Full octahedral group/List of all subgroups

The list of subgroups as shown in Full octahedral group, but including lists of all 48 permutations of the respective example solid.

Subgroups of order 24
{| class="collapsible open" style="width: 100%; text-align: center; border: 1px solid #999;" !colspan="2" bgcolor="#f0f0e0"| Th  A4 × C2   [3+,4]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; A4xC2; example solid.png
 * Subgroup of Oh; A4xC2; cycle graph.svg
 * Subgroup of Oh; A4xC2; matrix.svg
 * colspan="2"|
 * Subgroup of Oh; A4xC2; matrix.svg
 * colspan="2"|
 * colspan="2"|


 * }

Subgroups of order 12
{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999;" ! bgcolor="#f0f0e0" colspan="5"| D3d  Dih6   [2+,6]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; Dih6 03; example solid.png
 * Subgroup of Oh; Dih6 03; cycle graph.svg
 * Subgroup of Oh; Dih6 11; cycle graph.svg
 * Subgroup of Oh; Dih6 15; cycle graph.svg
 * Subgroup of Oh; Dih6 08; cycle graph.svg
 * Subgroup of Oh; Dih6 03; matrix.svg
 * Subgroup of Oh; Dih6 11; matrix.svg
 * Subgroup of Oh; Dih6 15; matrix.svg
 * Subgroup of Oh; Dih6 08; matrix.svg
 * colspan="5"|
 * Subgroup of Oh; Dih6 08; matrix.svg
 * colspan="5"|
 * colspan="5"|


 * }

Subgroups of order 8
{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999;" ! bgcolor="#e0f0f0" colspan="4"| D2h  C23 green   [2,2]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; C2^3 green 07; example solid.png
 * Subgroup of Oh; C2^3 green 07; cycle graph.svg
 * Subgroup of Oh; C2^3 green 16; cycle graph.svg
 * Subgroup of Oh; C2^3 green 23; cycle graph.svg
 * Subgroup of Oh; C2^3 07; matrix.svg
 * Subgroup of Oh; C2^3 16; matrix.svg
 * Subgroup of Oh; C2^3 green 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; C2^3 green 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#f0f0e0" colspan="4"| D2d  Dih4 blue orange   [2+,4]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; Dih4 blue orange 07; example solid.png
 * Subgroup of Oh; Dih4 blue orange 07; cycle graph.svg
 * Subgroup of Oh; Dih4 blue orange 16; cycle graph.svg
 * Subgroup of Oh; Dih4 blue orange 23; cycle graph.svg
 * Subgroup of Oh; Dih4 blue orange 07; matrix.svg
 * Subgroup of Oh; Dih4 blue orange 16; matrix.svg
 * Subgroup of Oh; Dih4 blue orange 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; Dih4 blue orange 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999;" ! bgcolor="#f0e0f0" colspan="4"| D4  Dih4 blue red   [2,4]+
 * rowspan="2" style="width:240px;"| Subgroup of Oh; Dih4 blue red 07; example solid.png
 * Subgroup of Oh; Dih4 blue red 07; cycle graph.svg
 * Subgroup of Oh; Dih4 blue red 16; cycle graph.svg
 * Subgroup of Oh; Dih4 blue red 23; cycle graph.svg
 * Subgroup of Oh; Dih4 blue red 07; matrix.svg
 * Subgroup of Oh; Dih4 blue red 16; matrix.svg
 * Subgroup of Oh; Dih4 blue red 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; Dih4 blue red 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }

Subgroups of order 6
{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999;" ! bgcolor="#f0e0f0" colspan="5"| D3  S3 blue   [2,3]+
 * rowspan="2" style="width:240px;"| Subgroup of Oh; S3 blue 03; example solid.png
 * Subgroup of Oh; S3 blue 03; cycle graph.svg
 * Subgroup of Oh; S3 blue 11; cycle graph.svg
 * Subgroup of Oh; S3 blue 15; cycle graph.svg
 * Subgroup of Oh; S3 blue 08; cycle graph.svg
 * Subgroup of Oh; S3 blue 03; matrix.svg
 * Subgroup of Oh; S3 blue 11; matrix.svg
 * Subgroup of Oh; S3 blue 15; matrix.svg
 * Subgroup of Oh; S3 blue 08; matrix.svg
 * colspan="5"|
 * Subgroup of Oh; S3 blue 08; matrix.svg
 * colspan="5"|
 * colspan="5"|


 * }

Subgroups of order 4
{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999;" ! bgcolor="#f0e0f0" colspan="4"| C4  C4 red   [4]+
 * rowspan="2" style="width:240px;"| Subgroup of Oh; C4 red 07; example solid.png
 * Subgroup of Oh; C4 red 07; cycle graph.svg
 * Subgroup of Oh; C4 red 16; cycle graph.svg
 * Subgroup of Oh; C4 red 23; cycle graph.svg
 * Subgroup of Oh; C4 red 07; matrix.svg
 * Subgroup of Oh; C4 red 16; matrix.svg
 * Subgroup of Oh; C4 red 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; C4 red 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#f0f0e0" colspan="7"| C2h = D1d  V inv green   [2+,2]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; V inv green 01; example solid.png
 * Subgroup of Oh; V inv green 01; cycle graph.svg
 * Subgroup of Oh; V inv green 06; cycle graph.svg
 * Subgroup of Oh; V inv green 05; cycle graph.svg
 * Subgroup of Oh; V inv green 14; cycle graph.svg
 * Subgroup of Oh; V inv green 02; cycle graph.svg
 * Subgroup of Oh; V inv green 21; cycle graph.svg
 * Subgroup of Oh; V inv green 01; matrix.svg
 * Subgroup of Oh; V inv green 06; matrix.svg
 * Subgroup of Oh; V inv green 05; matrix.svg
 * Subgroup of Oh; V inv green 14; matrix.svg
 * Subgroup of Oh; V inv green 02; matrix.svg
 * Subgroup of Oh; V inv green 21; matrix.svg
 * colspan="7"|
 * Subgroup of Oh; V inv green 21; matrix.svg
 * colspan="7"|
 * colspan="7"|

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#e0f0f0" colspan="4"| C2v  V yellow white   [2]
 * }
 * rowspan="2" style="width:240px;"| Subgroup of Oh; V yellow white 07; example solid.png
 * Subgroup of Oh; V yellow white 07; cycle graph.svg
 * Subgroup of Oh; V yellow white 16; cycle graph.svg
 * Subgroup of Oh; V yellow white 23; cycle graph.svg
 * Subgroup of Oh; V yellow white 07; matrix.svg
 * Subgroup of Oh; V yellow white 16; matrix.svg
 * Subgroup of Oh; V yellow white 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; V yellow white 23; matrix.svg
 * colspan="4"|
 * colspan="4"|

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#f0e0f0" colspan="4"| D2  V blue white   [2,2]+
 * }
 * rowspan="2" style="width:240px;"| Subgroup of Oh; V blue white; example solid.png
 * Subgroup of Oh; V blue white 07; cycle graph.svg
 * Subgroup of Oh; V blue white 16; cycle graph.svg
 * Subgroup of Oh; V blue white 23; cycle graph.svg
 * Subgroup of Oh; V blue white 07; matrix.svg
 * Subgroup of Oh; V blue white 16; matrix.svg
 * Subgroup of Oh; V blue white 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; V blue white 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }

Subgroups of order 2
{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#e0f0f0" colspan="4"| Cs = C1v  C2 yellow   [ ]
 * rowspan="2" style="width:240px;"| Subgroup of Oh; C2 yellow 07; example solid.png
 * Subgroup of Oh; C2 yellow 07; cycle graph.svg
 * Subgroup of Oh; C2 yellow 16; cycle graph.svg
 * Subgroup of Oh; C2 yellow 23; cycle graph.svg
 * Subgroup of Oh; C2 yellow 07; matrix.svg
 * Subgroup of Oh; C2 yellow 16; matrix.svg
 * Subgroup of Oh; C2 yellow 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; C2 yellow 23; matrix.svg
 * colspan="4"|
 * colspan="4"|

{| class="collapsible collapsed" style="width: 100%; text-align: center; border: 1px solid #999; border-bottom: 0;" ! bgcolor="#f0e0f0" colspan="4"| C2  C2 white   [2]+
 * }
 * rowspan="2" style="width:240px;"| Subgroup of Oh; C2 white 07; example solid.png
 * Subgroup of Oh; C2 white 07; cycle graph.svg
 * Subgroup of Oh; C2 white 16; cycle graph.svg
 * Subgroup of Oh; C2 white 23; cycle graph.svg
 * Subgroup of Oh; C2 white 07; matrix.svg
 * Subgroup of Oh; C2 white 16; matrix.svg
 * Subgroup of Oh; C2 white 23; matrix.svg
 * colspan="4"|
 * Subgroup of Oh; C2 white 23; matrix.svg
 * colspan="4"|
 * colspan="4"|


 * }