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File:Full octahedral group; subgroups Hasse diagram.svg

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Description
subgroups of S4 as subgroups of O a.k.a. [4,3]+
subgroups of S4 as subgroups of Oh a.k.a. [4,3]

The subgroups of the full octahedral group (w:Octahedral symmetry, v:Full octahedral group)

Actually there are 98 individual subgroups, but this diagram bundles them in 25 different kinds of subgroups, each denoted in Schoenflies and Coxeter notation.

The subgroups of O or [4,3]+ can be seen on the left side (in magenta boxes). On the right side all the subgroups that contain the inversion (the small black dot in the cycle graphs) repeat the same structure. Each of them is the product of C2 and a subgroup of O, to which it is connected by a light red edge. These light edges are drawn straight, regardless of the nodes in between.

There are 7 subgroups that are not subgroups of O, and do not contain the inversion. Their boxes are thinner, and so are the edges leading to them.

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Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".
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Date/TimeThumbnailDimensionsUserComment
current17:21, 7 May 2017Thumbnail for version as of 17:21, 7 May 20172,068 × 1,326 (595 KB)Watchduckcorrect colors in cycle graphs
00:03, 31 October 2016Thumbnail for version as of 00:03, 31 October 20162,068 × 1,326 (607 KB)Watchduck{{Information |Description ={{en|1=thumb|The subgroups of the Symmetric group S4 can be seen on the left side. The 25 different kinds of subgroups of the full octahedral group ([[w...

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