# subgroup structure of $S_4$

In the checklist of Young subgroups of $S_4,$ we locate $\langle(12)\rangle, \langle(13)\rangle, \langle(14)\rangle, \langle(23)\rangle, \langle(24)\rangle, \langle(34)\rangle,$ yet we do not locate $\langle(12)(34)\rangle, \langle(13)(24)\rangle,\langle(14)(23)\rangle,$ while they are all isomorphic to $S_2.$ I'm perplexed.

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palio 2022-07-25 20:46:51

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