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Homework Help: Number of subgroups of S4

  1. Feb 22, 2009 #1
    Not a true homework question, but I'm trying to find all subgroups of S4.

    Including the identity and the group itself, I've found 30. Is that correct?

    I've got groups such as:

    trivial

    s4

    alternating group

    {identity, (12)}, {identity, (13)} etc - 6 of these

    {identity, (123), (132)}, {identity, (124), (142)} etc - 4 of these

    {identity, (12)(34)}, {identity, (13)(24)} etc - 3 of these

    {identity, (1243), (14)(23), (1342)} etc - 3 of these

    {identity, (13), (24), (12)(34), (13)(24), (14)(23), (1234), (1432)} - 3 of these

    {identity, (12), (34), (12)(34)} etc - 3 of these

    {identity, (123), (132), (12), (23), (13)}, {identity, (124), (142), (12), (24), (14)} etc - 4 of these.

    {identity, (12)(34), (13)(24), (14)(23)}

    Am I missing any?
     
    Last edited: Feb 22, 2009
  2. jcsd
  3. Feb 23, 2009 #2

    Dick

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    Last edited by a moderator: Apr 24, 2017
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