How many subgroups are there in S4?

[TaylorWatts]

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?

 

[Dick]

Somebody else added them up too. http://planetmath.org/encyclopedia/SubgroupsOfS_4.html They got 29, but they didn't count S4 itself, I don't think. So you are at least pretty close to right. Check it out. Compare notes.