Can someone tell me how can I find all the subgroups of A4. I have the elements written down and I know there should be subgroups of order 2,3, 4 ( 6 is impossible ). I can't understand how to find the 3 and 4 order subgroups and I have surfed the internet but haven't ye found a satisfying answer.
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A subgroup of order 3 can be found by taking an element $a$ whose inverse is not itself, and take $\{e,a,a^{-1}\}$, where e denotes the neutral element.
For the subgroup of order 4, there are 3 elements with the same form, you should take a look at them. What other group of order 4 has the same multiplication table?
Pepijn
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