Subgroups of a permutation group The permutation group $S_{4}$ is defined as the group of all possible permutations of [1234].
i) Find the number of subgroups of $S_{4}$ that have order 2.
ii) A: { [1234], [2143], [3412], [4321] } and B: { [1234], [1243], [2134], [2143] }. Which of A and B are subgroups of $S_{4}$?
Trying to teach myself a Further Maths module on Groups is proving difficult when none of my teachers know the syllabus, any help would be appreciated! Thanks.

Hints:
i) If a subgroup has order two then there are exactly one trivial and one non-trivial element. Furthermore the nontrivial element $a\in G$ must fulfill $a^2=e$. So just check with of the elements of $S_4$ fulfill this requirement.
ii) Just check the subgroup axioms for $A$ and $B$.
