Show that the symmetric group $S_4$ has a subgroup of order $d$ for each $d|24$.
From Lagrange's theorem I know that if $G \le S_4$, then the order of $G$ necessarily divides $|S_4|=24$. However the question actually asks the converse of the Lagrange's theorem, so I cannot apply the theorem directly. (And I don't think I can apply it indirectly, either)
So my question is:
Instead of listing the subgroups in detail, is there a convenient way of proving the existence of subgroups of every $d|24$?