Alternating Group on 4 Letters/Subgroups

Subgroups of the Alternating Group on $4$ Letters
Let $A_4$ denote the alternating group on $4$ letters, whose Cayley table is given as:

The subsets of $A_4$ which form subgroups of $A_4$ are as follows:

Trivial:

Order $2$ subgroups:

Order $3$ subgroups:

Order $4$ subgroup: