Number of subgroups of order $4$ and $8$ in a group of order $72$

Question

Let $G$ be a group of order $72$. I want to calculate the number of subgroups of order $4$ and $8$ with GAP. How can I do? thanks in advance.

Answer 1

There are lots of possible values:

gap> Set(AllSmallGroups(72),g->List([4,8],n->Number(AllSubgroups(g),h->Order(h)=n)));
[ [ 1, 1 ], [ 1, 3 ], [ 1, 9 ], [ 3, 1 ], [ 7, 1 ], [ 7, 3 ], [ 9, 9 ], [ 15, 9 ],
  [ 19, 3 ], [ 19, 9 ], [ 27, 9 ], [ 51, 9 ], [ 55, 9 ] ]

For instance there are groups of order 72 that have 55 subgroups of order 4 and 9 subgroups of order 8.