[GAP Forum] subgroups of S_4

[ekpen ogiugo]

Dear forum,

gap> G:= SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap> H:= AllSubgroups(G);;
gap> Length(H);
30
gap> M:= List([1..30],i->Size(H[i]));
[ 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6,
6, 8, 8, 8, 12, 24 ]
gap> Collected(M);
[ [ 1, 1 ], [ 2, 9 ], [ 3, 4 ], [ 4, 7 ], [ 6, 4 ], [ 8, 3 ], [ 12, 1 ], [
24, 1 ] ]

gap> List([15..30],j->List([3..10],i->IsSubgroup(H[j],H[i])));
[ [ true, true, false, false, false, false, false, false ],
[ false, false, true, false, false, true, false, false ],
[ false, true, false, true, false, false, false, true ],
[ true, false, false, false, true, false, true, false ],
[ false, false, false, false, false, false, false, false],
[ true, false, false, false, false, false, false, false],
[ false, true, false, false, false, false, false, false ],
[ false, false, true, true, true, false, false, false ],
[ false, false, true, false, false, false, true, true ],
[ false, false, false, true, false, true, true, false ],
[ false, false, false, false, true, true, false, true ],
[ true, true, true, false, false, true, false, false ],
[ true, true, false, true, false, false, false, true ],
 [ true, true, false, false, true, false, true, false ],
[ true, true, false, false, false, false, false, false ],
 [ true, true, true, true, true, true, true, true ] ]
This is an illustration of order of subgroups in S4:(2,4),(2,6),(2,8),(2,12)
and(2,24).
Can someone help  me to write a program that can compute for subgroup order
of these pairs (2,4,24) and (2,4,8,24) in S4?
Thanks
Mike