Dear Sorouhesh,
If you want a more visual representation, you could also do this in
xgap (or Gap.app on the mac):
If G is your group and H is your subgroup, run
GraphicSubgroupLattice(G);
H;
Then (from the graphic subgroup lattice sheet) select the menu item:
Subgroups | Insert Vertices from GAP
Select the G and H on the sheet by shift-clicking them, then select the
menu item:
Subgroups | Intermediate Subgroups
However, this may use the GAP call that William pointed out underneath,
which you said had some problem. What problem did that have?
Best,
--Russ
On May 14, 2012, at 5:48 AM, muhammad shah wrote:
>
> Dear Sorouhesh,Here is a simple method for the solution of your problem.
> Load
> package SONATA.It contains a command Subgroups which find all subgroups
> of a group G. Then filter over this set for those which contain your
> specified subgroup h.
> For example I take s4 as G and its fifth subgroup as h then GAP gives:
> gap> LoadPackage("sonata");;
> gap> s_4:=(SymmetricGroup(IsPermGroup,4));
> Sym( [ 1 .. 4 ] )
> gap> allsubgrps:=Subgroups(s_4);;
> gap> Size(last);
> 30
> gap> h:=allsubgrps[5];
> Group([ (1,2) ])
> gap> Filtered(allsubgrps, t -> IsSubgroup(t,h));
> [ Group([ (1,2) ]), Group([ (1,2)(3,4), (1,2) ]), Group([ (1,3), (1,3,2) ]),
> Group([ (1,4), (1,4,2) ]), Group([ (1,3)(2,4), (1,4)(2,3), (1,2) ]),
> Group([ (1,3)(2,4), (1,4)(2,3), (2,4,3), (1,2) ]) ]
> gap>
> Regards,
> Muhammad Shah
>
>> Date: Mon, 14 May 2012 12:14:58 +0430
>> From: msorouh...@gmail.com
>> To: fo...@gap-system.org
>> Subject: [GAP Forum] Contain a fixed subgroup
>>
>> Suppose we have a finite group such that know all its subgroups. Now,
>> fix a certain subgroup in the group.Can we use GAP to list all
>> subgroups of the group that contain our fixed subgroup?
>> Best
>>
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