[GAP Forum] Contain a fixed subgroup

[Russ Woodroofe]

	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: msorouhesh at gmail.com
>> To: forum at 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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