[GAP Forum] Contain a fixed subgroup

[muhammad shah]

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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