[GAP Forum] Subgroup lattice of direct products of nonsolvable groups?

[Wei Mao]

Dear forum,

Currently the methods for LatticeSubgroups() work best with solvable groups, for nonsolvable ones the cyclic extension method has to be used, in conjunction with a perfect group library. For large nonsolvable groups the method always complains that the perfect residuum is too large.

The nonsolvable groups I am interested in are PGL(2,q)^n, i.e. the direct products of n copies of PGL(2,q), which have PSL(2,q)^n as the perfect residuums. For this specific type of groups, do we have nice ways of obtaining the subgroup lattice? One result that may be used is the Goursat's lemma, which states that the subdirect product of two groups can be described as a fiber product and vice versa. Is this a feasible direction for an algorithm?

Best,
Wei