Dear Forum members, Bruce Coletti asked: In GAP3.4.4, I want to
find all subgroups of G having a given size. Is there a way to
do this OTHER THAN searching G's lattice diagram? I am afraid
the straight answer is 'no'. However it may be worthwhile to add
a few remarks on available methods for looking into the lattice
of subgroups of a group, since we do get questions of a similar
kind more often. 1. Let me first assume that the group is given
in such a way that efficient computation with elements and
comparison of elements is possible, e.g. that the group is given
as a permutation group, or an Then there are essentially two
ways for determining the lattice of - The so-called 'cyclic
extension method' which constructs new subgroups as cyclic
extensions of already known ones, i.e. works 'bottom-up'. This
is the method presently used in GAP 3.4.4 e.g. by the command
'Lattice(G)' as described in section 7.74 of the manual. With no
further information given, it will only construct soluble
sbgroups, if it is given a