Dear Forum,

Mario Pineda Ruelas asked:

can any one tell me how to calculate a list of subgroups of S_3xS_3xS_3xS_3?

Since the group in question is relatively small, it is possible to compute
this list of subgroups with the GAP library function Lattice (): On my
Power Mac running at 120 MHz and 16 Megabytes of workspace, this takes
about 10 minutes. This, however, computes only the conjugacy classes of
subgroups. To compute the list of all subgroups, you will need about 60
Megabytes of workspace, and it takes around 45 minutes.

S := SymmetricGroup (3);
# Group( (1,3), (2,3) )

D := DirectProduct (S,S,S,S); # this is S_3xS_3xS_3xS_3, as a subgroup of
S_{12}
# Group( (1,3), (2,3), (4,6), (5,6), (7,9), (8,9), (10,12), (11,12) )

latt := LatticeSubgroups (D);
#latt is a record representing the subgroups of D
#latt.classes contains a list of the conjugacy classes of subgroups of D

#now generate a list containing all subgroups
sgrs := [];
for c in latt.classes do
Append (sgrs, Elements (c));
od;

Note that 16 Megabytes of workspace suffice to compute the subgroup lattice
of D, which contains 1569 conjugacy classes of subgroups. If you actually
need to compute a list of all 19244 subgroups of G, more workspace is
required.

If you need further assistance or would like the gzipped version of a file
containing the file, please contact me directly.

Hope this helps.

Burkhard Hofling.