On 14 Jan 1992,  Allan C. Wechsler posted

Regarding the meta-approach of descending through a series of subgroups,
how much leverage does properly selecting the chain give you? It seems
like the jump from <F2,B2,...> to <F2,B2,L2,R2,...> is pretty large.
There are probably other paths through the subgroup lattice.

Does anyone have a table of subgroups?

There hasn't been any response to this, seemingly, which is a pity.

In any event, I would like to know of any other well-known subgroups.
There are the slice group; double-slice group; U group; square group;
anti-slice group. How many others are there not mentioned here, that
people know of ?