The methods described above have been developed with a particular interest in the tables of marks of simple and almost simple groups. While it should be possible to adapt them to larger classes of groups, it should be noted that arguments involving Sylow subgroups (in particular Corollary 4.8) loose their meaning when the table of marks of a p-group is to be determined.
Table 4 in the appendix lists the numbers of subgroups and the numbers of conjugacy classes of subgroups for the following groups: all projective special linear groups of order ; the projective special linear groups for n = 3, 4, 5; the alternating groups for ; the symmetric groups for ; the unitary groups for n = 3, 4, 5 and ; the Suzuki group Sz(8); the symplectic group ; the Mathieu groups , , and plus their automorphism groups and ; the Janko groups , and ; and the McLaughlin group McL.
The complete tables of marks of these groups have been determined by the methods described above. These tables form a library which is part of GAP.
In [Buekenhout and Rees 1988] the poset structure of the Mathieu group is determined. The poset structure of the sporadic simple Janko group is determined in [Pahlings 1987]. The poset structure of the sporadic simple Janko group is determined in [Pfeiffer 1991]. Informations about parts of the subgroup lattice of the sporadic simple McLaughlin group McL can be found in [Diawara 1987].
A rather incomplete collection of facts about subgroups of the Mathieu groups is given in [Greenberg 1973]. In his review (MR 50#4731), P. Fong points out that ``this can not remain the last work on the subject.''