Some combinatorial aspects of finite Hamiltonian groups

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a nite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a nite Hamiltonian group.