On supersoluble like groups of automorphisms of compact Riemann surfaces

Let G be a not necessary full automorphism group of a compact Riemann surface of genus g. We found sharp bounds for $|G|$ in the terms of g when G belongs to one of the following classes of finite groups sharing similar properties with supersoluble groups: 2-nilpotent, with the Sylow tower of supersoluble type, with P-subnormal cyclic primary subgroups, widely supersoluble, with submodular Sylow subgroups, with submodular cyclic primary subgroups and strongly supersoluble.