Finite 2-groups Whose Length Of The Chain Of The Non-normal Subgroups Is At Most 2

Assume G is a finite 2-group.We say H1<H2<…<Hs is a chain of the non-normal subgroups of G if Hi(?)G,where 1 ? i ?s.and s is called the length of the chain.We use chn(G)to denote the maximum of the lengths of the chains of non-normal subgroups of G.In this paper,finite 2-groups in which chn(G)? 2 are completely classified up to isomorphism.