On a conjecture by Haipeng Qu

Abstract

Abstract In this note, we prove that D 8 × C 2 n - 3 {D_{8}\times C_{2}^{n-3}} is the non-elementary abelian 2-group of order 2 n {2^{n}} , n ≥ 3 {n\geq 3} , whose number of subgroups of possible orders is maximal. This solves a conjecture by Haipeng Qu. A formula for counting the subgroups of an (almost) extraspecial 2-group is also presented.