Planar subgroup lattices

Abstract

In this paper we determine all finite groups with planar subgroup lattices. For this, by Kuratowski’s theorem, we have to study subdivisions of the Kuratowski graphs K_3,3 and K₅ in the covering graph of the subgroup lattice of a finite group. It turns out that such a graph is planar if and only if it contains no subdivision of K_3,3.