Introduction to D[subscript]8 x D[subscript]8 and its Subgroup Lattice

Abstract

Let A and B be groups and consider the direct product A x B. In 1889, Edouard Goursat proved a theorem that provides the structure of subgroups in a direct product. The purpose of this study was to improve and make more effective this containment theorem for further use and to identify the extraspecial group of order 32 that lies inside of D[subscript]8 x D[subscript]8.