Computation of subgroup structures of groups leads to understanding them better and to being able to answer questions about them and the geometric objects they act on.

In this talk, we will focus on the computation of the whole subgroup structure of finite (simple) groups. We will briefly recall what is the subgroup lattice of a group and explain how Magma does to compute it. We will then give some last minute results on the sporadic simple groups and some applications of these results.