Finite space of nontrivial p-subgroups

Definition
Let $$G$$ be a finite group and $$p$$ be a prime number. The finite space of nontrivial $$p$$-subgroups of $$G$$ is a $$T_0$$-topological space whose points correspond to the nontrivial $$p$$-subgroups of $$G$$, and where the corresponding partial order is the same as the partial order by inclusion.

The simplicial complex associated with this finite space is sometimes termed the Brown complex.