  There exist spaces BSol(q) which are the classifying spaces of a family of
2-local finite groups based on certain fusion system over the Sylow 2-subgroups
of Spin_7(q). In this paper we calculate the cohomology of BSol(q) as an
algebra over the Steenrod algebra A_2. We also provide the calculation of the
cohomology algebra over A_2 of the finite group of Lie type G_2(q).
