For odd primes p, the E2 page of the LHS spectral sequence for the Sylow p-subgroups of GL_2(Z/p^n) and SL_2(Z/p^n) is independent of n>1, with stable elements described via fusion systems.
New Horizons in Pro-p Groups, du Sautoy, Segal and Shalev eds., Birkhauser (2000) 349-416
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On the modular cohomology of $GL_2(\mathbb{Z}/p^n)$ and $SL_2(\mathbb{Z}/p^n)$
For odd primes p, the E2 page of the LHS spectral sequence for the Sylow p-subgroups of GL_2(Z/p^n) and SL_2(Z/p^n) is independent of n>1, with stable elements described via fusion systems.