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Could someone tell me the subgroups lattice of $PSL(n,p^k)$ or could someone tell me sources I should read to know all about $Aut(PSL(n,p^k))$ and its subgroups lattice.

Thanks in advance.

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I write this answer to just leave this question from list of unanswered questions.
Thomas Connor and Dimitri Leemans has published an online Atlas of Subgroup Lattices of Finite Almost Simple Groups.

This atlas contains all subgroup lattices of almost simple groups G such that S≤G≤Aut(S) and S is a simple group of order less than 1 million appearing in the Atlas of Finite Groups by Conway et al. Some simple groups and almost simple groups or order larger than 1 million have also been included, but not in a systematic way.

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