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Thank you very much for your answer. If I understand correctly, the answer is $PSL(2,2^n)$ , $PSL(2,p)$ , $Sz(2,2^n)$ and $J_1$where their Sylow $2$-subgroups are elementer abelian, dihedral, Suzuki 2-group and elementer abelian, respectivly.
@user7212389: Dear idt, your answer is not true since you do not understand the question even if I ıty to say what i mean step by step you reject to understand.
