If a finite group G has a Hall π-subgroup H (π containing 2 and odd prime p), its non-p-soluble length is at most the generalized Fitting height of H; when H is soluble the bound is 2 times the 2-length of H plus 1.
Wilson, On the structure of compact torsion groups,Monatsh.Math.96, 57–66 (1983)
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Length parameters of finite groups and their Hall subgroups
If a finite group G has a Hall π-subgroup H (π containing 2 and odd prime p), its non-p-soluble length is at most the generalized Fitting height of H; when H is soluble the bound is 2 times the 2-length of H plus 1.