Siberian Federal University

We investigate the well-known hypothesis of D. R. Hughes that the full collineation group of a non-Desarguesian semifield projective plane of a finite order is solvable (the question 11.76 in Kourovka notebook was written down by N. D.Podufalov). The spread set method allows us to prove that any non- Desarguesian semifield plane of order pN, where p 1 (mod 4) is prime, does not admit an autotopism subgroup isomorphic to the dihedral group of order 8. As a corollary, we obtain the extensive list of simple non-Abelian groups which cannot be the autotopism subgroups