Dihedral group of order $8$ in an autotopism group of a semifield projective plane of odd order

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 $p^N$, where $p\equiv 1\pmod 4$ 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.