Finite digraphs with given regular automorphism groups

With five exceptions, every finite regular permutation group occurs as the automorphism group of a digraph.One of the corollaries: given a finite groupG of ordern, there is a commutative semigroupS of order 2n+2 such that AutSG. The problem whether a latticeL of order Cn with AutLG exists (for some constantC), remains open.