Completion of standard-like embeddings

Inequivalent standard-like observable sector embeddings in $Z_3$ orbifolds with two discrete Wilson lines, as determined by Casas, Mondragon and Mu~noz, are completed by examining all possible ways of embedding the hidden sector. The hidden sector embeddings are relevant to twisted matter in nontrivial representations of the Standard Model and to scenarios where supersymmetry breaking is generated in a hidden sector. We find a set of 175 models which have a hidden sector gauge group which is viable for dynamical supersymmetry breaking. Only four different hidden sector gauge groups are possible in these models.