Some subnormal embeddings of groups into groups with additional properties are established, and in particular, embeddings of countable groups into two-generated groups with some extra properties. The results obtained are generalizations of theorems of P. Hall, R. Dark, B. Neumann, H. Neumann and G. Higman on embeddings of that type. Through the consideration of subnormal embeddings of finite groups into finite groups with additional properties, a result of H. Heineken and J. Lennox is illustrated.