We present an algorithm for generating all derivative superstructures of a nonprimitive parent lattice. The algorithm has immediate application in important materials design problems such as modeling hexagonalclose-packed ͑hcp͒ alloys. Extending the work of Hart and Forcade ͓Phys. Rev. B 77, 224115 ͑2008͔͒ ͑which applies only to Bravais lattices͒, this approach applies to arbitrary multilattices. The algorithm enumerates superlattices and atomic configurations using permutation groups rather

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... n direct geometric comparisons. The key concept is to use the quotient group associated with each superlattice to determine all unique atomic configurations. The algorithm is very efficient; the run time scales linearly with the number of unique structures found. We demonstrate the algorithm in the important case of hcp-derived superstructures. In the list of enumerated hexagonal-close-packed derivative superstructures, we predict several as-yet-unobserved structures as likely candidates for new intermetallic prototypes.