Practical algorithm for identifying subgroups of space groups

The problem of identifying subgroups G’ of a space group G with respect to a conventional listing is considered. The properties of space groups and subgroups are given in terms of an algebraic rather than a geometric description. In this algebraic description, G’ is equivalent to one of the standard listings through a similarity transformation consisting of a linear unimodular component and a translation. A general algorithm is presented to determine which standard listing corresponds to subgroup G’. The algorithm is applied to a specific example, a subgroup of $D_{3d}^6$.