Structured latent attribute models (SLAMs) are a special family of discrete latent variable models widely used in the social and biological sciences. This work considers the problem of learning significant latent attribute patterns from a SLAM with potentially high-dimensional patterns. We address the theoretical identifiability issue, propose a penalized likelihood method for the selection of the attribute patterns, and further establish the selection consistency in the overfitted SLAM with diverging number of latent mixture components. The good performance of the proposed methodology is illustrated by simulation studies and two real datasets in educational assessment.