Recently, more and more applications represent data objects as sets of feature vectors or multi-instance objects. In this paper, we propose COSMIC, a method for deriving concept lattices from multi-instance data based on hierarchical density-based clustering. The found concepts correspond to groups or clusters of multi-instance objects having similar instances in common. We demonstrate that COSMIC outperforms compared methods with respect to efficiency and cluster quality and is capable to extract interesting patterns in multi-instance data sets.