Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum cost multicut problems defined on such graphs al- lows to optimize the number of the resulting segments along with the segment assignment. However, pairwise potentials limit the discriminative power of the employed motion models to translational differences. More complex models such as Euclidean or affine transformations call for higher-order potentials and a tractable inference in the resulting higher-order graphical models. In this paper, we (1) introduce a generalization of the minimum cost lifted multicut problem to hypergraphs, and (2) propose a simple primal feasible heuristic that allows for a reasonably efficient inference in instances of higher-order lifted multicut problem instances defined on point trajectory hypergraphs for motion segmentation. The resulting motion segmentations improve over the state-of-the-art on the FBMS-59 dataset.