SO(3) and SO(2) decompositions of numerical channel flow turbulence are performed. The decompositions are used to probe, characterize, and quantify anisotropic structures in the flow. Close to the wall, the anisotropic modes are dominant and reveal the flow structures. The dominance of the (j, m) = (2, 1) mode of the SO(3) decomposition in the buffer layer is associated with hairpin vortices. The SO(2) decomposition in planes parallel to the walls allows us also to access the regions very close to the wall. In those regions we have found that the strong enhancement of intermittency can be explained in terms of streaklike structures and their signatures in the m = 2 and m = 4 modes of the SO(2) decomposition.