Vortex solitons with the topological charge S = 3, and "quasivortex" (multipole) solitons, which exist instead of the vortices with S = 2 and 4, are constructed on a square lattice in the discrete nonlinear Schrödinger equation (true vortices with S = 2 were known before, but they are unstable). For each type of solitary wave, its stability interval is found, in terms of the intersite coupling constant. The interval shrinks with increase of S. At couplings above a critical value, oscillatory

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... tabilities set in, resulting in breakup of the vortex or quasivortex into lattice solitons with a lower vorticity. Such localized states may be observed in optical guiding structures, and in Bose-Einstein condensates loaded into optical lattices.