We demonstrate a cryogenically cooled Yb:LiYF(4) (Yb:YLF) laser with 224W linearly polarized output power (pump-power limited) and a slope efficiency of 68%. The beam quality is characterized by an M(2) approximately 1.1 at 60W output and M(2) approximately 2.6 at 180W output. This level of average laser power is approximately 2 orders of magnitude higher than demonstrated previously in cryogenic Yb:YLF. Yb:YLF is attractive for femtosecond pulse generation because of its wide gain bandwidth, and this demonstration shows the potential for high-average-power subpicosecond pulse lasers.