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Differential unitary space-time group codes are effective for multiple antenna wireless communications, especially in rapidly changing mobile environments. In this paper, we propose new unitary infinite subgroups for differential good space-time codes. The unitary subgroups are on the basis of Bruhat decomposition by the maximal torus and Weyl groups on Lie groups theory. Some interesting examples of the subgroups are given. However, it is shown that if the number of transmit antennas is odd, the good unitary subgroups cannot be constructed. Finally, a coded modulation system using the subgroup is proposed.