  Superadditivity relations characterize the distributions of coherence in
multipartite quantum systems. In this work, we investigate the superadditivity
relations related to the $l_1$-norm of coherence $C_{l_1}$ in multiqubit
quantum systems. Tighter superadditivity inequalities based on the $\alpha$-th
($\alpha\geqslant 1$) power of $l_1$-norm of coherence are presented for
multiqubit states under certain conditions, which include the existing results
as special cases. These superadditivity relations give rise to finer
characterization of the coherence distributions among the subsystems of a
multipartite system. A detailed example is presented.
