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Electromagnetic response is studied for clusters of subwavelength graphene-coated nanowires illuminated by a linearly polarized plane wave in the terahertz frequency range. The solution of the scattering problem is obtained with the Lorenz-Mie theory and multiple cylinder scattering formalism. The results show that normalized scattering cross-sections of nanowire clusters can be drastically changed by the symmetry breaking introduced into the cluster's design. This effect is due to excitation of dark modes and is observed only for the incident wave of TE polarization.