The packing geometry plays an important role in the molecular systems and its symmetry may be used in many systems of coupled cavities. We are focused on the description of the symmetry of single mode coupled cavities in each of them are placed a two-level atom. It is shown that the number of collective states is reduced with increasing of the local symmetry. In the case, when the system is reduced to the two cooperative distinguished subsystems consisted from atoms and field, the possibility of quantitative description of entanglement between these two subsystems becomes possible. Using the conception of discord and quantum mutual information the entanglement between these subsystems was estimated.