The effect of network topological features, specifically the modularity or the existence of communities in the network, on the control performance, remains an unexplored problem. In this work, we investigate the role of communities in feedback control in the framework of sparsity-promoting control and structured optimal control of a Laplacian dynamics defined on a network. We find that for modular networks, the community structures in the network correspond to feedback channels necessary for maintaining control performance, and result in an advantage in total control cost over non-modular networks as the cost of feedback channels becomes significant. For decentralized control, the best control performance is approached with a decomposition according to the communities. Thus, the communities act as the 'core' of sparse feedback control. We then discuss the significance of this conclusion in understanding the behavior and evolution of networks as well as guiding the design of control strategies for large-scale and complex systems.