<p>This study investigates the controllability of a general heterogeneous networked sampled-data system (HNSS) consisting of nonidentical node systems, where the inner coupling between any pair of nodes can be described by a unique matrix. The signals on control and transmission channels are sampled and held by zero-order holders, and the control sampling period of each node can be different. Necessary and sufficient controllability conditions are developed for the general HNSS, using the Smith normal form and matrix equations, respectively. The HNSS in specific topology or dynamic settings is discussed subsequently with easier-to-verify conditions derived. These heterogeneous factors have been determined to independently or jointly affect the controllability of networked sampled-data systems. Notably, heterogeneous sampling periods have the potential to enhance the overall controllability, but not for systems with some special dynamics. When the node dynamics are heterogeneous, the overall system can be controllable even if it is topologically uncontrollable. In addition, in several typical heterogeneous sampled-data multi-agent systems, pathological sampling of single-node systems will necessarily cause overall uncontrollability.</p>