Dependence of controllability of a networked dynamic system (NDS) on its structure is investigated in this paper. Each subsystem is permitted to have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT), to allow rational function dependence of system matrices on the first principle parameters. It is proven that controllability keeps to be a generic property for this kind of NDSs. Results are at first established for structural controllability of LFT-parameterized plants under a diagonalization assumption. Necessary and sufficient conditions are then established respectively for the NDS to have a fixed uncontrollable mode, to have a parameter-dependent uncontrollable mode, and to be structurally controllable, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and give some insights on how the NDS controllability is influenced by subsystem input-output relations, subsystem uncontrollable modes and subsystem interconnection topology.