This paper discusses the relationship between the level of symmetry in a system structure and loss of controllability. For a system consisting of a large number of modules, symmetrical structure is considered as the identity of modules and their interconnections. We especially dealt with three basic structures, such as ring-type, bus-type, and star-type structures. If the entire system becomes uncontrollable because of failures in a set of k submodules, this number k indicates the level of fault tolerance. On the other hand, the level of symmetry is evaluated by the number of transformations that keep the structure invariant. Through the evaluation of fault tolerance of three basic structures, we considered the relationship between lowering the level of symmetry and loss of controllability because of failures.