In this paper, the dynamics of rule 106, a Chua's hyper Bernoulli cellular automata rule, is studied and discussed from the viewpoint of symbolic dynamics. It is presented that rule 106 defines a chaotic subsystem which is topologically mixing and possesses the positive topologically entropy. An effective method of constructing its chaotic subsystems is proposed. Indeed, it is interesting to find that this rule is filled with infinitely many disjoint chaotic subsystems. Special attention is paid to each subsystem on which rule 106 is topologically mixing and possesses the positive topologically entropy. Therefore, it is natural to argue that the intrinsic complexity of rule 106 is high from this viewpoint.