In the field of network dynamics it has been suggested that statistical information of motifs, small subnetworks, can help in understanding global activity of the entire network. We present a counterexample where the relation between the stable synchronized activity modes and network connectivity was studied using the Hodgkin-Huxley brain dynamics model. Simulations indicate that small motifs of three nodes exhibit different synchronization modes depending on their local parameters such as delays, synaptic strength, and external drives. Thus the activity of a complex network composed of interconnected motifs cannot be extracted from the activity mode of each individual motif and is governed by local parameters. Finally, we exemplify how local dynamics ultimately enriches the ability of a network to generate diverse modes with a given motif structure.