One of the important features of Social Networks (SNs) is community structure detection. Several methods have been proposed to address this problem. One of the interesting methods is based on the famous Fuzzy C-Means (FCM) clustering algorithm. This method consists of three phases: spectral mapping, FCM clustering and modularity computation. Despite being very effective, this method is actually inefficient to deal with large-scale networks. A parallel implementation using GPUs is one of the feasible solutions to address this problem. Hence, this research presents a parallel implementation of FCM and modularity components of the algorithms. The implementation follows the hybrid CPU-GPU approach. We study the many factors affecting the performance speedups, such as the number of dimensions/features and the network size.