The social network built on top of mobile phone data has drawn increasing attention in recent years, due to its being far more accurate than its online counterpart in mirroring people's offline sociality. In this paper, we leverage a large dataset of mobile Call Detail Records (CDRs), provided by one of the primary Italian operators, to build the multiplex social network given by call and text message activities of the operator's subscribers. By discussing the multiplex network characteristics – ranging from ego-networks, dyads and triads all the way to cliques – the paper offers a comprehensive and thorough overview of human sociality as carried on through mobile phone; in addition, it highlights the need to consider more than one communication media when aiming to understand people's sociality.Finally, by investigating on-phone cliques, we show people's inclination to gather in cohesive and restricted groups of close friends, thus providing strong ominous indicators of where many recent online social networks, namely Snapchat, WeChat and others, are leading. © 2017 Elsevier B.V.