Multimode fibre optic communication systems, employing mode/mode group multiplexing, present challenges in accurately identifying numerous modes and mode groups for improved performance. In this study, we propose an intelligent identification model utilizing a fully convolutional neural network (CNN) to precisely identify multimode fibre modes and their clusters. The model is simulated and experimentally validated, considering noise influences on linear polarisation modes. Using a platform with OM2 multimode fibre and a multiplane optical conversion mode multiplexer, we capture optical field information for 10 modes and their corresponding mode groups. Extensive data are employed for training and validation, achieving a 100% recognition rate for all modes and mode groups in experiments. Notably, when employing a 44-photodetector array, an impressive 98.3% recognition efficiency is attained, showcasing the potential of deep learning in advancing multimode fibre optic communication systems.