Gene coexpression analysis is widely used to infer gene modules associated with diseases and other clinical traits. However, a systematic view and comparison of gene coexpression networks and modules across a cohort of tissues are more or less ignored. In this study, we first construct gene coexpression networks and modules of 52 GTEx tissues and cell lines. The network modules are enriched in many tissue-common functions like organelle membrane and tissue-specific functions. We then study the correlation of tissues from the network point of view. As a result, the network modules of most tissues are significantly correlated, indicating a general similar network pattern across tissues. However, the level of similarity among the tissues is different. The tissues closing in a physical location seem to be more similar in their coexpression networks. For example, the two adjacent tissues fallopian tube and bladder have the highest Fisher’s exact test p value 8.54E-291 among all tissue pairs. It is known that immune-associated modules are frequently identified in coexperssion modules. In this study, we found immune modules in many tissues like liver, kidney cortex, lung, uterus, adipose subcutaneous, and adipose visceral omentum. However, not all tissues have immune-associated modules, for example, brain cerebellum. Finally, by the clique analysis, we identify the largest clique of modules, in which the genes in each module are significantly overlapped with those in other modules. As a result, we are able to find a clique of size 40 (out of 52 tissues), indicating a strong correlation of modules across tissues. It is not surprising that the 40 modules are most commonly enriched in immune-related functions.