Genetic and molecular analysis of rare disease is made difficult by the small numbers of affected patients. Phenotypic comorbidity analysis can help rectify this by combining information from individuals with similar phenotypes and looking for overlap in terms of shared genes and underlying functional systems. However, few studies have combined comorbidity analysis with genomic data. We present a computational approach that connects patient phenotypes based on phenotypic co-occurence and uses genomic information related to the patient mutations to assign genes to the phenotypes, which are used to detect enriched functional systems. These phenotypes are clustered using network analysis to obtain functionally coherent phenotype clusters. We applied the approach to the DECIPHER database, containing phenotypic and genomic information for thousands of patients with heterogeneous rare disorders and copy number variants. Validity was demonstrated through overlap with known diseases, co-mention within the biomedical literature, semantic similarity measures, and patient cluster membership. These connected pairs formed multiple phenotype clusters, showing functional coherence, and mapped to genes and systems involved in similar pathological processes. Examples include claudin genes from the 22q11 genomic region associated with a cluster of phenotypes related to DiGeorge syndrome and genes related to the GO term anterior/posterior pattern specification associated with abnormal development. The clusters generated can help with the diagnosis of rare diseases, by suggesting additional phenotypes for a given patient and potential underlying functional systems. Other tools to find causal genes based on phenotype were also investigated. The approach has been implemented as a workflow, named PhenCo, which can be adapted to any set of patients for which phenomic and genomic data is available. Full details of the analysis, including the clusters formed, their constituent functional systems and underlying genes are given. Code to implement the workflow is available from GitHub.