The functional connectome has gained increased attention in the neuroscience community. In general, most network connectivity models are based on correlations between discrete-time series signals that only connect two different brain regions. However, these bivariate region-to-region models do not involve three or more brain regions that form a subnetwork. Here we propose a learning-based method to explore subnetwork biomarkers that are significantly distinguishable between two clinical cohorts. Learning on hypergraph is employed in our work. Specifically, we construct a hypergraph by exhaustively inspecting all possible subnetworks for all subjects, where each hyperedge connects a group of subjects demonstrating highly correlated functional connectivity behavior throughout the underlying subnetwork. The objective function of hypergraph learning is to jointly optimize the weights for all hyperedges which make the separation of two groups by the learned data representation be in the best consensus with the observed clinical labels. We deploy our method to find high order childhood autism biomarkers from rs-fMRI images. Promising results have been obtained from comprehensive evaluation on the discriminative power and generality in diagnosis of Autism.