Mammalian functional architecture flexibly adapts, transitioning from integration where information is distributed across the cortex, to segregation where information is focal in densely connected communities of brain regions. This flexibility in cortical brain networks is hypothesized to be driven by control signals originating from subcortical pathways, with the basal ganglia shifting the cortex towards integrated processing states and the cerebellum towards segregated states. In a sample of healthy human participants (N=242), we used fMRI to measure temporal variation in global brain networks while participants performed two tasks with similar cognitive demands (Stroop and Multi-Source Inference Task (MSIT)). Using the modularity index, we determined cortical networks shifted from integration (low modularity) at rest to high modularity during easier i.e. congruent (segregation). Increased task difficulty (incongruent) resulted in lower modularity in comparison to the easier counterpart indicating more integration of the cortical network. Influence of basal ganglia and cerebellum was measured using eigenvector centrality. Results correlated with decreases and increases in cortical modularity respectively, with only the basal ganglia influence preceding cortical integration. Our results support the theory the basal ganglia shifts cortical networks to integrated states due to environmental demand. Cerebellar influence correlates with shifts to segregated cortical states, though may not play a causal role.