Independent component analysis (ICA) has become a widely used method for extracting functional networks in the brain during rest and task. Historically, preferred ICA dimensionality has widely varied within the neuroimaging community, but typically varies between 20 and 100 components. This can be problematic when comparing results across multiple studies because of the impact ICA dimensionality has on the topology of its resultant components. Recent studies have demonstrated that ICA can be applied to peak activation coordinates archived in a large neuroimaging database (i.e., BrainMap Database) to yield whole-brain task-based co-activation networks. A strength of applying ICA to BrainMap data is that the vast amount of metadata in BrainMap can be used to quantitatively assess tasks and cognitive processes contributing to each component. In this study, we investigated the effect of model order on the distribution of functional properties across networks as a method for identifying the most informative decompositions of BrainMap-based ICA components. Our findings suggest dimensionality of 20 for low model order ICA to examine large-scale brain networks, and dimensionality of 70 to provide insight into how large-scale networks fractionate into sub-networks. We also provide a functional and organizational assessment of visual, motor, emotion, and interoceptive task co-activation networks as they fractionate from low to high model-orders.