Cognitive control, the ability to adapt thoughts and actions to shifting contexts and goals, is composed primarily of three distinct yet interrelated components: Inhibition, Shifting, and Updating. While prior research has examined the nature of different cognitive components as well as their inter-relationships, fewer studies examined whole-brain connectivity to predict individual differences for the three cognitive components and associated tasks. Here, using the Connectome-based Predictive Modelling (CPM) approach and open-access data from the Human Connectome Project, we built brain network models to successfully predict individual performance differences on the Flanker task, the Dimensional Change Card Sort task, and the 2-Back task, each putatively corresponding to Inhibition, Shifting, and Updating. We focused on grayordinate fMRI data collected during the 2-Back tasks after confirming superior predictive performance over resting-state and volumetric data. High cross-task prediction accuracy as well as joint recruitment of canonical networks, such as the frontoparietal and default-mode networks, suggest the existence of a common cognitive control factor. To directly investigate the relationships among the three cognitive control components, we developed new measures to disentangle their shared and unique aspects. Our analysis confirmed that a shared control component can be well predicted from functional connectivity patterns densely located around the frontoparietal, default-mode and dorsal attention networks. In contrast, the Shifting-specific and Inhibition-specific components exhibited lower cross-prediction performance, indicating their distinct and specialized roles. Notably, the Updating-specific component showed significant cross-prediction with the general control factor, suggesting its central role in cognitive control. Given the limitation that individual behavioral measures do not purely reflect the intended cognitive constructs, our study demonstrates the need to distinguish between common and specific components of cognitive control.