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The brain's rich club is a network of particularly densely interconnected regions, metabolically costly to maintain but central to the balance between functional segregation and integration. We assessed whether the rich club can accordingly be described as a control center of the brain, and present a systematic analysis of its involvement in maintenance of and traversal between various cognitively relevant functional states. Brain states were defined based on fMRI task-evoked and resting-state patterns of activity as provided by the Human Connectome Project (HCP). Using tools from network control theory (NCT), we computed the necessary effort needed for control of dynamics when the rich club, versus a size-matched set of low-degree peripheral regions, was prohibited from exerting control over dynamics. Control energy needed to traverse functional states was significantly higher, and stability of states significantly lower, when the set of peripheral regions was prohibited from control. Findings were stable across various rich-club and null model definitions and across different parameter settings. A region's contribution to optimal control processes was instead associated with its affiliation with certain intrinsic connectivity networks and its position on the visual-sensorimotor, but not sensory-transmodal cortical gradient. We accordingly report that the rich club was systematically less involved in control of dynamics than the size-matched set of peripheral regions. These results do not negate an integratory role of the rich club, but question its proposed role as a driver of control. Indeed, if it would inhabit such a role, we would have expected opposite results. Our findings fit with a position describing the rich club as a passive "data-highway" which, by means of its high connectivity, can be easily controlled by peripheral regions and thus facilitate relevant communication channels between them. We call for methodological expansions of the control theoretical toolbox allowing for elaborations on the temporal dynamics of control processes.