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Studies have revealed contributions of the cerebellum and subcortex to higher-order cognitive functions; however, it has been unclear whether such functional representations are preserved across the cortex, cerebellum, and subcortex. In this study, we use functional magnetic resonance imaging data with 103 cognitive tasks and construct three voxel-wise encoding and decoding models independently using cortical, cerebellar, and subcortical voxels. Representational similarity analysis reveals that the structure of task representations is preserved across the three brain parts. Principal component analysis visualizes distinct organizations of abstract cognitive functions in each part of the cerebellum and subcortex. More than 90% of the cognitive tasks are decodable from the cerebellum and subcortical activities, even for the novel tasks not included in model training. 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