The cerebral cortex may be organized into anatomical genetic modules, communities of brain regions with shared genetic influences via pleiotropy. Such modules could represent novel phenotypes amenable to large-scale gene discovery. This modular structure was investigated with network analysis of in vivo MRI of extended pedigrees, revealing a "multiscale" structure where smaller and larger modules exist simultaneously and in partially overlapping fashion across spatial scales, in contrast to prior work suggesting a specific number of cortical thickness modules. Inter-regional genetic correlations, gene co-expression patterns and computational models indicate that two simple organizational principles account for a large proportion of the apparent complexity in the network of genetic correlations. First, regions are strongly genetically correlated with their homologs in the opposite cerebral hemisphere. Second, regions are strongly genetically correlated with nearby regions in the same hemisphere, with an initial steep decrease in genetic correlation with anatomical distance, followed by a more gradual decline. Understanding underlying organizational principles of genetic influence is a critical step towards a mechanistic model of how specific genes influence brain anatomy and mediate neuropsychiatric risk.