No, organizations cannot be nested within a parent organization. Organizations are "flat", relative to each other.
Note that devices, device groups, content (apps and files) and users are sandboxed within an organization.
However, you can establish account hierarchy in terms of billing. This is recommended for customers who require their devices, device groups, content (apps and files) and users to be sandboxed by either client or department, but would like to consolidate and manage billing across all their organizations from one place. For more information about establishing billing account hierarchy, see this article.