Hierarchical decompositions of control systems are important for reducing the analysis and design of large scale systems. Such decompositions depend on the notion of abstraction: Given a large scale system and a desired property, one tries to extract an abstracted model with equivalent properties, while ignoring details that are irrelevant. Checking the property on the abstraction should be equivalent to checking the property on the original system. In this paper, we focus on large scale linear systems nad the property of stabilizability. This results in a hierarchy of linear abstractions that are equivalent from a stabilizability point of view. This is important as high level controller designs are guaranteed to have lower level implementations.