DNA tile based self-assembly provides a bottom-up approach to construct desired nanostructures. DNA tiles have been directly constructed from ssDNA and readily self-assembled into 2D lattices and 3D superstructures. However, for more complex lattice designs including algorithmic assemblies requiring larger tile sets, a more modular approach could prove useful. This paper reports a new DNA 'sub-tile' strategy to easily create whole families of programmable tiles. Here, we demonstrate the stability and flexibility of our sub-tile structures by constructing 3-, 4- and 6-arm DNA tiles that are subsequently assembled into 2D lattices and 3D nanotubes according to a hierarchical design. Assembly of sub-tiles, tiles, and superstructures was analyzed using polyacrylamide gel electrophoresis and atomic force microscopy. DNA tile self-assembly methods provide a bottom-up approach to create desired nanostructures; the sub-tile strategy adds a useful new layer to this technique. Complex units can be made from simple parts. The sub-tile approach enables the rapid redesign and prototyping of complex DNA tile sets and tiles with asymmetric designs.