Columnar nanostructures and liquid crystals are an important class of self-assembled organic materials that are making great impact on several optoelectronic technologies like transistors, solar cells, ferroelectric switches or light-emitting diodes. These materials are typically produced by the ordered stacking of functional molecules with a discotic shape. We have here studied related assemblies from a unique class of molecules, Subphthalocyanines, having instead a rigid conical shape and strong axial dipole moment. In solution, these molecules organize into non-centrosymmetric supramolecular columnar polymers that show intriguing dual-mode self-assembly and chiral self-sorting processes, as a result of the intrinsic monomer chirality. In condensed phases, the generation of liquid crystalline materials that can be efficiently aligned in the presence of electric fields and that exhibit permanent or switchable net polarization is observed. This is a novel and appealing attribute that may have important implications in, for instance, technologies that require an efficient directional transport of charges or memory devices combining ferroelectric and semiconducting properties.