Despite the widespread exploration and availability of parcellations for the functional connectome, parcellations designed for the structural connectome are comparatively limited. Current research suggests that there may be no single "correct" parcellation and that the human brain is intrinsically a multiresolution entity. In this work, we propose the Continuous Structural Connectivitity-based, Nested (CoCoNest) family of parcellations-a fully data-driven, multiresolution family of parcellations derived from structural connectome data. The CoCoNest family is created using agglomerative (bottom-up) clustering and error-complexity pruning, which strikes a balance between the complexity of each parcellation and how well it preserves patterns in vertex-level, high-resolution connectivity data. We draw on a comprehensive battery of internal and external evaluation metrics to show that the CoCoNest family is competitive with or outperforms widely used parcellations in the literature. Additionally, we show how the CoCoNest family can serve as an exploratory tool for researchers to investigate the multiresolution organization of the structural connectome.