We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For this, we construct invariants attached to a given hypersurface that serve as obstructions to embeddability. We further study the embeddability problem for real-analytic submanifolds of higher codimension and answer a question by Forstneri\v c.