The notion of QL-operations constructed from overlap and grouping functions is introduced and their properties are studied. The conditions under which QL-operations are QL-implications functions are analyzed. We show that those QL-implication functions are richer than QL-implications derived from t-norms and positive t-conorms. The intersection among QL-implication functions and other classes of fuzzy implication functions constructed from overlap and grouping functions is provided. We present an application to the generation of fuzzy subsethood and derived entropy measures.