  The structure of overlapping subdivergences, which appear in the perturbative
expansions of quantum field theory, is analyzed using algebraic lattice theory.
It is shown that for specific QFTs the sets of subdivergences of Feynman
diagrams form algebraic lattices. This class of QFTs includes the Standard
model. In kinematic renormalization schemes, in which tadpole diagrams vanish,
these lattices are semimodular. This implies that the Hopf algebra of Feynman
diagrams is graded by the coradical degree or equivalently that every maximal
forest has the same length in the scope of BPHZ renormalization. As an
application of this framework a formula for the counter terms in
zero-dimensional QFT is given together with some examples of the enumeration of
primitive or skeleton diagrams.
