  We classify Haag-dual Poincar\'e covariant subsystems $\B\subset \F$ of a
graded-local net $\F$ on 4D Minkowski spacetime which satisfies standard
assumptions and has trivial superselection structure. The result applies to the
canonical field net $\F_\A$ of a net $\A$ of local observables satisfying
natural assumptions. As a consequence, provided that it has no nontrivial
internal symmetries, such an observable net $\A$ is generated by (the abstract
versions of) the local energy-momentum tensor density and the observable local
gauge currents which appear in the algebraic formulation of the quantum Noether
theorem. Moreover, for a net $\A$ of local observables as above, we also
classify the Poincar\'e covariant local extensions $\B \supset \A$ which
preserve the dynamics.
