All the supersymmetric configurations of N=4, d=4 supergravity

All the supersymmetric configurations of pure, ungauged, N=4, d=4 supergravity are classified in a formalism that keeps manifest the S and T dualities of the theory. We also find simple equations that need to be satisfied by the configurations to be classical solutions of the theory. While the solutions associated to null Killing vectors were essentially classified by Tod (a classification that we refine), we find new configurations and solutions associated to timelike Killing vectors that do not satisfy Tod's rigidity hypothesis (hence, they have a nontrivial U(1) connection) and whose supersymmetry projector is associated to 1-dimensional objects (strings), although they have a trivial axion field.