  M-theory preons -- solutions of eleven-dimensional supergravity preserving 31
supersymmetries -- have recently been shown to be locally maximally
supersymmetric. This implies that if preons exist they are quotients of
maximally supersymmetric solutions. In this paper we show that no such
quotients exist. This is achieved by reducing the problem to quotients by
cyclic groups in the image of the exponential map, for which there already
exists a partial classification, which is completed in the present paper.
