Infinitesimal conformal transformations of ℝn are always polynomial and finitely generated when n > 2. Here we prove that the Lie algebra of infinitesimal conformal polynomial transformations over ℝn, n > 2, is maximal in the Lie algebra of polynomial vector fields. When n is greater than 2 and p, q are such that p + q = n, this implies the maximality of an embedding of so(p + 1, q + 1, ℝ) into polynomial vector fields that was revisited in recent works about equivariant quantizations. It also refines a similar but weaker theorem by V. I. Ogievetsky.