F_p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve

Let f be the finite field of order q2. It is sometimes attributed to Serre that any curve F -covered by the Hermitian curve Hq+1 : Yq+1 = xq + x is also F -maximal. For prime numbers q we show that every F -maximal curve X of genus g ≤ 2 with | Aut(X) | > 84(g - 1) is Galois-covered by Hq+1. The hypothesis on | Aut(X) | is sharp, since there exists an F -maximal curve X for q = 71 of genus g = 7 with | Aut(X) | = 84(7 - 1) which is not Galois-covered by the Hermitian curve H72.