Number fields unramified away from 2

Consider the set of number fields unramified away from 2, i.e., unramified outside {2, infinity}. We show that there do not exist any such fields of degrees 9 through 15. As a consequence, the following simple groups are ruled out for being the Galois group of an extension which is unramified away from 2: Mathieu groups M-11 and M-12, PSL(3, 3), and alternating groups A(j) for 8 < j < 16 (values j <= 8 were previously known). (c) 2010 Elsevier Inc. All rights reserved.