18.116 (2014)

Given a finite 2-group $G$ of order $2^n$, does there exist a finite set $S$ of rational primes such that $|S| \leqslant n$ and $G$ is a quotient group of the absolute Galois group of the maximal 2-extension of $\mathbb{Q}$ unramified outside $S \cup \{\infty\}$? This is true for $p$-groups, $p$ odd, as noted by Serre.