  We present a consistency condition for 8d ${\cal N} = 1$ supergravity
theories with non-trivial global structure $G/Z$ for the non-Abelian gauge
group, based on an anomaly involving the $Z$ 1-form center symmetry. The
interplay with other Swampland criteria identifies the majority of 8d theories
with gauge group $G/Z$, which have no string theory realization, as
inconsistent quantum theories when coupled to gravity. While this condition is
equivalent to geometric properties of elliptic K3 surfaces in F-theory
compactifications, it constrains the unexplored landscape of gauge groups in
other 8d string models.
