jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of ‘anomaly interplay’, which uses functoriality of cobordism and naturality of the jats:italicη</jats:italic>-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including jats:italicS</jats:italic>jats:sub3</jats:sub>, jats:italicA</jats:italic>jats:sub4</jats:sub>, jats:italicQ</jats:italic>jats:sub8</jats:sub>, and SL(2jats:italic,</jats:italic> 𝔽jats:sub3</jats:sub>).</jats:p>jats:pIn the case of finite abelian groups, it is well known that anomalies can be ‘truncated’ in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with jats:italicA</jats:italic>jats:sub4</jats:sub> symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the SL(2jats:italic,</jats:italic> 𝔽jats:sub3</jats:sub>) symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a ℤjats:italic/</jats:italic>3 extension of SL(2jats:italic,</jats:italic> 𝔽jats:sub3</jats:sub>).</jats:p>