“Miso makes a soup loaded with flavour that saves you the hassle of making stock.” – Y. Ottolenghi [19] We present MiSoSouP, a suite of algorithms for extracting highquality approximations of the most interesting subgroups, according to different interestingness measures, from a random sample of a transactional dataset. We describe a new formulation of these measures that makes it possible to approximate them using sampling. We then discuss how pseudodimension, a key concept from statistical learning theory, relates to the sample size needed to obtain an high-quality approximation of the most interesting subgroups. We prove an upper bound on the pseudodimension of the problem at hand, which results in small sample sizes. Our evaluation on real datasets shows that MiSoSouP outperforms state-of-the-art algorithms offering the same guarantees, and it vastly speeds up the discovery of subgroups w.r.t. analyzing the whole dataset.