A closed subgroup of a semisimple algebraic group G is said to be G‐irreducible if it lies in no proper parabolic subgroup of G. We prove a number of results concerning such subgroups. Firstly they have only finitely many overgroups in G; secondly, with some specified exceptions, there exist G‐irreducible subgroups of type A1; and thirdly, we prove an embedding theorem for G‐irreducible subgroups.

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