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Classification of Certain Subgroups of G2

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type G2, focusing on the case of number fields and p-adic fields. In the same context we characterize the rational conjugacy classes of A2 subgroups of G2. Having obtained the concrete characterization, we then relate it to the more abstract characterization which can be given in terms of Galois cohomology. We note that these results on A2 subgroups were simultaneously and independently developed in the work of Hooda whereas the results on tori were simultaneously and independently developed in the work of Beli-Gille-Lee.