We prove that any connected
2
2
–compact group is classified by its
2
2
–adic root datum, and in particular the exotic
2
2
–compact group
DI
(
4
)
\operatorname {DI}(4)
, constructed by Dwyer–Wilkerson, is the only simple
2
2
–compact group not arising as the
2
2
–completion of a compact connected Lie group. Combined with our earlier work with Møller and Viruel for
p
p
odd, this establishes the full classification of
p
p
–compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected
p
p
–compact groups and root data over the
p
p
–adic integers. As a consequence we prove the maximal torus conjecture, giving a one-to-one correspondence between compact Lie groups and finite loop spaces admitting a maximal torus. Our proof is a general induction on the dimension of the group, which works for all primes. It refines the Andersen–Grodal–Møller–Viruel methods by incorporating the theory of root data over the
p
p
–adic integers, as developed by Dwyer–Wilkerson and the authors. Furthermore we devise a different way of dealing with the rigidification problem by utilizing obstruction groups calculated by Jackowski–McClure–Oliver in the early 1990s.