  In analogy to the theory of nilpotent orbit in finite-dimensional semisimple
Lie algebras, it is known that the principal $\mathfrak{sl}_2$ subalgebras can
be constructed in hyperbolic Kac-Moody Lie algebras. We obtained a series of
$\mathfrak{sl}_2$ subalgebras in rank 2 symmetric hyperbolic Kac-Moody Lie
algebras by extending the aforementioned construction. We present this result
and also discuss $\mathfrak{sl}_2$ modules obtained by the action of the
$\mathfrak{sl}_2$ subalgebras on the original Lie algebras.
