This paper is motivated by a theorem of the author [Tsukuba J. Math. 9, 117-131 (1985; Zbl 0581.53044)], which asserts that a compact quaternionic submanifold in a quaternionic Kähler manifold is homologically volume minimizing. Let M be a quaternionic symmetric space and \({\mathfrak g}\) the Lie algebra of the group of all isometries on M. The classification of quaternionic submanifolds in M is reduced to that of complex simple subalgebras of index 1 in \({\mathfrak g}^{{\mathbb{C}}}\). In the case that M is of classical type quaternionic submanifolds in M are completely classified by the use of the representation theory of complex simple Lie algebras. This classification enables us to investigate the homology classes represented by quaternionic submanifolds.