The present article is the final part of a series on the classification
of the totally geodesic submanifolds of the irreducible Riemannian
symmetric spaces of rank 2. After this problem has been solved
for the 2-Grassmannians in my papers [7] and [8], and for
the space $\mathrm{SU}(3)/\mathrm{SO}(3)$ in Section 6 of [9],
we now solve
the classification for the remaining irreducible Riemannian
symmetric spaces of rank 2 and compact type:
$\mathrm{SU}(6)/\mathrm{Sp}(3)$,
$\mathrm{SO}(10)/\mathrm{U}(5)$,
$E_{6}/(\mathrm{U}(1) \cdot \mathrm{Spin}(10))$,
$E_{6}/F_{4}$, $G_{2}/\mathrm{SO}(4)$,
$\mathrm{SU}(3)$, $\mathrm{Sp}(2)$ and $G_{2}$.
Similarly as for the spaces already investigated in the earlier
papers, it turns out that for many of the spaces investigated
here, the earlier classification of the maximal totally geodesic
submanifolds of Riemannian symmetric spaces by Chen and Nagano
([5], \S9) is incomplete. In particular, in the spaces $\mathrm{Sp}(2)$,
$G_{2}/\mathrm{SO}(4)$ and $G_{2}$, there exist maximal totally geodesic
submanifolds, isometric to 2- or 3-dimensional spheres, which
have a ``skew'' position in the ambient space in the sense
that their geodesic diameter is strictly larger than the geodesic
diameter of the ambient space. They are all missing from [5].