  Let $\Lambda$ be an artin algebra and $\mathcal{C}$ be a functorially finite
subcategory of mod$\Lambda$ which contains $\Lambda$ or $D\Lambda$. We use the
concept of the infinite radical of $\mathcal{C}$ and show that $\mathcal{C}$
has an additive generator if and only if rad$^\infty_{\mathcal{C}}$ vanishes.
In this case we describe the morphisms in powers of the radical of
$\mathcal{C}$ in terms of its irreducible morphisms. Moreover, under a mild
assumption, we prove that $\mathcal{C}$ is of finite representation type if and
only if any family of monomorphisms (epimorphisms) between indecomposable
objects in $\mathcal{C}$ is noetherian (conoetherian). Also, by using injective
envelopes, projective covers, left $\mathcal{C}$-approximations and right
$\mathcal{C}$-approximations of simple $\Lambda$-modules, we give other
criteria to describe whether $\mathcal{C}$ is of finite representation type. In
addition, we give a nilpotency index of the radical of $\mathcal{C}$ which is
independent from the maximal length of indecomposable $\Lambda$-modules in
$\mathcal{C}$.
