In higher dimension, quotient singularities are still log terminal. Fix $n>0$ and let $H\subset\mathbb{C}{\mathbb{P}}^{n+1}$ be a smooth degree $d$ hypersurface. The affine cone over $H$ has only canonical singularities iff $d\leq n+1$.

In particular, the ordinary double point $x^{2}+y^{2}+z^{2}+t^{2}=0$ has only canonical singularities but it is not a quotient singularity.

The hypersurface singularities of type $A-D-E$ are canonical.