  A left Bol loop is a loop satisfying $x(y(xz)) = (x(yx))z$. The commutant of
a loop is the set of elements which commute with all elements of the loop. In a
finite Bol loop of odd order or of order $2k$, $k$ odd, the commutant is a
subloop. We investigate conditions under which the commutant of a Bol loop is
not a subloop. In a finite Bol loop of order relatively prime to 3, the
commutant generates an abelian group of order dividing the order of the loop.
This generalizes a well-known result for Moufang loops. After describing all
extensions of a loop $K$ such that $K$ is in the left and middle nuclei of the
resulting loop, we show how to construct classes of Bol loops with non-subloop
commutant. In particular, we obtain all Bol loops of order 16 with non-subloop
commutant.
