  We prove that large cardinals need not generally exhibit their large cardinal
nature in HOD. For example, a supercompact cardinal $\kappa$ need not be weakly
compact in HOD, and there can be a proper class of supercompact cardinals in
$V$, none of them weakly compact in HOD, with no supercompact cardinals in HOD.
Similar results hold for many other types of large cardinals, such as
measurable and strong cardinals.
