  The cold dark matter scenario of hierarchical large-scale structure formation
predicts the existence of abundant subhalos around large galaxies. However, the
number of observed dwarf galaxies is far from this theoretical prediction,
suggesting that most of the subhalos could be dark or quite faint.
Gravitational lensing is a powerful tool to probe the mass distribution
directly irrespective of whether it is visible or dark. Time delay anomalies in
strongly lensed quasar systems are complementary to flux ratio anomalies in
probing dark matter substructure in galaxies. Here we propose that lensed
gravitational waves detected by the third-generation ground detectors with
quite accurate time delay measurements could be a much better tool for this
study than conventional techniques. Combined with good quality images of lensed
host galaxies identified by the electromagnetic counterpart measurements,
lensed GW signals could make the systematic errors caused by dark matter
substructures detectable at several percent levels, depending on their mass
functions, internal distribution of subhalos and lensing system configuration.
