  We report the largest sample of candidate strong gravitational lenses
belonging to the Survey of Gravitationally-lensed Objects in HSC Imaging for
group-to-cluster scale (SuGOHI-c) systems. These candidates are compiled from
the S18A data release of the Hyper Suprime-Cam Subaru Strategic Program
(HSC-SSP) Survey. We visually inspect $\sim39,500$ galaxy clusters, selected
from several catalogs, overlapping with the Wide, Deep, and UltraDeep fields,
spanning the cluster redshift range $0.05<z_{cl}<1.38$. We discover 641
candidate lens systems, of which 536 are new. From the full sample, 47 are
almost certainly bonafide lenses, 181 of them are highly probable lenses and
413 are possible lens systems. Additionally, we present 131 lens candidates at
galaxy-scale serendipitously discovered during the inspection. We obtained
spectroscopic follow-up of 10 candidates using the X-shooter. With this
follow-up, we confirm 8 systems as strong gravitational lenses. Of the
remaining two, one of the sources is too faint to detect any emission, and the
other has a tentative redshift close to the lens redshift, but additional arcs
in this system are yet to be observed spectroscopically. Since the HSC-SSP is
an ongoing survey, we expect to find $\sim600$ definite or probable lenses
using this procedure and even more if combined with other lens finding methods.
