Sigma Quattro H has a Sigma SA Bayonet lens mount and currently there are 77 native lenses available for this mount.
Sigma Quattro H doesn't have a sensor based image stabilization system but 29 of these lenses already comes with optical image stabilization.
Since Sigma Quattro H has a APS-H sensor, it has a focal length multiplier of 1.3x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on Quattro H.
You may also also be interested in these:
Sigma Quattro H Lenses with Image Stabilization
Sigma Quattro H Lenses with Weather Sealings