You want to be careful with 308 Win subsonic loads. It is pretty easy to stick a bullet down the bore and if you are not paying attention, fire a second round behind it. Either use lube on the bullet or regular (read OFTEN) run a lubed patch down the bore will help prevent sticking a bullet in the bore.
Powder like Trailboss revolutionized large case subsonics but Trailboss is pretty hard to find these days.
Lapua makes a 308 bullet specifically for subsonics. It is 200gr with a rebated boat-tail and a thin gilded jacket. They do not need lube.
Shorter, lighter subsonics will wildly overpenetrate pretty much anything. Longer projectiles, like the 208 AMAX will become unstable on impact and tumble in flesh.