It's difficult, (if not impossible), and expensive to kill crabgrass, without killing everything, once it's mature.
You can pull up as much of it as practical, before it goes to seed, and use a pre-emergent crab grass preventer next year.
This is done by either using a fertilizer with crabgrass preventer built in, or a pre-emergent weed preventer in spray form.
You apply the first treatment early, like in March, or April. And, I would apply again in June, for a few years. After you get control of it, you can try just applying it, in the spring only. It needs to be watered in well, or lots of rain, after application.
I use generic Baracade, (Prodiamine 65 WDG), it's been the most cost effective way to treat acreage.
It took many years to finally figure out what it would take to get complete control of mine.