I have 59.74 %ile, 474256 CRL and 35,395 SC rank in JEE Mains. Can I get admission in any NIT, IIIT or GFTI?

With this rank, it is difficult for you to get into any NIT, IIIT, GFTI's. 

However, I'll suggest you to go for state level counselling and some private colleges there you'll get some advantages too. 

I would also suggest you to use some college predictors. It will help you in getting ideas of various