The N200 can fit coolers up to 160mm
in height http://www.coolermaster.com/case/mini-tower/n200/
The Hyper 212 LED Turbo is 163mm
For a G4560, the Cryorig M9i would be more than enough (even the stock cooler will suffice).
Note that your H110 motherboard *might* need a BIOS update (if it doesn't have already) for that G4560 to work.