The Pentium G3220 is a 4th generation Intel processor and it comes with the Intel® HD Graphics controller.
You can check it in the below image:
This graphics controller supports same features than the HD 4400 and the others. It is important to mention that Intel® graphics controllers do not support DVI Dual Link. With the DVI Single Link you can get a resolution up to 1900x1200 but this also depends on the computer manufacturer. Sometimes in case of an OEM system, they can set limitations on the graphics controllers including certain resolutions.
You can check this link for more information about the 4th Generation Intel® Core™ Processor Graphics (formerly codenamed Haswell):