I have calculated it as 516.
The selection of 3 points out of 16 can be done in 16C3 = 560.
This include points that are collinear. If you calculate the number of collinear lines with 3 grid points then you will get 44 such lines.
So, final number of possible triangles are 560 -44 = 516
This stackexchange Q&A helped me to solve this: https://math.stackexchange.com/a/634131
Please consider counting these 4 lines too