At the moment this is a list of order 4 magic squares .
It's going to become a detailed article about the topic.

The characteristic masks on the left of the collapsible tables are the pattern of fields without blue or green background. They are the exclusive or of the four masks shown below each magic square.

The types named by roman numerals are the usual way to order magic squares by the position of complement pairs:
http://www.magic-squares.net/order4list.htm
http://gaspalou.fr/magic-squares/transformation.htm

0 in corner (208 squares) [ edit ]
2 of type VI

2 of type VI

2 of type XI

2 of type XII

12 of type I

12 of type II

12 of type III

2 of type VI

2 of type VI

2 of type IX

2 of type VIII

24 of type V

24 of type IV

24 of type VI

24 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type VI

2 of type IX

2 of type VIII

2 of type VI

2 of type VI

2 of type VI

2 of type VI

6 of type IX

6 of type VIII

6 of type IX

6 of type VIII

Magic sum quadruples [ edit ]

To be continued [ edit ]
24 of type V

24 of type IV

2 of type XI

2 of type XII

6 of type VII

6 of type X

6 of type VII

6 of type X

2 of type VII

2 of type X

2 of type VII

2 of type X