Step 1: Identify the nature of the numbers.
All options are perfect squares:
\[
121 = 11^2,\quad 144 = 12^2,\quad 169 = 13^2,\quad 225 = 15^2
\]
Step 2: Analyze the base numbers.
11, 13, 15 are odd numbers
12 is an even number
Step 3: Identify the odd one out.
Only 144 is the square of an even number. All others are squares of odd numbers.
Conclusion: The number that does not belong in the group is:
144