Hi,
Your best bet is to check the compatibility matrix:
https://www.cisco.com/c/en/us/td/docs/wireless/compatibility/matrix/compatibility-matrix.html#wp99531
4400 WLC Supports up to code 7.x
Minimum Code for APs:
AP 3602i - 7.1.91.0 (Supported)
AP 1131 - 3.1.59.24 (Supported)
AP 1142 - 5.2.157.0 (Supported)
AP 1252 - 4.2.61.0 (Supported)
So they are all compatible BUT:
The 4400 is a very old WLC and is no longer supported by Cisco.
The code required for the 3600 is 7.1.191.0 but anything lower than 8.x code is generally not recommended in a deployment.
At the very least you should run the latest 7.x code which I believe all APs support and the 4400 does too. Ideally you would be looking at refreshing the 1131 and 1252 APs as well as your WLC. The 1142 and 3602s are still within reasonable hardware refresh timelines (in my opinion).
Ric
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