Check if it also wakes up automatically from being completely shut down. If so, there is probably a BIOS option configured to automatically turn it on. If this is the case, enter the BIOS setup by pressing Esc (for most HP laptops) when booting up, and look for a scheduled wake-up time.
If it doesn't wake from complete shutdown, some process is waking it up then. Are you sure you've checked all of the scheduled tasks? There can be multiple folders in the task scheduler which it would be in. Is there a backup program running?
You could also use software like SysInternals Process Monitor to look at what processes are launching right at 11:30am. If a certain process runs every day right at that time, that would be a clue to what is causing the problem.
You could also just dump the running process list by running
tasklist > file.txt at 11:29 and 11:31. This will create a text file with a list of all the processes running. You could then DIFF these files to see what is running which wasn't before. If you'd like to load the lists into Excel to make it easier to analyze, you can use
tasklist /FO CSV > file.txt to dump a csv file which can be imported into Excel.