Hi rskern,
It sounds like you would like to know what can be customized in Control Center, and I want to help.
The Control Center can't have your Calendar app, but you can adjust Control Center as seen here:
Use and customize Control Center on your iPhone, iPad, and iPod touch - Apple Support
You might instead be happy to know that you can add a Calendar widget to your Today View, which would let you easily access Calendar events from Notification Center, the Lock screen, and the Home screen:
Use widgets on your iPhone, iPad, and iPod touch - Apple Support
Good luck!
Thanks for using the Apple Support Communities.