Chances are is that what you have is Alacantara (artificial suede) and not suede, which is actually the bottom layer of the leather hide. Most upholsters don't use suede anymore in auto interiors as they try to get as much out of the leather hide as they can.
Alacantara is a very nice material, but you have to treat it carefully. I use Swissvax Alacanta cleaner for it as it is purposely made for this material. Since alacantara is a very delicate material, what you do is spray the solution lightly onto the surfaces. After that, basically take a nice microfiber cloth and lightly pat the surfaces to gently work in the cleaner. After, just let the cleaner naturally dry. You also want to try to avoid using a brush, or rubbing the material with any force.
I absolutely love alacantara and the looks it provides. Such a great material, however it is finicky.