No, only clean by hand and with water.

The upper part, where the coffee runs in, is NOT washed, but I let the coffee blacken it. Rinse briefly with water but nothing else.
That doesn't answer the question of dishwasher suitability. My opinion... I would never do it!

No way - a layer develops on the material and then it is neither attractive nor appetising. This happened to me with my very first mocha pot.

Aluminium should never be put in the dishwasher.

I think so - but I always wash this part by hand.