I would say with 3 weeks to do it in, you probably could do about 5 islands (not 6) plus Athens if you're young and flexible, willing to travel at night sometimes. Our advice would differ a great deal depending on WHEN you plan to go... PLEASE share your exact dates of Athens arrival/departure.
In general if your dates are in August, the islands you mention will be absolutely HEAVING with holiday-makers, not a single metre of sand to spread your beach towel on, and all ferries busses jammed as well. Crete would be the exception simply because it is so large that you can escape the crowds. You may have to look at some less-visited islands, if you want more breathing room ... I have some delightful ones to suggest if you'll just share a bit more.
Another consideration is BUDGET. You have selected (aside from Crete) the MOST touristic islands, thus the most expensive. What is your Euro budget per day for EVERYTHING (lodging, food, drink, transport, misc).
It also always helps if you can give an idea of your interests. Is it mainly for beach and sunshine, with a bit of nightlife? Or are you into ruins and history, do you like hiking, are you interested in small villages where you can encounter authentic Greek life a bit.? What are your priorities.