U.S. Military Command during WWII

I have some troubles during reading Eisenhower's biography. Can't recognize his role during WWII time. Is he the supreme commander during war? Is he higher in rank compared to MacArthur? So after a bit of googling and looking through Wikipedia, I can conceptualize the wartime command structure into this diagram. - The U.S. system puts the President (in this case, FDR) as the Commander in Chief - [Joint Chiefs of Staff](http://en.wikipedia.org/wiki/Joint_Chiefs_of_Staff), the committee consists of each armed forces chief, serves as the supreme command structure of the military. - William D. Leahy (U.S. Navy) is the highest rank military officer during WWII - During WWII, the Air Forces serve under U.S. Amry. Arnold also hold the rank as Army General. - People in this diagram are listed only the top rank officers after WWII, all of them were promoted to General of the Army or Fleet Admiral (five-star general) in late 1944.