First off, the War of the Austrian Succession was more properly the War of the Bohemian Succession. Maria Theresa was the eldest daughter of an Emperor without sons who had inherited the throne from his older brother whose only son had died. There had been an agreement that if the younger brother failed to produce a son that the elder brother's daughters (the Queen of Poland and the Queen of Bavaria) would have superior inheritance rights over the younger brother's daughters. The Queen of Bavaria then claimed the Kingdom of Bohemia without making claims against Austria or Hungary. This was significant because Bohemia was one of the 7 electors, and after France bribed, threatened and cajoled the Bishop-Electors of Mainz, Trier and Cologne, the vote of Bohemia was sufficient to make the King of Bavaria the Holy Roman Emperor.
Second, Spain had lost all of her possessions is Italy as a result of the War of the Spanish Succession. Sicily and Naples seem to be Spain's color. The old King of Spain had fathered new children with his second Italian wife. This second wife wanted possessions in Italy to set up her sons as Kings of Dukes. Specifically, she wanted Parma.
Third, while France wanted to break the power of the House of Austria within Germany, France also had her then long term goal of seizing the Southern portions of what is today Belgium principally to advance their frontier to a highly defensible river but also to take in the Francophone Walloons.
None of these three central focuses of the war exist as Supply Centers.
Frederick the Great and the awesome Prussian Army was largely a thing of the next generation. Frederick never really faced the Austrian Army during this war. Austria was fighting the French in the Low Countries and in Southern Germany and the Spanish and the French in both Northern and Southern Italy throughout the war. The top two Austrian generals were von Khevenhüller and von Traun. The Prussians faced von Traun only once and were soundly defeated. Aside from this one brief campaign in which von Traun was sent with a real army to evict the Prussians from Moravia, von Traun spent nearly the entire war in Italy, while von Khevenhüller evicted the French from Southern Germany and forced the Bavarians out of Bohemia.