I recently bought the quarter eagle flag on ebay and only this morning when I woke up I noticed that austria seems to be missing. Does anyone have an idea why? The wikipedia entry didn't say much .
Picture of woodcut at the very top of the page: https://en.wikipedia.org/wiki/Coats_of_arms_of_the_Holy_Roman_Empire
Does the flag you bought feature the exact same eagle that you linked to? You’re right, that one doesn’t seem to feature Austria – others do, however. The HRE consisted of so many parts, it would have been impossible to show all of them on one coat of arms, and there was no fixed rule how the Quarter Eagle should look, so whenever someone commissioned or designed one, the decision to include certain parts of the HRE was quite arbitrary. For example, this one does feature Austria (on the left) and also Tyrol, I think – hard to tell without colour.
Another thing to bear in mind is that many depictions of the Quarter Eagle didn’t show for example the most important duchies, but rather a selection of the different estates of the realm. Take this example of the eagle: each of the 12 feathers features a different estate of the realm, for instance cities, dukes, counts, etc., plus the electors at the top, and – interestingly enough – four others coats of arms surrounding the eagle, each representing one of the other anointed European kings (England, Scotland, France and Sicily). More information on this particular eagle (painted 1495, Innsbruck) here.
The simple answer is /u/stefan2494's. Everyone who had a Quarter Eagle made could and effectively had to choose which of the hundreds of Imperial subjects he wanted represented.
The term "Quarter Eagle" itself does not mean 1/4 eagle but is a shortening of "Quaternion Eagle", Quaternia being the HRE's holy order of estates (1606 woodcut) meant to represent a god-given division of the Empire's population from duke to peasant. As such people often focused on their estate, for example a Free City using a Quarter Eagle mainly composed of other Free Cities, or getting "a bit of each".
For a more symbolic explanation, the eagle (and other regalia of that kind) is meant to represent the Empire in total with the shields showing a selection of subjects. Since the Habsburgs dominated the title of Holy Roman Emperor from 1452 (Frederick III) onwards, their hereditary lands were of course not subject to but personal property of the Emperor and are thus not commonly depicted in these kinds of things.
EDIT: Estates are not classes. Wrong context.