What was the percent of the Soviet territory that was under Nazi control at maximum extent?
A widely cited figure is "500,000 sq mi of Russian territory" occupied by Nazi Germany, but it does not seem plausible because of the imprecise choice of wording.
Wikipedia says (without providing a reference), that in course of Operation Barbarossa Germany captured 1.3 mln km2 until the end of 1941 plus a maximum of 0.65 mln km2 later. That would be a total of 1.95 mln km2.
Properly, this should be divided by Soviet land area as of 22 June 1941, but I've been unable to find this figure. I substitute the 1991 figure, which is only a little bit lower.
1.95 / ( 22.27 or more ) * 100% = 8.8% (or less)
That's not a terribly easy question as the numbers and definitions are in dispute. For example, do you mean occupied, military presence, or actually subjugated, and if subjugated how much resistance? Then do you include Soviet occupied Poland? If Poland, then what about Finland? Since the Russians practiced slash and burn, do you include territory which was more-or-less unable to be occupied?
The amount of land under control can be seen here and here. Both maps are from the same period and both show some very different maps. It appears that the most that the Germans were able to hold indisputably was somewhere around a third of the territory of the Soviet Union west of the Urals. The broader chart suggest closer to half of the territory west of the Urals.
Of course, both of those estimates exclude Siberia.