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SciFi Armies

Done reading about WW1, I got to thinking about the organization of armies on a SciFi scale. What exactly do you call those mega-groupings? I mean, you need enough people to occupy an planet.

For the US, military groupings are as follows:

Squad
Platoon
Company
Battalion
Brigade
Division
Corps
Field Army
Army Group
Theater
Army (field army, est 100,000)
Group (army group, est 500,000)
Theater (est 5-10 million)

And now we get into the SF stuff.

League (multiple theaters, est. 20-50 million)
Sector (multiple leagues, est. 200-500 million)
Quadrant (multiple sectors, estimate 1 billion+)
Solar (multiple quadrants, estimate 5-10 billion+)