It won an Emmy this year for best comedy series, while Aniston won best comedy actress.
The seven categories are: most creative, most inspirational, best series, best comedy, musician of the year, best commentary and "most adorable video ever".
Along with best original screenplay, best comedy series and daytime serial, there's a new category being featured, best video game writing.
It also has a Golden Globe nomination for best musical or comedy series.
However, they were both pipped by Lena Dunham, creator and star of sitcom Girls, which also won best comedy TV series.
Comedy Central's "Daily Show" won the Emmy for best variety, music or comedy series for a ninth year.
The show's writers Steven Levitan and Jeffrey Richman won for best writing in a comedy series.
"Modern Family" also claimed the Emmy for best directing in a comedy series, given to Michael Alan Spiller.
They will compete with Friday Night Dinner and Sky series Spy for best new comedy, while Jack Whitehall and Hugh Bonneville are both up for best TV comedy actor for their roles in the shows.
The ladies competing for best lead actress in a comedy series conspired on a gag when their category was called.
Alec Baldwin repeated his Emmy success at the Globes, winning the best actor in a TV comedy or musical series award.
He's perhaps best known for playing JD in the American comedy series Scrubs, but now actor Zach Braff is preparing for his UK theatre debut.
The writers of Louis claimed the prize for comedy series and Lena Dunham's Girls was named best new TV series.
Radio 4's comedy series Cabin Pressure, featuring Benedict Cumberbatch and Roger Allam, has been nominated for best radio programme along with James Joyce's Ulysses, a Radio 4 dramatisation to mark Bloomsday, the day in June when the book's events take place.
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