Lindsay Lohan Getting HANDS ON with Max from The Wanted

12/8/2012 8:20 AM PST

Lindsay Lohan -- Getting Hands On with Max George from The Wanted [PHOTO]

Lindsay Lohan staked her claim to new beau Max George from The Wanted ... throwing her arm around him at a club in New York City last night following their show at Madison Square Garden.

As TMZ first reported, Lindsay has been by Max's side the last few days, even riding with the band on their tour bus. We're told Max has been the aggressor in the "relationship" from the start, but that Lindsay isn't looking for anything serious right now.

Which is probably for the best ... she might be a little busy for the next 8-12 months.