Theoretically, you could finish second even with 15 points. And win the group with just 5 points. But, in reality what are the records? Is it Arsenal (with 13 points) this season and Monaco (with 11 points) this season?
Most points achieved in the group stage, not winning the group (2nd): Manchester City, 15, 2013-2014.
Most points achieved in the group stage, yet knocked out (3rd): Napoli, 12, 2013-2014.
Fewest points achieved in the group stage, yet advanced: Milan, 5, 1994-1995.‡
‡ Prior to 1995-1996 season two points were awarded for a win instead of three.