AA 3153 then AA 3864 at Charlotte
Omaha → Charlotte → Hilton Head
Timetable, Charlotte time
16:38AA 3153 from Omaha at the gate
15:54AA 3864 to Hilton Head leaves the gate
23 h 16 apart on the timetable, overnight
AA 3864 leaves 23 h 16 after AA 3153 arrives on the timetable: more than half a day, so not a connection we count.