On tab 1, I have a column where each cell in that column has a group of numbers, and another column where that group of numbers is associated with a name. Example:
Entered as an array formula (Ctrl-Shift-Enter) and copied down, this works:
=INDEX($B$1:$B$4,MATCH(TRUE,ISNUMBER(SEARCH(","&D8&",",","&$A$1:$A$4&",")),0))