Word for “all the groups an item belongs to”?
Solution 1:
For parent-child relationships, ancestor works, or ancestor groups if you need to be explicit. An ancestor is a parent or parent of an ancestor. You could also use containing, inclusive, or maybe superordinate.
Solution 2:
Hypernyms.
Fuji is a hyponym of apple. Apple is a hyponym of fruit. But Fuji is also a hyponym of fruit. And fruit and apple are both hypernyms of Fuji.