Use dropdown menus with an autocomplete-enabled text search, and only show the next selection level of the previous has been selected.
Company: ▼ ACME inc
Component: ▼ Foobar
Group: ▼ Bazgroup
Offer the option to bookmark selections (maybe even incomplete selections like
folder subfolder ___).
Usually I would advise against dropdowns, but in ...
I assume that you will show all available information to make this decision "somewhere near" (in a table, in columns prior to the number column), and concentrate on the number field.
The maximum changes, so it must be displayed all the time. From your question, the minimum seems to be 0 for all cases - if that's not the case, display the minimum as well.