If I understand correctly, then ...
a plant belongs to a single division
a division belongs to single family
a family belongs to single genus
These all seem to be one-to-many relationships, assuming it's not possible for a plant to be in two divisions (at the same time).
So, I would have a division field in the plant table, a family field in the division table, etc.
This gives the maximum flexibility since, if a plant needs relocating to a new division then only a single change is necessary, if a whole division of plants gets moved to a new family, then that is only a single change ... etc.
Hope that helps.