Do I need a permit in order to sublease my home?

Yes, generally you need a permit if you have a condominium (bostadsrätt) or tenancy-apartment (hyresrätt). Exceptions can be made if you rent out a room. Having a permission to sublease is important for both the landlord's and tenant's safety. 

The rules vary depending on if you subleas a condominium or a tenancy-apartment. If you're subleasing a tenancy-apartment, you will need a permission from your landlord/administrator. If you, have a condominium you'll need a permit from the housing cooperative, which implies different rules and regulations. You can always create an account for free.