H&M are the only chain shops with proper fashion... but other big ones are Kappahl, Lindex, Gina Tricot, Monki.
Brands:
Acne
Hope
Ida Sjöstedt (designed Sophia’s wedding dress)
Filippa K
Rodebjer (CPV:s boring pantsuits, but they do a cracking caftan)
Totême
Ahlvar
Cheap Monday
Nudie jeans
Dagmar
Maria Westerlind
Whyred
All I can think of atm.