Though many answers are given, I believe one of important powerful [types of] magic is [the] power of house-elves to fulfill their master's command. House-elves have their own brand of wandless magic that only they have access to, as do many other magical creatures. The upper limits of Elf magic are not known, however it is incredibly versatile and allows them to perform very powerful magic.
Kreacher was able to return from Voldemort's cave just because his master ordered to do so. The cave had an extremely powerful dark magical barrier to forbid such from happening, placed there by none other than the greatest dark Lord of all time, Voldemort. However despite this, Kreacher succeeded where even Dumbledore did not. They can apparate from anywhere even Hogwarts.
Dobby could disarm wizards with a flick of fingers, duel any wizard and perform dark magic. He hexed the barrier that leads to Platform Nine and Three Quarters, a very powerful magical barrier, so that Harry Potter and his friends could not enter.
No doubt they had a different and very powerful [type of] magic.
— Quora user Piyush Tiwari
