Se contrefoutre belong to the 3
rd group.
Se contrefoutre is conjugated the same way that verbs that end in :
-tre
Se contrefoutre is conjugated with
auxiliary être.
Se contrefoutre is a defective verb.
It can not be conjugated in all possible forms.
French verb se contrefoutre is a reflexive verb which is always reflexive. So it is always conjugated with a reflexive pronoun.