Subgroup structure of special linear group:SL(2,3)

This article gives information on the subgroup structure of special linear group:SL(2,3), which is the special linear group of degree two over field:F3. Note that this field has three elements $$0,1,2$$ and we have $$2 = -1$$.

Sylow subgroups
We are considering the group $$SL(2,q)$$ with $$q = p^r$$ a prime power, $$q = 3, p = 3, r = 1$$. The prime $$p = 3$$ is the characteristic prime.

Sylow subgroups for the prime 3
The prime 3 is the characteristic prime $$p$$, so we compare with the general information on $$p$$-Sylow subgroups of $$SL(2,q)$$.

Sylow subgroups for the prime 2
We are in the subcase where $$\ell = 2$$ ($$\ell$$ being the prime for which we are taking Sylow subgroups) and $$q \equiv 3 \pmod 8$$.