According to Wikipedia the cardinality of $O(n,q)$ depends on the properties of the field we're working over. These are the results:

I'm considering both $O^+$ and $O^−$. The definitions: Suppose $V$ is a vector space on which the orthogonal group $G$ acts, then $V=L_1\oplus L_2\oplus\dots\oplus L_m\oplus W$, with $L_i$ hyperbolic lines and $W\le V$ contains no singular vectors. If $W=0$, then $G$ is of plus type. If $\dim(W)=2$, then $G$ is of minus type. If $W$ is one-dimensional then $G$ has odd dimension.

As for the question: I'm studying the Sylow subgroups of these groups. The cardinalities of a Sylow $q$-subgroup of $O(2n+1,q)$ (see picture) would be $q^{n^2}$ and for the last two $q^{n(n-1)}$. I'm now wondering how the Sylow $q$-subgroups of these orthogonal groups look like, i.e. what is their structure? What matrices generate such a Sylow subgroup? In addition, I would like to know how the normalizers look like.

Note: I don't need lengthy proofs (or even any proofs), results only suffice.

Thanks in advance.