Given a 4-dimensional complex space $T$, we consider the flag manifolds $F_{d_1,\ldots,d_m}(T)=\{(S_1,\ldots,S_m)\ |\ \textrm{dim}S_i=d_i, \ \ S_1\subset S_2\subset\ldots\subset S_m\}$. The $S_i$ are subspaces of $T$. My question is: how/why we can see that the action of the group $SL(4,\mathbb{C})$ over the flag is transitive, i.e, we can always find a $g\in SL(4,\mathbb{C}$ such thay for every two $[S_1,\ldots,S_m],[S_1',\ldots,S_m']$ we have that $g(S_1)=S_1',\ldots,g(S_m)=S_m'$.
And also, why we don't have one transitive action when we consider the group $SU(2,2)$?