From Wikipedia
According to basic results of linear algebra, any two complete flags in an $n$-dimensional vector space $V$ over a field $F$ are no different from each other from a geometric point of view. That is to say, the general linear group acts transitively on the set of all complete flags.
So I understad that a point in a flag manifold $X_{1}\subset X_{2}\subset ...\subset X_{n} = X$ is a $n$-hyperplane regardless some subspace $V_{i},i<n$ is missing in the sequence.
1-Is this correct?
2-If so; is there a generalization of the flag manifold in the sense that a point in the manifold (or a more general space) represents something geometrically more complicated/general than an $n$-hyperplane?
EDIT: In response to the answer of @Nicolas Hemelsoet
I do not see the thing clearly . I am trying to visualize the point in a flag manifold apart from knowing what the definition of the flag is.
Let´s see the last parapgraph of this article https://rigtriv.wordpress.com/2008/01/17/grassmannians-and-flag-varieties/ I understand that there is not something like a (spatial) "flag" in some space but a collection of {a point, a line, a plane, a $3$-plane... a $k$-plane} in different subspaces (one of each is contained in the following one). But the data that maps for example the line in $V_{1}$ with the plane in $V_{2}$ are not part of the specification of the (flag) manifold?