The family \(A\) of analytic functions \(f\) of the unit disk \(\Delta\), equipped with the topology of uniform convergence in compact subsets forms a locally convex linear space. Let \(B_0:=\{\omega\in A |\omega(0)=0, |\omega|0\}=\{p\in A |p\prec {1+z \over 1-z}\} =s({1+z \over 1-z}) . \] The Krein-Milman theorem guarantees that a subordination family has \textit{extreme points} \(\text{ E} s(F)\neq \emptyset\), and these reconstruct \(s(F)\), i.~e. \(\overline{\text{ co}} \text{ E} s(F)=\overline{\text{ co}} s(F)\), \(\overline{\text{ co}} M\) denoting the closed convex hull of \(M\). The Herglotz representation formula shows via Choquet's theorem that \[ \text{ E} P=\{{1+xz \over 1-xz} ||x|=1\}. \] It is easy to see that in subordination families for every extreme point \(f\in \text{ E} s(F)\) (or \(f\in \text{ E} \overline{\text{ co}} s(F)\)), and \(f\prec g\), it follows that also \(g\in \text{ E} s(F)\) (or \(g\in \text{ E} \overline{\text{ co}} s(F)\), respectively) [W. Koepf: Extrempunkte und Stützpunkte in Familien nicht-verschwindender analytischer Funktionen; \(PhD\) thesis, Free University Berlin (1984)]. Hence the extreme points are large with respect to \(\prec\). A similar statement holds for the \textit{support points} of a linear functional \(L\). In the case of \(P\), the set of extreme points is smallest possible and consists only of the maximal elements w.~r.~t.\ \(\prec\). The authors show under which conditions for \(F\) this situation occurs. In contrast, for \(B_0\) one has \[ \text{ E} B_0= \{f\in B_0 |\int_0^{2\pi} \log (1-|f(e^{it})|) dt=-\infty\} \] Hence in this case, the set of extreme points is rather large. The article informs about the situation for general \(F\) which lies between the two extremes. Furthermore the set of support points of subordination families is considered. Finally, extreme point results for functions subordinate to convex, starlike and close-to-convex functions are given. Similar results for functions normalized by \(f(0)=1\) and \(f\neq 0\) can be found in [Complex Variables, Theory Appl. 8, 153-171 (1987; Zbl 0622.30002)].