Satmar traces back to the Yismach Moshe, who was a Talmid of the Tzanzer Rav.
All Chassidusen come from the Maggid. The Rebbe Reb Meilech was a Talmid of the Maggid. The Chozeh of Lublin was his Talmid. Most of today’s dynasties come from Talmidim of the Chozeh.
Among the Chozeh’s Talmidim are the Ropshitzer, the Peshis’cher, the Ziditchover (Kamarna, eventually Tosch), and the B’nei Yisas’char (Munkatch). From the Ropshitzer there is Tzanz (Bobov, Klozenberg, Satmar) and Belz, and from the Peshis’cher there is Kotzk (Ger) and Vorka (Amshinov). The first Vizhnitzer Rebbe was a grandson of Reb Yaakov Kappel, a Talmid of the Baal Shem Tov, and a son in law of the Rizhiner.
There are dynasties that start from Talmidei Hamaggid: The Baal Hatanya, Reb Aharon Hagadol of Karlin and his Talmid Reb Shlomo of Karlin (Stolin-Karlin, Slonim), Reb Aharon of Tchernobel (Skver, Rachmestrivke). From the Maggid’s son, Reb Avraham Hamalach, comes Rizhin (Bayan, Alechsander)
You can really check out Wikipedia for more information: http://en.wikipedia.org/wiki/Hasidic_dynasty