There are 6 rites and 23 autonomous Churches or Churches sui juris in the Catholic Church. Roman Church (Latin) is the only Rite in the Western Church. The Mozarabic and Gallican Churches came in the Latin tradition as separate Churches, but were absorbed into the Latin Church. Now they do not have separate identity
In the Eastern Churches , there are 22 autonomous Churches (Churches sui iuris) under five Rites. The Holy See's Annuario Pontificio gives the following list of Eastern Catholic Churches with the principal see of each and the countries (or larger political areas) where they have ecclesiastical jurisdiction, to which are here added the date of union or foundation in parenthesis and the membership in brackets. The total membership is about 16,336,000.Eastern Churches
I. Alexandrean:
1. Coptic Church (Patriarchate): Cairo, [163,849], Egypt (1741)
2. Ethiopian Catholic Church (Metropolia): Addis Ababa, [208,093], Ethiopia, Eritrea (1846)
II. Antiochean or West Syrian:
1. Maronite Church (Patriarchate): Bkerke, [3,105,278], Lebanon, Cyprus, Jordan, Israel, Palestinian Authority, Egypt, Syria, Argentina, Brazil, United States, Australia, Canada, Mexico (Never separated: union re-affirmed 1182)
2. Syriac Church (Patriarchate): Beirut,[131,692], Lebanon, Iraq, Jordan, Kuwait, Palestinian Authority, Egypt, Sudan, Syria, Turkey, United States and Canada, Venezuela (1781)
3. Syro-Malankara Church (Major Archepiscopate): Trivandrum, [412,640], India, United States (1930)
III. Armenian:
1. Armenian Church (Patriarchate): Beirut, [375,182], Lebanon, Iran, Iraq, Egypt, Syria, Turkey, Jordan, Palestinian Authority, Ukraine, France, Greece, Latin America, Argentina, Romania, United States, Canada, Eastern Europe (1742)
IV. Chaldean or East Syrian:
1. Chaldean Church (Patriarchate): Baghdad, [418,194], Iraq, Iran, Lebanon, Egypt, Syria, Turkey, United States (1692)
2. Syro-Malabar Church (Major Archepiscopate): Ernakulam, [3,902,089], India, Middle East, Europe, America (Never separated)
V. Byzantine or Constantinopolitan:
1. Albanian Church (Apostolic Administration): [3,510], Albania (1628)
2. Belarusian Church (No established hierarchy at present): [10,000], Belarus (1596)
3. Bulgarian Church (Apostolic Exarchate): Sofia, [10,107], Bulgaria (1861)
4. Križevci Church (An Eparchy and an Apostolic Exarchate): Križevci, Ruski Krstur [21,480] + [22,653], Croatia, Serbia, and Montenegro (1611)
5. Greek Byzantine Church (Two Apostolic Exarchates): Athens, [2,325], Greece, Turkey (1829)
6. Hungarian Church (An Eparchy and an Apostolic Exarchate): Nyiregyháza, [290,000], Hungary (1646)
7. Italo-Albanian Church (Two Eparchies and a Territorial Abbacy): [63,240], Italy (Never separated)
8. Macedonian Church (An Apostolic Exarchate): Skopje, [11,491], Republic of Macedonia (1918)
9. Melkite Greek Church (Patriarchate): Damascus, [1,346,635], Syria, Lebanon, Jordan, Israel, Brazil, United States, Canada, Mexico, Iraq, Egypt and Sudan, Kuwait, Australia, Venezuela, Argentina (1726)
10. Romanian Church (Major Archiepiscopate): Blaj, [776,529] Romania, United States (1697)
11. Russian Church (Two Apostolic Exarchates, at present with no published hierarchs): Russia, China (1905); currently about 20 parishes and communities scattered around the world, including five in Russia itself, answering to bishops of other jurisdictions
12. Ruthenian Church (A sui juris Metropolia, an Eparchy, and an Apostolic Exarchate): Uzhhorod, Pittsburgh, [594,465], United States, Ukraine, Czech Republic (1646)
13. Slovak Church (Metropolia and an eparchy): Prešov, [243,335], Slovakia, Canada (1646)
14. Ukrainian Catholic Church (Major Archiepiscopate): Kiev, [4,223,425], Ukraine, Poland, United States, Canada, Great Britain, Australia, Germany and Scandinavia, France, Brazil, Argentina (1595)
Note: Georgian Byzantine-Rite Catholics are not recognized as a particular Church (cf. canon 27 of the Code of Canons of the Eastern Churches). The majority of Eastern Catholic Christians in the Georgian Republic worship under the form of the Armenian liturgical rite.
Ukranian Church, with just more than 4 million faithful, is the largest Eastern Catholic Church. The Syro-Malabar Church, with just less than 4 million faithful, is the second largest Eastern Catholic Church.
As seen above, some Churches are Patriarchal, some are Major Archiepiscopal , some are Metropolitan and some are Episcopal. Some Churches are only Apostolic Exarchates. Patriarchate is a form of government, an autonomous, self-governing federation of dioceses under the jurisdiction of a chief bishop, called "patriarch" and his synod. Patriarchates have existed from ancient times. Pope, the head of the Universal Church is also the Patriarch of the Roman Church.
Seven Churches are Patriarchal now. They are Rome (The Latin), Alexandria of the Copts (residence in Cairo), Alexandria-Antioch-Jerusalem of the Melchites (titular, resident in Damascus), Antioch of the Maronites (Bkerke',Lebanon), Antioch of the Syrians (Beirut), Babylon of the Chaldean (Baghdad),Cilicia of the Armenian (Beirut).
Most of the Eastern Churches had once left the Catholic Church, but later got reunited. There are only three Churches that never separated from the Catholic Church. They are Maronite, Syro-Malabar and Italo-Albanian.
The Indian Catholic Church is a composition of the Latin, the Syro-Malabar and the Syro-Malankara Churches, which keep their own identity.