For those pilgrims whose lives are affected by the feudal system--that is, may ultimately owe military service to a lord--I would include the Knight, the Squire (the knight's son and candidate for knighthood), and the Franklin (a landowner, usually in a rural setting, one level below the aristocracy but part of the feudal system).
Pilgrims who have religious responsibilities include the Friar, Summoner (a secular official of some ecclesiastical courts), Clerk (although he could be part of the city group, he's most likely to become part of the religious establishment--for example, his tale is highly moral), Pardoner, Prioress, Monk, Nun's Priest, Second Nun, Canon's Yeoman (part of the religious group by default as the servant of a Canon), Parson.
Those pilgrims in the city group include the Miller, Reeve (functions as the overseer of an estate, sometimes as a sheriff), Cook, Man-of-Law, Wife of Bath, Merchant, Physician, Shipman, Manciple (usually worked in the Inns of Court as a steward).
Chaucer himself could go either into the city group or the feudal group, but I would argue that, given what we know of his background, he fits well into the feudal group. We believe Chaucer spent a good part of his life as a diplomat and negotiator for the government and Court, and he therefore would have some level of feudal responsibility.
[Another way to categorize the pilgrims in The Canterbury Tales is as follows.]
Pilgrims who are related to the feudal system include the Knight, the Squire, the Franklin (a "free man" in feudal society), the Reeve (a steward on a feudal manor), the Plowman, and the Yeoman (who works for the Knight and Squire).
Pilgrims related to the city include the Wife of Bath (a seamstress), the Miller, the clerk (a student), the Man of Law (a lawyer), the Manciple (who buys supplies for a court and works with lawyers), the Merchant, the Physician, the Shipman, the Guildsmen (a guild was similar to a labor union/trade organization), and the Cook (who works for the Guildsmen).
Those related to the church include the Pardoner (who granted indulgences), the Prioress (a nun who is charge of a convent), the Friar, the Monk, the Summoner (who summons, or calls, people to the church court), the Parson, the Second Nun, and the Nun's Priest.