You are correct in noting that our Sunday lectionary cycle revolves around the synoptic gospels of Matthew (year A), Mark (year B) and Luke (year C) yet we don’t have a year dedicated to reading from the gospel of John. The only times we hear accounts from the fourth evangelist are occasionally in the seasons of Advent, Christmas, Lent and Easter, but not during ordinary time (i.e. the majority of weeks during the calendar year when we’re not in one of the particular seasons listed above.)
In general, the synoptic gospels lend themselves more easily to brief, succinct and self-contained readings. John’s Gospel contains significantly fewer healings, miracle stories, and episodic narrative events, replacing them instead with notably long monologues by Jesus that don’t lend themselves as easily to public proclamation. That said, some of the better-known stories from John which do make an appearance during particular seasons are the story of the man born blind, the woman at the well, the raising of Lazarus, the foot washing, and doubting Thomas.