In Lumen Gentium 8 we find the words, "Haec Ecclesia [...] subsistit in Ecclesia catholica..." ("This Church [...] subsists in the Catholic Church").
The Acta Synodalia Sacrosancti Concilii Oecumenici Vaticani II is a collection of all of the speeches, debates, and written submissions of the Council Fathers at Vatican II. For example, it is well known that "subsistit in" replaced the original formulation of "est" due to an intervention during the Council.
According to the Acta Synodalia of Vatican II, what is the meaning of "subsistit in"? What did the Council Fathers mean by subsistit in and why did they use this term to convey the relation between the Church of Christ and the Catholic Church?
Note: I am only interested in the interpretation of subsistit in with respect to the Acta Synodalia. Strong answers will include insight into central discussions and debates that took place at the Council as well as the names of the parties who put forward various positions.