Back in the 1980s, Archbishop Lefebvre of the Society of St. Pius X consecrated four priests as bishops without the Pope's approval. Does this action make the Society schismatic?
Societies of Apostolic Life, "without taking religious vows, pursue the apostolic purpose proper to each society. Living a fraternal life in common in their own special manner, they strive for the perfection of charity through the observance of the constitutions" [Canon 731]. The Society of S Pius X is constituted as a Society of Apostolic Life with the canonical approval of the Bishop of Fribourg [Canon 579]. Such Societies, "since they are dedicated in a special way to the service of God and of the whole Church, are in a particular manner subject to its supreme authority" [Canon 590].
The Society itself says
Archbishop Lefebvre consecrated four priests as bishops in 1998 without authority, an act which was schismatic under Canon Law [Canon 751] and resulted in all five being excommunicated by Pope John Paul II.
In 2009, Pope Benedict XVI remitted the excommunication of the four bishops consecrated without authority by Archbishop Lefebvre, and explained in an apostolic letter:
He went on
This mirrors the Society's own statement.
Pope Benedict then dealt with the status of the Society and its ministers:
Thus although the ministers within the SSPX who were illegitimately consecrated have been released from the individual penalty of that schismatic act, the fact that they belong to an organisation constituted as a Society of Apostolic Life which has reservations about the authority of the Pope and the Second Vatican Council [cf Canon 590] means that they cannot minister within the Church: they remain under interdict.
Because the Society itself (in the second sentence quoted at the top of this answer) has set itself to be the authority to determine if "time-honoured teachings are obscured or seemingly contradicted," it remains schismatic.