Founded 1870, antitrust 1911:
https://en.wikipedia.org/wiki/Standard_Oil
Crude prices in that time frame (and beyond):
https://commons.wikimedia.org/wiki/File:Oil_Prices_Since_186...
Production in that time frame (having trouble finding a nice long time-series chart):
https://en.wikipedia.org/wiki/History_of_the_petroleum_indus...
If we want to make a strong claim of harmful monopoly[0], we should not expect to see a massive surge in production combined with an impressive decrease in price.
[0]Here I use the term "harmful monopoly" to refer to a firm that has both market power (can influence prices by controlling supply) and uses it to increase its own profits. What we see instead is a time period where we do indeed have a dominant firm, but one behaving as if it were in a competitive market.
The important characteristics of a competitive market here are low barriers to entry/exit, and a commodity product. There were incredibly low barriers to entry/exit, and oil has, for nearly its entire existence as a product in the modern age, been a commodity.