Doctor Strange is shown to have a passion for music trivia as we see way back before he joins the Masters of the Mystic Arts. In Doctor Strange, whilst performing surgery he is also doing a music "trivia quiz" with the nurses to impress with his knowledge.
Doctor Strange: Feels So Good, Chuck Mangione, 1977. Seriously, Billy, you said this one would be hard.
Billy: Hah! It’s 1978.
Doctor Strange: No, Billy, while Feels So Good may have charted in 1978, the album was released in December, 1977.
Billy: No, no. Wikipedia says the...
Doctor Strange: Check again.
Billy: When did you…?
Doctor that is helping Stephen: Where do you store all this useless information?
Doctor Strange: Useless? The man charted a top ten hit with a Flugelhorn. Status, Billy?
Doctor Strange
With that established, whilst it could be argued he is referring to 'The Fab Four' (aka The Beatles) it is more likely this is a call back to his music trivia knowledge. In that case he is most likely referring to a band from the 60s who were indeed named 'The Fantastic Four'.
The Fantastic Four did indeed chart in the 60s several times, so it is likely this is what he is referring to here.