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The Irish actor, 47, scooped up Best Actor in a Motion Picture: Drama at the Globes on Monday for his much-praised performance in Christopher Nolan's latest drama.
Others overlooked by the SAG nominating committee include Jeremy Strong ("Succession") and the "Jury Duty" cast.
"Succession" dominated the SAG Award nominations for TV, but Jeremy Strong's snub was just one of a few curious quirks by the Screen Actors Guild.
"Killers of the Flower Moon" and "Oppenheimer" will lead film nominees, while "Succession" and "The Bear" will lead TV dramas and comedies.
Dominic West has revealed he would love to play the role of the King's great-great grandfather.