Guillermo del Toro's fantasy romance received 13 nominations, including best picture.
World War Two drama Dunkirk follows with eight nominations, while Three Billboards Outside Ebbing, Missouri received seven.
British stars shortlisted include Gary Oldman, Sally Hawkins and a pair of Daniels - Day-Lewis and Kaluuya.
Greta Gerwig has landed a best director nomination for Lady Bird, one of nine films shortlisted for the best picture award.
Others include Steven Spielberg's The Post, gay romance Call Me By Your Name and Winston Churchill drama Darkest Hour.