All four of the girls who share the lead role in Matilda the Musical have been jointly named in the best actress in a musical category at the Olivier theatre awards, one of 10 nominations for the show.

Not only did Matilda have more nominations than any other production, it was shortlisted in every possible category.

The shortlists were announced at a London hotel on Thursday by Roger Allam and Nancy Carroll, recipients last year of the best actor and best actress awards.

In the non-musical categories, comedies picked up the most awards, with One Man, Two Guvnors and The Ladykillers getting five each.

But it was Matilda – which started life in Stratford-on-Avon, transferred to the Cambridge theatre in the West End and is heading to New York next year – that dominated. In the best new musical category it will go up against Shrek the Musical, Ghost the Musical, the National's London Road and Betty Blue Eyes, which closed early because not enough people saw it.

There were also nominations for Matilda in choreography, lighting, set design, costumes and sound, and one for its director, Matthew Warchus, who will compete with Sean Foley for The Ladykillers, Nicholas Hytner for One Man, Two Guvnors and Rufus Norris for London Road.

If the four girls win in the best actress in a musical category, they will follow the success of the three Billys when Billy Elliot did so well at the Oliviers in 2006. They are up against Sarah Lancashire (Betty Blue Eyes), Scarlett Strallen (Singin' in the Rain) and Kate Fleetwood (London Road).

The nominees for best actor in a musical are Bertie Carvel for his monstrous Miss Trunchbull in Matilda, Nigel Lindsay in Shrek, Reece Shearsmith in Betty Blue Eyes and Paulo Szot in South Pacific.

There was another joint nomination in the best actor category, with Benedict Cumberbatch and Jonny Lee Miller named as one for their role in Frankenstein at the National, in which they alternated the roles of monster and doctor. They will both soon be rival Sherlock Holmeses, with Miller cast as the detective for a US TV version.

Cumberbatch and Miller will be up against Jude Law (Anna Christie at the Donmar Warehouse), Douglas Hodge (Inadmissible Evidence, also at the Donmar), David Haig (The Madness of George III) and James Corden, who has reprised his starring role in One Man, Two Guvnors on Broadway.

In the best actress category Lesley Manville was nominated for her lead role in Mike Leigh's play Grief at the National, along with Celia Imrie for Noises Off, Kristin Scott Thomas for Betrayal, Ruth Wilson for Anna Christie and Marcia Warren for her portrayal of the nice Mrs Wilberforce in The Ladykillers.

The best new play category is between One Man, Two Guvnors, The Ladykillers, Collaborators and Jumpy, which was at the Royal Court and transfers to the West End this year. The best revival nominations are Anna Christie, Flare Path, Noises Off and Much Ado About Nothing, which starred David Tennant and Catherine Tate.

The best supporting role nominees are Mark Addy (Collaborators), Oliver Chris (One Man), Johnny Flynn (Jerusalem), Bryony Hannah (The Children's Hour) and Sheridan Smith (Flare Path).

The Oliviers also reward dance and opera. In the latter categories, English National Opera came out top, taking five of the eight nominations. The best new opera production category will be fought between Castor and Pollux, A Midsummer Night's Dream, The Passenger (all ENO) and Clemency, a Royal Opera and Scottish Opera co-commission that was in Linbury Studio in Covent Garden, London.

There was controversy last year when not a single dancer was nominated in the dance categories. Not so in 2012, with the shortlist for outstanding achievement in dance revealed as Edward Watson for The Metamorphosis at Covent Garden; Sylvie Guillem for 6,000 Miles Away at Sadler's Wells and Tommy Franzen for Some Like it Hip Hop at the Peacock. They are joined by the design team for the Royal Ballet's Alice's Adventures in Wonderland.

The Oliviers will be presented on 15 April at the Royal Opera House. While not as long or as lavish as the Tonys, organisers are these days aiming to give Broadway a run for its money. Julian Bird, the chief executive of the Society of London Theatre, said: "We want to put London theatre on the world map. There are two great theatre capitals in the world and we both deserve great awards ceremonies."