If you based it purely on 'the rules' (not updated for William's children) you'd have had:
While the Queen is alive:
Prince Charles
Prince William (Prince George, Charlotte, Louis)
Prince Harry (Archie, ?)
Princess Anne
Peter (Savannah, Isla)
Zara (Mia, Lena)
Prince Andrew
Princess Beatrice
Princess Eugenie (August)
Prince Edward
Princess Louisa
Prince James
After the Queen dies, the only ones affected would be Charles' branch:
Prince Charles
Prince William (Prince George, Princess Charlotte, Prince Louis)
Prince Harry (Prince Archie, Princess ?)