Light Alliance:
I am only talking about Earls as most of Counts and Viscount follow Dumbledore and Marquis houses withdrew from politics centuries ago. Dumbledore himself is a Viscount, but he does not hold the Lordship as they are a branch family. Along with his 5 votes of Chief Warlock, he holds 3 votes for Order of Melin.
Potters, Bones, Longbottom, Kingsley, Diggory, Fawley, Shafiq, McMillian, Prewets (Fred and George are heir, Molly is a Prewet and according to Prewet family rules twins takes precedence over any other child of direct line.), McKinnon (on the verge of extinction just like Potters with only a girl in Harry's year left)
Currently led by Amelia Bones and Augusta Longbottom
Dark Alliance:
Nott, Lestrange (in prison, heiress being raised by Malfoy, seat is dormant), Carrows, Yaxley, Rosier, Parkinson, Flint, Bulstrode, Mort, Malfoy (are Counts but their cousins in France are Earl's and have a lot of sway in France so they are a major part of dark alliance),
Blacks (used to be a part but never officially and Regulus was only heir at that time)
Currently led by Nott and Malfoys lead Counts and Viscounts.
Grey Alliance:
Greengrass, Slughorn, Crouch (will pass on to a cousin after Barty Crouch Sr.), Avery, Selwyn, Burge, Gamp, McDougal, Rowle.
Currently led by Greengrass