Rock
Metal
Folk
Alternative

All other genres are subtypes of those… Punk is a subgenre of alternative, grindcore is a subgenre of metal, etc.
References :

Hard Rock

Metal

Contemporary Rock

Alternative

I that doesn’t help, go on wikipedia.com, it always helps me
References :

* 2 Tone
* Acid rock
* Afro-punk
* Alternative metal
* Alternative rock
* Anatolian rock
* Art punk
* Art rock
* Avant-garde metal
* Avant-rock
* Avant-progressive rock
* Baroque pop
* Beat
* Bisrock
* Black metal
* Blackened death metal
* Blues-rock
* Boogaloo
* Brazilian rock
* Britpop
* Bubblegum pop
* C86
* Canterbury sound
* Cello rock
* Celtic punk
* Celtic rock
* Chicano rock
* Christcore
* Christian rock
* Christian metal
* Coldwave
* Comedy rock
* Country rock
* Cowpunk
* Crossover thrash
* Crust punk
* Cuddlecore
* Dance-punk
* Dance-rock
* Dark cabaret
* Darkwave
* Death ‘n’ roll
* Deathcore
* Deathgrind
* Death metal
* Death rock
* Doom metal
* Dream pop
* Electro Punk
* Emo
* Experimental rock
* Folk rock
* Folk metal
* Folk punk
* Freakbeat
* Funk rock
* Garage rock
* Garage punk
* German rock
* Glam metal
* Glam punk
* Glam rock

* Goregrind
* Gothic metal
* Gothic rock
* Grebo
* Grindcore
* Groove metal
* Group Sounds
* Grunge
* Gypsy punk
* Hatecore
* Hard rock
* Hardcore punk
* Heartland rock
* Heavy metal
* Horror punk
* Indie pop
* Indie rock
* Indorock
* Industrial metal
* Industrial rock
* Instrumental rock
* Iranian rock
* J-ska
* Jam rock
* Jangle pop
* Jazz rock
* Jersey Shore sound
* Krautrock
* Latin rock
* Lo-fi
* Lovers rock
* Madchester
* Manila sound
* Mathcore
* Math rock
* Melodic black metal
* Melodic death metal
* Melodic hardcore
* Metalcore
* Mod
* Mod revival
* Nardcore
* Nazi punk
* Neo-classical metal
* Neo-folk
* Neo-prog
* Neo-psychedelia
* New prog
* New Romantic
* New wave
* Nintendocore
* Noisecore
* Noise pop
* Noise rock
* No wave
* Nu metal
* Oi!
* Ostrock
* Pagan rock
* Pinoy rock
* Pop punk
* Pop rock

* Pornogrind
* Post-punk
* Post-punk revival
* Post-hardcore
* Post-grunge
* Post-metal
* Post-rock
* Power pop
* Power metal
* Power violence
* Progressive folk
* Progressive metal
* Progressive rock
* Protopunk
* Power pop
* Psychedelic rock
* Psych-Folk
* Psychobilly
* Punk rock
* Punta rock
* Queercore
* Raga rock
* Rapcore
* Rap metal
* Rap rock
* Riot Grrrl
* Rock
* Rock Against Communism
* Rock and roll
* Rockabilly
* Rock en Español
* Rockoson
* Rocksteady
* Russian rock
* Sadcore
* Samba-rock
* Screamo
* Shoegazing
* Shock rock
* Ska punk
* Skate punk
* Skate rock
* Sludge metal
* Soft rock
* Southern rock
* Space rock
* Speed metal
* Stoner metal
* Stoner rock
* Street punk
* Sunshine pop
* Surf music
* Surf rock
* Swamp rock
* Symphonic metal
* Symphonic rock
* Synth pop
* Thrash metal
* Thrashcore
* Trash rock
* Trip rock
* Twee pop
* Viking metal
* Wagnerian rock
* Wizard rock
* Zeuhl
References :