Does a Quickened Spell have a Somatic component?

Does a quickened spell still require the components it usually does (verbal, somatic, and material)? For example, can a silenced or grappled wizard still cast a quickened dispel magic?
Quicken Spell makes a spell quick; you still need all the components normally required for a quickened spell. If you want help casting spells while grappled, you need Still Spell. If you want help casting spells while silenced, you need Silent Spell.