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Sufi orders exists among the Shi'a, but they are strongly disapproved of by the Ayatollahs and don't really operate openly in Iran. They are seen as rivals for spiritual authority and are often regarded as crypto-Sunni (every Shi'a Sufi order is an offshoot of a Sunni order and only became Shi'a during the Safavid period).
Historically, Sufism is an integrally Sunni phenomenon and was only grafted into a Shi'a mileu much later. All the great Sufis were Sunni: Bayazid Bistami, Imam Junayd, al-Hallaj, Abdullah Ansari, al-Qushayri, al-Ghazali, al-Suhrawardi, Abu Madyan, 'Abdul-Qadir al-Jilani, Muinuddin Chishti, Bahauddin Naqshband, Ibn 'Arabi, Ibn Sab'in, Mevlana Jalaluddin Rumi, Ibn Barrajan, Ibn Mashish, Abu'l Hasan ash-Shadhili, Ahmad Zarruq, etc.
Sufism was officially supported by the majority of Sunni political dynasties, like the later Abbasids, the Idrisis in Morocco, the Mamluks, and most significantly, the Ottomans.
The vast majority of Sunni 'ulama either accept Sufism as legitimate, or are members of Sufi tariqas themselves.
Shaykh al-Yaqoubi of Syria is a Shadhili-Darqawi; Habib 'Umar ibn Hafiz and Habib 'Ali al-Jifri of Yemen are Ba'Alawi; Shaykh 'Ali al-Jumu'ah (former Grand Mufti of Egypt) is a Shadhili; Shaykh Salahuddin al-Misri is a Tijani; 'Abdullah bin Bayyah of Mauritania is a Shadhili; Akhtar Raza Khan (Grand Mufti of India) and Muneeb-ur-Rahman (Grand Mufti of Pakistan) are both Qadiri; Hafiz Sabri Koci (the late Grand Mufti of Albania) was a Tijani; most of the major 'ulama of West Africa are Qadiri or Tijani. In the U.S., Zaid Shakir is a Shadhili-'Alawi, Ninowy is a Shadhili-Siddiqi, Yahya Rhodus is Ba'Alawi, Na'eem Abdul-Wali is a Naqshbandi.