There's a general provision, in addition to the specific provisions.
Quoting 720 ILCS 5/3‑5(b)
Unless the statute describing the offense provides otherwise, or the period of limitation is extended by Section 3‑6, a prosecution for any offense not designated in Subsection (a) must be commenced within 3 years after the commission of the offense if it is a felony, or within one year and 6 months after its commission if it is a misdemeanor.