Is unlawful taking of a vehicle a lesser included crime than carjacking?

Defendant argues People v. Montoya (2004) 33 Cal.4th 1031, supports his contention. In Montoya, the greater offense was carjacking and the lesser offense was unlawful taking of a vehicle. The court analyzed the situation as follows: "Applying the elements test to the two offenses here, the crime of unlawfully taking a vehicle is not a lesser included offense of carjacking because a person can commit a carjacking without necessarily committing an unlawful taking of a vehicle." (Id. at p. 1035.)