Warrior Ancient and Medieval Rules

I have a list question on the Patrician Romans. I'm at work, so I'm
working from memory (not having the list book at hand), but here it
is:

The Patrician Roman list allows for an Alan allied general. This
general is listed as being HC L, B, and Sh. Under the Alan troop
types that can be taken are also HC L, B, Sh elements, but they have
the option of any or all being upgraded to EHC. It does not appear
that the general element can also be upgraded in the same manner. Is
this true? Or could the general element also be upgraded at the same
cost as the allied troop elements?

I noticed the same situation in other Imperial Warrior lists that
have Alan allies, so just wanted to make sure how it is handled.

Thanks,

Peter