A suborder is a set of related expression elements which are more strictly ordered with respect to each other than they are with respect to other expression elements. This is my own term. I offer the English adverbs probably, eagerly, entirely as my only example, so far. These are, respectively, sentence adverb, manner adverb, and degree adverb. Each of these can occur alone in several positions. In general, while two adverbs of the same type may not co-occur in English clauses, adverbs of differing types may co-occur:
Harry will eagerly eat the fish entirely, probably.
Putting aside such examples with an intonation break (comma intonation), we also get
Probably Harry will eagerly eat the fish entirely.
But when the positions of any two of these adverbs are interchanged, we get bad results:
*Probably Harry will entirely eat the fish eagerly.
*Eagerly Harry will probably eat the fish entirely.
*Eagerly Harry will entirely eat the fish probably.
*Entirely Harry will eagerly eat the fish probably.
*Entirely Harry will probably eat the fish eagerly.
Thus these adverbs make up a suborder. Perhaps other adverbs of the three types sentence adverb, manner adverb, and degree adverb work similarly. In McCawley's theory (The Syntactic Phenomena of English), these adverb types are, respectively, sentence modifiers, V-bar modifiers, and V modifiers, but I don't see how this, if true, accounts for their order with respect to each other.