Aren't players required to choose a subclass? Most of the characters (at least up to episode 5, since I haven't gone any further) seem to have both class and subclass:  


Akatsuki: Class - Assassin; Subclass - Tracker  
Shiroe: Class - Enchanter; Subclass - Scribe
Nyanta: Class - Swashbuckler; Subclass - Chef
Serara: Class - Druid; Subclass - Maid


However, Naotsugu (whose Class is Guardian) appears to not have a Subclass.   

From the Classes and the Subclasses page on Log Horizon Wiki, one can tell that once a player starts playing Elder Tale he has to choose a Class, which cannot be changed again. However, one also gathers that Subclasses, on the other hand, are changeable, but the site says nothing about whether or not a player is required to have one.

Does this mean that Subclasses are not required?
Or was Naotsugu's class just not yet revealed/unknown?
The wiki page you referenced for Naotsugu has been updated saying that he has the Border Patrol Subclass.

On a side note if Elder Tale is anything like most MMORPGs a subclass is not chosen until you have gained a couple levels and there is no advantage for not having one. So it would make sense that most players would pick a subclass to start leveling it right away.