The modern Greek military ranks are based partly on the Byzantine ones, partly on ancient ones and partly on British ones:
Air Force
Category Greek rank Transliteration British Equivalent NATO
General Officers
Πτέραρχος Pterarkhos Air Chief Marshal (Lit. "wing-commander") OF-9
Αντιπτέραρχος Antipterarkhos Air Marshal (Lit. "vice-wing-commander") OF-8
Υποπτέραρχος Hypopterarkhos Air Vice-Marshal (lit. "under-wing-commander") OF-7
Ταξίαρχος Αεροπορίας Taxiarkhos Aeroporias Air Commodore (lit. "air brigadier") OF-6
Senior Officers
Σμήναρχος Smenarkhos Group Captain (lit "flock commander") OF-5
Αντισμήναρχος Antismenarkhos Wing Commander (lit. "vice-flock-commander") OF-4
Επισμηναγός Epismenagos Squadron Leader (lit. "over-flock-leader") OF-3
Junior Officers
Σμηναγός Smenagos Flight Lieutenant (lit. "flock-leader") OF-2
Υποσμηναγός Hyposmenagos Flying Officer (lit. "under-flock-leader") OF-1
Ανθυποσμηναγός Anthyposmenagos Pilot Officer (lit. "vice-under-flock-leader") OF-1
Army
Category Greek Rank Transliteration English Equivalent NATO
General Officers
[Στρατἀρχης Stratarkhis Field-Marshal (lit. "army commander") OF-10, no longer used]
Στρατηγός Stratigos General OF-9
Αντιστράτηγος Antistratigos Lieutenant General (lit. "vice-general") OF-8
Υποστράτηγος Ypostratigos Major General (lit. "under-general") OF-7
Ταξίαρχος Taxiarkhos Brigadier General (lit. "brigade-leader") OF-6
Field Grade Officers
Συνταγματάρχης Syntagmatarkhis Colonel (lit. "regiment-commander") OF-5
Αντισυνταγματάρχης Antisyntagmatarkhis Lieutenant Colonel (lit. "vice-regiment-commander") OF-4
Ταγματάρχης Tagmatarkhis Major (lit. "battalion-commander") OF-3
Company Grade Officers
Λοχαγός Lokhagos Captain (lit. "company-leader") OF-2
Υπολοχαγός Ypolokhagos Lieutenant (lit. "under-company-leader") OF-1
Ανθυπολοχαγός Anthypolokhagos Second Lieutenant (lit. "vice-under-company-leader") OF-1
Navy
Category Greek Rank Transliteration English Equivalent NATO
Flag Officers
Ναύαρχος Navarkhos Admiral OF-9
Αντιναύαρχος Antinavarkhos Vice Admiral OF-8
Υποναύαρχος Yponavarkhos Rear Admiral (lit. "under-admiral") OF-7
Αρχιπλοίαρχος Arkhiploiarkhos Commodore (lit. "chief captain") OF-6
Senior Officers
Πλοίαρχος Ploiarkhos Captain OF-5
Αντιπλοίαρχος Antiploiarkhos Commander (lit. "vice-captain") OF-4
Πλωτάρχης Plotarkhis Lieutenant Commander (lit. "boat commander") OF-3
Junior Officers
Υποπλοίαρχος Ypoploiarkhos Lieutenant (lit. "under-captain") OF-2
Ανθυποπλοίαρχος Anthypoploiarkhos Sub-Lieutenant (lit. "vice-under-captain") OF-1
Σημαιοφόρος Simaiophoros Ensign (lit. "flag-bearer") OF-1
And if you want Byzantine complexity, take a look at Imperial Russian military ranks...
http://en.wikipedia.org/wiki/Russian_military_ranks#1722-1917