The clarinet commonly used in military is the A - flat clarinet. Also know as the A clarinet and Ab clarinet. It is a member of the clarinet family, it is one of the soprano clarinets. The A flat clarinet is used for transposing. It is played by advanced professional clarinetists. The A clarinet is pitched higher than the Bb clarinet.
It is used mostly in the military, in classical music, Choirs, in orchestras and sometimes in Jazz. The A flat clarinet is much smaller than Bb and the Eb, that is why it is also called piccolo clarinet which means small in Italian. Only few companies produce the A flat clarinet.
First, let's define military band for the layperson. Military bands aren't necessarily those comprised of military personnel or for military use. They are any band that play music while marching or in formation. Clarinets used in military bands are most often the Bb or soprano clarinet.
Eb, bass, and alto clarinets can all be found in marching or military bands but are far less popular. Oboes and other instruments with a double reed aren't often found because of their sensitivity to the weather and the possibility of damages.