If mounted, weapons such as these could be hung from the saddle. If on foot or on horse, they could be hung from the soldier's belt or tucked into the belt.
Two examples from art showing a mace and flail tucked into a belt:
https://commons.wikimedia.org/wiki/File:DisasterOfMari1266.JPG
https://i.pinimg.com/originals/e2/12/a2/e212a2ed3cb01f1376303fbd0d2833ed.jpg - the complete artwork from which this detail is from is at https://www.metmuseum.org/toah/works-of-art/1970.301.3/
Swords are sometimes worn through a belt in a similar manner:
The katana is a famous example of a sword worn like this. Often, the scabbards of swords designed to be worn like this have flared mouths of other features that will stop them from slipping through the belt. The head of a mace will provide similar security.
Many maces have strap holes in their hafts:
The straps that would have gone through these holes could have been used as wrist straps, to prevent the weapon from being dropped, and to hang the weapon from the saddle.
This flail, assumed probably to be a Victorian replica:
has a groove in the grip which could have been used to attach a strap (perhaps via a metal ring sitting in the groove).
Some weapons have hooks allowing them to be hung from a belt or saddle:
