This is a description of the actual individual floral symmetry (rather than the symmetry of any flower head as a whole which 'panicle', 'globular' or 'umbel' might describe).
If the flower possesses radial symmetry, like a clock-face or magnetic compass with the line of symmetry passing vertically through the centre, then it is described as actinomorphic [radiating 'star-like' from the centre]. Examples are Daisy, Marsh Marigold or Welsh Poppy
Zygomorphic flowers possess bi-lateral symmetry, where the flower has a mirror image counterpart across a plane of symmetry, much like Himalayan Balsam or Snapdragon.
These are flowers that look like they might have radial symmetry, but actually might have one (or an odd number) longer or shorter than the others, so are actually slightly zygomorphic. Examples include Brooklime one of many Speedwells which have four petals, apparently arranged radially, but one is smaller than the others and another is larger than the rest, or Mullein where one petal is slightly wider than the rest.
These flowers having no axis of symmetry at all. Examples are Lords and Ladies or Arum Lily which have twisting spathes and no petals. Strictly speaking, these aren't the flowers, but the outward appearance is one of asymmetry.
Peloric flowers are genetic aberrations (or purposely bred) flowers that normally have Zygomorphic flowers but instead have (at least one) actinomorphic flowers instead. Some cultivated garden flowers are peloric. Foxglove is prone to natural pelorism.