Just a short categorization of the four most important family of knots. Some might argue the selections I've made.
| Task | Overhand | Bowline | Alpine | Figure eight | Half hitches |
|---|---|---|---|---|---|
| Stopper | Overhand knot | - | - | Figure of eight knot | - |
| Binding | Square knot | - | - | Packers knot | Corned beef knot |
| Fixed end loop | Overhand loop | Bowline | Alpine butterfly bend loop | Retreaded figure of eight loop | - |
| Fixed mid loop | Overhand loop | - | Alpine butterfly loop | Directional figure eight | - |
| Double loops | - | Double bowline | Double alpine butterfly | Bunny ears | - |
| Tripple loops | - | Tripple bowline | Tripple alpine butterfly | Double figure of eigh tripple loop | - |
| Slip loops | Overhand noose | Running bowline | - | -Siberian hitch | Two half hitches |
| Adjustable loop | - | - | - | HFP Slippery 8 loop | Tautline hitch |
| Bends | Fishermans knot | Sheet bend | Alpine butterfly bend | Flemish bend | - |
| Middle hitch | - | - | - | - | Clove hitch |
| End hitch | Halter hitch | - | - | Siberian hitch | Two half hitches |
| Lengthwise pull hitch | - | - | - | - | Rolling hitch |
| Shortenings | Overhand loop | - | Alpine butterfly loop | Directional figure eight | Sheepshank |
Each of the knot families fills this many knot categories:
Overhand: 8/13
Bowline: 5/13
Alpine butterfly: 6/13
Figure eight: 11/13
Half hitches: 7/13
Which makes the Figure eight the most complete family of knots. Missing knots in the lengthwise pull hitch and mid hitch categories only.