Can I take cuttings from my hedges?

Folks, can anyone advise me on taking cuttings from hedges, please? I have a beautiful hedge in my garden comprising of beech, privet, and hawthorn and my husband has recently trimmed it down. I have another area that I would like to plant with hedging and instead of buying expensive plants from a garden centre, I thought it might be possible to take cuttings from the existing hedge.

I am a novice gardener, so I really need to know if I can do this and if so, how?

Many thanks, Jay

Beech - no
Privet - yes
Hawthorn - no

Needless to say, the least interesting one is the easiest to propagate ;-)

Resin

Darn it! Thanks Resin... I appreciate your advice. Last year I tried the rooting powder and it didn't work on ANY of them! Must not have green fingers!

How do the garden centres do it? They must start somewhere?... sorry if I'm a bit dense but I really do want to learn...

Many thanks, Jay

Beech and Hawthorn are usually raised from seeds

Resin

Oh, okay... maybe I will just buy them in the end!

Thanks for your time :)

Jay