friendly, gentle, light, little, playful
good, hard, hefty (BrE), mighty, powerful, violent

give sb/sth
Harry gave him a hefty shove and he fell down.

with a shove
She sent him off with a little shove.

forcefully, hard, roughly
I shoved hard until the door opened.

gently, playfully
practically
aside, away, back
He shoved me roughly aside.

open
She shoved open the door.

down, in
She shoved the letter in a drawer.

into, out of, through
A leaflet was shoved through my letter box. (BrE)
A leaflet was shoved through my mail slot. (AmE)

to
He was shoved to the ground.

push and shove
The crowd was pushing and shoving to get a better view.

shove your hands in your pockets, shove your hands into your pockets
shove sb out of the way
shove your way past sb/sth, shove your way through sth
We shoved our way through the crowd.

Shove is used with these nouns as the object:
finger, fist, way