If there a way to create a formula that will pull the numerical values of COLUMN F but a range?

For example...=SUMIF(H:H,?????,F:F)

I want the ???? to add all the quantities in column F if the letter in column H is between A-H, (then another formula I-N, and O-Z)

COLUMN H = ALL MY DATA HERE IS A FORMULA THAT SHOWS FIRST CHARACTER (A - Z)
COLUMN F = MY QUANTITIES (in numbers)

Thanks for any input you can provide.