In order to book an upgradable fare on United you have to buy a ticket in fare class W or higher. Here are the fare classes above W.
V
Q
H
U
E
M
B
Y
Only airlines could convolute something so simple as the ordering of the alphabet.
Related
Research from Natalia Emanuel, Emma Harrington, and Amanda Pallais highlights
The following was published in Dealerscope Magazine in December 2010: