Stieg Larsson's posthumous novel The Girl with the Dragon Tattoo -- originally Men Who Hate Women in Swedish -- is almost entirely composed of conflict. The story itself, although tightly plotted, is almost secondary to the constant conflict between characters, events, and history.
Since the main plot has two threads -- one starring Mikael Blomkvist and one starring Lisbeth Salander -- there are two main conflicts. Blomkvist's involves his search for truth in the face of lies, and Salander's involves her fight against a male-dominated, abusive world.
Blomkvist's conflict is best described in the mode of Character vs. Character; his investigation into a decades-old murder is at first scorned and then actively discouraged by others. All of the obstacles he faces are put into place by other people.
Salander's conflict is best described in the mode of Character vs. Society; she has been abused seemingly from birth by men -- always men, a recurring theme in Larsson's books -- and has developed a personal moral system based on this abuse. In her mind, the ends always justify the means, and if society forgives and enables people to do bad things, it is her job to punish them.
The Girl With the Dragon Tattoo is a wonderful novel written by Steig Larsson. This Swedish book is filled with twists and turns, adventure and mystery, love and hate. I would definitely say the main conflict is Blomkvist's search to find the truth behind Harriet's disappearance. This is what the entire book is centered around so it is safe to say this is the most prominent conflict.