I've never really liked the term "patriarchy". Before this is written off as exhibit Q of patriarchy in action let me add that much of my PhD was about the psychology of prejudice, and I don't think that a word like patriarchy really does prejudice right.
For one thing it's focused entirely on gender, but what about the other kinds of prejudice? Like 80 years ago it would be fair to say we were in a WASPiarchy, but these days jews aren't really resented in most of North America, and Irish and Italian Americans are no longer (by the bizarre logic of prejudice-land) "races" so much as flavors of whiteness. Plus there's a shifting miasma of other prejudices. Depending where you are there's a smartiarchy or a dumyarchy, and there is an omnipresent and exceptionally powerful cooliarchy (tied in heavily, but not exclusively, to the beautiarchy).
I'm not trying to be glib here - Gender based prejudice is almost certainly the most common form of prejudice in terms of raw frequency of occurrence, and leads to lots of Really Bad Things. The set of stats I found in a quick google search had Black men making a slightly higher median income than white women at all levels of education - though they were reasonably close, and both dwarfed by White men's income (1995 stats makes it slightly old data). And of course, the statistics on rape are just mind-bogglingly evil. But I don't think it's easy to compare suffering side by side. Women are at a far higher risk of being raped, Blacks are at a far higher risk of being imprisoned... I don't think you can even start to contemplate questions like: "how many years in jail would you trade for being raped once". It simply defies humanity to do so. Suffering on this kind of scale is just horrible wherever it is found. And it's not just gender and race. People with mental disorders, for example, can suffer social stigmas that put them at elevated risks of alcoholism and suicide, and poor people are basically screwed every which way to Sunday (especially in the States where they get lousy health care, if any at all). So we're living in a patri-whity-neurotypic-wealthiarchy for starters.
On a more philosophical note, as Wikipedia puts it "The English suffix -archy (from Greek αρχή, rule) denotes leadership and government." Prejudice certainly can be codified into, and enforced by government (see Crow, Jim) but most modern prejudice has little to nothing to do with government, and very little to do with leadership either. In fact, a lot of it takes place at non-conscious levels, merely shaping expectancies rather than directing commandments at people - and people's level of prejudiced actions (at least the non-overt modern kinds) seems to ebb and flow with their level of insecurity. That's not a governing principle, it's people just being shitty to each other when they're feeling defensive.
That isn't to say that prejudice doesn't shape society - the types of roles people get shunted in to, and how easy it is for them to flourish there matter (see the enormous wage disparities). And anything that encourages or excuses aggression can lead to physical assaults and their coverups. But that doesn't make it an "archy: any more than other strong social force are. People feel compelled to surround themselves with other people and have friends, and will massively rearange their worlds to get it, indeed will put up with massive amounts of abuse to get it, but we don't live in a sociarchy do we? Really?