I'm not sure whether you mean: "Why did the Great Depression not give rise to radical groups" or "Why did the Great Depression not give rise to Nazis" so I'll try and answer them both.

But the US absolutely had radical political movements during the Great Depression - Charles Coughlin led a popular but incredibly anti-semetic and at times pro-fascist radio show, The Bonus Army marched on Washington D.C. and the Business Plot attempted to overthrow American democracy, the German American Bund was pro-Nazi and held a 20,000 person strong rally in Madison Square Garden, FDR himself radically redesigned the way in which the state would function.

As to why they were never as successful as the Nazis or why the Nazis existed in Germany but not in America let's compare the two countries a little. America had an entrenched 2 party system, with both parties being mass parties who appealed widely to the general public, the US has a mature democratic culture which placed emphasis on the importance of democracy and liberty. Germany was an immature democracy and had been an almost absolute monarchy which was extremely militarised and nationalistic with great emphasis placed on the military, it had mobilized to a far greater degree than America and lost the war, then had fought a civil war as a Communist revolution broke out, in which the state armed and sanctioned "free corps" various armed veteran groups who were allowed to coexist with the army. German democracy was immature and contained a large number of parties with narrow appeals (The Nazis were noted as being the only party which could actually claim considerable support from all sections of society). Germany also had large amounts of antisemitism before WW1.

The Nazi party was formed after WW1 and received around 5% of the votes in national elections but rose to prominence during 1929 when the Young Plan became an issue. The Young Plan was a renegotiation of Germany's reparations, in which the Weimar government negotiated a smaller debt which they were given more time to pay off. But renegotiating Germany's reparations meant they accepted Germany's war guilt and the Nazis strong opposition to this was popular with the media who backed them over the government. When the Great Depression hit the Nazis were prominent within media coverage and were able to claim that German Democracy was a failure given that it had overseen 3 disasters in 11 years (the German civil war, hyperinflation, and the Great Depression).

The Nazis were, therefore, a prominently placed political party, with broad appeal, fighting against an unpopular incumbent party and advocated for the end of a democracy which had lasted for 11 years, was imposed upon Germany, and was stricken by a number of crises and this was created by a far more militarized and antisemitic culture. The US never had a party like the Nazis who were similarly positioned before the Great Depression. The closest equivalent could maybe be the KKK who were rapidly declining in numbers due to various scandals and weren't a political party. And the US has unfavourable laws against 3rd parties.

Sources:

Ian Kershaw - Hitler, 1889-1936: Hubris

Adrian Weale - The SS: A New History

Joshua Rothman - When Bigotry Paraded Through The Streets