Based on web search results, here are some common punk genres and how dystopian stories using these genres tend to be:

- **Cyberpunk**: This is the original punk genre that emerged in the 1980s and influenced many others. It involves a high-tech, low-life setting where advanced technology such as artificial intelligence, cybernetics, and hacking coexists with social decay, inequality, and crime. Cyberpunk stories are usually very dystopian, depicting a bleak and oppressive future where corporations and governments have too much power and individuals struggle to survive and resist.
- **Steampunk**: This is a genre that combines elements of science fiction and fantasy with Victorian-era aesthetics and technology. It imagines a world where steam power is the dominant form of energy and enables inventions such as airships, automatons, and time machines. Steampunk stories can be dystopian or utopian, depending on how the technology is used and how it affects society. Some steampunk stories explore themes such as imperialism, class conflict, and social reform.
- **Dieselpunk**: This is a genre that is similar to steampunk but focuses on the interwar period (1918-1939) and the early stages of World War II. It features diesel-based technology such as tanks, planes, submarines, and robots, as well as art deco and noir styles. Dieselpunk stories are often dystopian, portraying a world where fascism, totalitarianism, and war are rampant and where heroes fight against tyranny and oppression.
- **Biopunk**: This is a genre that deals with the implications of biotechnology, genetic engineering, and biohacking. It depicts a world where humans can modify themselves or other organisms with DNA manipulation, cybernetics, or nanotechnology. Biopunk stories are usually dystopian, showing the dangers of unethical experimentation, corporate exploitation, and biological warfare.
- **Solarpunk**: This is a genre that is relatively new and optimistic compared to other punk genres. It envisions a future where renewable energy sources such as solar power are widely used and where society is more egalitarian, diverse, and ecological. Solarpunk stories are utopian or at least hopeful, highlighting the potential of human creativity, cooperation, and innovation to solve environmental and social problems.

These are just some examples of punk genres. There are many more variations and combinations that can be found in literature, film, music, art, and fashion.

Source: 
Punk rock - Wikipedia. https://en.wikipedia.org/wiki/Punk_rock
Different punk: A to Z of punk genres - Sorcerer of Tea. https://sorcereroftea.com/punkpunk-a-to-z-of-punk-genres/
Types of Punk Genres - HubPages. https://discover.hubpages.com/literature/types-of-punk-genres
A Guide to the Different Punk Subgenres - Musician Wave. https://www.musicianwave.com/punk-subgenres/
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