Basically an add to Fizz's answer. Large industries certainly draw subsidies. But there are a couple of nuances worth pointing out, largely to do with GAAP accounting and tax law in the US as it applies generally to business operations in the United States, and those that apply specifically to oil, gas and mining.
General Accounting and Tax Law Considerations
The reason for this nuance is that these organizations that run these studies take an expansive view of subsidies. In the ODI study mentioned by Fizz, subsidies are broken down into three main groupings, Capex (exploratory, R&D), Opex (manufacturing) and consumer. In the Capex bucket, the ODI explicitly calls out the R&D tax credit, as research and development keep the US on the cutting edge. This is not a subsidy unique to oil and gas exploration and manufacturing. You could eliminate it entirely, but it offers salutary, outside benefits across industry, and across the government/private sector divide. Other items that are routinely categorized as "subsidies" from this group include the Master Limited Partnership, which avoids double taxation-- a sound and foundational policy goal of the US tax system, Domestic Manufacturing Deduction-- which encourages domestic manufacturing generally, and the foreign tax credit. (same sources for all). As far as I could tell the ODI study made no attempt to differentiate these types of "subsidies", but we know they included at least one of them, the R&D credit.
Specific Accounting Considerations for the Oil and Gas Industries
The question is why the US cannot eliminate "subsidies". One reason is that we have to account for these assets and expenses somehow, and GAAP better practices appear to be in conflict with the WTO's definition of subsidy (maximization of tax revenue). The two big ticket ones here are depletion allowance and intangible drilling costs both of which one could infer are in the ODI report. For small independent producers, petro reserves are required to be capitalized. Any asset on the books is required to be depreciated, again not specific to this industry. Likewise the intangible drilling costs from an accounting perspective one could easily argue that the rules are very penal to the oil and gas industry as $0 assets should be written off immediately, not over time. I think it's more incumbent on those suggesting that we get rid of these subsidies suggest what their plan is from a tax and accounting policy perspective.