The Russian Football Union (RFU) imposed the punishments after sections of Torpedo fans were found to have shown the symbols during a clash that saw a number of crowd disturbances.
Torpedo will pay the RFU 200,000 rubles while they will also have to face Rubin Kazan and Ural at the Eduard Streltsov Stadium without fans next month.
The club have not yet finished serving a stadium closure decision imposed in March when sections of the club's supporters were found to have racially abused Zenit striker Hulk.
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