Police have also raided offices of companies linked to the ferry’s owners.
Search teams are continuing to recover bodies from the submerged hull of the passenger ferry.
One survivor has described taking the agonizing decision to save himself as the ship capsized and water washed away students he was trying to rescue.
The number of people known to have died in the accident has reached 150, with another 152 still missing, most of them teenage children from a single school in Ansan, outside the capital Seoul.
An emotional memorial service took place near the school on Wednesday, with friends and family members laying flowers in front of photographs of some of those who died.
The government is under strong public pressure to find out why the ferry capsized.
Twenty-two of the 29 members of the ferry’s crew survived and prosecutors say the 11 arrested were on the bridge when the ship listed and sank within two hours of distress signals being sent.
Companies associated with Incheon-based Chonghaejin Marine Company, which owned the 6,825-tonne Sewol ferry, have also been raided by police as part of the investigation.
Authorities have issued 30-day travel bans to more than 70 executives connected with Chonghaejin and its affiliates while they are investigated on possible charges ranging from criminal negligence to embezzlement.
“We will also make efforts to retrieve profits made out of criminal acts and track down hidden assets to support financial compensations for [potential] lawsuits by families of the victims and the missing,” a prosecutor told AFP.
Survivors have spoken of the struggle to save the hundreds of passengers trapped below the tilting decks as cargo containers toppled into the sea.
Reports suggest that passengers were told to remain in their rooms and cabins as the ship listed, amid confusion on the bridge over whether to order them to abandon ship.
The first distress call from the sinking ferry was made from a mobile phone by a boy with a shaking voice, officials told Reuters.
His plea for help was followed by about 20 other emergency calls from children on board the ship.
A crew member quoted by local media said that attempts to launch lifeboats were unsuccessful because the ship was listing too severely. Only two of the vessel’s 46 lifeboats were reported to have been deployed.
South Korean President Park Geun-hye has condemned the conduct of some of the crew, calling it “akin to murder”.
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