I create QTableview and uses QSqlTableModel. She contains 7 columns. Columns 0 and 6 is hide.

ui->tableView->hideColumn(0);

ui->tableView->hideColumn(6);

And i create a column 7 and set it QPushButton

model->insertColumn(7);

model->setHeaderData(7, Qt::Horizontal, QString(""));

QPushButton* button = new QPushButton(..., ui->tableView);

ui->tableView->setIndexWidget(model->index(i,7), button);

Sortin is enabled. After sort by some column i create column 7 in the same way.

See screen