Hi,
It depends. If it's only for you, then you can create custom fields of the table "order" via the menu Display>Custom fields and store the informations there.
If it's for a plugin for the public, then you want to store that in the column order_payment_params of hikashop_order.
You should have your data serialized in that column and you should have an object with attributes.
For example:
$data = new stdClass();
$data->subscription_id = $subscription_id;
// etc for the rest of the data
$order = new stdClass();
$order->order_id = $order_id;
$order->order_payment_params = $data;
$orderClass = hikashop_get('class.order');
$orderClass->save($order);