Your question is difficult to understand because of the overloaded names in JIRA. "subtask" in JIRA is used both as an issue-type "name" and as an issue-type classification. For example, I believe out of the box JIRA comes with a subtask (classification) by the name of "Technical Task" as well as another subtask by the name of "Sub Task". Both of them have titles: the Summary field.
It would be possible to show the parent of a subtask in issue navigator but you'd need a custom report to show the subtasks for the parent issue. One exception is in the Board (JIRA Agile) where you can show issues grouped by their parent item.
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