Assuming you are using JIRA Cloud, have a look here: https://confluence.atlassian.com/cloud/manage-groups-744721627.html
You can add them to the 'site-admins' group to give the next level up from 'administrators' permission.
You can't give System Administrator privileges in Cloud as that is reserved for Atlassian support staff only:
In addition to these groups, there are two default groups that are used by Atlassian support staff. You can't edit these groups or add users to them:
The 'sysadmin' user from these groups can log into your site to provide support to you and to perform certain system maintenance tasks. This user automatically has full application access but does not count towards your license limit, no matter which groups it is placed in.
The account is only used by Atlassian. You may notice logins by this user even without having raised a support request. This is because certain types of system maintenance involve our automated systems performing tasks using this account.
Hope this helps a bit.
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