übergeordnet
superior
Standing at a higher level in a hierarchy or ranking system.
Die Abteilungsleiter berichten an die übergeordnete Geschäftsführung.
The department heads report to the superior executive management.

higher-level / superior
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superior
Standing at a higher level in a hierarchy or ranking system.
Die Abteilungsleiter berichten an die übergeordnete Geschäftsführung.
The department heads report to the superior executive management.

'Übergeordnet' (higher-level/superior) is the past participle of the verb 'überordnen'. It is made up of 'über' and 'ordnen' and literally means to place something 'above' something else in an order or hierarchy.
Das Wohl der Kinder ist allen anderen Interessen übergeordnet.
The well-being of the children takes priority over all other interests.
When you want to express to whom or what something is superior, you use the dative. The structure is: [thing A] ist [thing B in the dative] übergeordnet.
Die Zentrale in Berlin ist allen regionalen Büros übergeordnet.
The headquarters in Berlin is superior to all regional offices.
The context makes the meaning clear: If 'übergeordnet' (higher-level/superior) refers to people or institutions, e.g. 'die übergeordnete Behörde' (the superior authority), it is about hierarchy. If it refers to abstract things, e.g. 'das übergeordnete Ziel' (the overarching goal), it is about importance or generality.
Der Manager muss sich an die übergeordnete Direktion wenden.
The manager has to contact the superior directorate.
general
'allgemein' and 'übergeordnet' can both describe something that does not refer only to one small individual case. 'allgemein' often means: valid for many things or not very detailed. 'übergeordnet', on the other hand, means: it is on a higher level and groups other points under it. The words can be confused when talking about topics, goals, or terms. 'Allgemein' fits when a statement is broad or not very specific. 'Übergeordnet' fits when there is a clear structure, for example a main topic with subtopics.

Das übergeordnete Ziel des Kurses ist, sicherer Deutsch zu sprechen.
The overarching goal of the course is to speak German more confidently.
Im Bericht stehen zuerst allgemeine Informationen über das Projekt.
The report first gives general information about the project.