festnehmen
to arrest
To take a person who is suspected of a crime into custody in the name of the law; to arrest.
Die Polizei hat den Verdächtigen nach einer kurzen Verfolgung festgenommen.
The police arrested the suspect after a short chase.

to arrest
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to arrest
To take a person who is suspected of a crime into custody in the name of the law; to arrest.
Die Polizei hat den Verdächtigen nach einer kurzen Verfolgung festgenommen.
The police arrested the suspect after a short chase.

'Festnehmen' (to arrest) is a separable verb. In a main clause, the prefix 'fest' goes to the end of the sentence. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Polizei nimmt den Dieb auf frischer Tat fest.
The police arrest the thief in the act.
The verb is made up of the adverb 'fest' (firmly) and the verb 'nehmen' (to take). The literal meaning is therefore to 'take someone firmly' or 'hold someone firmly', which describes the meaning 'verhaften' (to arrest) well.
Der Ladendetektiv hielt den Dieb fest, bis die Polizei kam, um ihn festzunehmen.
The store detective held the thief until the police came to arrest him.
This verb is used almost exclusively in the context of police, law, and crime. The typical subject of the sentence is 'die Polizei' (the police) or another authority.
Die Polizei konnte den Einbrecher noch am Tatort festnehmen.
The police were able to arrest the burglar at the scene of the crime.
to take
'nehmen' and 'festnehmen' are connected when a person is no longer allowed to leave freely. Here, 'nehmen' mainly fits in fixed expressions such as 'gefangen nehmen' (to take prisoner) or 'in Gewahrsam nehmen' (to take into custody). 'festnehmen' is the normal verb when the police stop a suspected person and take them away. The words can be confused because 'festnehmen' contains the idea of 'nehmen'. Even so, you do not simply say 'die Polizei nimmt den Mann'; normally you say 'die Polizei nimmt den Mann fest' or 'verhaftet ihn' (arrests him).

Am Bahnhof nimmt die Polizei einen Verdächtigen fest.
At the train station, the police arrest a suspect.
Die Wachen nehmen den Einbrecher gefangen.
The guards take the burglar prisoner.