"The Rings of Power" Vanity Fair article

[William Cloud Hicklin]

Command armies? When she is the head of the state, she certainly directs her armies... the strategy if not the tactics.

Yes, but note Appendix B: "when the Shadow passed, Celeborn came forth and led the host of Lorien over Anduin in many boats. They took Dol Guldur, and Galadriel threw down its walls and laid bare its pits, and the forest was cleansed." Which I read as saying that the Lord of the Galadhrim was the military commander, the general and warrior, and the Lady's role was more magical and mystical. (Note also the parallel phrasing to Luthien's destruction of Sauron's tower on Tol-in-Gaurhoth long before: again, Luthien put forth her power after Huan, and Beren sort of, had already defeated Sauron and driven him off.)

I suppose it's worth mentioning that Elrond (who clearly was a general, at least during the First War of the Rings) was present at the battle of Dagorlad and the siege of Barad-dur with Gil-galad, as was Thranduil's father Oropher, but Galadriel makes no mention of having been there herself.