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We present a detailed characterization of the Kepler-411 system (KOI 1781).This system was previously known to host two transiting planets: one with aperiod of 3 days ($R=2.4R_\oplus$; Kepler-411b) and one with a period of 7.8days ($R=4.4R_\oplus$; Kepler-411c), as well as a transiting planetarycandidate with a 58-day period ($R=3.3R_\oplus$; KOI 1781.03) from Keplerphotometry. Here, we combine Kepler photometry data and new transit timingvariation (TTV) measurements from all the Kepler quarters with previousadaptive-optics imaging results, and dynamical simulations, in order toconstrain the properties of the Kepler-411 system. From our analysis, we obtainmasses of 25.6$\pm$2.6$M_\oplus$ for Kepler-411b and 26.4$\pm$5.9 $M_\oplus$for Kepler-411c, and we confirm the planetary nature of KOI 1781.03 with a massof 15.2$\pm$5.1$M_\oplus$, hence the name Kepler-411d. Furthermore, by assumingnear-coplanarity of the system (mutual inclination below $30^\circ$), wediscover a nontransiting planet, Kepler-411e, with a mass of10.8$\pm$1.1$M_\oplus$ on a 31.5-day orbit, which has a strong dynamicalinteraction with Kepler-411d. With densities of $1.71\pm0.39$~g\,cm$^{-3}$ and$2.32\pm0.83$~g\,cm$^{-3}$, both Kepler-411c and Kepler-411d belong to thegroup of planets with a massive core and a significant fraction of volatiles.Although Kepler-411b has a sub-Neptune size, it belongs to the group of rockyplanets.

Kepler-411: a four-planet system with an active host star