Finite Group Databasebeta

← D₁₆×C₇₆₉ #37589771

Subgroups — D₁₆×C₇₆₉ #37589771

Order 24608.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×C₇₆₉	C₂	1	2	yes	maximal, complemented
2	C₁₆×C₇₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₇₆₉	—	2	2	no	—
4	C₈×C₇₆₉	C₂²	1	1	yes	characteristic
5	C₂²×C₇₆₉	—	4	2	no	—
6	C₄×C₇₆₉	D₄	1	1	yes	characteristic
7	C₂×C₇₆₉	—	8	2	no	—
8	C₂×C₇₆₉	D₈	1	1	yes	characteristic
9	C₇₆₉	D₁₆	1	1	yes	characteristic, direct product factor, Sylow
10	D₁₆	C₇₆₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	D₈	C₂×C₇₆₉	1	2	yes	complemented
12	C₁₆	C₂×C₇₆₉	1	1	yes	characteristic, complemented
13	D₄	—	2	2	no	—
14	C₈	C₂²×C₇₆₉	1	1	yes	characteristic
15	C₂²	—	4	2	no	—
16	C₄	D₄×C₇₆₉	1	1	yes	characteristic
17	C₂	—	8	2	no	—
18	C₂	D₈×C₇₆₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₆₉	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₇₆₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₆₉ ◁ C₄×C₇₆₉ ◁ C₈×C₇₆₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. D₈×C₇₆₉	C₂	semidirect
2. C₁₆×C₇₆₉	C₂	semidirect
9. C₇₆₉	D₁₆	direct (N × H)
10. D₁₆	C₇₆₉	direct (N × H)
11. D₈	C₂×C₇₆₉	semidirect
12. C₁₆	C₂×C₇₆₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₈×C₇₆₉	2
C₁₆×C₇₆₉	2
D₁₆	769