Subgroups — Dic₈₅₆₉ #46804643

Order 34276.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₉×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₇₇₉	—	11	1	no	maximal, Hall
4	Dic₄₅₁	—	19	1	no	maximal, Hall
5	C₂×C₁₉×C₄₁	D₁₁	1	1	yes	characteristic
6	C₂×C₁₁×C₄₁	D₁₉	1	1	yes	characteristic
7	Dic₂₀₉	—	41	1	no	maximal, Hall
8	C₁₉×C₄₁	Dic₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₁₉	D₄₁	1	1	yes	characteristic
11	C₁₁×C₁₉	Dic₄₁	1	1	yes	characteristic, complemented, Hall
12	Dic₄₁	—	209	1	no	Hall
13	C₂×C₄₁	D₂₀₉	1	1	yes	characteristic
14	Dic₁₉	—	451	1	no	Hall
15	Dic₁₁	—	779	1	no	Hall
16	C₄₁	Dic₂₀₉	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₉	D₄₅₁	1	1	yes	characteristic
18	C₂×C₁₁	D₇₇₉	1	1	yes	characteristic
19	C₁₉	Dic₄₅₁	1	1	yes	characteristic, complemented, Sylow
20	C₁₁	Dic₇₇₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	8569	1	no	Sylow
22	C₂	D₈₅₆₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₅₆₉
commutator, hypocenter	C₁₁×C₁₉×C₄₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₉×C₄₁	C₂
LCS	G ▷ C₁₁×C₁₉×C₄₁
UCS	C₁ ◁ C₂

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

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