Subgroups — Dic₈₆₁₉ #46828131

Order 34476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₈₇₃	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₆₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₇×C₁₆₉	D₃	1	1	yes	characteristic
5	C₁₇×C₁₆₉	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₆₆₃	—	13	1	no	maximal
7	Dic₅₀₇	—	17	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₁₇	D₁₃	1	1	yes	characteristic
9	C₂×C₃×C₁₆₉	D₁₇	1	1	yes	characteristic
10	Dic₂₂₁	—	39	1	no	—
11	Dic₁₆₉	—	51	1	no	Hall
12	C₃×C₁₃×C₁₇	Dic₁₃	1	1	yes	characteristic
13	C₃×C₁₆₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₇	D₃₉	1	1	yes	characteristic
15	C₂×C₁₆₉	D₅₁	1	1	yes	characteristic
16	C₁₃×C₁₇	Dic₃₉	1	1	yes	characteristic
17	Dic₅₁	—	169	1	no	Hall
18	C₁₆₉	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
19	Dic₃₉	—	221	1	no	—
20	C₂×C₃×C₁₇	D₁₆₉	1	1	yes	characteristic
21	C₂×C₃×C₁₃	D₂₂₁	1	1	yes	characteristic
22	Dic₁₇	—	507	1	no	Hall
23	Dic₁₃	—	663	1	no	—
24	C₃×C₁₇	Dic₁₆₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₃	Dic₂₂₁	1	1	yes	characteristic
26	C₂×C₁₇	D₅₀₇	1	1	yes	characteristic
27	C₂×C₁₃	D₆₆₃	1	1	yes	characteristic
28	C₁₇	Dic₅₀₇	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	Dic₆₆₃	1	1	yes	characteristic
30	Dic₃	—	2873	1	no	Hall
31	C₂×C₃	D₂₈₇₃	1	1	yes	characteristic
32	C₄	—	8619	1	no	Sylow
33	C₃	Dic₂₈₇₃	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₈₆₁₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₈₆₁₉
commutator, hypocenter	C₃×C₁₇×C₁₆₉	C₄
Frattini	C₂×C₁₃	D₆₆₃
Fitting, cosocle	C₂×C₃×C₁₇×C₁₆₉	C₂
socle, prime radical	C₂×C₃×C₁₃×C₁₇	D₁₃
LCS	G ▷ C₃×C₁₇×C₁₆₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₁₇×C₁₆₉	C₄	semidirect
5. C₁₇×C₁₆₉	Dic₃	semidirect
13. C₃×C₁₆₉	Dic₁₇	semidirect
18. C₁₆₉	Dic₅₁	semidirect
24. C₃×C₁₇	Dic₁₆₉	semidirect
28. C₁₇	Dic₅₀₇	semidirect
33. C₃	Dic₂₈₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₇×C₁₆₉	2
Dic₂₈₇₃	3
Dic₆₆₃	13
Dic₅₀₇	17

Subgroups — Dic8619 #46828131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₈₆₁₉ #46828131