Subgroups — C₃⋊Dic₂₈₇₇ #46828607

Order 34524.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₈₇₇	—	3	4	no	maximal
3	C₃²×C₇×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₃₇	D₃	1	4	yes	—
5	C₃⋊Dic₄₁₁	—	7	1	no	maximal, Hall
6	Dic₉₅₉	—	9	1	no	Hall
7	C₃×C₇×C₁₃₇	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₁₃₇	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₃₇	C₃⋊D₃	1	1	yes	characteristic
10	Dic₄₁₁	—	21	4	no	—
11	C₃²×C₁₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₁₃₇	D₂₁	1	4	yes	—
14	Dic₁₃₇	—	63	1	no	Hall
15	C₃×C₁₃₇	Dic₂₁	1	4	yes	complemented
16	C₂×C₁₃₇	C₃⋊D₂₁	1	1	yes	characteristic
17	C₃⋊Dic₂₁	—	137	1	no	maximal, Hall
18	C₁₃₇	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₇	D₁₃₇	1	1	yes	characteristic
20	Dic₂₁	—	411	4	no	—
21	C₃²×C₇	Dic₁₃₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₄₁₁	1	4	yes	—
23	C₃⋊Dic₃	—	959	1	no	Hall
24	Dic₇	—	1233	1	no	Hall
25	C₃×C₇	Dic₄₁₁	1	4	yes	complemented
26	C₂×C₃²	D₉₅₉	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₄₁₁	1	1	yes	characteristic
28	Dic₃	—	2877	4	no	—
29	C₃²	Dic₉₅₉	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₄₁₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₈₇₇	1	4	yes	—
32	C₄	—	8631	1	no	Sylow
33	C₃	Dic₂₈₇₇	1	4	yes	complemented
34	C₂	C₃⋊D₂₈₇₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₂₈₇₇
commutator, hypocenter	C₃²×C₇×C₁₃₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₇×C₁₃₇	C₂
LCS	G ▷ C₃²×C₇×C₁₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₃₇	C₄	semidirect
7. C₃×C₇×C₁₃₇	Dic₃	semidirect
11. C₃²×C₁₃₇	Dic₇	semidirect
12. C₇×C₁₃₇	C₃⋊Dic₃	semidirect
15. C₃×C₁₃₇	Dic₂₁	semidirect
18. C₁₃₇	C₃⋊Dic₂₁	semidirect
21. C₃²×C₇	Dic₁₃₇	semidirect
25. C₃×C₇	Dic₄₁₁	semidirect
29. C₃²	Dic₉₅₉	semidirect
30. C₇	C₃⋊Dic₄₁₁	semidirect
33. C₃	Dic₂₈₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₁₃₇	2
Dic₂₈₇₇	3
C₃⋊Dic₄₁₁	7
C₃⋊Dic₂₁	137

Subgroups — C3⋊Dic2877 #46828607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊Dic₂₈₇₇ #46828607