Subgroups — C₃⋊(C₇⋊Dic₃₇₁) #44528372

Order 31164.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇²×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₇⋊Dic₃₇₁	—	3	1	no	maximal, Hall
3	C₃×C₇²×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₅₃	D₃	1	1	yes	characteristic
5	Dic₁₁₁₃	—	7	8	no	maximal
6	C₇²×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₅₃	D₇	1	8	yes	—
8	Dic₃₇₁	—	21	8	no	—
9	C₃×C₇×C₅₃	Dic₇	1	8	yes	complemented
10	C₂×C₇×C₅₃	D₂₁	1	8	yes	—
11	Dic₁₅₉	—	49	1	no	Hall
12	C₃⋊(C₇⋊Dic₇)	—	53	1	no	maximal, Hall
13	C₇×C₅₃	Dic₂₁	1	8	yes	complemented
14	C₂×C₃×C₅₃	C₇⋊D₇	1	1	yes	characteristic
15	C₂×C₃×C₇²	D₅₃	1	1	yes	characteristic
16	Dic₅₃	—	147	1	no	Hall
17	C₇⋊Dic₇	—	159	1	no	Hall
18	C₃×C₅₃	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇²	Dic₅₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
21	C₂×C₇²	D₁₅₉	1	1	yes	characteristic
22	Dic₂₁	—	371	8	no	—
23	C₅₃	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented, Sylow
24	C₇²	Dic₁₅₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	D₃₇₁	1	8	yes	—
26	Dic₇	—	1113	8	no	—
27	C₃×C₇	Dic₃₇₁	1	8	yes	complemented
28	C₂×C₇	D₁₁₁₃	1	8	yes	—
29	Dic₃	—	2597	1	no	Hall
30	C₇	Dic₁₁₁₃	1	8	yes	complemented
31	C₂×C₃	C₇⋊D₃₇₁	1	1	yes	characteristic
32	C₄	—	7791	1	no	Sylow
33	C₃	C₇⋊Dic₃₇₁	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₃⋊(C₇⋊D₃₇₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₇⋊D₃₇₁)
commutator, hypocenter	C₃×C₇²×C₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₅₃	C₂
LCS	G ▷ C₃×C₇²×C₅₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₇²×C₅₃	C₄	semidirect
6. C₇²×C₅₃	Dic₃	semidirect
9. C₃×C₇×C₅₃	Dic₇	semidirect
13. C₇×C₅₃	Dic₂₁	semidirect
18. C₃×C₅₃	C₇⋊Dic₇	semidirect
19. C₃×C₇²	Dic₅₃	semidirect
23. C₅₃	C₃⋊(C₇⋊Dic₇)	semidirect
24. C₇²	Dic₁₅₉	semidirect
27. C₃×C₇	Dic₃₇₁	semidirect
30. C₇	Dic₁₁₁₃	semidirect
33. C₃	C₇⋊Dic₃₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇²×C₅₃	2
C₇⋊Dic₃₇₁	3
Dic₁₁₁₃	7
C₃⋊(C₇⋊Dic₇)	53

Subgroups — C3⋊(C7⋊Dic371) #44528372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊Dic₃₇₁) #44528372