Subgroups — D₃₂₅₇₁ #72303261

Order 65142.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₈₅₇	—	3	1	no	maximal
3	C₃×C₇×C₁₁×C₄₇	D₃	1	1	yes	characteristic
4	D₄₆₅₃	—	7	1	no	maximal, Hall
5	D₃₆₁₉	—	9	1	no	Hall
6	D₂₉₆₁	—	11	1	no	maximal, Hall
7	C₉×C₁₁×C₄₇	D₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₁×C₄₇	D₉	1	1	yes	characteristic, complemented, Hall
9	D₁₅₅₁	—	21	1	no	—
10	C₇×C₉×C₄₇	D₁₁	1	1	yes	characteristic, complemented, Hall
11	D₉₈₇	—	33	1	no	—
12	C₃×C₁₁×C₄₇	D₂₁	1	1	yes	characteristic
13	D₆₉₃	—	47	1	no	maximal, Hall
14	D₅₁₇	—	63	1	no	Hall
15	C₃×C₇×C₄₇	D₃₃	1	1	yes	characteristic
16	D₄₂₃	—	77	1	no	Hall
17	C₇×C₉×C₁₁	D₄₇	1	1	yes	characteristic, complemented, Hall
18	D₃₂₉	—	99	1	no	Hall
19	C₁₁×C₄₇	D₆₃	1	1	yes	characteristic, complemented, Hall
20	D₂₃₁	—	141	1	no	—
21	C₉×C₄₇	D₇₇	1	1	yes	characteristic, complemented, Hall
22	C₇×C₄₇	D₉₉	1	1	yes	characteristic, complemented, Hall
23	D₁₄₁	—	231	1	no	—
24	C₃×C₇×C₁₁	D₁₄₁	1	1	yes	characteristic
25	D₉₉	—	329	1	no	Hall
26	D₇₇	—	423	1	no	Hall
27	C₃×C₄₇	D₂₃₁	1	1	yes	characteristic
28	D₆₃	—	517	1	no	Hall
29	C₉×C₁₁	D₃₂₉	1	1	yes	characteristic, complemented, Hall
30	D₄₇	—	693	1	no	Hall
31	C₇×C₁₁	D₄₂₃	1	1	yes	characteristic, complemented, Hall
32	D₃₃	—	987	1	no	—
33	C₇×C₉	D₅₁₇	1	1	yes	characteristic, complemented, Hall
34	C₄₇	D₆₉₃	1	1	yes	characteristic, complemented, Sylow
35	D₂₁	—	1551	1	no	—
36	C₃×C₁₁	D₉₈₇	1	1	yes	characteristic
37	D₁₁	—	2961	1	no	Hall
38	C₃×C₇	D₁₅₅₁	1	1	yes	characteristic
39	D₉	—	3619	1	no	Hall
40	D₇	—	4653	1	no	Hall
41	C₁₁	D₂₉₆₁	1	1	yes	characteristic, complemented, Sylow
42	C₉	D₃₆₁₉	1	1	yes	characteristic, complemented, Sylow
43	C₇	D₄₆₅₃	1	1	yes	characteristic, complemented, Sylow
44	D₃	—	10857	1	no	—
45	C₃	D₁₀₈₅₇	1	1	yes	characteristic
46	C₂	—	32571	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁×C₄₇	C₂
Frattini	C₃	D₁₀₈₅₇
socle	C₃×C₇×C₁₁×C₄₇	D₃
LCS	G ▷ C₇×C₉×C₁₁×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₁₁×C₄₇	C₂	semidirect
7. C₉×C₁₁×C₄₇	D₇	semidirect
8. C₇×C₁₁×C₄₇	D₉	semidirect
10. C₇×C₉×C₄₇	D₁₁	semidirect
17. C₇×C₉×C₁₁	D₄₇	semidirect
19. C₁₁×C₄₇	D₆₃	semidirect
21. C₉×C₄₇	D₇₇	semidirect
22. C₇×C₄₇	D₉₉	semidirect
29. C₉×C₁₁	D₃₂₉	semidirect
31. C₇×C₁₁	D₄₂₃	semidirect
33. C₇×C₉	D₅₁₇	semidirect
34. C₄₇	D₆₉₃	semidirect
41. C₁₁	D₂₉₆₁	semidirect
42. C₉	D₃₆₁₉	semidirect
43. C₇	D₄₆₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₉×C₁₁×C₄₇	2
D₁₀₈₅₇	3
D₄₆₅₃	7
D₂₉₆₁	11
D₆₉₃	47

Subgroups — D32571 #72303261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₂₅₇₁ #72303261