Subgroups — D₇×D₉×C₇₁ #31822014

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇×C₇₁	—	3	1	no	maximal
5	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×C₇₁	—	3	1	no	—
7	D₃×C₇×C₇₁	—	3	1	no	—
8	C₃×D₇×C₇₁	D₃	1	1	yes	characteristic
9	C₂×D₉×C₇₁	—	7	1	no	maximal, Hall
10	C₂×D₇×C₇₁	—	9	1	no	Hall
11	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic
12	C₂×C₉×C₇₁	—	7	1	no	—
13	D₉×C₇₁	—	7	1	no	—
14	D₉×C₇₁	D₇	1	1	yes	characteristic, direct product factor
15	C₂×C₇×C₇₁	—	9	1	no	—
16	D₇×C₇₁	—	9	1	no	—
17	D₇×C₇₁	D₉	1	1	yes	characteristic, direct product factor
18	C₂×D₃×C₇₁	—	21	1	no	—
19	C₉×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₇₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇₁	—	7	1	no	—
22	D₃×C₇₁	—	3	1	no	—
23	D₃×C₇₁	—	21	1	no	—
24	C₂²×C₇₁	—	63	1	no	Hall
25	D₇×D₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₃×C₇₁	D₃×D₇	1	1	yes	characteristic
27	C₂×C₇₁	—	7	1	no	—
28	C₂×C₇₁	—	9	1	no	—
29	C₂×C₇₁	—	63	1	no	—
30	D₆₃	C₂×C₇₁	1	1	yes	characteristic, complemented
31	C₉×D₇	C₂×C₇₁	1	1	yes	characteristic, complemented
32	C₇×D₉	C₂×C₇₁	1	1	yes	characteristic, complemented
33	D₃×D₇	—	3	1	no	—
34	C₇₁	D₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₇×C₉	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
36	D₂₁	—	3	1	no	—
37	C₃×D₇	D₃×C₇₁	1	1	yes	characteristic
38	D₃×C₇	—	3	1	no	—
39	C₂×D₉	—	7	1	no	Hall
40	C₂×D₇	—	9	1	no	Hall
41	C₃×C₇	C₂×D₃×C₇₁	1	1	yes	characteristic
42	C₂×C₉	—	7	1	no	—
43	D₉	—	7	1	no	—
44	D₉	D₇×C₇₁	1	1	yes	characteristic, direct product factor
45	C₂×C₇	—	9	1	no	—
46	D₇	—	9	1	no	—
47	D₇	D₉×C₇₁	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	21	1	no	—
49	C₉	C₂×D₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
50	C₇	C₂×D₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	21	1	no	—
54	C₂²	—	63	1	no	Sylow
55	C₃	D₃×D₇×C₇₁	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	63	1	no	—

	subgroup	G/H
center, hypercenter	C₇₁	D₇×D₉
commutator, cosocle, hypocenter	C₇×C₉	C₂²×C₇₁
Frattini	C₃	D₃×D₇×C₇₁
Fitting	C₇×C₉×C₇₁	C₂²
socle	C₃×C₇×C₇₁	C₂×D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇₁×D₆₃	C₂	semidirect
2. C₇×D₉×C₇₁	C₂	semidirect
3. C₉×D₇×C₇₁	C₂	semidirect
5. C₇×C₉×C₇₁	C₂²	semidirect
14. D₉×C₇₁	D₇	direct (N × H)
17. D₇×C₇₁	D₉	direct (N × H)
19. C₉×C₇₁	C₂×D₇	semidirect
20. C₇×C₇₁	C₂×D₉	semidirect
25. D₇×D₉	C₇₁	direct (N × H)
30. D₆₃	C₂×C₇₁	semidirect
31. C₉×D₇	C₂×C₇₁	semidirect
32. C₇×D₉	C₂×C₇₁	semidirect
34. C₇₁	D₇×D₉	direct (N × H)
35. C₇×C₉	C₂²×C₇₁	semidirect
44. D₉	D₇×C₇₁	direct (N × H)
47. D₇	D₉×C₇₁	direct (N × H)
49. C₉	C₂×D₇×C₇₁	semidirect
50. C₇	C₂×D₉×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇₁×D₆₃	2
C₇×D₉×C₇₁	2
C₉×D₇×C₇₁	2
D₃×D₇×C₇₁	3
C₂×D₉×C₇₁	7
D₇×D₉	71

Subgroups — D7×D9×C71 #31822014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₉×C₇₁ #31822014