Subgroups — C₇×D₉×D₇₁ #31822012

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₆₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₇₁	—	3	1	no	maximal
5	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₂₁₃	—	3	1	no	—
7	D₃×C₇×C₇₁	—	3	1	no	—
8	C₃×C₇×D₇₁	D₃	1	1	yes	characteristic
9	D₉×D₇₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×D₇₁	—	9	1	no	Hall
11	C₃×C₇×C₇₁	C₂×D₃	1	1	yes	characteristic
12	D₆₃₉	C₂×C₇	1	1	yes	characteristic, complemented
13	C₉×D₇₁	C₂×C₇	1	1	yes	characteristic, complemented
14	D₉×C₇₁	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₇×C₇₁	—	9	1	no	—
16	C₇×D₇₁	—	9	1	no	—
17	C₇×D₇₁	D₉	1	1	yes	characteristic, direct product factor
18	D₃×D₇₁	—	3	1	no	—
19	C₉×C₇₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₇₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	D₂₁₃	—	3	1	no	—
22	C₃×D₇₁	D₃×C₇	1	1	yes	characteristic
23	D₃×C₇₁	—	3	1	no	—
24	C₂×D₇₁	—	9	1	no	Hall
25	C₂×C₇×D₉	—	71	1	no	maximal, Hall
26	C₃×C₇₁	C₂×D₃×C₇	1	1	yes	characteristic
27	C₂×C₇₁	—	9	1	no	—
28	D₇₁	—	9	1	no	—
29	D₇₁	C₇×D₉	1	1	yes	characteristic, direct product factor
30	C₂×C₇×C₉	—	71	1	no	—
31	C₇×D₉	—	71	1	no	—
32	C₇×D₉	D₇₁	1	1	yes	characteristic, direct product factor
33	C₂×D₃×C₇	—	213	1	no	—
34	C₇₁	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
35	C₇×C₉	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₇	—	71	1	no	—
37	D₃×C₇	—	3	1	no	—
38	D₃×C₇	—	213	1	no	—
39	C₂×D₉	—	71	1	no	Hall
40	C₂²×C₇	—	639	1	no	Hall
41	C₃×C₇	D₃×D₇₁	1	1	yes	characteristic
42	C₂×C₉	—	71	1	no	—
43	D₉	—	71	1	no	—
44	D₉	C₇×D₇₁	1	1	yes	characteristic, direct product factor
45	C₂×C₇	—	9	1	no	—
46	C₂×C₇	—	71	1	no	—
47	C₂×C₇	—	639	1	no	—
48	C₂×D₃	—	213	1	no	—
49	C₉	C₂×C₇×D₇₁	1	1	yes	characteristic, complemented, Sylow
50	C₇	D₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	71	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	213	1	no	—
54	C₂²	—	639	1	no	Sylow
55	C₃	D₃×C₇×D₇₁	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	71	1	no	—
58	C₂	—	639	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₉×D₇₁
commutator, cosocle, hypocenter	C₉×C₇₁	C₂²×C₇
Frattini	C₃	D₃×C₇×D₇₁
Fitting	C₇×C₉×C₇₁	C₂²
socle	C₃×C₇×C₇₁	C₂×D₃
LCS	G ▷ C₉×C₇₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₆₃₉	C₂	semidirect
2. C₇×D₉×C₇₁	C₂	semidirect
3. C₇×C₉×D₇₁	C₂	semidirect
5. C₇×C₉×C₇₁	C₂²	semidirect
9. D₉×D₇₁	C₇	direct (N × H)
12. D₆₃₉	C₂×C₇	semidirect
13. C₉×D₇₁	C₂×C₇	semidirect
14. D₉×C₇₁	C₂×C₇	semidirect
17. C₇×D₇₁	D₉	direct (N × H)
19. C₉×C₇₁	C₂²×C₇	semidirect
20. C₇×C₇₁	C₂×D₉	semidirect
29. D₇₁	C₇×D₉	direct (N × H)
32. C₇×D₉	D₇₁	direct (N × H)
34. C₇₁	C₂×C₇×D₉	semidirect
35. C₇×C₉	C₂×D₇₁	semidirect
44. D₉	C₇×D₇₁	direct (N × H)
49. C₉	C₂×C₇×D₇₁	semidirect
50. C₇	D₉×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₆₃₉	2
C₇×D₉×C₇₁	2
C₇×C₉×D₇₁	2
D₃×C₇×D₇₁	3
D₉×D₇₁	7
C₂×C₇×D₉	71

Subgroups — C7×D9×D71 #31822012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₉×D₇₁ #31822012