Subgroups — C₉×D₇×D₇₁ #31822011

Order 17892.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₄₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₇₁	C₃	1	1	yes	maximal, characteristic
5	C₇×C₉×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₄₉₇	C₂×C₃	1	1	yes	characteristic
7	C₃×D₇×C₇₁	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×D₇₁	C₂×C₃	1	1	yes	characteristic
9	C₂×C₉×D₇₁	—	7	1	no	maximal, Hall
10	D₇×D₇₁	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₇₁	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₉×C₇₁	—	7	1	no	—
13	C₉×D₇₁	—	7	1	no	—
14	C₉×D₇₁	D₇	1	1	yes	characteristic, direct product factor
15	D₄₉₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×D₇₁	C₂×C₉	1	1	yes	characteristic, complemented
17	D₇×C₇₁	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×D₇₁	—	7	1	no	—
19	C₉×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₇₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇₁	—	7	1	no	—
22	C₃×D₇₁	—	7	1	no	—
23	C₃×D₇₁	C₃×D₇	1	1	yes	characteristic
24	C₂×D₇₁	—	7	1	no	Hall
25	C₂×C₉×D₇	—	71	1	no	maximal, Hall
26	C₃×C₇₁	C₂×C₃×D₇	1	1	yes	characteristic
27	C₂×C₇₁	—	7	1	no	—
28	D₇₁	—	7	1	no	—
29	D₇₁	C₉×D₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇×C₉	—	71	1	no	—
31	C₉×D₇	—	71	1	no	—
32	C₉×D₇	D₇₁	1	1	yes	characteristic, direct product factor
33	C₂×C₃×D₇	—	71	1	no	—
34	C₇₁	C₂×C₉×D₇	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	C₃×D₇	—	71	1	no	—
38	C₃×D₇	C₃×D₇₁	1	1	yes	characteristic
39	C₂²×C₉	—	497	1	no	Hall
40	C₂×D₇	—	71	1	no	Hall
41	C₃×C₇	C₂×C₃×D₇₁	1	1	yes	characteristic
42	C₂×C₉	—	7	1	no	—
43	C₂×C₉	—	71	1	no	—
44	C₂×C₉	—	497	1	no	—
45	C₂×C₇	—	71	1	no	—
46	D₇	—	71	1	no	—
47	D₇	C₉×D₇₁	1	1	yes	characteristic, direct product factor
48	C₂²×C₃	—	497	1	no	—
49	C₉	D₇×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₇	C₂×C₉×D₇₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	C₂×C₃	—	71	1	no	—
53	C₂×C₃	—	497	1	no	—
54	C₂²	—	497	1	no	Sylow
55	C₃	C₃×D₇×D₇₁	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	71	1	no	—
58	C₂	—	497	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₇×D₇₁
commutator, hypocenter	C₇×C₇₁	C₂²×C₉
Frattini	C₃	C₃×D₇×D₇₁
Fitting	C₇×C₉×C₇₁	C₂²
socle, cosocle	C₃×C₇×C₇₁	C₂²×C₃
prime radical	C₃×D₇×D₇₁	C₃
LCS	G ▷ C₇×C₇₁
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₄₉₇	C₂	semidirect
2. C₉×D₇×C₇₁	C₂	semidirect
3. C₇×C₉×D₇₁	C₂	semidirect
5. C₇×C₉×C₇₁	C₂²	semidirect
10. D₇×D₇₁	C₉	direct (N × H)
14. C₉×D₇₁	D₇	direct (N × H)
15. D₄₉₇	C₂×C₉	semidirect
16. C₇×D₇₁	C₂×C₉	semidirect
17. D₇×C₇₁	C₂×C₉	semidirect
19. C₉×C₇₁	C₂×D₇	semidirect
20. C₇×C₇₁	C₂²×C₉	semidirect
29. D₇₁	C₉×D₇	direct (N × H)
32. C₉×D₇	D₇₁	direct (N × H)
34. C₇₁	C₂×C₉×D₇	semidirect
35. C₇×C₉	C₂×D₇₁	semidirect
47. D₇	C₉×D₇₁	direct (N × H)
49. C₉	D₇×D₇₁	direct (N × H)
50. C₇	C₂×C₉×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₉×D₄₉₇	2
C₉×D₇×C₇₁	2
C₇×C₉×D₇₁	2
C₃×D₇×D₇₁	3
C₂×C₉×D₇₁	7
C₂×C₉×D₇	71

Subgroups — C9×D7×D71 #31822011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₇×D₇₁ #31822011