Subgroups — C₁₁×D₉×D₇₁ #43244653

Order 28116.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₆₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₁×D₇₁	—	3	1	no	maximal
5	C₉×C₁₁×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₂₁₃	—	3	1	no	—
7	D₃×C₁₁×C₇₁	—	3	1	no	—
8	C₃×C₁₁×D₇₁	D₃	1	1	yes	characteristic
9	C₂×C₁₁×D₇₁	—	9	1	no	Hall
10	D₉×D₇₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₁×C₇₁	C₂×D₃	1	1	yes	characteristic
12	C₂×C₁₁×C₇₁	—	9	1	no	—
13	C₁₁×D₇₁	—	9	1	no	—
14	C₁₁×D₇₁	D₉	1	1	yes	characteristic, direct product factor
15	D₆₃₉	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₉×D₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented
17	D₉×C₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₃×D₇₁	—	3	1	no	—
19	C₁₁×C₇₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₉×C₇₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	D₂₁₃	—	3	1	no	—
22	C₃×D₇₁	D₃×C₁₁	1	1	yes	characteristic
23	D₃×C₇₁	—	3	1	no	—
24	C₂×C₁₁×D₉	—	71	1	no	maximal, Hall
25	C₂×D₇₁	—	9	1	no	Hall
26	C₃×C₇₁	C₂×D₃×C₁₁	1	1	yes	characteristic
27	C₂×C₉×C₁₁	—	71	1	no	—
28	C₁₁×D₉	—	71	1	no	—
29	C₁₁×D₉	D₇₁	1	1	yes	characteristic, direct product factor
30	C₂×C₇₁	—	9	1	no	—
31	D₇₁	—	9	1	no	—
32	D₇₁	C₁₁×D₉	1	1	yes	characteristic, direct product factor
33	C₂×D₃×C₁₁	—	213	1	no	—
34	C₉×C₁₁	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
35	C₇₁	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₁	—	71	1	no	—
37	D₃×C₁₁	—	3	1	no	—
38	D₃×C₁₁	—	213	1	no	—
39	C₂²×C₁₁	—	639	1	no	Hall
40	C₂×D₉	—	71	1	no	Hall
41	C₃×C₁₁	D₃×D₇₁	1	1	yes	characteristic
42	C₂×C₁₁	—	9	1	no	—
43	C₂×C₁₁	—	71	1	no	—
44	C₂×C₁₁	—	639	1	no	—
45	C₂×C₉	—	71	1	no	—
46	D₉	—	71	1	no	—
47	D₉	C₁₁×D₇₁	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	213	1	no	—
49	C₁₁	D₉×D₇₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₉	C₂×C₁₁×D₇₁	1	1	yes	characteristic, complemented, 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×C₁₁×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	C₁₁	D₉×D₇₁
commutator, cosocle, hypocenter	C₉×C₇₁	C₂²×C₁₁
Frattini	C₃	D₃×C₁₁×D₇₁
Fitting	C₉×C₁₁×C₇₁	C₂²
socle	C₃×C₁₁×C₇₁	C₂×D₃
LCS	G ▷ C₉×C₇₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₆₃₉	C₂	semidirect
2. C₁₁×D₉×C₇₁	C₂	semidirect
3. C₉×C₁₁×D₇₁	C₂	semidirect
5. C₉×C₁₁×C₇₁	C₂²	semidirect
10. D₉×D₇₁	C₁₁	direct (N × H)
14. C₁₁×D₇₁	D₉	direct (N × H)
15. D₆₃₉	C₂×C₁₁	semidirect
16. C₉×D₇₁	C₂×C₁₁	semidirect
17. D₉×C₇₁	C₂×C₁₁	semidirect
19. C₁₁×C₇₁	C₂×D₉	semidirect
20. C₉×C₇₁	C₂²×C₁₁	semidirect
29. C₁₁×D₉	D₇₁	direct (N × H)
32. D₇₁	C₁₁×D₉	direct (N × H)
34. C₉×C₁₁	C₂×D₇₁	semidirect
35. C₇₁	C₂×C₁₁×D₉	semidirect
47. D₉	C₁₁×D₇₁	direct (N × H)
49. C₁₁	D₉×D₇₁	direct (N × H)
50. C₉	C₂×C₁₁×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×D₆₃₉	2
C₁₁×D₉×C₇₁	2
C₉×C₁₁×D₇₁	2
D₃×C₁₁×D₇₁	3
D₉×D₇₁	11
C₂×C₁₁×D₉	71

Subgroups — C11×D9×D71 #43244653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₉×D₇₁ #43244653