Subgroups — C₁₁×D₉×D₁₉ #21418975

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₁×D₁₉	—	3	1	no	maximal
5	C₉×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₅₇	—	3	1	no	—
7	D₃×C₁₁×C₁₉	—	3	1	no	—
8	C₃×C₁₁×D₁₉	D₃	1	1	yes	characteristic
9	C₂×C₁₁×D₁₉	—	9	1	no	Hall
10	D₉×D₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₁×C₁₉	C₂×D₃	1	1	yes	characteristic
12	C₂×C₁₁×C₁₉	—	9	1	no	—
13	C₁₁×D₁₉	—	9	1	no	—
14	C₁₁×D₁₉	D₉	1	1	yes	characteristic, direct product factor
15	C₂×C₁₁×D₉	—	19	1	no	maximal, Hall
16	D₁₇₁	C₂×C₁₁	1	1	yes	characteristic, complemented
17	C₉×D₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₉×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
19	D₃×D₁₉	—	3	1	no	—
20	C₁₁×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₉×C₁₁	—	19	1	no	—
22	C₁₁×D₉	—	19	1	no	—
23	C₁₁×D₉	D₁₉	1	1	yes	characteristic, direct product factor
24	C₉×C₁₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₂×D₃×C₁₁	—	57	1	no	—
26	D₅₇	—	3	1	no	—
27	C₃×D₁₉	D₃×C₁₁	1	1	yes	characteristic
28	D₃×C₁₉	—	3	1	no	—
29	C₉×C₁₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×D₁₉	—	9	1	no	Hall
31	C₂×C₃×C₁₁	—	19	1	no	—
32	D₃×C₁₁	—	3	1	no	—
33	D₃×C₁₁	—	57	1	no	—
34	C₃×C₁₉	C₂×D₃×C₁₁	1	1	yes	characteristic
35	C₂²×C₁₁	—	171	1	no	Hall
36	C₂×C₁₉	—	9	1	no	—
37	D₁₉	—	9	1	no	—
38	D₁₉	C₁₁×D₉	1	1	yes	characteristic, direct product factor
39	C₂×D₉	—	19	1	no	Hall
40	C₃×C₁₁	D₃×D₁₉	1	1	yes	characteristic
41	C₂×C₁₁	—	9	1	no	—
42	C₂×C₁₁	—	19	1	no	—
43	C₂×C₁₁	—	171	1	no	—
44	C₁₉	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₉	—	19	1	no	—
46	D₉	—	19	1	no	—
47	D₉	C₁₁×D₁₉	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	57	1	no	—
49	C₁₁	D₉×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
50	C₉	C₂×C₁₁×D₁₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	19	1	no	—
52	D₃	—	3	1	no	—
53	D₃	—	57	1	no	—
54	C₂²	—	171	1	no	Sylow
55	C₃	D₃×C₁₁×D₁₉	1	1	yes	characteristic
56	C₂	—	9	1	no	—
57	C₂	—	19	1	no	—
58	C₂	—	171	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	D₉×D₁₉
commutator, hypocenter	C₉×C₁₉	C₂²×C₁₁
Frattini	C₃	D₃×C₁₁×D₁₉
Fitting	C₉×C₁₁×C₁₉	C₂²
socle	C₃×C₁₁×C₁₉	C₂×D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₇₁	C₂	semidirect
2. C₁₁×D₉×C₁₉	C₂	semidirect
3. C₉×C₁₁×D₁₉	C₂	semidirect
5. C₉×C₁₁×C₁₉	C₂²	semidirect
10. D₉×D₁₉	C₁₁	direct (N × H)
14. C₁₁×D₁₉	D₉	direct (N × H)
16. D₁₇₁	C₂×C₁₁	semidirect
17. C₉×D₁₉	C₂×C₁₁	semidirect
18. D₉×C₁₉	C₂×C₁₁	semidirect
20. C₁₁×C₁₉	C₂×D₉	semidirect
23. C₁₁×D₉	D₁₉	direct (N × H)
24. C₉×C₁₉	C₂²×C₁₁	semidirect
29. C₉×C₁₁	C₂×D₁₉	semidirect
38. D₁₉	C₁₁×D₉	direct (N × H)
44. C₁₉	C₂×C₁₁×D₉	semidirect
47. D₉	C₁₁×D₁₉	direct (N × H)
49. C₁₁	D₉×D₁₉	direct (N × H)
50. C₉	C₂×C₁₁×D₁₉	semidirect

Subgroups — C11×D9×D19 #21418975

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×D₉×D₁₉ #21418975