Subgroups — C₂×C₁₁×D₁₇₁ #21418988

Order 7524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₂²×C₁₁
Frattini	C₃	C₂×C₁₁×D₅₇
Fitting	C₂×C₉×C₁₁×C₁₉	C₂
socle	C₂×C₃×C₁₁×C₁₉	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₇₁	C₂	direct (N × H)
2. C₂×C₉×C₁₁×C₁₉	C₂	semidirect
4. C₉×C₁₁×C₁₉	C₂²	semidirect
8. C₂×D₁₇₁	C₁₁	direct (N × H)
10. C₂×C₁₁×C₁₉	D₉	semidirect
13. C₂×C₉×C₁₉	C₂×C₁₁	semidirect
14. D₁₇₁	C₂×C₁₁	direct (N × H)
16. C₁₁×C₁₉	C₂×D₉	semidirect
17. C₂×C₉×C₁₁	D₁₉	semidirect
19. C₉×C₁₉	C₂²×C₁₁	semidirect
23. C₉×C₁₁	C₂×D₁₉	semidirect
29. C₂×C₁₉	C₁₁×D₉	semidirect
34. C₂×C₁₁	D₁₇₁	direct (N × H)
35. C₁₉	C₂×C₁₁×D₉	semidirect
36. C₂×C₉	C₁₁×D₁₉	semidirect
39. C₁₁	C₂×D₁₇₁	direct (N × H)
40. C₉	C₂×C₁₁×D₁₉	semidirect
46. C₂	C₁₁×D₁₇₁	direct (N × H)

Subgroups — C2×C11×D171 #21418988

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₁₁×D₁₇₁ #21418988