Subgroups — D₃×C₁₁×D₇×C₁₉ #31798310

Order 17556.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₁×D₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₇×C₁₉	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₇×C₁₉	—	3	1	no	—
7	C₁₁×D₇×C₁₉	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₁×C₁₉	—	3	1	no	—
9	C₂×D₃×C₁₁×C₁₉	—	7	1	no	maximal, Hall
10	D₃×D₇×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₁₁×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₁×C₁₉	—	7	1	no	—
13	D₃×C₁₁×C₁₉	—	7	1	no	—
14	D₃×C₁₁×C₁₉	D₇	1	1	yes	characteristic, direct product factor
15	D₃×C₁₁×D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₁₁×C₁₉	—	21	1	no	Hall
17	C₁₉×D₂₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₃×C₇×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×D₇×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₃×C₁₁×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
21	C₂×D₇×C₁₉	—	3	1	no	Hall
22	C₁₁×D₂₁	C₂×C₁₉	1	1	yes	characteristic, complemented
23	D₃×C₇×C₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₃×C₁₁×D₇	C₂×C₁₉	1	1	yes	characteristic, complemented
25	C₂×C₁₁×C₁₉	—	3	1	no	—
26	C₂×C₁₁×C₁₉	—	7	1	no	—
27	C₂×C₁₁×C₁₉	—	21	1	no	—
28	C₃×C₇×C₁₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₁×D₇	—	3	1	no	Hall
30	C₂×C₇×C₁₉	—	3	1	no	—
31	D₇×C₁₉	—	3	1	no	—
32	D₇×C₁₉	D₃×C₁₁	1	1	yes	characteristic, direct product factor
33	C₃×C₇×C₁₁	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₁₉	—	7	1	no	Hall
35	C₁₁×C₁₉	D₃×D₇	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₇×C₁₁	—	3	1	no	—
37	C₁₁×D₇	—	3	1	no	—
38	C₁₁×D₇	D₃×C₁₉	1	1	yes	characteristic, direct product factor
39	C₇×C₁₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₁₁	—	7	1	no	Hall
41	C₂×C₃×C₁₉	—	7	1	no	—
42	D₃×C₁₉	—	7	1	no	—
43	D₃×C₁₉	C₁₁×D₇	1	1	yes	characteristic, direct product factor
44	D₃×D₇	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
45	C₇×C₁₁	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
46	C₂²×C₁₉	—	21	1	no	Hall
47	C₂×C₃×C₁₁	—	7	1	no	—
48	D₃×C₁₁	—	7	1	no	—
49	D₃×C₁₁	D₇×C₁₉	1	1	yes	characteristic, direct product factor
50	C₃×C₁₉	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
51	C₂²×C₁₁	—	21	1	no	Hall
52	D₂₁	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented
53	C₃×D₇	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented
54	D₃×C₇	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented
55	C₂×C₁₉	—	3	1	no	—
56	C₂×C₁₉	—	7	1	no	—
57	C₂×C₁₉	—	21	1	no	—
58	C₃×C₁₁	C₂×D₇×C₁₉	1	1	yes	characteristic, complemented, Hall
59	C₂×D₇	—	3	1	no	Hall
60	C₂×C₁₁	—	3	1	no	—
61	C₂×C₁₁	—	7	1	no	—
62	C₂×C₁₁	—	21	1	no	—
63	C₃×C₇	C₂²×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Hall
64	C₁₉	D₃×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₇	—	3	1	no	—
66	D₇	—	3	1	no	—
67	D₇	D₃×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor
68	C₂×D₃	—	7	1	no	Hall
69	C₁₁	D₃×D₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₇	C₂×D₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	7	1	no	—
72	D₃	—	7	1	no	—
73	D₃	C₁₁×D₇×C₁₉	1	1	yes	characteristic, direct product factor
74	C₂²	—	21	1	no	Sylow
75	C₃	C₂×C₁₁×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₉×D₂₁	C₂	semidirect
2. D₃×C₇×C₁₁×C₁₉	C₂	semidirect
3. C₃×C₁₁×D₇×C₁₉	C₂	semidirect
5. C₃×C₇×C₁₁×C₁₉	C₂²	semidirect
7. C₁₁×D₇×C₁₉	D₃	direct (N × H)
10. D₃×D₇×C₁₉	C₁₁	direct (N × H)
11. C₇×C₁₁×C₁₉	C₂×D₃	semidirect
14. D₃×C₁₁×C₁₉	D₇	direct (N × H)
15. D₃×C₁₁×D₇	C₁₉	direct (N × H)
17. C₁₉×D₂₁	C₂×C₁₁	semidirect
18. D₃×C₇×C₁₉	C₂×C₁₁	semidirect
19. C₃×D₇×C₁₉	C₂×C₁₁	semidirect
20. C₃×C₁₁×C₁₉	C₂×D₇	semidirect
22. C₁₁×D₂₁	C₂×C₁₉	semidirect
23. D₃×C₇×C₁₁	C₂×C₁₉	semidirect
24. C₃×C₁₁×D₇	C₂×C₁₉	semidirect
28. C₃×C₇×C₁₉	C₂²×C₁₁	semidirect
32. D₇×C₁₉	D₃×C₁₁	direct (N × H)
33. C₃×C₇×C₁₁	C₂²×C₁₉	semidirect
35. C₁₁×C₁₉	D₃×D₇	direct (N × H)
38. C₁₁×D₇	D₃×C₁₉	direct (N × H)
39. C₇×C₁₉	C₂×D₃×C₁₁	semidirect
43. D₃×C₁₉	C₁₁×D₇	direct (N × H)
44. D₃×D₇	C₁₁×C₁₉	direct (N × H)
45. C₇×C₁₁	C₂×D₃×C₁₉	semidirect
49. D₃×C₁₁	D₇×C₁₉	direct (N × H)
50. C₃×C₁₉	C₂×C₁₁×D₇	semidirect
52. D₂₁	C₂×C₁₁×C₁₉	semidirect
53. C₃×D₇	C₂×C₁₁×C₁₉	semidirect
54. D₃×C₇	C₂×C₁₁×C₁₉	semidirect
58. C₃×C₁₁	C₂×D₇×C₁₉	semidirect
63. C₃×C₇	C₂²×C₁₁×C₁₉	semidirect
64. C₁₉	D₃×C₁₁×D₇	direct (N × H)
67. D₇	D₃×C₁₁×C₁₉	direct (N × H)
69. C₁₁	D₃×D₇×C₁₉	direct (N × H)
70. C₇	C₂×D₃×C₁₁×C₁₉	semidirect
73. D₃	C₁₁×D₇×C₁₉	direct (N × H)
75. C₃	C₂×C₁₁×D₇×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×D₂₁	2
D₃×C₇×C₁₁×C₁₉	2
C₃×C₁₁×D₇×C₁₉	2
C₂×C₁₁×D₇×C₁₉	3
C₂×D₃×C₁₁×C₁₉	7
D₃×D₇×C₁₉	11
D₃×C₁₁×D₇	19

Subgroups — D3×C11×D7×C19 #31798310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₁×D₇×C₁₉ #31798310