Subgroups — D₃×C₇×C₁₁×C₁₉⋊C₃ #39911884

Order 26334.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₁×C₁₉⋊C₃	—	3	1	no	maximal
4	C₇×C₁₁×C₁₉⋊C₃	—	2	1	no	—
5	C₇×C₁₁×C₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₁×C₁₉⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₁×C₁₉	—	3	1	no	Hall
9	D₃×C₇×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₁×C₁₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₁×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₃×C₇×C₁₁	—	19	1	no	maximal, Hall
13	D₃×C₁₁×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
14	C₂×C₁₁×C₁₉⋊C₃	—	3	1	no	—
15	C₃×C₇×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
16	D₃×C₇×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented
17	C₂×C₇×C₁₉⋊C₃	—	3	1	no	—
18	C₃²×C₇×C₁₁	—	19	1	no	Hall
19	C₃×C₁₁×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
20	C₁₁×C₁₉⋊C₃	—	2	1	no	—
21	C₁₁×C₁₉⋊C₃	D₃×C₇	1	1	yes	characteristic, direct product factor
22	C₂×C₃×C₇×C₁₁	—	57	1	no	—
23	D₃×C₇×C₁₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁×C₁₉	—	3	1	no	Hall
25	C₃×C₇×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
26	C₇×C₁₉⋊C₃	—	2	1	no	—
27	C₇×C₁₉⋊C₃	D₃×C₁₁	1	1	yes	characteristic, direct product factor
28	D₃×C₁₉⋊C₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇×C₁₉	—	3	1	no	Hall
30	C₃×C₇×C₁₁	—	19	1	no	—
31	C₃×C₇×C₁₁	—	38	1	no	—
32	C₃×C₇×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
33	C₁₁×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	C₃×D₃×C₁₁	—	19	1	no	Hall
35	C₃×C₁₉⋊C₃	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₁	—	3	1	no	Hall
37	C₇×C₁₉	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
38	C₃×D₃×C₇	—	19	1	no	Hall
39	D₃×C₁₉	C₃×C₇×C₁₁	1	1	yes	characteristic, complemented
40	C₂×C₁₉⋊C₃	—	3	1	no	—
41	C₃²×C₁₁	—	19	1	no	Hall
42	C₇×C₁₁	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₁₁	—	57	1	no	—
44	D₃×C₁₁	C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
45	C₃²×C₇	—	19	1	no	Hall
46	C₃×C₁₉	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	—	2	1	no	—
48	C₁₉⋊C₃	D₃×C₇×C₁₁	1	1	yes	characteristic, direct product factor
49	C₂×C₃×C₇	—	57	1	no	—
50	D₃×C₇	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
51	C₂×C₁₉	—	3	1	no	Hall
52	C₃×C₁₁	—	19	1	no	—
53	C₃×C₁₁	—	38	1	no	—
54	C₃×C₁₁	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
55	C₂×C₁₁	—	3	1	no	Hall
56	C₃×C₇	—	19	1	no	—
57	C₃×C₇	—	38	1	no	—
58	C₃×C₇	C₂×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented
59	C₁₉	C₃×D₃×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	19	1	no	Hall
61	C₂×C₇	—	3	1	no	Hall
62	C₁₁	D₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
63	C₃²	—	19	1	no	Sylow
64	C₇	D₃×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	—	57	1	no	—
66	D₃	C₇×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
67	C₃	—	19	1	no	—
68	C₃	—	38	1	no	—
69	C₃	C₂×C₇×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₃×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₁₉⋊C₃	C₂	semidirect
2. D₃×C₇×C₁₁×C₁₉	C₃	semidirect
5. C₇×C₁₁×C₁₉⋊C₃	D₃	direct (N × H)
6. C₃×C₇×C₁₁×C₁₉	C₂×C₃	semidirect
7. D₃×C₁₁×C₁₉⋊C₃	C₇	direct (N × H)
9. D₃×C₇×C₁₉⋊C₃	C₁₁	direct (N × H)
10. C₃×C₁₁×C₁₉⋊C₃	C₂×C₇	semidirect
11. C₇×C₁₁×C₁₉	C₃×D₃	semidirect
13. D₃×C₁₁×C₁₉	C₃×C₇	semidirect
15. C₃×C₇×C₁₉⋊C₃	C₂×C₁₁	semidirect
16. D₃×C₇×C₁₉	C₃×C₁₁	semidirect
19. C₃×C₁₁×C₁₉	C₂×C₃×C₇	semidirect
21. C₁₁×C₁₉⋊C₃	D₃×C₇	direct (N × H)
23. D₃×C₇×C₁₁	C₁₉⋊C₃	direct (N × H)
25. C₃×C₇×C₁₉	C₂×C₃×C₁₁	semidirect
27. C₇×C₁₉⋊C₃	D₃×C₁₁	direct (N × H)
28. D₃×C₁₉⋊C₃	C₇×C₁₁	direct (N × H)
32. C₃×C₇×C₁₁	C₂×C₁₉⋊C₃	semidirect
33. C₁₁×C₁₉	C₃×D₃×C₇	semidirect
35. C₃×C₁₉⋊C₃	C₂×C₇×C₁₁	semidirect
37. C₇×C₁₉	C₃×D₃×C₁₁	semidirect
39. D₃×C₁₉	C₃×C₇×C₁₁	semidirect
42. C₇×C₁₁	D₃×C₁₉⋊C₃	direct (N × H)
44. D₃×C₁₁	C₇×C₁₉⋊C₃	direct (N × H)
46. C₃×C₁₉	C₂×C₃×C₇×C₁₁	semidirect
48. C₁₉⋊C₃	D₃×C₇×C₁₁	direct (N × H)
50. D₃×C₇	C₁₁×C₁₉⋊C₃	direct (N × H)
54. C₃×C₁₁	C₂×C₇×C₁₉⋊C₃	semidirect
58. C₃×C₇	C₂×C₁₁×C₁₉⋊C₃	semidirect
59. C₁₉	C₃×D₃×C₇×C₁₁	semidirect
62. C₁₁	D₃×C₇×C₁₉⋊C₃	direct (N × H)
64. C₇	D₃×C₁₁×C₁₉⋊C₃	direct (N × H)
66. D₃	C₇×C₁₁×C₁₉⋊C₃	direct (N × H)
69. C₃	C₂×C₇×C₁₁×C₁₉⋊C₃	semidirect

Maximal subgroups

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

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

Subgroups — D3×C7×C11×C19⋊C3 #39911884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×C₁₁×C₁₉⋊C₃ #39911884