Subgroups — D₃×D₁₉×C₄₃⋊C₃ #44441007

Order 29412.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₉×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₉×C₄₃⋊C₃	—	3	1	no	maximal
6	C₃×C₁₉×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₁₉×C₄₃⋊C₃	—	2	1	no	—
8	D₁₉×C₄₃⋊C₃	—	3	1	no	—
9	D₁₉×C₄₃⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₄₃×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×D₁₉×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₁₉×C₄₃⋊C₃	—	3	1	no	—
14	C₂×D₁₉×C₄₃	—	3	1	no	Hall
15	C₃×C₁₉×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₉×C₄₃⋊C₃	—	2	1	no	—
17	C₁₉×C₄₃⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₄₃	—	3	1	no	—
19	D₁₉×C₄₃	—	3	1	no	—
20	D₁₉×C₄₃	C₃×D₃	1	1	yes	characteristic, complemented
21	C₂×D₃×C₄₃⋊C₃	—	19	1	no	maximal, Hall
22	C₁₉×C₄₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₄₃⋊C₃	—	19	1	no	—
24	D₃×C₄₃⋊C₃	—	19	1	no	—
25	D₃×C₄₃⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
26	C₃×D₃×D₁₉	—	43	1	no	maximal, Hall
27	C₂×D₃×C₄₃	—	19	1	no	—
28	C₂²×C₄₃⋊C₃	—	57	1	no	—
29	C₃×C₄₃⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
30	C₃×D₅₇	—	43	1	no	—
31	C₃×D₃×C₁₉	—	43	1	no	—
32	C₃²×D₁₉	—	43	1	no	—
33	C₂×C₃×C₄₃	—	19	1	no	—
34	D₃×C₄₃	—	19	1	no	—
35	D₃×C₄₃	C₃×D₁₉	1	1	yes	characteristic, complemented
36	C₂×C₄₃⋊C₃	—	3	1	no	—
37	C₂×C₄₃⋊C₃	—	19	1	no	—
38	C₂×C₄₃⋊C₃	—	38	1	no	—
39	C₂×C₄₃⋊C₃	—	57	1	no	—
40	C₂×C₃×D₁₉	—	129	1	no	—
41	D₃×D₁₉	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
42	C₂²×C₄₃	—	57	1	no	Hall
43	C₃²×C₁₉	—	43	1	no	Hall
44	C₃×C₄₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
45	C₄₃⋊C₃	—	2	1	no	—
46	C₄₃⋊C₃	D₃×D₁₉	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₁₉	—	129	1	no	—
48	D₅₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
49	C₃×D₁₉	—	43	1	no	—
50	C₃×D₁₉	—	86	1	no	—
51	C₃×D₁₉	—	129	1	no	—
52	C₃×D₁₉	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
53	D₃×C₁₉	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
54	C₂×C₄₃	—	3	1	no	—
55	C₂×C₄₃	—	19	1	no	—
56	C₂×C₄₃	—	57	1	no	—
57	C₂×D₁₉	—	3	1	no	Hall
58	C₃×C₁₉	—	43	1	no	—
59	C₃×C₁₉	—	86	1	no	—
60	C₃×C₁₉	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented
61	C₄₃	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₁₉	—	3	1	no	—
63	D₁₉	—	3	1	no	—
64	D₁₉	D₃×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
65	C₂×C₃×D₃	—	817	1	no	Hall
66	C₁₉	C₂×D₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	817	1	no	—
68	C₃×D₃	—	43	1	no	—
69	C₃×D₃	—	817	1	no	—
70	C₂²×C₃	—	2451	1	no	—
71	C₂×D₃	—	19	1	no	—
72	C₃²	—	43	1	no	Sylow
73	C₂×C₃	—	19	1	no	—
74	C₂×C₃	—	817	1	no	—
75	C₂×C₃	—	1634	1	no	—
76	C₂×C₃	—	129	1	no	—
77	C₂×C₃	—	2451	1	no	—
78	D₃	—	19	1	no	—
79	D₃	D₁₉×C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	57	1	no	Sylow
81	C₃	—	43	1	no	—
82	C₃	—	86	1	no	—
83	C₃	C₂×D₁₉×C₄₃⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	19	1	no	—
86	C₂	—	57	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₄₃	C₂²×C₃
LCS	G ▷ C₃×C₁₉×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₇×C₄₃⋊C₃	C₂	semidirect
2. D₃×C₁₉×C₄₃⋊C₃	C₂	semidirect
3. C₃×D₁₉×C₄₃⋊C₃	C₂	semidirect
4. D₃×D₁₉×C₄₃	C₃	semidirect
6. C₃×C₁₉×C₄₃⋊C₃	C₂²	semidirect
9. D₁₉×C₄₃⋊C₃	D₃	direct (N × H)
10. C₄₃×D₅₇	C₂×C₃	semidirect
11. D₃×C₁₉×C₄₃	C₂×C₃	semidirect
12. C₃×D₁₉×C₄₃	C₂×C₃	semidirect
15. C₃×C₁₉×C₄₃	C₂²×C₃	semidirect
17. C₁₉×C₄₃⋊C₃	C₂×D₃	semidirect
20. D₁₉×C₄₃	C₃×D₃	semidirect
22. C₁₉×C₄₃	C₂×C₃×D₃	semidirect
25. D₃×C₄₃⋊C₃	D₁₉	direct (N × H)
29. C₃×C₄₃⋊C₃	C₂×D₁₉	semidirect
35. D₃×C₄₃	C₃×D₁₉	semidirect
41. D₃×D₁₉	C₄₃⋊C₃	direct (N × H)
44. C₃×C₄₃	C₂×C₃×D₁₉	semidirect
46. C₄₃⋊C₃	D₃×D₁₉	direct (N × H)
48. D₅₇	C₂×C₄₃⋊C₃	semidirect
52. C₃×D₁₉	C₂×C₄₃⋊C₃	semidirect
53. D₃×C₁₉	C₂×C₄₃⋊C₃	semidirect
60. C₃×C₁₉	C₂²×C₄₃⋊C₃	semidirect
61. C₄₃	C₃×D₃×D₁₉	semidirect
64. D₁₉	D₃×C₄₃⋊C₃	direct (N × H)
66. C₁₉	C₂×D₃×C₄₃⋊C₃	semidirect
79. D₃	D₁₉×C₄₃⋊C₃	direct (N × H)
83. C₃	C₂×D₁₉×C₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₅₇×C₄₃⋊C₃	2
D₃×C₁₉×C₄₃⋊C₃	2
C₃×D₁₉×C₄₃⋊C₃	2
D₃×D₁₉×C₄₃	3
C₂×D₁₉×C₄₃⋊C₃	3
C₂×D₃×C₄₃⋊C₃	19
C₃×D₃×D₁₉	43

Subgroups — D3×D19×C43⋊C3 #44441007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₉×C₄₃⋊C₃ #44441007