Subgroups — D₃×D₄×C₁₉ #11744976

Order 912.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×C₁₉	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#67	C₂	1	2	yes	maximal, complemented
4	C₁₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₁₉	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₁₉	C₂²	1	2	yes	complemented
8	C₂×D₃×C₁₉	—	2	4	no	—
9	C₂×D₃×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×D₃×C₁₉	C₂²	1	2	yes	complemented
11	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	Dic₃×C₁₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₁₉	—	3	2	no	—
14	D₄×C₁₉	—	3	2	no	—
15	D₄×C₁₉	—	3	1	no	—
16	D₄×C₁₉	D₃	1	1	yes	characteristic, direct product factor
17	C₂×C₄×C₁₉	—	3	1	no	—
18	C₂×C₃×C₁₉	—	2	2	no	—
19	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
20	D₃×C₁₉	—	2	2	no	—
21	D₃×C₁₉	D₄	1	2	yes	direct product factor
22	C₂²×C₁₉	—	3	1	no	—
23	C₂²×C₁₉	—	3	2	no	—
24	C₂²×C₁₉	—	6	4	no	—
25	C₂²×C₁₉	C₂×D₃	1	2	yes	complemented
26	C₄×C₁₉	—	3	1	no	—
27	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
28	C₃×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented, Hall
29	D₃×D₄	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂×C₁₉	—	2	2	no	—
31	C₂×C₁₉	—	3	2	no	—
32	C₂×C₁₉	—	6	2	no	—
33	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
34	C₂²×D₃	C₂×C₁₉	1	2	yes	complemented
35	C₃×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
36	#67	C₂×C₁₉	1	2	yes	complemented
37	D₁₂	C₂×C₁₉	1	1	yes	characteristic, complemented
38	C₄×D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
39	C₁₉	D₃×D₄	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×D₄	—	3	1	no	Sylow
41	C₂²×C₃	C₂²×C₁₉	1	2	yes	complemented
42	C₂×D₃	—	2	4	no	—
43	C₂×D₃	C₂²×C₁₉	1	1	yes	characteristic
44	C₂×D₃	C₂²×C₁₉	1	2	yes	complemented
45	C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
46	Dic₃	C₂²×C₁₉	1	1	yes	characteristic, complemented
47	C₂³	—	3	2	no	—
48	D₄	—	3	2	no	—
49	D₄	—	3	1	no	—
50	D₄	D₃×C₁₉	1	1	yes	characteristic, direct product factor
51	C₂×C₄	—	3	1	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	C₂³×C₁₉	1	1	yes	characteristic
54	D₃	—	2	2	no	—
55	D₃	D₄×C₁₉	1	2	yes	direct product factor
56	C₂²	—	3	1	no	—
57	C₂²	—	3	2	no	—
58	C₂²	—	6	4	no	—
59	C₂²	C₂×D₃×C₁₉	1	2	yes	complemented
60	C₄	—	3	1	no	—
61	C₄	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
62	C₃	C₂×D₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
63	C₂	—	2	2	no	—
64	C₂	—	3	2	no	—
65	C₂	—	6	2	no	—
66	C₂	C₂²×D₃×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₁₉
Frattini	C₂	C₂²×D₃×C₁₉
Fitting	C₃×D₄×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂³
hypercenter	D₄×C₁₉	D₃
hypocenter	C₃	C₂×D₄×C₁₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ D₄×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃×C₁₉	C₂	semidirect
2. C₃×D₄×C₁₉	C₂	semidirect
3. C₁₉×#67	C₂	semidirect
4. C₁₉×D₁₂	C₂	semidirect
5. C₄×D₃×C₁₉	C₂	semidirect
7. C₂²×C₃×C₁₉	C₂²	semidirect
10. C₂×D₃×C₁₉	C₂²	semidirect
11. C₃×C₄×C₁₉	C₂²	semidirect
12. Dic₃×C₁₉	C₂²	semidirect
16. D₄×C₁₉	D₃	direct (N × H)
21. D₃×C₁₉	D₄	direct (N × H)
25. C₂²×C₁₉	C₂×D₃	semidirect
27. C₄×C₁₉	C₂×D₃	semidirect
28. C₃×C₁₉	C₂×D₄	semidirect
29. D₃×D₄	C₁₉	direct (N × H)
34. C₂²×D₃	C₂×C₁₉	semidirect
35. C₃×D₄	C₂×C₁₉	semidirect
36. #67	C₂×C₁₉	semidirect
37. D₁₂	C₂×C₁₉	semidirect
38. C₄×D₃	C₂×C₁₉	semidirect
39. C₁₉	D₃×D₄	direct (N × H)
41. C₂²×C₃	C₂²×C₁₉	semidirect
44. C₂×D₃	C₂²×C₁₉	semidirect
45. C₃×C₄	C₂²×C₁₉	semidirect
46. Dic₃	C₂²×C₁₉	semidirect
50. D₄	D₃×C₁₉	direct (N × H)
55. D₃	D₄×C₁₉	direct (N × H)
59. C₂²	C₂×D₃×C₁₉	semidirect
61. C₄	C₂×D₃×C₁₉	semidirect
62. C₃	C₂×D₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₃×C₁₉	2
C₃×D₄×C₁₉	2
C₁₉×#67	2
C₁₉×D₁₂	2
C₄×D₃×C₁₉	2
C₂×D₄×C₁₉	3
D₃×D₄	19

Subgroups — D3×D4×C19 #11744976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₄×C₁₉ #11744976