Subgroups — C₂²×C₃×C₁₉×#3862 #45692763

Order 33516.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×#3862	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₉×#3862	C₃	1	3	yes	maximal, direct product factor
3	C₂²×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₉×#3862	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂×C₁₉×#3862	C₂×C₃	1	9	yes	direct product factor
6	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	3	yes	complemented
7	C₂²×C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	maximal
8	C₂²×C₇²×C₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₁₉×#3862	C₂²×C₃	1	3	yes	direct product factor
10	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	—	7	6	no	—
12	C₂×C₇²×C₁₉	C₂×C₃²	1	3	yes	complemented
13	C₂²×C₃×#3862	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₇×C₁₉	—	3	2	no	—
15	C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	2	yes	complemented
16	C₂²×C₁₉×ΓL(1,𝔽₈)	—	7	6	no	—
17	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
18	C₇²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×#3862	C₂×C₁₉	1	3	yes	direct product factor
20	C₂×C₃×C₇×C₁₉	—	3	6	no	—
21	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	6	yes	complemented
22	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	18	no	—
23	C₂²×C₃²×C₁₉	—	49	1	no	Hall
24	C₂²×C₃×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented
25	C₂²×#3862	C₃×C₁₉	1	3	yes	direct product factor
26	C₂²×C₇×C₁₉	—	3	2	no	—
27	C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
28	C₃×#3862	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₇×C₁₉	—	3	2	no	—
30	C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
31	C₁₉×ΓL(1,𝔽₈)	—	7	6	no	—
32	C₂×C₃²×C₁₉	—	49	3	no	—
33	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	3	yes	complemented
34	C₂×#3862	C₂×C₃×C₁₉	1	9	yes	direct product factor
35	C₂×C₇×C₁₉	—	3	6	no	—
36	C₂×C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	6	yes	complemented
37	C₂²×C₃×ΓL(1,𝔽₈)	—	7	2	no	—
38	C₂²×C₃×C₁₉	—	49	3	no	—
39	C₂²×C₃×C₁₉	#3862	1	1	yes	characteristic, direct product factor
40	C₂²×C₇²	C₃²×C₁₉	1	1	yes	characteristic, complemented, Hall
41	C₃²×C₁₉	—	49	1	no	Hall
42	C₃×C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
43	#3862	C₂²×C₃×C₁₉	1	3	yes	direct product factor
44	C₇×C₁₉	—	3	2	no	—
45	C₇×C₁₉	C₂²×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
46	C₂×C₃×ΓL(1,𝔽₈)	—	7	6	no	—
47	C₂×C₃×C₁₉	—	49	9	no	—
48	C₂×C₃×C₁₉	C₂×#3862	1	3	yes	direct product factor
49	C₂×C₇²	C₂×C₃²×C₁₉	1	3	yes	complemented
50	C₂²×C₃×C₇	—	3	2	no	—
51	C₂²×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
52	C₂²×ΓL(1,𝔽₈)	—	7	6	no	—
53	C₂²×C₁₉	C₃×#3862	1	1	yes	characteristic, direct product factor, Hall
54	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
55	C₃×C₁₉	—	49	3	no	—
56	C₃×C₁₉	C₂²×#3862	1	1	yes	characteristic, direct product factor
57	C₇²	C₂²×C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	3	6	no	—
59	C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	6	yes	complemented
60	C₂×ΓL(1,𝔽₈)	—	7	18	no	—
61	C₂×C₁₉	C₂×C₃×#3862	1	3	yes	direct product factor
62	C₂²×C₃²	—	49	1	no	Hall
63	C₂²×C₇	—	3	2	no	—
64	C₂²×C₇	C₃×C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
65	C₃×C₇	—	3	2	no	—
66	C₃×C₇	C₂²×C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
67	ΓL(1,𝔽₈)	—	7	6	no	—
68	C₁₉	C₂²×C₃×#3862	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×C₃²	—	49	3	no	—
70	C₂×C₇	—	3	6	no	—
71	C₂×C₇	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	1	6	yes	complemented
72	C₂²×C₃	—	49	3	no	—
73	C₂²×C₃	C₁₉×#3862	1	1	yes	characteristic, direct product factor
74	C₃²	—	49	1	no	Sylow
75	C₇	—	3	2	no	—
76	C₇	C₂²×C₃×C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
77	C₂×C₃	—	49	9	no	—
78	C₂×C₃	C₂×C₁₉×#3862	1	3	yes	direct product factor
79	C₂²	C₃×C₁₉×#3862	1	1	yes	characteristic, direct product factor, Sylow
80	C₃	—	49	3	no	—
81	C₃	C₂²×C₁₉×#3862	1	1	yes	characteristic, direct product factor
82	C₂	C₂×C₃×C₁₉×#3862	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₁₉	#3862
commutator, cosocle, hypocenter	C₇²	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇²×C₁₉	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×#3862	C₂	direct (N × H)
2. C₂²×C₁₉×#3862	C₃	direct (N × H)
3. C₂²×C₃×C₇²×C₁₉	C₃	semidirect
4. C₃×C₁₉×#3862	C₂²	direct (N × H)
5. C₂×C₁₉×#3862	C₂×C₃	direct (N × H)
6. C₂×C₃×C₇²×C₁₉	C₂×C₃	semidirect
8. C₂²×C₇²×C₁₉	C₃²	semidirect
9. C₁₉×#3862	C₂²×C₃	direct (N × H)
10. C₃×C₇²×C₁₉	C₂²×C₃	semidirect
12. C₂×C₇²×C₁₉	C₂×C₃²	semidirect
13. C₂²×C₃×#3862	C₁₉	direct (N × H)
15. C₂²×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
18. C₇²×C₁₉	C₂²×C₃²	semidirect
19. C₂×C₃×#3862	C₂×C₁₉	direct (N × H)
21. C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
24. C₂²×C₃×C₇²	C₃×C₁₉	semidirect
25. C₂²×#3862	C₃×C₁₉	direct (N × H)
27. C₂²×C₇×C₁₉	C₃×ΓL(1,𝔽₈)	semidirect
28. C₃×#3862	C₂²×C₁₉	direct (N × H)
30. C₃×C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
33. C₂×C₃×C₇²	C₂×C₃×C₁₉	semidirect
34. C₂×#3862	C₂×C₃×C₁₉	direct (N × H)
36. C₂×C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
39. C₂²×C₃×C₁₉	#3862	direct (N × H)
40. C₂²×C₇²	C₃²×C₁₉	semidirect
42. C₃×C₇²	C₂²×C₃×C₁₉	semidirect
43. #3862	C₂²×C₃×C₁₉	direct (N × H)
45. C₇×C₁₉	C₂²×C₃×ΓL(1,𝔽₈)	semidirect
48. C₂×C₃×C₁₉	C₂×#3862	direct (N × H)
49. C₂×C₇²	C₂×C₃²×C₁₉	semidirect
51. C₂²×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	semidirect
53. C₂²×C₁₉	C₃×#3862	direct (N × H)
56. C₃×C₁₉	C₂²×#3862	direct (N × H)
57. C₇²	C₂²×C₃²×C₁₉	semidirect
59. C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
61. C₂×C₁₉	C₂×C₃×#3862	direct (N × H)
64. C₂²×C₇	C₃×C₁₉×ΓL(1,𝔽₈)	semidirect
66. C₃×C₇	C₂²×C₁₉×ΓL(1,𝔽₈)	semidirect
68. C₁₉	C₂²×C₃×#3862	direct (N × H)
71. C₂×C₇	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	semidirect
73. C₂²×C₃	C₁₉×#3862	direct (N × H)
76. C₇	C₂²×C₃×C₁₉×ΓL(1,𝔽₈)	semidirect
78. C₂×C₃	C₂×C₁₉×#3862	direct (N × H)
79. C₂²	C₃×C₁₉×#3862	direct (N × H)
81. C₃	C₂²×C₁₉×#3862	direct (N × H)
82. C₂	C₂×C₃×C₁₉×#3862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×#3862	2
C₂²×C₁₉×#3862	3
C₂²×C₃×C₇²×C₁₉	3
C₂²×C₃×C₁₉×ΓL(1,𝔽₈)	7
C₂²×C₃×#3862	19

Subgroups — C22×C3×C19×#3862 #45692763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₁₉×#3862 #45692763