Subgroups — Dic₃×C₁₉×#3861 #45691930

Order 33516.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic
2	C₇²×Dic₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₉×#3861	—	3	1	no	maximal
4	C₃×C₁₉×#3861	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×#3861	—	2	1	no	—
6	C₂×C₁₉×#3861	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
8	Dic₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	maximal
9	C₄×C₇²×C₁₉	—	3	1	no	Hall
10	C₁₉×#3861	—	2	1	no	—
11	C₁₉×#3861	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
14	C₂×C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic
15	Dic₃×#3861	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₇×Dic₃×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
17	C₄×C₁₉×ΓL(1,𝔽₈)	—	21	8	no	—
18	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
19	C₇²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×#3861	C₂×C₁₉	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	—
22	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
23	C₂×C₁₉×ΓL(1,𝔽₈)	—	14	8	no	—
24	C₃×Dic₃×C₁₉	—	49	1	no	Hall
25	C₇²×Dic₃	C₃×C₁₉	1	1	yes	characteristic, complemented
26	C₄×#3861	—	3	1	no	—
27	C₄×C₇×C₁₉	—	3	8	no	—
28	C₃×#3861	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
30	C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
31	C₁₉×ΓL(1,𝔽₈)	—	14	8	no	—
32	C₂×C₃²×C₁₉	—	49	1	no	—
33	C₂×C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
34	C₂×#3861	—	2	1	no	—
35	C₂×#3861	D₃×C₁₉	1	1	yes	characteristic
36	C₂×C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	8	yes	—
37	Dic₃×ΓL(1,𝔽₈)	—	7	8	no	—
38	C₃×C₄×C₁₉	—	147	1	no	—
39	Dic₃×C₁₉	#3861	1	1	yes	characteristic, direct product factor
40	C₄×C₇²	—	3	1	no	Hall
41	C₃²×C₁₉	—	49	1	no	Hall
42	C₃×C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
43	#3861	—	2	1	no	—
44	#3861	Dic₃×C₁₉	1	1	yes	characteristic, direct product factor
45	C₇×C₁₉	Dic₃×ΓL(1,𝔽₈)	1	8	yes	complemented
46	C₂×C₃×ΓL(1,𝔽₈)	—	7	8	no	—
47	C₂×C₃×C₁₉	—	49	1	no	—
48	C₂×C₃×C₁₉	—	98	1	no	—
49	C₂×C₃×C₁₉	C₂×#3861	1	1	yes	characteristic
50	C₂×C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic
51	C₇×Dic₃	C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
52	C₄×ΓL(1,𝔽₈)	—	21	8	no	—
53	C₄×C₁₉	—	3	1	no	Hall
54	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
55	C₃×C₁₉	—	49	1	no	—
56	C₃×C₁₉	—	98	1	no	—
57	C₃×C₁₉	C₄×#3861	1	1	yes	characteristic, complemented
58	C₇²	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	8	yes	—
60	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
61	C₂×ΓL(1,𝔽₈)	—	14	8	no	—
62	C₂×C₁₉	D₃×#3861	1	1	yes	characteristic
63	C₃×Dic₃	—	49	1	no	Hall
64	C₄×C₇	—	3	8	no	—
65	C₃×C₇	C₄×C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
66	ΓL(1,𝔽₈)	—	7	8	no	—
67	ΓL(1,𝔽₈)	—	14	8	no	—
68	C₁₉	Dic₃×#3861	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×C₃²	—	49	1	no	—
70	C₂×C₇	D₃×C₁₉×ΓL(1,𝔽₈)	1	8	yes	—
71	C₃×C₄	—	147	1	no	—
72	Dic₃	C₁₉×#3861	1	1	yes	characteristic, direct product factor
73	C₃²	—	49	1	no	Sylow
74	C₇	Dic₃×C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
75	C₂×C₃	—	49	1	no	—
76	C₂×C₃	—	98	1	no	—
77	C₂×C₃	C₂×C₁₉×#3861	1	1	yes	characteristic
78	C₄	—	3	1	no	Sylow
79	C₃	—	49	1	no	—
80	C₃	—	98	1	no	—
81	C₃	C₄×C₁₉×#3861	1	1	yes	characteristic, complemented
82	C₂	D₃×C₁₉×#3861	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃×#3861
commutator, hypocenter	C₃×C₇²	C₃×C₄×C₁₉
Frattini	C₂	D₃×C₁₉×#3861
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×#3861	C₂
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₇²×Dic₃×C₁₉	C₃	semidirect
4. C₃×C₁₉×#3861	C₄	semidirect
11. C₁₉×#3861	Dic₃	direct (N × H)
12. C₃×C₇²×C₁₉	C₃×C₄	semidirect
15. Dic₃×#3861	C₁₉	direct (N × H)
16. C₇×Dic₃×C₁₉	ΓL(1,𝔽₈)	semidirect
19. C₇²×C₁₉	C₃×Dic₃	semidirect
25. C₇²×Dic₃	C₃×C₁₉	semidirect
28. C₃×#3861	C₄×C₁₉	semidirect
29. C₃×C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
39. Dic₃×C₁₉	#3861	direct (N × H)
42. C₃×C₇²	C₃×C₄×C₁₉	semidirect
44. #3861	Dic₃×C₁₉	direct (N × H)
45. C₇×C₁₉	Dic₃×ΓL(1,𝔽₈)	semidirect
51. C₇×Dic₃	C₁₉×ΓL(1,𝔽₈)	semidirect
57. C₃×C₁₉	C₄×#3861	semidirect
58. C₇²	C₃×Dic₃×C₁₉	semidirect
65. C₃×C₇	C₄×C₁₉×ΓL(1,𝔽₈)	semidirect
68. C₁₉	Dic₃×#3861	direct (N × H)
72. Dic₃	C₁₉×#3861	direct (N × H)
74. C₇	Dic₃×C₁₉×ΓL(1,𝔽₈)	semidirect
81. C₃	C₄×C₁₉×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×#3861	2
C₇²×Dic₃×C₁₉	3
C₄×C₁₉×#3861	3
Dic₃×C₁₉×ΓL(1,𝔽₈)	7
Dic₃×#3861	19

Subgroups — Dic3×C19×#3861 #45691930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×C₁₉×#3861 #45691930