Subgroups — D₃×C₁₉×#3861 #30660846

Order 16758.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#3861	—	3	1	no	maximal
4	C₁₉×#3861	—	2	1	no	—
5	C₁₉×#3861	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	maximal
8	C₂×C₇²×C₁₉	—	3	1	no	Hall
9	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
10	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×#3861	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
13	C₂×C₁₉×ΓL(1,𝔽₈)	—	21	8	no	—
14	C₃×#3861	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
17	C₁₉×ΓL(1,𝔽₈)	—	14	8	no	—
18	C₃×D₃×C₁₉	—	49	1	no	Hall
19	D₃×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented
20	C₂×#3861	—	3	1	no	—
21	C₂×C₇×C₁₉	—	3	8	no	—
22	C₃²×C₁₉	—	49	1	no	Hall
23	C₃×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
24	#3861	—	2	1	no	—
25	#3861	D₃×C₁₉	1	1	yes	characteristic, direct product factor
26	C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
27	D₃×ΓL(1,𝔽₈)	—	7	8	no	—
28	C₂×C₃×C₁₉	—	147	1	no	—
29	D₃×C₁₉	#3861	1	1	yes	characteristic, direct product factor
30	C₂×C₇²	—	3	1	no	Hall
31	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
32	C₃×C₁₉	—	49	1	no	—
33	C₃×C₁₉	—	98	1	no	—
34	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
35	C₇²	C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
36	D₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
37	C₂×ΓL(1,𝔽₈)	—	21	8	no	—
38	C₂×C₁₉	—	3	1	no	Hall
39	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
40	ΓL(1,𝔽₈)	—	7	8	no	—
41	ΓL(1,𝔽₈)	—	14	8	no	—
42	C₁₉	D₃×#3861	1	1	yes	characteristic, direct product factor, Sylow
43	C₃×D₃	—	49	1	no	Hall
44	C₂×C₇	—	3	8	no	—
45	C₃²	—	49	1	no	Sylow
46	C₇	D₃×C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
47	C₂×C₃	—	147	1	no	—
48	D₃	C₁₉×#3861	1	1	yes	characteristic, direct product factor
49	C₃	—	49	1	no	—
50	C₃	—	98	1	no	—
51	C₃	C₂×C₁₉×#3861	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3861	C₂	semidirect
2. D₃×C₇²×C₁₉	C₃	semidirect
5. C₁₉×#3861	D₃	direct (N × H)
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
10. C₇²×C₁₉	C₃×D₃	semidirect
11. D₃×#3861	C₁₉	direct (N × H)
12. D₃×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
14. C₃×#3861	C₂×C₁₉	semidirect
15. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. D₃×C₇²	C₃×C₁₉	semidirect
23. C₃×C₇²	C₂×C₃×C₁₉	semidirect
25. #3861	D₃×C₁₉	direct (N × H)
26. C₇×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
29. D₃×C₁₉	#3861	direct (N × H)
34. C₃×C₁₉	C₂×#3861	semidirect
35. C₇²	C₃×D₃×C₁₉	semidirect
36. D₃×C₇	C₁₉×ΓL(1,𝔽₈)	semidirect
39. C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
42. C₁₉	D₃×#3861	direct (N × H)
46. C₇	D₃×C₁₉×ΓL(1,𝔽₈)	semidirect
48. D₃	C₁₉×#3861	direct (N × H)
51. C₃	C₂×C₁₉×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₉×#3861	2
D₃×C₇²×C₁₉	3
C₂×C₁₉×#3861	3
D₃×C₁₉×ΓL(1,𝔽₈)	7
D₃×#3861	19

Subgroups — D3×C19×#3861 #30660846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×#3861 #30660846