Subgroups — C₃×D₁₉×#3861 #30660789

Order 16758.

240 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	C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	D₁₉×#3861	C₃	1	3	yes	maximal, direct product factor
4	C₁₉×#3861	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×ΓL(1,𝔽₈)×D₁₉	—	7	8	no	maximal
7	C₇²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
9	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×#3861	—	19	1	no	maximal, Hall
11	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
12	ΓL(1,𝔽₈)×D₁₉	—	7	24	no	—
13	C₃×#3861	D₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
15	C₁₉×ΓL(1,𝔽₈)	—	7	24	no	—
16	C₃²×D₁₉	—	49	1	no	Hall
17	C₂×C₃×C₇²	—	19	1	no	—
18	C₂×#3861	—	19	3	no	—
19	C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
20	C₃²×C₁₉	—	49	1	no	Hall
21	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
22	#3861	C₃×D₁₉	1	3	yes	direct product factor
23	C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
24	C₂×C₃×ΓL(1,𝔽₈)	—	133	8	no	—
25	C₃×D₁₉	—	49	3	no	—
26	C₃×D₁₉	#3861	1	1	yes	characteristic, direct product factor
27	C₂×C₇²	—	19	1	no	Hall
28	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
29	C₃×C₁₉	—	49	3	no	—
30	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
31	C₇²	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	19	8	no	—
33	C₂×ΓL(1,𝔽₈)	—	133	24	no	—
34	D₁₉	C₃×#3861	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	8	yes	complemented
36	ΓL(1,𝔽₈)	—	7	24	no	—
37	C₁₉	C₂×C₃×#3861	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃²	—	931	1	no	Hall
39	C₂×C₇	—	19	8	no	—
40	C₃²	—	49	1	no	Sylow
41	C₇	C₃×ΓL(1,𝔽₈)×D₁₉	1	8	yes	complemented
42	C₂×C₃	—	19	1	no	—
43	C₂×C₃	—	931	3	no	—
44	C₃	—	49	3	no	—
45	C₃	D₁₉×#3861	1	1	yes	characteristic, direct product factor
46	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₉×#3861
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3861	C₂	semidirect
2. C₃×C₇²×D₁₉	C₃	semidirect
3. D₁₉×#3861	C₃	direct (N × H)
4. C₁₉×#3861	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. C₇²×D₁₉	C₃²	semidirect
9. C₇²×C₁₉	C₂×C₃²	semidirect
11. C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
13. C₃×#3861	D₁₉	direct (N × H)
14. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
21. C₃×C₇²	C₃×D₁₉	semidirect
22. #3861	C₃×D₁₉	direct (N × H)
23. C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
26. C₃×D₁₉	#3861	direct (N × H)
30. C₃×C₁₉	C₂×#3861	semidirect
31. C₇²	C₃²×D₁₉	semidirect
34. D₁₉	C₃×#3861	direct (N × H)
35. C₃×C₇	ΓL(1,𝔽₈)×D₁₉	semidirect
37. C₁₉	C₂×C₃×#3861	semidirect
41. C₇	C₃×ΓL(1,𝔽₈)×D₁₉	semidirect
45. C₃	D₁₉×#3861	direct (N × H)

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
C₃×C₇²×D₁₉	3
D₁₉×#3861	3
C₃×ΓL(1,𝔽₈)×D₁₉	7
C₂×C₃×#3861	19

Subgroups — C3×D19×#3861 #30660789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₉×#3861 #30660789