Subgroups — C₃×D₁₉×#3862 #30660791

Order 16758.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	D₁₉×#3862	C₃	1	3	yes	maximal, direct product factor
4	C₁₉×#3862	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×ΓL(1,𝔽₈)×D₁₉	—	7	2	no	maximal
7	C₇²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
9	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×#3862	—	19	1	no	maximal, Hall
11	C₃×C₇×D₁₉	—	3	2	no	—
12	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	2	yes	complemented
13	ΓL(1,𝔽₈)×D₁₉	—	7	6	no	—
14	C₃×#3862	D₁₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₇×C₁₉	—	3	2	no	—
16	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
17	C₁₉×ΓL(1,𝔽₈)	—	7	6	no	—
18	C₃²×D₁₉	—	49	1	no	Hall
19	C₂×C₃×C₇²	—	19	1	no	—
20	C₂×#3862	—	19	3	no	—
21	C₇×D₁₉	—	3	2	no	—
22	C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
23	C₃²×C₁₉	—	49	1	no	Hall
24	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
25	#3862	C₃×D₁₉	1	3	yes	direct product factor
26	C₇×C₁₉	—	3	2	no	—
27	C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
28	C₂×C₃×ΓL(1,𝔽₈)	—	133	2	no	—
29	C₃×D₁₉	—	49	3	no	—
30	C₃×D₁₉	#3862	1	1	yes	characteristic, direct product factor
31	C₂×C₇²	—	19	1	no	Hall
32	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
33	C₃×C₁₉	—	49	3	no	—
34	C₃×C₁₉	C₂×#3862	1	1	yes	characteristic, complemented
35	C₇²	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₇	—	19	2	no	—
37	C₂×C₃×C₇	—	57	2	no	—
38	C₂×ΓL(1,𝔽₈)	—	133	6	no	—
39	D₁₉	C₃×#3862	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₇	—	3	2	no	—
41	C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	2	yes	complemented
42	ΓL(1,𝔽₈)	—	7	6	no	—
43	C₁₉	C₂×C₃×#3862	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃²	—	931	1	no	Hall
45	C₂×C₇	—	19	2	no	—
46	C₂×C₇	—	57	2	no	—
47	C₃²	—	49	1	no	Sylow
48	C₇	—	3	2	no	—
49	C₇	C₃×ΓL(1,𝔽₈)×D₁₉	1	2	yes	complemented
50	C₂×C₃	—	19	1	no	—
51	C₂×C₃	—	931	3	no	—
52	C₃	—	49	3	no	—
53	C₃	D₁₉×#3862	1	1	yes	characteristic, direct product factor
54	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₉×#3862
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×#3862	C₂	semidirect
2. C₃×C₇²×D₁₉	C₃	semidirect
3. D₁₉×#3862	C₃	direct (N × H)
4. C₁₉×#3862	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. C₇²×D₁₉	C₃²	semidirect
9. C₇²×C₁₉	C₂×C₃²	semidirect
12. C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
14. C₃×#3862	D₁₉	direct (N × H)
16. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
24. C₃×C₇²	C₃×D₁₉	semidirect
25. #3862	C₃×D₁₉	direct (N × H)
27. C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
30. C₃×D₁₉	#3862	direct (N × H)
34. C₃×C₁₉	C₂×#3862	semidirect
35. C₇²	C₃²×D₁₉	semidirect
39. D₁₉	C₃×#3862	direct (N × H)
41. C₃×C₇	ΓL(1,𝔽₈)×D₁₉	semidirect
43. C₁₉	C₂×C₃×#3862	semidirect
49. C₇	C₃×ΓL(1,𝔽₈)×D₁₉	semidirect
53. C₃	D₁₉×#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
C₃×C₁₉×#3862	2
C₃×C₇²×D₁₉	3
D₁₉×#3862	3
C₃×ΓL(1,𝔽₈)×D₁₉	7
C₂×C₃×#3862	19

Subgroups — C3×D19×#3862 #30660791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₉×#3862 #30660791