Subgroups — C₃×#19150309 #30660784

Order 16758.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#87705	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150309	C₃	1	3	yes	maximal, direct product factor
4	C₇×#87705	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×D₇×C₁₉⋊C₃	—	7	1	no	maximal
7	C₃×#11716326	—	7	1	no	maximal
8	C₁₉×C₇⋊D₇	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#87705	D₇	1	1	yes	characteristic, complemented
10	C₃×C₇×C₁₉⋊C₃	—	7	1	no	—
11	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×ΓL(1,𝔽₈)⋊D₇	—	19	1	no	maximal, Hall
13	C₃×D₇×C₁₉	—	7	1	no	—
14	C₃×D₇×C₁₉	—	7	1	no	—
15	C₃×D₇×C₁₉	—	21	2	no	—
16	#11716326	—	7	3	no	—
17	D₇×C₁₉⋊C₃	—	7	3	no	—
18	C₃×C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
19	C₃×C₇×C₁₉	—	3	2	no	—
20	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₃×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
22	#87705	C₃×D₇	1	3	yes	complemented
23	C₇×C₁₉⋊C₃	—	7	3	no	—
24	C₂×C₃×C₁₉⋊C₃	—	49	1	no	Hall
25	C₃×C₇⋊D₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
26	ΓL(1,𝔽₈)⋊D₇	—	19	3	no	—
27	D₇×C₁₉	—	7	1	no	—
28	D₇×C₁₉	—	7	1	no	—
29	D₇×C₁₉	—	21	2	no	—
30	C₃×C₁₉⋊C₃	—	7	1	no	Hall
31	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
32	C₇×ΓL(1,𝔽₈)	—	19	3	no	—
33	C₇×C₁₉	—	3	2	no	—
34	C₇×C₁₉	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
35	C₇×C₁₉	C₃²×D₇	1	1	yes	characteristic, complemented
36	C₃²×D₇	—	133	1	no	—
37	C₃×AGL(1,𝔽₇)	—	133	1	no	—
38	C₂×C₃×C₁₉	—	49	1	no	—
39	C₂×C₁₉⋊C₃	—	49	3	no	—
40	C₇⋊D₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
41	C₃²×C₇	—	133	1	no	—
42	C₃×ΓL(1,𝔽₈)	—	19	1	no	—
43	C₃×C₁₉	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented
44	C₁₉⋊C₃	—	7	3	no	—
45	C₇²	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
46	C₃×D₇	—	7	1	no	—
47	C₃×D₇	—	21	2	no	—
48	C₃×D₇	—	21	1	no	—
49	C₃×D₇	—	133	3	no	—
50	AGL(1,𝔽₇)	—	133	3	no	—
51	C₂×C₁₉	—	49	1	no	Hall
52	C₃×C₇	—	3	2	no	—
53	C₃×C₇	—	133	3	no	—
54	C₃×C₇	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
55	C₃×C₇	#11716326	1	1	yes	characteristic, complemented
56	ΓL(1,𝔽₈)	—	19	3	no	—
57	C₁₉	C₃×ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃²	—	931	1	no	Hall
59	D₇	—	7	1	no	—
60	D₇	—	21	2	no	—
61	D₇	—	21	1	no	—
62	C₃²	—	133	1	no	Sylow
63	C₇	—	3	2	no	—
64	C₇	C₃×#11716326	1	1	yes	characteristic, complemented
65	C₇	C₃×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
66	C₂×C₃	—	147	1	no	—
67	C₂×C₃	—	931	3	no	—
68	C₃	—	133	3	no	—
69	C₃	#19150309	1	1	yes	characteristic, direct product factor
70	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#19150309
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×C₇×#87705	C₂	semidirect
2. C₃×C₁₉×C₇⋊D₇	C₃	semidirect
3. #19150309	C₃	direct (N × H)
4. C₇×#87705	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
8. C₁₉×C₇⋊D₇	C₃²	semidirect
9. C₃×#87705	D₇	semidirect
11. C₇²×C₁₉	C₂×C₃²	semidirect
20. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
21. C₃×C₇×C₁₉	C₃×D₇	semidirect
22. #87705	C₃×D₇	semidirect
25. C₃×C₇⋊D₇	C₁₉⋊C₃	semidirect
31. C₃×C₇²	C₂×C₁₉⋊C₃	semidirect
34. C₇×C₁₉	C₃×AGL(1,𝔽₇)	semidirect
35. C₇×C₁₉	C₃²×D₇	semidirect
40. C₇⋊D₇	C₃×C₁₉⋊C₃	semidirect
43. C₃×C₁₉	ΓL(1,𝔽₈)⋊D₇	semidirect
45. C₇²	C₂×C₃×C₁₉⋊C₃	semidirect
54. C₃×C₇	D₇×C₁₉⋊C₃	semidirect
55. C₃×C₇	#11716326	semidirect
57. C₁₉	C₃×ΓL(1,𝔽₈)⋊D₇	semidirect
64. C₇	C₃×#11716326	semidirect
65. C₇	C₃×D₇×C₁₉⋊C₃	semidirect
69. C₃	#19150309	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×C₇×#87705	2
C₃×C₁₉×C₇⋊D₇	3
#19150309	3
C₃×D₇×C₁₉⋊C₃	7
C₃×#11716326	7
C₃×ΓL(1,𝔽₈)⋊D₇	19

Subgroups — C3×#19150309 #30660784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19150309 #30660784