Subgroups — C₃×#19150312 #30660788

Order 16758.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14584116	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150312	C₃	1	3	yes	maximal, direct product factor
4	#14584116	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#11716322	—	7	1	no	maximal
7	C₃×#11716322	—	7	7	no	maximal
8	C₇²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×#87705	—	7	1	no	—
10	C₃×#87705	—	7	7	no	—
11	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×#3861	—	19	1	no	maximal, Hall
13	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	7	yes	complemented
15	#11716322	—	7	3	no	—
16	#11716322	—	7	21	no	—
17	C₃×#3861	—	19	1	no	Hall
18	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	7	yes	complemented
20	#87705	—	7	3	no	—
21	#87705	—	7	21	no	—
22	C₃×D₁₉⋊C₃	—	49	1	no	Hall
23	C₂×C₃×C₇²	—	57	1	no	—
24	C₂×#3861	—	19	3	no	—
25	C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	7	yes	complemented
27	C₃×C₁₉⋊C₃	—	49	1	no	Hall
28	C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
29	#3861	—	19	3	no	—
30	C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
31	C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	7	yes	complemented
32	C₂×C₃×ΓL(1,𝔽₈)	—	133	1	no	—
33	C₂×C₃×ΓL(1,𝔽₈)	—	133	7	no	—
34	C₃×D₁₉	#3861	1	1	yes	characteristic, complemented
35	D₁₉⋊C₃	—	49	3	no	—
36	C₂×C₇²	—	57	1	no	Hall
37	C₃×ΓL(1,𝔽₈)	—	133	1	no	—
38	C₃×ΓL(1,𝔽₈)	—	133	7	no	—
39	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
40	C₁₉⋊C₃	—	49	3	no	—
41	C₇²	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃×C₇	—	19	1	no	—
43	C₂×C₃×C₇	—	57	7	no	—
44	C₂×ΓL(1,𝔽₈)	—	133	3	no	—
45	C₂×ΓL(1,𝔽₈)	—	133	21	no	—
46	D₁₉	C₃×#3861	1	1	yes	characteristic, complemented, Hall
47	C₃×C₇	#11716322	1	1	yes	characteristic, complemented
48	C₃×C₇	#11716322	1	7	yes	complemented
49	ΓL(1,𝔽₈)	—	133	3	no	—
50	ΓL(1,𝔽₈)	—	133	21	no	—
51	C₁₉	C₂×C₃×#3861	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃²	—	931	1	no	Hall
53	C₂×C₇	—	19	1	no	—
54	C₂×C₇	—	57	7	no	—
55	C₃²	—	931	1	no	Sylow
56	C₇	C₃×#11716322	1	1	yes	characteristic, complemented
57	C₇	C₃×#11716322	1	7	yes	complemented
58	C₂×C₃	—	57	1	no	—
59	C₂×C₃	—	931	3	no	—
60	C₃	—	931	3	no	—
61	C₃	#19150312	1	1	yes	characteristic, direct product factor
62	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#19150312
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×#14584116	C₂	semidirect
2. C₃×C₇²×D₁₉	C₃	semidirect
3. #19150312	C₃	direct (N × H)
4. #14584116	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
8. C₇²×D₁₉	C₃²	semidirect
11. C₇²×C₁₉	C₂×C₃²	semidirect
13. C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
14. C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
18. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
25. C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
26. C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
28. C₃×C₇²	D₁₉⋊C₃	semidirect
30. C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
31. C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
34. C₃×D₁₉	#3861	semidirect
39. C₃×C₁₉	C₂×#3861	semidirect
41. C₇²	C₃×D₁₉⋊C₃	semidirect
46. D₁₉	C₃×#3861	semidirect
47. C₃×C₇	#11716322	semidirect
48. C₃×C₇	#11716322	semidirect
51. C₁₉	C₂×C₃×#3861	semidirect
56. C₇	C₃×#11716322	semidirect
57. C₇	C₃×#11716322	semidirect
61. C₃	#19150312	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×#14584116	2
C₃×C₇²×D₁₉	3
#19150312	3
C₃×#11716322	7
C₂×C₃×#3861	19

Subgroups — C3×#19150312 #30660788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19150312 #30660788