Subgroups — C₃⋊#19150298 #30660833

Order 16758.

108 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	C₇×D₃₉₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150298	—	3	1	no	maximal
4	C₁₉×#3861	—	2	1	no	—
5	C₁₉×#3861	D₃	1	1	yes	characteristic, complemented
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	ΓL(1,𝔽₈)×D₅₇	—	7	1	no	maximal
8	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	—	7	1	no	maximal
9	C₇×D₁₃₃	—	3	1	no	Hall
10	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₃×C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
12	C₃×C₁₉×ΓL(1,𝔽₈)	—	14	3	no	—
13	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃⋊#64423	—	19	1	no	maximal, Hall
15	D₃₉₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	C₇×D₅₇	—	7	1	no	—
17	ΓL(1,𝔽₈)⋊D₁₉	—	21	1	no	—
18	ΓL(1,𝔽₈)×D₁₉	—	21	1	no	—
19	C₃×#3861	D₁₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₇×C₁₉	—	2	3	no	—
21	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
24	C₁₉×ΓL(1,𝔽₈)	—	14	6	no	—
25	C₁₉×ΓL(1,𝔽₈)	—	14	3	no	—
26	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
27	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
28	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
29	C₃×D₅₇	—	49	1	no	Hall
30	C₇×D₂₁	—	19	1	no	—
31	#64423	—	57	1	no	—
32	D₁₃₃	—	3	1	no	—
33	C₇×D₁₉	—	21	1	no	—
34	C₃²×C₁₉	—	98	1	no	Hall
35	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
36	#3861	—	2	1	no	—
37	#3861	D₅₇	1	1	yes	characteristic, complemented
38	C₇×C₁₉	—	2	3	no	—
39	C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
41	C₃⋊AGL(1,𝔽₇)	—	133	1	no	—
42	D₃×ΓL(1,𝔽₈)	—	133	1	no	—
43	D₅₇	—	7	1	no	—
44	C₃×D₁₉	—	147	1	no	—
45	C₇×D₇	—	57	1	no	Hall
46	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
47	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
48	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
49	C₃×C₁₉	—	98	1	no	—
50	C₃×C₁₉	—	98	1	no	—
51	C₃×C₁₉	#64423	1	1	yes	characteristic, complemented
52	C₇²	C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
53	D₂₁	—	19	1	no	—
54	D₃×C₇	—	133	1	no	—
55	C₂×ΓL(1,𝔽₈)	—	399	1	no	—
56	AGL(1,𝔽₇)	—	399	1	no	—
57	D₁₉	—	21	1	no	Hall
58	C₃×C₇	—	2	3	no	—
59	C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic, complemented
60	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
61	ΓL(1,𝔽₈)	—	7	1	no	—
62	ΓL(1,𝔽₈)	—	14	6	no	—
63	ΓL(1,𝔽₈)	—	14	3	no	—
64	ΓL(1,𝔽₈)	—	14	1	no	—
65	ΓL(1,𝔽₈)	—	14	1	no	—
66	ΓL(1,𝔽₈)	—	14	1	no	—
67	C₁₉	C₃⋊#64423	1	1	yes	characteristic, complemented, Sylow
68	C₃×D₃	—	931	1	no	Hall
69	C₂×C₇	—	399	1	no	—
70	D₇	—	57	1	no	—
71	C₃²	—	49	1	no	Sylow
72	C₇	—	2	3	no	—
73	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	1	1	yes	characteristic, complemented
74	C₇	ΓL(1,𝔽₈)×D₅₇	1	1	yes	characteristic, complemented
75	C₂×C₃	—	2793	1	no	—
76	D₃	—	133	1	no	—
77	C₃	—	98	1	no	—
78	C₃	—	98	1	no	—
79	C₃	#19150298	1	1	yes	characteristic, complemented
80	C₂	—	399	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×#3861	C₂	semidirect
2. C₇×D₃₉₉	C₃	semidirect
5. C₁₉×#3861	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
13. C₇²×C₁₉	C₃×D₃	semidirect
15. D₃₉₉	ΓL(1,𝔽₈)	semidirect
19. C₃×#3861	D₁₉	semidirect
21. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
22. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
35. C₃×C₇²	C₃×D₁₉	semidirect
37. #3861	D₅₇	semidirect
39. C₇×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
40. C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
51. C₃×C₁₉	#64423	semidirect
52. C₇²	C₃×D₅₇	semidirect
59. C₃×C₇	ΓL(1,𝔽₈)×D₁₉	semidirect
60. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
67. C₁₉	C₃⋊#64423	semidirect
73. C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	semidirect
74. C₇	ΓL(1,𝔽₈)×D₅₇	semidirect
79. C₃	#19150298	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
C₇×D₃₉₉	3
#19150298	3
ΓL(1,𝔽₈)×D₅₇	7
C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	7
C₃⋊#64423	19

Subgroups — C3⋊#19150298 #30660833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19150298 #30660833