Subgroups — C₃⋊#19150304 #30660839

Order 16758.

76 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	C₇×D₃₉₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150304	—	3	1	no	maximal
4	C₁₉×#3862	—	2	1	no	—
5	C₁₉×#3862	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)	—	14	1	no	—
12	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊#64422	—	19	1	no	maximal, Hall
14	D₃₉₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₇×D₅₇	—	7	1	no	—
16	ΓL(1,𝔽₈)⋊D₁₉	—	21	1	no	—
17	ΓL(1,𝔽₈)×D₁₉	—	21	1	no	—
18	C₃×#3862	D₁₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₁₉	—	6	1	no	—
20	C₃×C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
23	C₁₉×ΓL(1,𝔽₈)	—	7	1	no	—
24	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
25	C₁₉×ΓL(1,𝔽₈)	—	14	1	no	—
26	C₃×D₅₇	—	49	1	no	Hall
27	C₇×D₂₁	—	19	1	no	—
28	#64422	—	57	1	no	—
29	D₁₃₃	—	3	1	no	—
30	C₇×D₁₉	—	21	1	no	—
31	C₃²×C₁₉	—	98	1	no	Hall
32	C₃×C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented
33	#3862	—	2	1	no	—
34	#3862	D₅₇	1	1	yes	characteristic, complemented
35	C₇×C₁₉	—	6	1	no	—
36	C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
37	C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
38	C₃⋊AGL(1,𝔽₇)	—	133	1	no	—
39	D₃×ΓL(1,𝔽₈)	—	133	1	no	—
40	D₅₇	—	7	1	no	—
41	C₃×D₁₉	—	147	1	no	—
42	C₇×D₇	—	57	1	no	Hall
43	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
44	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
45	C₃×C₁₉	—	98	1	no	—
46	C₃×C₁₉	—	98	1	no	—
47	C₃×C₁₉	#64422	1	1	yes	characteristic, complemented
48	C₇²	C₃×D₅₇	1	1	yes	characteristic, complemented, Sylow
49	D₂₁	—	19	1	no	—
50	D₃×C₇	—	133	1	no	—
51	C₂×ΓL(1,𝔽₈)	—	399	1	no	—
52	AGL(1,𝔽₇)	—	399	1	no	—
53	D₁₉	—	21	1	no	Hall
54	C₃×C₇	—	6	1	no	—
55	C₃×C₇	ΓL(1,𝔽₈)×D₁₉	1	1	yes	characteristic, complemented
56	C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	7	1	no	—
58	ΓL(1,𝔽₈)	—	7	1	no	—
59	ΓL(1,𝔽₈)	—	14	1	no	—
60	ΓL(1,𝔽₈)	—	14	1	no	—
61	C₁₉	C₃⋊#64422	1	1	yes	characteristic, complemented, Sylow
62	C₃×D₃	—	931	1	no	Hall
63	C₂×C₇	—	399	1	no	—
64	D₇	—	57	1	no	—
65	C₃²	—	98	1	no	Sylow
66	C₇	—	6	1	no	—
67	C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	1	1	yes	characteristic, complemented
68	C₇	ΓL(1,𝔽₈)×D₅₇	1	1	yes	characteristic, complemented
69	C₂×C₃	—	2793	1	no	—
70	D₃	—	133	1	no	—
71	C₃	—	98	1	no	—
72	C₃	—	98	1	no	—
73	C₃	#19150304	1	1	yes	characteristic, complemented
74	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×#3862	C₂	semidirect
2. C₇×D₃₉₉	C₃	semidirect
5. C₁₉×#3862	D₃	semidirect
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
12. C₇²×C₁₉	C₃×D₃	semidirect
14. D₃₉₉	ΓL(1,𝔽₈)	semidirect
18. C₃×#3862	D₁₉	semidirect
20. C₃×C₇×C₁₉	AGL(1,𝔽₇)	semidirect
21. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
32. C₃×C₇²	C₃×D₁₉	semidirect
34. #3862	D₅₇	semidirect
36. C₇×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
37. C₇×C₁₉	C₃⋊AGL(1,𝔽₇)	semidirect
47. C₃×C₁₉	#64422	semidirect
48. C₇²	C₃×D₅₇	semidirect
55. C₃×C₇	ΓL(1,𝔽₈)×D₁₉	semidirect
56. C₃×C₇	ΓL(1,𝔽₈)⋊D₁₉	semidirect
61. C₁₉	C₃⋊#64422	semidirect
67. C₇	C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	semidirect
68. C₇	ΓL(1,𝔽₈)×D₅₇	semidirect
73. C₃	#19150304	semidirect

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
C₇×D₃₉₉	3
#19150304	3
ΓL(1,𝔽₈)×D₅₇	7
C₃⋊(ΓL(1,𝔽₈)⋊D₁₉)	7
C₃⋊#64422	19

Subgroups — C3⋊#19150304 #30660839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19150304 #30660839