Subgroups — D₃×C₇×#87704 #30660813

Order 16758.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#87704	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#87704	—	3	1	no	maximal
4	C₇×#87704	—	2	1	no	—
5	C₇×#87704	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×#87704	C₇	1	1	yes	maximal, characteristic, direct product factor
8	D₃×C₇×C₁₉⋊C₃	—	7	1	no	maximal
9	C₂×C₇²×C₁₉	—	3	1	no	Hall
10	C₃×#87704	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃×C₇×C₁₉⋊C₃	—	7	1	no	—
12	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	D₃×C₇×ΓL(1,𝔽₈)	—	19	1	no	maximal, Hall
14	D₃×C₇×C₁₉	—	3	2	no	—
15	D₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	D₃×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic, complemented
17	C₂×#87704	—	3	1	no	—
18	C₂×C₇×C₁₉⋊C₃	—	21	1	no	—
19	C₃×C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
20	C₃×C₇×C₁₉	—	3	2	no	—
21	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₃×C₇×C₁₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	#87704	—	2	1	no	—
24	#87704	D₃×C₇	1	1	yes	characteristic, direct product factor
25	C₇×C₁₉⋊C₃	—	7	1	no	—
26	C₇×C₁₉⋊C₃	—	14	1	no	—
27	D₃×C₁₉⋊C₃	—	7	1	no	Hall
28	D₃×C₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
29	C₂×C₇×ΓL(1,𝔽₈)	—	57	1	no	—
30	C₂×C₇×C₁₉	—	3	1	no	—
31	C₂×C₇×C₁₉	—	3	1	no	—
32	C₂×C₇×C₁₉	—	9	2	no	—
33	C₃×C₁₉⋊C₃	—	7	1	no	Hall
34	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	C₇×ΓL(1,𝔽₈)	—	19	1	no	—
36	C₇×ΓL(1,𝔽₈)	—	38	1	no	—
37	C₇×C₁₉	—	3	2	no	—
38	C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₇×C₁₉	C₃×D₃×C₇	1	1	yes	characteristic, complemented
40	C₃×D₃×C₇	—	133	1	no	—
41	D₃×ΓL(1,𝔽₈)	—	19	1	no	—
42	D₃×C₁₉	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
43	C₂×C₁₉⋊C₃	—	21	1	no	—
44	C₂×C₇²	—	3	1	no	Hall
45	C₃²×C₇	—	133	1	no	—
46	C₃×ΓL(1,𝔽₈)	—	19	1	no	—
47	C₃×C₁₉	C₂×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
48	C₁₉⋊C₃	—	7	1	no	—
49	C₁₉⋊C₃	—	14	1	no	—
50	C₇²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃×C₇	—	399	1	no	—
52	D₃×C₇	—	3	2	no	—
53	D₃×C₇	C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
54	D₃×C₇	#87704	1	1	yes	characteristic, direct product factor
55	C₂×ΓL(1,𝔽₈)	—	57	1	no	—
56	C₂×C₁₉	—	3	1	no	Hall
57	C₃×C₇	—	3	2	no	—
58	C₃×C₇	—	266	1	no	—
59	C₃×C₇	—	133	1	no	—
60	C₃×C₇	C₂×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
61	C₃×C₇	C₂×#87704	1	1	yes	characteristic, complemented
62	ΓL(1,𝔽₈)	—	19	1	no	—
63	ΓL(1,𝔽₈)	—	38	1	no	—
64	C₁₉	D₃×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
65	C₃×D₃	—	133	1	no	Hall
66	C₂×C₇	—	3	1	no	—
67	C₂×C₇	—	3	1	no	—
68	C₂×C₇	—	9	2	no	—
69	C₃²	—	133	1	no	Sylow
70	C₇	—	3	2	no	—
71	C₇	D₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
72	C₇	D₃×#87704	1	1	yes	characteristic, direct product factor
73	C₂×C₃	—	399	1	no	—
74	D₃	C₇×#87704	1	1	yes	characteristic, direct product factor
75	C₃	—	266	1	no	—
76	C₃	—	133	1	no	—
77	C₃	C₂×C₇×#87704	1	1	yes	characteristic, complemented
78	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₃×#87704
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#87704	C₂	semidirect
2. D₃×C₇²×C₁₉	C₃	semidirect
5. C₇×#87704	D₃	direct (N × H)
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. D₃×#87704	C₇	direct (N × H)
10. C₃×#87704	C₂×C₇	semidirect
12. C₇²×C₁₉	C₃×D₃	semidirect
15. D₃×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
16. D₃×C₇×C₁₉	C₃×C₇	semidirect
21. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. C₃×C₇×C₁₉	C₂×C₃×C₇	semidirect
24. #87704	D₃×C₇	direct (N × H)
28. D₃×C₇²	C₁₉⋊C₃	semidirect
34. C₃×C₇²	C₂×C₁₉⋊C₃	semidirect
38. C₇×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
39. C₇×C₁₉	C₃×D₃×C₇	semidirect
42. D₃×C₁₉	C₇×ΓL(1,𝔽₈)	semidirect
47. C₃×C₁₉	C₂×C₇×ΓL(1,𝔽₈)	semidirect
50. C₇²	D₃×C₁₉⋊C₃	semidirect
53. D₃×C₇	C₇×C₁₉⋊C₃	semidirect
54. D₃×C₇	#87704	direct (N × H)
60. C₃×C₇	C₂×C₇×C₁₉⋊C₃	semidirect
61. C₃×C₇	C₂×#87704	semidirect
64. C₁₉	D₃×C₇×ΓL(1,𝔽₈)	semidirect
71. C₇	D₃×C₇×C₁₉⋊C₃	semidirect
72. C₇	D₃×#87704	direct (N × H)
74. D₃	C₇×#87704	direct (N × H)
77. C₃	C₂×C₇×#87704	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×#87704	2
D₃×C₇²×C₁₉	3
C₂×C₇×#87704	3
D₃×#87704	7
D₃×C₇×C₁₉⋊C₃	7
D₃×C₇×ΓL(1,𝔽₈)	19

Subgroups — D3×C7×#87704 #30660813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×#87704 #30660813