Subgroups — D₃×C₂₉×AGL(1,𝔽₇) #20300627

Order 7308.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×ΓL(1,𝔽₈)×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×C₃⋊AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₉×AGL(1,𝔽₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×AGL(1,𝔽₇)	—	3	1	no	maximal
6	C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂₉×D₂₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×ΓL(1,𝔽₈)×C₂₉	—	3	1	no	—
11	C₂₉×AGL(1,𝔽₇)	—	2	1	no	—
12	C₂₉×AGL(1,𝔽₇)	—	3	1	no	—
13	C₂₉×AGL(1,𝔽₇)	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₃×D₃×C₂₉	—	7	1	no	maximal, Hall
15	C₂×D₇×C₂₉	—	3	1	no	Hall
16	C₃×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
17	ΓL(1,𝔽₈)×C₂₉	—	2	1	no	—
18	ΓL(1,𝔽₈)×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₂₉	—	7	1	no	—
20	C₃×D₃×C₂₉	—	7	1	no	—
21	C₃×D₃×C₂₉	—	7	1	no	—
22	C₂×C₇×C₂₉	—	3	1	no	—
23	D₇×C₂₉	—	3	1	no	—
24	D₇×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₂₉	—	21	1	no	—
26	C₂×D₃×C₂₉	—	7	1	no	—
27	C₃²×C₂₉	—	7	1	no	Hall
28	D₃×AGL(1,𝔽₇)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₉	—	7	1	no	—
31	C₂×C₃×C₂₉	—	7	1	no	—
32	C₂×C₃×C₂₉	—	14	1	no	—
33	C₂×C₃×C₂₉	—	21	1	no	—
34	C₂×C₃×C₂₉	—	21	1	no	—
35	D₃×C₂₉	—	7	1	no	—
36	D₃×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
37	C₃⋊AGL(1,𝔽₇)	C₂×C₂₉	1	1	yes	characteristic, complemented
38	D₃×ΓL(1,𝔽₈)	C₂×C₂₉	1	1	yes	characteristic, complemented
39	C₃×AGL(1,𝔽₇)	C₂×C₂₉	1	1	yes	characteristic, complemented
40	C₂²×C₂₉	—	21	1	no	Hall
41	C₃×C₂₉	—	7	1	no	—
42	C₃×C₂₉	—	14	1	no	—
43	C₃×C₂₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
44	D₃×D₇	C₃×C₂₉	1	1	yes	characteristic, complemented
45	C₂×AGL(1,𝔽₇)	—	3	1	no	—
46	C₃×ΓL(1,𝔽₈)	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₂₉	—	3	1	no	—
48	C₂×C₂₉	—	7	1	no	—
49	C₂×C₂₉	—	21	1	no	—
50	D₂₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
51	C₃×D₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
52	D₃×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
53	C₂×ΓL(1,𝔽₈)	—	3	1	no	—
54	AGL(1,𝔽₇)	—	2	1	no	—
55	AGL(1,𝔽₇)	—	3	1	no	—
56	AGL(1,𝔽₇)	D₃×C₂₉	1	1	yes	characteristic, direct product factor
57	C₂×C₃×D₃	—	7	1	no	Hall
58	C₂₉	D₃×AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×D₇	—	3	1	no	Hall
60	C₃×C₇	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
61	ΓL(1,𝔽₈)	—	2	1	no	—
62	ΓL(1,𝔽₈)	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	7	1	no	—
64	C₃×D₃	—	7	1	no	—
65	C₃×D₃	—	7	1	no	—
66	C₂×C₇	—	3	1	no	—
67	D₇	—	3	1	no	—
68	D₇	C₃×D₃×C₂₉	1	1	yes	characteristic, complemented
69	C₂²×C₃	—	21	1	no	—
70	C₂×D₃	—	7	1	no	—
71	C₃²	—	7	1	no	Sylow
72	C₇	C₂×C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	7	1	no	—
74	C₂×C₃	—	7	1	no	—
75	C₂×C₃	—	14	1	no	—
76	C₂×C₃	—	21	1	no	—
77	C₂×C₃	—	21	1	no	—
78	D₃	—	7	1	no	—
79	D₃	C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
80	C₂²	—	21	1	no	Sylow
81	C₃	—	7	1	no	—
82	C₃	—	14	1	no	—
83	C₃	C₂×C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	7	1	no	—
86	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₃×AGL(1,𝔽₇)
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₂₉	C₂²×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. D₃×ΓL(1,𝔽₈)×C₂₉	C₂	semidirect
2. C₂₉×C₃⋊AGL(1,𝔽₇)	C₂	semidirect
3. C₃×C₂₉×AGL(1,𝔽₇)	C₂	semidirect
4. D₃×D₇×C₂₉	C₃	semidirect
6. C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	semidirect
7. C₂₉×D₂₁	C₂×C₃	semidirect
8. D₃×C₇×C₂₉	C₂×C₃	semidirect
9. C₃×D₇×C₂₉	C₂×C₃	semidirect
13. C₂₉×AGL(1,𝔽₇)	D₃	direct (N × H)
16. C₃×C₇×C₂₉	C₂²×C₃	semidirect
18. ΓL(1,𝔽₈)×C₂₉	C₂×D₃	semidirect
24. D₇×C₂₉	C₃×D₃	semidirect
28. D₃×AGL(1,𝔽₇)	C₂₉	direct (N × H)
29. C₇×C₂₉	C₂×C₃×D₃	semidirect
36. D₃×C₂₉	AGL(1,𝔽₇)	direct (N × H)
37. C₃⋊AGL(1,𝔽₇)	C₂×C₂₉	semidirect
38. D₃×ΓL(1,𝔽₈)	C₂×C₂₉	semidirect
39. C₃×AGL(1,𝔽₇)	C₂×C₂₉	semidirect
43. C₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
44. D₃×D₇	C₃×C₂₉	semidirect
46. C₃×ΓL(1,𝔽₈)	C₂²×C₂₉	semidirect
50. D₂₁	C₂×C₃×C₂₉	semidirect
51. C₃×D₇	C₂×C₃×C₂₉	semidirect
52. D₃×C₇	C₂×C₃×C₂₉	semidirect
56. AGL(1,𝔽₇)	D₃×C₂₉	direct (N × H)
58. C₂₉	D₃×AGL(1,𝔽₇)	direct (N × H)
60. C₃×C₇	C₂²×C₃×C₂₉	semidirect
62. ΓL(1,𝔽₈)	C₂×D₃×C₂₉	semidirect
68. D₇	C₃×D₃×C₂₉	semidirect
72. C₇	C₂×C₃×D₃×C₂₉	semidirect
79. D₃	C₂₉×AGL(1,𝔽₇)	direct (N × H)
83. C₃	C₂×C₂₉×AGL(1,𝔽₇)	semidirect

Subgroups — D3×C29×AGL(1,𝔽7) #20300627

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₂₉×AGL(1,𝔽₇) #20300627