Subgroups — C₂×C₂₉×C₃⋊AGL(1,𝔽₇) #20300638

Order 7308.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₂₉	C₃⋊AGL(1,𝔽₇)
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×ΓL(1,𝔽₈)×C₂₉	C₂	semidirect
2. C₂₉×C₃⋊AGL(1,𝔽₇)	C₂	direct (N × H)
3. C₂×C₂₉×D₂₁	C₃	semidirect
5. C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	semidirect
6. C₂×C₃×C₇×C₂₉	C₂×C₃	semidirect
7. C₂₉×D₂₁	C₂×C₃	semidirect
9. C₂×ΓL(1,𝔽₈)×C₂₉	D₃	semidirect
13. C₃×C₇×C₂₉	C₂²×C₃	semidirect
15. ΓL(1,𝔽₈)×C₂₉	C₂×D₃	semidirect
18. C₂×C₇×C₂₉	C₃×D₃	semidirect
23. C₂×C₃⋊AGL(1,𝔽₇)	C₂₉	direct (N × H)
24. C₇×C₂₉	C₂×C₃×D₃	semidirect
28. C₂×C₃×C₂₉	AGL(1,𝔽₇)	semidirect
30. C₂×C₃×ΓL(1,𝔽₈)	C₂×C₂₉	semidirect
31. C₃⋊AGL(1,𝔽₇)	C₂×C₂₉	direct (N × H)
35. C₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
36. C₂×D₂₁	C₃×C₂₉	semidirect
38. C₃×ΓL(1,𝔽₈)	C₂²×C₂₉	semidirect
40. C₂×C₂₉	C₃⋊AGL(1,𝔽₇)	direct (N × H)
41. C₂×C₃×C₇	C₂×C₃×C₂₉	semidirect
42. D₂₁	C₂×C₃×C₂₉	semidirect
44. C₂×ΓL(1,𝔽₈)	D₃×C₂₉	semidirect
47. C₂₉	C₂×C₃⋊AGL(1,𝔽₇)	direct (N × H)
49. C₃×C₇	C₂²×C₃×C₂₉	semidirect
51. ΓL(1,𝔽₈)	C₂×D₃×C₂₉	semidirect
54. C₂×C₇	C₃×D₃×C₂₉	semidirect
59. C₇	C₂×C₃×D₃×C₂₉	semidirect
63. C₂×C₃	C₂₉×AGL(1,𝔽₇)	semidirect
68. C₃	C₂×C₂₉×AGL(1,𝔽₇)	semidirect
70. C₂	C₂₉×C₃⋊AGL(1,𝔽₇)	direct (N × H)

Subgroups — C2×C29×C3⋊AGL(1,𝔽7) #20300638

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₉×C₃⋊AGL(1,𝔽₇) #20300638