Subgroups — C₂×C₃×ΓL(1,𝔽₈)⋊D₂₉ #20300636

Order 7308.

120 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	C₃×ΓL(1,𝔽₈)⋊D₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₂₀₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×ΓL(1,𝔽₈)⋊D₂₉	C₃	1	3	yes	maximal, direct product factor
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	C₃×D₂₀₃	C₂×C₃	1	2	yes	complemented
8	C₂×ΓL(1,𝔽₈)×C₂₉	C₂×C₃	1	3	yes	complemented
9	ΓL(1,𝔽₈)⋊D₂₉	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃²×D₂₉	—	7	1	no	maximal, Hall
11	C₂×D₂₀₃	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	ΓL(1,𝔽₈)×C₂₉	C₂²×C₃	1	3	yes	complemented
14	C₂×C₃²×C₂₉	—	7	1	no	—
15	C₃²×D₂₉	—	7	2	no	—
16	C₂×C₇×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₂₀₃	C₂×C₃²	1	2	yes	complemented
18	C₂×C₃×D₂₉	—	7	3	no	—
19	C₂×C₃×D₂₉	—	7	1	no	—
20	C₃²×C₂₉	—	7	1	no	Hall
21	C₂×C₃×AGL(1,𝔽₇)	—	29	1	no	maximal, Hall
22	C₇×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₂₉	—	7	3	no	—
24	C₂×C₃×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
25	C₃×D₂₉	—	7	6	no	—
26	C₃×D₂₉	—	7	2	no	—
27	C₂×C₃×ΓL(1,𝔽₈)	D₂₉	1	1	yes	characteristic, complemented
28	C₃×AGL(1,𝔽₇)	—	29	2	no	—
29	C₂×D₂₉	—	7	1	no	Hall
30	C₃×C₂₉	—	7	3	no	—
31	C₃×C₂₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
32	C₂×C₃×D₇	—	29	1	no	—
33	C₂×AGL(1,𝔽₇)	—	29	3	no	—
34	C₃×ΓL(1,𝔽₈)	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
35	C₂×C₂₉	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	D₂₉	—	7	2	no	—
37	C₂×C₃×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented
38	C₃×D₇	—	29	2	no	—
39	C₂×ΓL(1,𝔽₈)	C₃×D₂₉	1	3	yes	complemented
40	AGL(1,𝔽₇)	—	29	6	no	—
41	C₂²×C₃²	—	203	1	no	Hall
42	C₂₉	C₂×C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₇	—	29	1	no	Hall
44	C₃×C₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
45	ΓL(1,𝔽₈)	C₂×C₃×D₂₉	1	3	yes	complemented
46	C₂×C₃²	—	7	1	no	—
47	C₂×C₃²	—	203	2	no	—
48	C₂×C₇	C₃²×D₂₉	1	1	yes	characteristic, complemented
49	D₇	—	29	2	no	—
50	C₂²×C₃	—	203	3	no	—
51	C₂²×C₃	—	203	1	no	—
52	C₃²	—	7	1	no	Sylow
53	C₇	C₂×C₃²×D₂₉	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃	—	7	3	no	—
55	C₂×C₃	—	203	6	no	—
56	C₂×C₃	—	203	2	no	—
57	C₂×C₃	ΓL(1,𝔽₈)⋊D₂₉	1	1	yes	characteristic, direct product factor
58	C₂²	—	203	1	no	Sylow
59	C₃	—	7	3	no	—
60	C₃	C₂×ΓL(1,𝔽₈)⋊D₂₉	1	1	yes	characteristic, direct product factor
61	C₂	—	203	2	no	—
62	C₂	C₃×ΓL(1,𝔽₈)⋊D₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₂₉
commutator, hypocenter	C₇×C₂₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₂×C₃

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. C₃×ΓL(1,𝔽₈)⋊D₂₉	C₂	direct (N × H)
3. C₂×C₃×D₂₀₃	C₃	semidirect
4. C₂×ΓL(1,𝔽₈)⋊D₂₉	C₃	direct (N × H)
5. C₃×ΓL(1,𝔽₈)×C₂₉	C₂²	semidirect
6. C₂×C₃×C₇×C₂₉	C₂×C₃	semidirect
7. C₃×D₂₀₃	C₂×C₃	semidirect
8. C₂×ΓL(1,𝔽₈)×C₂₉	C₂×C₃	semidirect
9. ΓL(1,𝔽₈)⋊D₂₉	C₂×C₃	direct (N × H)
11. C₂×D₂₀₃	C₃²	semidirect
12. C₃×C₇×C₂₉	C₂²×C₃	semidirect
13. ΓL(1,𝔽₈)×C₂₉	C₂²×C₃	semidirect
16. C₂×C₇×C₂₉	C₂×C₃²	semidirect
17. D₂₀₃	C₂×C₃²	semidirect
22. C₇×C₂₉	C₂²×C₃²	semidirect
24. C₂×C₃×C₂₉	AGL(1,𝔽₇)	semidirect
27. C₂×C₃×ΓL(1,𝔽₈)	D₂₉	semidirect
31. C₃×C₂₉	C₂×AGL(1,𝔽₇)	semidirect
34. C₃×ΓL(1,𝔽₈)	C₂×D₂₉	semidirect
35. C₂×C₂₉	C₃×AGL(1,𝔽₇)	semidirect
37. C₂×C₃×C₇	C₃×D₂₉	semidirect
39. C₂×ΓL(1,𝔽₈)	C₃×D₂₉	semidirect
42. C₂₉	C₂×C₃×AGL(1,𝔽₇)	semidirect
44. C₃×C₇	C₂×C₃×D₂₉	semidirect
45. ΓL(1,𝔽₈)	C₂×C₃×D₂₉	semidirect
48. C₂×C₇	C₃²×D₂₉	semidirect
53. C₇	C₂×C₃²×D₂₉	semidirect
57. C₂×C₃	ΓL(1,𝔽₈)⋊D₂₉	direct (N × H)
60. C₃	C₂×ΓL(1,𝔽₈)⋊D₂₉	direct (N × H)
62. C₂	C₃×ΓL(1,𝔽₈)⋊D₂₉	direct (N × H)

Subgroups — C2×C3×ΓL(1,𝔽8)⋊D29 #20300636

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×ΓL(1,𝔽₈)⋊D₂₉ #20300636