Subgroups — AGL(1,𝔽₇)×D₂₉₃ #37590029

Order 24612.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)⋊D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	AGL(1,𝔽₇)×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	ΓL(1,𝔽₈)×D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₂₉₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	ΓL(1,𝔽₈)×C₂₉₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₅₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₂₉₃	C₂×C₃	1	1	yes	characteristic, complemented
8	D₇×C₂₉₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₃×D₂₉₃	—	7	1	no	maximal, Hall
10	C₇×C₂₉₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₂₉₃	—	7	1	no	—
12	C₃×D₂₉₃	—	7	1	no	—
13	C₃×D₂₉₃	—	14	1	no	—
14	C₂×D₂₉₃	—	7	1	no	Hall
15	C₃×C₂₉₃	—	14	1	no	Hall
16	C₂×C₂₉₃	—	7	1	no	—
17	D₂₉₃	—	7	1	no	—
18	D₂₉₃	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
19	C₂₉₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
20	C₂×AGL(1,𝔽₇)	—	293	1	no	maximal, Hall
21	C₂×ΓL(1,𝔽₈)	—	293	1	no	—
22	AGL(1,𝔽₇)	—	293	1	no	—
23	AGL(1,𝔽₇)	D₂₉₃	1	1	yes	characteristic, direct product factor
24	C₂×D₇	—	293	1	no	Hall
25	ΓL(1,𝔽₈)	C₂×D₂₉₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	293	1	no	—
27	D₇	—	293	1	no	—
28	D₇	C₃×D₂₉₃	1	1	yes	characteristic, complemented
29	C₂²×C₃	—	2051	1	no	Hall
30	C₇	C₂×C₃×D₂₉₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	2051	1	no	—
32	C₂×C₃	—	4102	1	no	—
33	C₂×C₃	—	7	1	no	—
34	C₂²	—	2051	1	no	Sylow
35	C₃	—	14	1	no	Sylow
36	C₂	—	2051	1	no	—
37	C₂	—	7	1	no	—
38	C₂	—	293	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₂₉₃	C₂²×C₃
LCS	G ▷ C₇×C₂₉₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)⋊D₂₉₃	C₂	semidirect
2. AGL(1,𝔽₇)×C₂₉₃	C₂	semidirect
3. ΓL(1,𝔽₈)×D₂₉₃	C₂	semidirect
4. D₇×D₂₉₃	C₃	semidirect
5. ΓL(1,𝔽₈)×C₂₉₃	C₂²	semidirect
6. D₂₀₅₁	C₂×C₃	semidirect
7. C₇×D₂₉₃	C₂×C₃	semidirect
8. D₇×C₂₉₃	C₂×C₃	semidirect
10. C₇×C₂₉₃	C₂²×C₃	semidirect
18. D₂₉₃	AGL(1,𝔽₇)	direct (N × H)
19. C₂₉₃	C₂×AGL(1,𝔽₇)	semidirect
23. AGL(1,𝔽₇)	D₂₉₃	direct (N × H)
25. ΓL(1,𝔽₈)	C₂×D₂₉₃	semidirect
28. D₇	C₃×D₂₉₃	semidirect
30. C₇	C₂×C₃×D₂₉₃	semidirect

Maximal subgroups

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

subgroup	index
ΓL(1,𝔽₈)⋊D₂₉₃	2
AGL(1,𝔽₇)×C₂₉₃	2
ΓL(1,𝔽₈)×D₂₉₃	2
D₇×D₂₉₃	3
C₂×C₃×D₂₉₃	7
C₂×AGL(1,𝔽₇)	293

Subgroups — AGL(1,𝔽7)×D293 #37590029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₇)×D₂₉₃ #37590029