Subgroups — AGL(1,𝔽₇)×C₇₃⋊C₃ #22604107

Order 9198.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#15690446	C₃	1	1	yes	maximal, characteristic, complemented
3	#15690445	C₃	1	1	yes	maximal, characteristic, complemented
4	AGL(1,𝔽₇)×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
5	D₇×C₇₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	#13095276	C₂×C₃	1	1	yes	characteristic, complemented
7	#13095275	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₇₃⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	ΓL(1,𝔽₈)×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₇₃⋊C₃	—	7	1	no	maximal, Hall
11	D₇×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇₃⋊C₃	—	7	1	no	Hall
13	C₇×C₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₇₃	—	7	1	no	—
15	C₂×C₇₃⋊C₃	—	7	1	no	—
16	C₂×C₇₃⋊C₃	—	7	1	no	—
17	C₂×C₇₃⋊C₃	—	7	1	no	—
18	C₃×C₇₃	—	7	1	no	—
19	C₇₃⋊C₃	—	7	1	no	—
20	C₇₃⋊C₃	—	7	1	no	—
21	C₇₃⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor
22	C₂×C₇₃	—	7	1	no	Hall
23	C₃×AGL(1,𝔽₇)	—	73	1	no	maximal, Hall
24	C₇₃	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
25	C₃×ΓL(1,𝔽₈)	—	73	1	no	Hall
26	C₃×D₇	—	73	1	no	—
27	AGL(1,𝔽₇)	—	73	1	no	—
28	AGL(1,𝔽₇)	—	73	1	no	—
29	AGL(1,𝔽₇)	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
30	C₃×C₇	—	73	1	no	—
31	ΓL(1,𝔽₈)	—	73	1	no	—
32	ΓL(1,𝔽₈)	—	73	1	no	—
33	ΓL(1,𝔽₈)	C₂×C₇₃⋊C₃	1	1	yes	characteristic, complemented
34	C₂×C₃²	—	511	1	no	Hall
35	D₇	C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
36	C₃²	—	511	1	no	Sylow
37	C₇	C₂×C₃×C₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	7	1	no	—
39	C₂×C₃	—	511	1	no	—
40	C₂×C₃	—	511	1	no	—
41	C₂×C₃	—	511	1	no	—
42	C₃	—	7	1	no	—
43	C₃	—	73	1	no	—
44	C₃	—	511	1	no	—
45	C₃	—	511	1	no	—
46	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₇₃	C₂×C₃²
LCS	G ▷ C₇×C₇₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)×C₇₃⋊C₃	C₂	semidirect
2. #15690446	C₃	semidirect
3. #15690445	C₃	semidirect
4. AGL(1,𝔽₇)×C₇₃	C₃	semidirect
5. D₇×C₇₃⋊C₃	C₃	semidirect
6. #13095276	C₂×C₃	semidirect
7. #13095275	C₂×C₃	semidirect
8. C₇×C₇₃⋊C₃	C₂×C₃	semidirect
9. ΓL(1,𝔽₈)×C₇₃	C₂×C₃	semidirect
11. D₇×C₇₃	C₃²	semidirect
13. C₇×C₇₃	C₂×C₃²	semidirect
21. C₇₃⋊C₃	AGL(1,𝔽₇)	direct (N × H)
24. C₇₃	C₃×AGL(1,𝔽₇)	semidirect
29. AGL(1,𝔽₇)	C₇₃⋊C₃	direct (N × H)
33. ΓL(1,𝔽₈)	C₂×C₇₃⋊C₃	semidirect
35. D₇	C₃×C₇₃⋊C₃	semidirect
37. C₇	C₂×C₃×C₇₃⋊C₃	semidirect

Subgroups — AGL(1,𝔽7)×C73⋊C3 #22604107

Conjugacy classes of subgroups

Complements

Subgroups — AGL(1,𝔽₇)×C₇₃⋊C₃ #22604107