Subgroups — ΓL(1,𝔽₈)⋊(D₆₇⋊C₃) #22554739

Order 8442.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#14584204	C₃	1	1	yes	maximal, characteristic, complemented
3	#14584203	C₃	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₈)⋊D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	(C₆₇⋊C₃)⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented
6	#13064105	C₂×C₃	1	1	yes	characteristic, complemented
7	#13064104	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₆₇⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
9	ΓL(1,𝔽₈)×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₆₇⋊C₃	—	7	1	no	maximal, Hall
11	D₄₆₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₆₇⋊C₃	—	7	1	no	Hall
13	C₇×C₆₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×D₆₇	—	7	1	no	—
15	D₆₇⋊C₃	—	7	1	no	—
16	D₆₇⋊C₃	—	7	1	no	—
17	D₆₇⋊C₃	—	7	1	no	—
18	C₃×C₆₇	—	7	1	no	—
19	C₆₇⋊C₃	—	7	1	no	—
20	C₆₇⋊C₃	—	7	1	no	—
21	C₆₇⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	D₆₇	—	7	1	no	Hall
23	C₃×AGL(1,𝔽₇)	—	67	1	no	maximal, Hall
24	C₆₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
25	C₃×ΓL(1,𝔽₈)	—	67	1	no	Hall
26	C₃×D₇	—	67	1	no	—
27	AGL(1,𝔽₇)	—	67	1	no	—
28	AGL(1,𝔽₇)	—	67	1	no	—
29	AGL(1,𝔽₇)	—	67	1	no	—
30	C₃×C₇	—	67	1	no	—
31	ΓL(1,𝔽₈)	—	67	1	no	—
32	ΓL(1,𝔽₈)	—	67	1	no	—
33	ΓL(1,𝔽₈)	D₆₇⋊C₃	1	1	yes	characteristic, complemented
34	C₂×C₃²	—	469	1	no	Hall
35	D₇	—	67	1	no	Hall
36	C₃²	—	469	1	no	Sylow
37	C₇	C₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	469	1	no	—
39	C₂×C₃	—	469	1	no	—
40	C₂×C₃	—	469	1	no	—
41	C₂×C₃	—	469	1	no	—
42	C₃	—	7	1	no	—
43	C₃	—	67	1	no	—
44	C₃	—	469	1	no	—
45	C₃	—	469	1	no	—
46	C₂	—	469	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₆₇	C₂×C₃²
LCS	G ▷ C₇×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)×C₆₇⋊C₃	C₂	semidirect
2. #14584204	C₃	semidirect
3. #14584203	C₃	semidirect
4. ΓL(1,𝔽₈)⋊D₆₇	C₃	semidirect
5. (C₆₇⋊C₃)⋊D₇	C₃	semidirect
6. #13064105	C₂×C₃	semidirect
7. #13064104	C₂×C₃	semidirect
8. C₇×C₆₇⋊C₃	C₂×C₃	semidirect
9. ΓL(1,𝔽₈)×C₆₇	C₂×C₃	semidirect
11. D₄₆₉	C₃²	semidirect
13. C₇×C₆₇	C₂×C₃²	semidirect
21. C₆₇⋊C₃	AGL(1,𝔽₇)	semidirect
24. C₆₇	C₃×AGL(1,𝔽₇)	semidirect
33. ΓL(1,𝔽₈)	D₆₇⋊C₃	semidirect
37. C₇	C₃×D₆₇⋊C₃	semidirect

Subgroups — ΓL(1,𝔽8)⋊(D67⋊C3) #22554739

Conjugacy classes of subgroups

Complements

Subgroups — ΓL(1,𝔽₈)⋊(D₆₇⋊C₃) #22554739