Subgroups — ΓL(1,𝔽₈)×D₆₇⋊C₁₁ #44526281

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×C₆₇⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₆₇⋊C₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₆₇⋊C₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₆₇⋊C₁₁	—	7	1	no	maximal, Hall
5	ΓL(1,𝔽₈)×D₆₇	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×C₆₇⋊C₁₁	—	7	1	no	Hall
7	D₆₇⋊C₁₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
8	ΓL(1,𝔽₈)×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₇×D₆₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₆₇⋊C₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×ΓL(1,𝔽₈)	—	67	1	no	maximal, Hall
13	C₃×D₆₇	—	7	1	no	Hall
14	C₁₁×ΓL(1,𝔽₈)	—	67	1	no	Hall
15	C₃×C₆₇	—	7	1	no	Hall
16	C₂×C₇×C₁₁	—	67	1	no	Hall
17	D₆₇	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
18	C₇×C₁₁	—	67	1	no	Hall
19	C₆₇	C₂×C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₁₁	—	469	1	no	Hall
21	C₂×ΓL(1,𝔽₈)	—	67	1	no	Hall
22	C₃×C₁₁	—	469	1	no	Hall
23	C₂×C₁₁	—	67	1	no	Hall
24	ΓL(1,𝔽₈)	D₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇	—	67	1	no	Hall
26	C₁₁	—	67	1	no	Sylow
27	C₇	C₃×D₆₇⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	469	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₆₇	C₂×C₃×C₁₁
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⋊C₁₁	C₂	semidirect
2. C₇×D₆₇⋊C₁₁	C₃	semidirect
3. C₇×C₆₇⋊C₁₁	C₂×C₃	semidirect
5. ΓL(1,𝔽₈)×D₆₇	C₁₁	semidirect
7. D₆₇⋊C₁₁	ΓL(1,𝔽₈)	direct (N × H)
8. ΓL(1,𝔽₈)×C₆₇	C₂×C₁₁	semidirect
9. C₇×D₆₇	C₃×C₁₁	semidirect
10. C₆₇⋊C₁₁	C₂×ΓL(1,𝔽₈)	semidirect
11. C₇×C₆₇	C₂×C₃×C₁₁	semidirect
17. D₆₇	C₁₁×ΓL(1,𝔽₈)	semidirect
19. C₆₇	C₂×C₁₁×ΓL(1,𝔽₈)	semidirect
24. ΓL(1,𝔽₈)	D₆₇⋊C₁₁	direct (N × H)
27. C₇	C₃×D₆₇⋊C₁₁	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)×C₆₇⋊C₁₁	2
C₇×D₆₇⋊C₁₁	3
C₃×D₆₇⋊C₁₁	7
ΓL(1,𝔽₈)×D₆₇	11
C₂×C₁₁×ΓL(1,𝔽₈)	67

Subgroups — ΓL(1,𝔽8)×D67⋊C11 #44526281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₈)×D₆₇⋊C₁₁ #44526281