Subgroups — C₁₁×#14584196 #44526255

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#13064104	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₁×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁×D₆₇⋊C₃	—	7	1	no	maximal, Hall
5	#14584196	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₆₇⋊C₃	—	7	1	no	Hall
7	C₁₁×D₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	#13064104	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	C₇×D₆₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₆₇	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	D₆₇⋊C₃	—	7	1	no	Hall
14	C₁₁×ΓL(1,𝔽₈)	—	67	1	no	Hall
15	C₆₇⋊C₃	—	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	D₆₇⋊C₃	1	1	yes	characteristic, complemented, 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)	—	67	1	no	Hall
25	C₂×C₇	—	67	1	no	Hall
26	C₁₁	#14584196	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₁₁×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	469	1	no	Hall
29	C₃	—	469	1	no	Sylow
30	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	#14584196
commutator, cosocle, hypocenter	C₇×C₆₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#13064104	C₂	semidirect
2. C₇×C₁₁×D₆₇	C₃	semidirect
3. C₇×C₁₁×C₆₇	C₂×C₃	semidirect
5. #14584196	C₁₁	direct (N × H)
7. C₁₁×D₆₇	ΓL(1,𝔽₈)	semidirect
8. #13064104	C₂×C₁₁	semidirect
9. C₇×D₆₇	C₃×C₁₁	semidirect
10. C₁₁×C₆₇	C₂×ΓL(1,𝔽₈)	semidirect
11. C₇×C₆₇	C₂×C₃×C₁₁	semidirect
17. D₆₇	C₁₁×ΓL(1,𝔽₈)	semidirect
18. C₇×C₁₁	D₆₇⋊C₃	semidirect
19. C₆₇	C₂×C₁₁×ΓL(1,𝔽₈)	semidirect
26. C₁₁	#14584196	direct (N × H)
27. C₇	C₁₁×D₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#13064104	2
C₇×C₁₁×D₆₇	3
C₁₁×D₆₇⋊C₃	7
#14584196	11
C₂×C₁₁×ΓL(1,𝔽₈)	67

Subgroups — C11×#14584196 #44526255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#14584196 #44526255