Finite Group Databasebeta

← C₁₁×D₁₃×C₆₇ #34062530

Subgroups — C₁₁×D₁₃×C₆₇ #34062530

Order 19162.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₁×C₆₇	—	13	1	no	maximal, Hall
4	C₁₃×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₆₇	D₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₁₁×D₁₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₁₃	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₆₇	—	13	1	no	Hall
9	C₆₇	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
10	D₁₃	C₁₁×C₆₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁	—	13	1	no	Hall
12	C₁₃	C₂×C₁₁×C₆₇	1	1	yes	characteristic, complemented, Sylow
13	C₁₁	D₁₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₆₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₁×C₆₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₆₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₁×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₆₇	C₂	semidirect
2. D₁₃×C₆₇	C₁₁	direct (N × H)
4. C₁₃×C₆₇	C₂×C₁₁	semidirect
5. C₁₁×C₆₇	D₁₃	direct (N × H)
6. C₁₁×D₁₃	C₆₇	direct (N × H)
7. C₁₁×C₁₃	C₂×C₆₇	semidirect
9. C₆₇	C₁₁×D₁₃	direct (N × H)
10. D₁₃	C₁₁×C₆₇	direct (N × H)
12. C₁₃	C₂×C₁₁×C₆₇	semidirect
13. C₁₁	D₁₃×C₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×C₆₇	2
D₁₃×C₆₇	11
C₂×C₁₁×C₆₇	13
C₁₁×D₁₃	67