Finite Group Databasebeta

← C₁₁×C₁₃×D₆₇ #34062529

Subgroups — C₁₁×C₁₃×D₆₇ #34062529

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	C₁₃×D₆₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×D₆₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₆₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₁×C₁₃	—	67	1	no	maximal, Hall
7	C₁₁×C₁₃	D₆₇	1	1	yes	characteristic, direct product factor, Hall
8	D₆₇	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₆₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₃	—	67	1	no	Hall
11	C₂×C₁₁	—	67	1	no	Hall
12	C₁₃	C₁₁×D₆₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	C₁₃×D₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	D₆₇
commutator, cosocle, hypocenter	C₆₇	C₂×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₆₇	C₂
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×C₆₇	C₂	semidirect
2. C₁₃×D₆₇	C₁₁	direct (N × H)
3. C₁₁×D₆₇	C₁₃	direct (N × H)
4. C₁₃×C₆₇	C₂×C₁₁	semidirect
5. C₁₁×C₆₇	C₂×C₁₃	semidirect
7. C₁₁×C₁₃	D₆₇	direct (N × H)
8. D₆₇	C₁₁×C₁₃	direct (N × H)
9. C₆₇	C₂×C₁₁×C₁₃	semidirect
12. C₁₃	C₁₁×D₆₇	direct (N × H)
13. C₁₁	C₁₃×D₆₇	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
C₁₃×D₆₇	11
C₁₁×D₆₇	13
C₂×C₁₁×C₁₃	67