Finite Group Databasebeta

← C₂×C₁₃×C₆₇⋊C₁₁ #34062528

Subgroups — C₂×C₁₃×C₆₇⋊C₁₁ #34062528

Order 19162.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₆₇⋊C₁₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃×C₆₇	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₆₇⋊C₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
5	C₆₇⋊C₁₁	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₁×C₁₃	—	67	1	no	maximal, Hall
7	C₁₁×C₁₃	—	67	1	no	Hall
8	C₂×C₆₇	C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
9	C₆₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₁₃	C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁	—	67	1	no	Hall
12	C₁₃	C₂×C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₁	—	67	1	no	Sylow
14	C₂	C₁₃×C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₆₇⋊C₁₁	C₂	direct (N × H)
2. C₂×C₁₃×C₆₇	C₁₁	semidirect
3. C₂×C₆₇⋊C₁₁	C₁₃	direct (N × H)
4. C₁₃×C₆₇	C₂×C₁₁	semidirect
5. C₆₇⋊C₁₁	C₂×C₁₃	direct (N × H)
8. C₂×C₆₇	C₁₁×C₁₃	semidirect
9. C₆₇	C₂×C₁₁×C₁₃	semidirect
10. C₂×C₁₃	C₆₇⋊C₁₁	direct (N × H)
12. C₁₃	C₂×C₆₇⋊C₁₁	direct (N × H)
14. C₂	C₁₃×C₆₇⋊C₁₁	direct (N × H)

Maximal subgroups

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

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