Finite Group Databasebeta

← C₁₁×D₇×C₁₉₃ #44446155

Subgroups — C₁₁×D₇×C₁₉₃ #44446155

Order 29722.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁×C₁₉₃	—	7	1	no	maximal, Hall
3	D₇×C₁₉₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₁₉₃	D₇	1	1	yes	characteristic, direct product factor, Hall
5	C₇×C₁₉₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₉₃	—	7	1	no	Hall
7	C₁₉₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₁₁×D₇	C₁₉₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁	C₂×C₁₉₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁	—	7	1	no	Hall
11	D₇	C₁₁×C₁₉₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁	D₇×C₁₉₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₂×C₁₁×C₁₉₃	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₁×C₁₉₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₉₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₁×C₁₉₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₁₉₃	C₂	semidirect
3. D₇×C₁₉₃	C₁₁	direct (N × H)
4. C₁₁×C₁₉₃	D₇	direct (N × H)
5. C₇×C₁₉₃	C₂×C₁₁	semidirect
7. C₁₉₃	C₁₁×D₇	direct (N × H)
8. C₁₁×D₇	C₁₉₃	direct (N × H)
9. C₇×C₁₁	C₂×C₁₉₃	semidirect
11. D₇	C₁₁×C₁₉₃	direct (N × H)
12. C₁₁	D₇×C₁₉₃	direct (N × H)
13. C₇	C₂×C₁₁×C₁₉₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₁₉₃	2
C₂×C₁₁×C₁₉₃	7
D₇×C₁₉₃	11
C₁₁×D₇	193