Finite Group Databasebeta

← C₃×C₃₁×D₁₉₁ #48001007

Subgroups — C₃×C₃₁×D₁₉₁ #48001007

Order 35526.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₁₉₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃₁×C₁₉₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₉₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₉₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
6	D₁₉₁	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
7	C₁₉₁	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₃₁	—	191	1	no	maximal, Hall
9	C₃×C₃₁	D₁₉₁	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃₁	—	191	1	no	Hall
11	C₃₁	C₃×D₁₉₁	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	191	1	no	Hall
13	C₃	C₃₁×D₁₉₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	191	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₉₁
commutator, cosocle, hypocenter	C₁₉₁	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₁₉₁	C₂
LCS	G ▷ C₁₉₁
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₁×C₁₉₁	C₂	semidirect
2. C₃₁×D₁₉₁	C₃	direct (N × H)
3. C₃₁×C₁₉₁	C₂×C₃	semidirect
4. C₃×D₁₉₁	C₃₁	direct (N × H)
5. C₃×C₁₉₁	C₂×C₃₁	semidirect
6. D₁₉₁	C₃×C₃₁	direct (N × H)
7. C₁₉₁	C₂×C₃×C₃₁	semidirect
9. C₃×C₃₁	D₁₉₁	direct (N × H)
11. C₃₁	C₃×D₁₉₁	direct (N × H)
13. C₃	C₃₁×D₁₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₁×C₁₉₁	2
C₃₁×D₁₉₁	3
C₃×D₁₉₁	31
C₂×C₃×C₃₁	191