Finite Group Databasebeta

← C₂×D₄₁×C₁₉₁ #44531208

Subgroups — C₂×D₄₁×C₁₉₁ #44531208

Order 31324.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₁×C₁₉₁	C₂	1	2	yes	maximal, direct product factor
3	C₄₁×C₁₉₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂²×C₁₉₁	—	41	1	no	maximal, Hall
5	C₂×C₁₉₁	—	41	2	no	—
6	C₂×C₁₉₁	D₄₁	1	1	yes	characteristic, direct product factor
7	C₁₉₁	C₂×D₄₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×D₄₁	C₁₉₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₄₁	C₂×C₁₉₁	1	1	yes	characteristic, complemented
10	D₄₁	C₂×C₁₉₁	1	2	yes	direct product factor
11	C₄₁	C₂²×C₁₉₁	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	41	1	no	Sylow
13	C₂	—	41	2	no	—
14	C₂	D₄₁×C₁₉₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₉₁	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂²×C₁₉₁
Frattini	C₁	G
Fitting, socle	C₂×C₄₁×C₁₉₁	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₁₉₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×C₁₉₁	C₂	semidirect
2. D₄₁×C₁₉₁	C₂	direct (N × H)
3. C₄₁×C₁₉₁	C₂²	semidirect
6. C₂×C₁₉₁	D₄₁	direct (N × H)
7. C₁₉₁	C₂×D₄₁	direct (N × H)
8. C₂×D₄₁	C₁₉₁	direct (N × H)
9. C₂×C₄₁	C₂×C₁₉₁	semidirect
10. D₄₁	C₂×C₁₉₁	direct (N × H)
11. C₄₁	C₂²×C₁₉₁	semidirect
14. C₂	D₄₁×C₁₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×C₁₉₁	2
D₄₁×C₁₉₁	2
C₂²×C₁₉₁	41
C₂×D₄₁	191