Finite Group Databasebeta

← C₂×D₈₀₈₃ #44568277

Subgroups — C₂×D₈₀₈₃ #44568277

Order 32332.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₀₈₃	C₂	1	2	yes	maximal, direct product factor
3	C₅₉×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃₇	—	59	1	no	maximal, Hall
5	C₂×C₁₃₇	D₅₉	1	1	yes	characteristic, complemented
6	D₁₃₇	—	59	2	no	—
7	C₂×D₅₉	—	137	1	no	maximal, Hall
8	C₁₃₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₅₉	D₁₃₇	1	1	yes	characteristic, complemented
10	D₅₉	—	137	2	no	—
11	C₅₉	C₂×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	8083	1	no	Sylow
13	C₂	—	8083	2	no	—
14	C₂	D₈₀₈₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₀₈₃
commutator, cosocle, hypocenter	C₅₉×C₁₃₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅₉×C₁₃₇	C₂
LCS	G ▷ C₅₉×C₁₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×C₁₃₇	C₂	semidirect
2. D₈₀₈₃	C₂	direct (N × H)
3. C₅₉×C₁₃₇	C₂²	semidirect
5. C₂×C₁₃₇	D₅₉	semidirect
8. C₁₃₇	C₂×D₅₉	semidirect
9. C₂×C₅₉	D₁₃₇	semidirect
11. C₅₉	C₂×D₁₃₇	semidirect
14. C₂	D₈₀₈₃	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×C₅₉×C₁₃₇	2
D₈₀₈₃	2
C₂×D₁₃₇	59
C₂×D₅₉	137