Finite Group Databasebeta

← C₂×D₁₄₂₁₃ #72291981

Subgroups — C₂×D₁₄₂₁₃ #72291981

Order 56852.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₄₂₁₃	C₂	1	2	yes	maximal, direct product factor
3	C₆₁×C₂₃₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₂₃₃	—	61	1	no	maximal, Hall
5	C₂×C₂₃₃	D₆₁	1	1	yes	characteristic, complemented
6	D₂₃₃	—	61	2	no	—
7	C₂×D₆₁	—	233	1	no	maximal, Hall
8	C₂₃₃	C₂×D₆₁	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₆₁	D₂₃₃	1	1	yes	characteristic, complemented
10	D₆₁	—	233	2	no	—
11	C₆₁	C₂×D₂₃₃	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	14213	1	no	Sylow
13	C₂	—	14213	2	no	—
14	C₂	D₁₄₂₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₄₂₁₃
commutator, cosocle, hypocenter	C₆₁×C₂₃₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₆₁×C₂₃₃	C₂
LCS	G ▷ C₆₁×C₂₃₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×C₂₃₃	C₂	semidirect
2. D₁₄₂₁₃	C₂	direct (N × H)
3. C₆₁×C₂₃₃	C₂²	semidirect
5. C₂×C₂₃₃	D₆₁	semidirect
8. C₂₃₃	C₂×D₆₁	semidirect
9. C₂×C₆₁	D₂₃₃	semidirect
11. C₆₁	C₂×D₂₃₃	semidirect
14. C₂	D₁₄₂₁₃	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×C₆₁×C₂₃₃	2
D₁₄₂₁₃	2
C₂×D₂₃₃	61
C₂×D₆₁	233