Finite Group Databasebeta

← C₂×D₃×C₂₆₄₇ #44540909

Subgroups — C₂×D₃×C₂₆₄₇ #44540909

Order 31764.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂₆₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₆₄₇	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₂₆₄₇	—	3	1	no	maximal, Hall
4	C₃×C₂₆₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₆₄₇	—	3	2	no	—
6	C₂×C₂₆₄₇	D₃	1	1	yes	characteristic, direct product factor
7	C₂₆₄₇	C₂×D₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×D₃	C₂₆₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃	C₂×C₂₆₄₇	1	1	yes	characteristic, complemented
10	D₃	C₂×C₂₆₄₇	1	2	yes	direct product factor
11	C₂²	—	3	1	no	Sylow
12	C₃	C₂²×C₂₆₄₇	1	1	yes	characteristic, complemented, Sylow
13	C₂	—	3	2	no	—
14	C₂	D₃×C₂₆₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₆₄₇	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₂₆₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₆₄₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₂₆₄₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₂₆₄₇	C₂	semidirect
2. D₃×C₂₆₄₇	C₂	direct (N × H)
4. C₃×C₂₆₄₇	C₂²	semidirect
6. C₂×C₂₆₄₇	D₃	direct (N × H)
7. C₂₆₄₇	C₂×D₃	direct (N × H)
8. C₂×D₃	C₂₆₄₇	direct (N × H)
9. C₂×C₃	C₂×C₂₆₄₇	semidirect
10. D₃	C₂×C₂₆₄₇	direct (N × H)
12. C₃	C₂²×C₂₆₄₇	semidirect
14. C₂	D₃×C₂₆₄₇	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×C₃×C₂₆₄₇	2
D₃×C₂₆₄₇	2
C₂²×C₂₆₄₇	3
C₂×D₃	2647