Finite Group Databasebeta

← C₃×D₇×C₆₄₃ #41008870

Subgroups — C₃×D₇×C₆₄₃ #41008870

Order 27006.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₆₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₆₄₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₆₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₆₄₃	—	7	1	no	maximal, Hall
5	C₃×C₆₄₃	D₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₆₄₃	—	7	1	no	Hall
7	C₆₄₃	C₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₃×D₇	C₆₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₆₄₃	1	1	yes	characteristic, complemented, Hall
10	D₇	C₃×C₆₄₃	1	1	yes	characteristic, direct product factor, Hall
11	C₇	C₂×C₃×C₆₄₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	7	1	no	Hall
13	C₃	D₇×C₆₄₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₆₄₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₆₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₆₄₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₆₄₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₆₄₃	C₂	semidirect
2. D₇×C₆₄₃	C₃	direct (N × H)
3. C₇×C₆₄₃	C₂×C₃	semidirect
5. C₃×C₆₄₃	D₇	direct (N × H)
7. C₆₄₃	C₃×D₇	direct (N × H)
8. C₃×D₇	C₆₄₃	direct (N × H)
9. C₃×C₇	C₂×C₆₄₃	semidirect
10. D₇	C₃×C₆₄₃	direct (N × H)
11. C₇	C₂×C₃×C₆₄₃	semidirect
13. C₃	D₇×C₆₄₃	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×C₇×C₆₄₃	2
D₇×C₆₄₃	3
C₂×C₃×C₆₄₃	7
C₃×D₇	643