Finite Group Databasebeta

← D₃×C₇×C₆₄₁ #41002178

Subgroups — D₃×C₇×C₆₄₁ #41002178

Order 26922.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₆₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₇×C₆₄₁	—	3	1	no	maximal, Hall
3	C₇×C₆₄₁	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₆₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₆₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₆₄₁	—	3	1	no	Hall
7	C₆₄₁	D₃×C₇	1	1	yes	characteristic, direct product factor, Sylow
8	D₃×C₇	C₆₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇	C₂×C₆₄₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇	—	3	1	no	Hall
11	C₇	D₃×C₆₄₁	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₇×C₆₄₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₇×C₆₄₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₆₄₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₇×C₆₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₆₄₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₇×C₆₄₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₆₄₁	C₂	semidirect
3. C₇×C₆₄₁	D₃	direct (N × H)
4. D₃×C₆₄₁	C₇	direct (N × H)
5. C₃×C₆₄₁	C₂×C₇	semidirect
7. C₆₄₁	D₃×C₇	direct (N × H)
8. D₃×C₇	C₆₄₁	direct (N × H)
9. C₃×C₇	C₂×C₆₄₁	semidirect
11. C₇	D₃×C₆₄₁	direct (N × H)
12. D₃	C₇×C₆₄₁	direct (N × H)
13. C₃	C₂×C₇×C₆₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₇×C₆₄₁	2
C₂×C₇×C₆₄₁	3
D₃×C₆₄₁	7
D₃×C₇	641