Finite Group Databasebeta

← D₃×C₆₇×C₇₉ #44540870

Subgroups — D₃×C₆₇×C₇₉ #44540870

Order 31758.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₆₇×C₇₉	—	3	1	no	maximal, Hall
3	C₆₇×C₇₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₇₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₃×C₆₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇₉	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
7	C₃×C₆₇	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇₉	—	3	1	no	Hall
9	C₂×C₆₇	—	3	1	no	Hall
10	C₇₉	D₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
11	C₆₇	D₃×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₆₇×C₇₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₆₇×C₇₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₆₇×C₇₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₆₇×C₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₆₇×C₇₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₆₇×C₇₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₆₇×C₇₉	C₂	semidirect
3. C₆₇×C₇₉	D₃	direct (N × H)
4. D₃×C₇₉	C₆₇	direct (N × H)
5. D₃×C₆₇	C₇₉	direct (N × H)
6. C₃×C₇₉	C₂×C₆₇	semidirect
7. C₃×C₆₇	C₂×C₇₉	semidirect
10. C₇₉	D₃×C₆₇	direct (N × H)
11. C₆₇	D₃×C₇₉	direct (N × H)
12. D₃	C₆₇×C₇₉	direct (N × H)
13. C₃	C₂×C₆₇×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₆₇×C₇₉	2
C₂×C₆₇×C₇₉	3
D₃×C₇₉	67
D₃×C₆₇	79