Finite Group Databasebeta

← C₃×C₆₇×D₅₉ #37557430

Subgroups — C₃×C₆₇×D₅₉ #37557430

Order 23718.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₉×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₇×D₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅₉×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₆₇	—	59	1	no	maximal, Hall
5	C₃×D₅₉	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₆₇	D₅₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅₉	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₆₇	—	59	1	no	Hall
9	D₅₉	C₃×C₆₇	1	1	yes	characteristic, direct product factor, Hall
10	C₆₇	C₃×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₅₉	C₂×C₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	59	1	no	Hall
13	C₃	C₆₇×D₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	59	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₆₇	D₅₉
commutator, cosocle, hypocenter	C₅₉	C₂×C₃×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₅₉×C₆₇	C₂
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₃×C₆₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₉×C₆₇	C₂	semidirect
2. C₆₇×D₅₉	C₃	direct (N × H)
3. C₅₉×C₆₇	C₂×C₃	semidirect
5. C₃×D₅₉	C₆₇	direct (N × H)
6. C₃×C₆₇	D₅₉	direct (N × H)
7. C₃×C₅₉	C₂×C₆₇	semidirect
9. D₅₉	C₃×C₆₇	direct (N × H)
10. C₆₇	C₃×D₅₉	direct (N × H)
11. C₅₉	C₂×C₃×C₆₇	semidirect
13. C₃	C₆₇×D₅₉	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×C₅₉×C₆₇	2
C₆₇×D₅₉	3
C₂×C₃×C₆₇	59
C₃×D₅₉	67