Finite Group Databasebeta

← C₃×D₃₂₈₇ #34089359

Subgroups — C₃×D₃₂₈₇ #34089359

Order 19722.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₇₃	—	19	1	no	maximal, Hall
5	C₃×C₁₇₃	D₁₉	1	1	yes	characteristic, complemented, Hall
6	D₁₇₃	—	19	1	no	Hall
7	C₁₇₃	C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
8	C₃×D₁₉	—	173	1	no	maximal, Hall
9	C₃×C₁₉	D₁₇₃	1	1	yes	characteristic, complemented, Hall
10	D₁₉	—	173	1	no	Hall
11	C₁₉	C₃×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	—	3287	1	no	Hall
13	C₃	D₃₂₈₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	3287	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₂₈₇
commutator, cosocle, hypocenter	C₁₉×C₁₇₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₇₃	C₂
LCS	G ▷ C₁₉×C₁₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₁₇₃	C₂	semidirect
2. D₃₂₈₇	C₃	direct (N × H)
3. C₁₉×C₁₇₃	C₂×C₃	semidirect
5. C₃×C₁₇₃	D₁₉	semidirect
7. C₁₇₃	C₃×D₁₉	semidirect
9. C₃×C₁₉	D₁₇₃	semidirect
11. C₁₉	C₃×D₁₇₃	semidirect
13. C₃	D₃₂₈₇	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×C₁₉×C₁₇₃	2
D₃₂₈₇	3
C₃×D₁₇₃	19
C₃×D₁₉	173