Finite Group Databasebeta

← D₃×C₂₉×C₁₇₉ #44528239

Subgroups — D₃×C₂₉×C₁₇₉ #44528239

Order 31146.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₂₉×C₁₇₉	—	3	1	no	maximal, Hall
3	C₂₉×C₁₇₉	D₃	1	1	yes	characteristic, direct product factor, Hall
4	D₃×C₁₇₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇₉	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₇₉	—	3	1	no	Hall
7	C₁₇₉	D₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
8	D₃×C₂₉	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₂₉	C₂×C₁₇₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₉	—	3	1	no	Hall
11	C₂₉	D₃×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
12	D₃	C₂₉×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
13	C₃	C₂×C₂₉×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉×C₁₇₉	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₂₉×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₇₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂₉×C₁₇₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×C₁₇₉	C₂	semidirect
3. C₂₉×C₁₇₉	D₃	direct (N × H)
4. D₃×C₁₇₉	C₂₉	direct (N × H)
5. C₃×C₁₇₉	C₂×C₂₉	semidirect
7. C₁₇₉	D₃×C₂₉	direct (N × H)
8. D₃×C₂₉	C₁₇₉	direct (N × H)
9. C₃×C₂₉	C₂×C₁₇₉	semidirect
11. C₂₉	D₃×C₁₇₉	direct (N × H)
12. D₃	C₂₉×C₁₇₉	direct (N × H)
13. C₃	C₂×C₂₉×C₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₉×C₁₇₉	2
C₂×C₂₉×C₁₇₉	3
D₃×C₁₇₉	29
D₃×C₂₉	179