Finite Group Databasebeta

← C₃×C₂₉×C₁₂₇⋊C₃ #45684113

Subgroups — C₃×C₂₉×C₁₂₇⋊C₃ #45684113

Order 33147.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂₉×C₁₂₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₂₉×C₁₂₇	C₃²	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₂₇⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₂₇	C₃×C₂₉	1	1	yes	characteristic, complemented
6	C₁₂₇⋊C₃	C₃×C₂₉	1	3	yes	direct product factor
7	C₃²×C₂₉	—	127	1	no	maximal, Hall
8	C₁₂₇	C₃²×C₂₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₂₉	—	127	3	no	—
10	C₃×C₂₉	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
11	C₂₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃²	—	127	1	no	Sylow
13	C₃	—	127	3	no	—
14	C₃	C₂₉×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₂₉	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×C₁₂₇	C₃	semidirect
2. C₂₉×C₁₂₇⋊C₃	C₃	direct (N × H)
3. C₂₉×C₁₂₇	C₃²	semidirect
4. C₃×C₁₂₇⋊C₃	C₂₉	direct (N × H)
5. C₃×C₁₂₇	C₃×C₂₉	semidirect
6. C₁₂₇⋊C₃	C₃×C₂₉	direct (N × H)
8. C₁₂₇	C₃²×C₂₉	semidirect
10. C₃×C₂₉	C₁₂₇⋊C₃	direct (N × H)
11. C₂₉	C₃×C₁₂₇⋊C₃	direct (N × H)
14. C₃	C₂₉×C₁₂₇⋊C₃	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×C₂₉×C₁₂₇	3
C₂₉×C₁₂₇⋊C₃	3
C₃×C₁₂₇⋊C₃	29
C₃²×C₂₉	127