Finite Group Databasebeta

← C₃⁴×C₁₂₇⋊C₃ #44525155

Subgroups — C₃⁴×C₁₂₇⋊C₃ #44525155

Order 30861.

5328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₂₇⋊C₃	C₃	1	120	yes	maximal, direct product factor
2	C₃⁴×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₂₇⋊C₃	C₃²	1	1170	yes	direct product factor
4	C₃³×C₁₂₇	C₃²	1	40	yes	complemented
5	C₃²×C₁₂₇	C₃³	1	130	yes	complemented
6	C₃×C₁₂₇⋊C₃	C₃³	1	1080	yes	direct product factor
7	C₃×C₁₂₇	C₃⁴	1	40	yes	complemented
8	C₁₂₇⋊C₃	C₃⁴	1	81	yes	direct product factor
9	C₃⁵	—	127	1	no	maximal, Sylow
10	C₁₂₇	C₃⁵	1	1	yes	characteristic, complemented, Sylow
11	C₃⁴	—	127	120	no	—
12	C₃⁴	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
13	C₃³	—	127	1170	no	—
14	C₃³	C₃×C₁₂₇⋊C₃	1	40	yes	direct product factor
15	C₃²	—	127	1080	no	—
16	C₃²	C₃²×C₁₂₇⋊C₃	1	130	yes	direct product factor
17	C₃	—	127	81	no	—
18	C₃	C₃³×C₁₂₇⋊C₃	1	40	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃⁴	C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₁₂₇	C₃⁵
Frattini	C₁	G
Fitting, socle	C₃⁴×C₁₂₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃⁴

Complements

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

N	H ≅ G/N	type
1. C₃³×C₁₂₇⋊C₃	C₃	direct (N × H)
2. C₃⁴×C₁₂₇	C₃	semidirect
3. C₃²×C₁₂₇⋊C₃	C₃²	direct (N × H)
4. C₃³×C₁₂₇	C₃²	semidirect
5. C₃²×C₁₂₇	C₃³	semidirect
6. C₃×C₁₂₇⋊C₃	C₃³	direct (N × H)
7. C₃×C₁₂₇	C₃⁴	semidirect
8. C₁₂₇⋊C₃	C₃⁴	direct (N × H)
10. C₁₂₇	C₃⁵	semidirect
12. C₃⁴	C₁₂₇⋊C₃	direct (N × H)
14. C₃³	C₃×C₁₂₇⋊C₃	direct (N × H)
16. C₃²	C₃²×C₁₂₇⋊C₃	direct (N × H)
18. C₃	C₃³×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
C₃³×C₁₂₇⋊C₃	3
C₃⁴×C₁₂₇	3
C₃⁵	127