Subgroups — C₃×C₂₇×C₁₂₇⋊C₃ #44525080

Order 30861.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₃×#16812178	C₃	1	2	yes	maximal, complemented
3	C₂₇×C₁₂₇⋊C₃	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₂₇×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
6	C₃×#11765917	C₉	1	2	yes	—
7	C₉×C₁₂₇⋊C₃	C₉	1	6	yes	—
8	C₉×C₁₂₇⋊C₃	C₃²	1	3	yes	—
9	#16812178	C₃²	1	6	yes	complemented
10	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
11	C₂₇×C₁₂₇	C₃²	1	3	yes	complemented
12	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
13	C₃×C₁₂₇⋊C₃	C₂₇	1	9	yes	direct product factor
14	C₃×C₁₂₇⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₁₂₇	C₃×C₉	1	2	yes	—
16	C₉×C₁₂₇	C₃³	1	1	yes	characteristic
17	#11765917	C₃×C₉	1	6	yes	—
18	C₃×C₁₂₇	C₃×C₂₇	1	3	yes	complemented
19	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
20	C₁₂₇⋊C₃	C₃×C₂₇	1	9	yes	direct product factor
21	C₃²×C₂₇	—	127	1	no	maximal, Sylow
22	C₁₂₇	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
23	C₃²×C₉	—	127	1	no	—
24	C₃×C₂₇	—	127	2	no	—
25	C₃×C₂₇	—	127	9	no	—
26	C₃×C₂₇	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃³	—	127	1	no	—
28	C₃×C₉	—	127	2	no	—
29	C₃×C₉	—	127	6	no	—
30	C₃×C₉	—	127	3	no	—
31	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
32	C₂₇	—	127	6	no	—
33	C₂₇	C₃×C₁₂₇⋊C₃	1	3	yes	direct product factor
34	C₃²	—	127	3	no	—
35	C₃²	—	127	9	no	—
36	C₃²	C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
37	C₉	—	127	6	no	—
38	C₉	C₉×C₁₂₇⋊C₃	1	2	yes	—
39	C₉	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
40	C₃	—	127	9	no	—
41	C₃	C₂₇×C₁₂₇⋊C₃	1	3	yes	direct product factor
42	C₃	C₃×C₉×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₂₇	C₁₂₇⋊C₃
commutator, hypocenter	C₁₂₇	C₃²×C₂₇
Frattini	C₉	C₃²×C₁₂₇⋊C₃
Fitting	C₃×C₂₇×C₁₂₇	C₃
socle	C₃²×C₁₂₇	C₃×C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₉
cosocle	C₉×C₁₂₇	C₃³
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
2. C₃×#16812178	C₃	semidirect
3. C₂₇×C₁₂₇⋊C₃	C₃	direct (N × H)
4. C₃×C₂₇×C₁₂₇	C₃	semidirect
9. #16812178	C₃²	semidirect
11. C₂₇×C₁₂₇	C₃²	semidirect
13. C₃×C₁₂₇⋊C₃	C₂₇	direct (N × H)
18. C₃×C₁₂₇	C₃×C₂₇	semidirect
20. C₁₂₇⋊C₃	C₃×C₂₇	direct (N × H)
22. C₁₂₇	C₃²×C₂₇	semidirect
26. C₃×C₂₇	C₁₂₇⋊C₃	direct (N × H)
33. C₂₇	C₃×C₁₂₇⋊C₃	direct (N × H)
41. C₃	C₂₇×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×C₉×C₁₂₇⋊C₃	3
C₃×#16812178	3
C₂₇×C₁₂₇⋊C₃	3
C₃×C₂₇×C₁₂₇	3
C₃²×C₂₇	127

Subgroups — C3×C27×C127⋊C3 #44525080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₇×C₁₂₇⋊C₃ #44525080