Subgroups — C₃×(C₁₂₇⋊C₃)⋊C₂₇ #44525200

Order 30861.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₂₇⋊C₃)⋊C₂₇	C₃	1	9	yes	maximal, direct product factor
2	C₃×#16812186	C₃	1	3	yes	maximal, complemented
3	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#16812186	C₃²	1	9	yes	complemented
5	C₃²×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
6	C₃×#11765917	C₉	1	1	yes	characteristic
7	C₃×#11765917	C₃²	1	1	yes	characteristic
8	C₉×C₁₂₇⋊C₃	C₉	1	6	yes	—
9	C₉×C₁₂₇⋊C₃	C₃²	1	3	yes	—
10	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic
11	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
12	C₃×C₁₂₇⋊C₃	C₂₇	1	9	yes	complemented
13	C₃×C₁₂₇⋊C₃	C₃×C₉	1	3	yes	—
14	C₉×C₁₂₇	C₃×C₉	1	3	yes	—
15	#11765917	C₃×C₉	1	2	yes	—
16	#11765917	C₃×C₉	1	3	yes	—
17	#11765917	C₃³	1	1	yes	characteristic
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	complemented
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	3	no	—
25	C₃×C₂₇	—	127	9	no	—
26	C₃³	—	127	1	no	—
27	C₃×C₉	—	127	1	no	—
28	C₃×C₉	—	127	1	no	—
29	C₃×C₉	—	127	6	no	—
30	C₃×C₉	—	127	3	no	—
31	C₃×C₉	#11765919	1	1	yes	characteristic
32	C₂₇	—	127	9	no	—
33	C₃²	—	127	9	no	—
34	C₃²	—	127	3	no	—
35	C₃²	C₃×#11765919	1	1	yes	characteristic
36	C₉	—	127	1	no	—
37	C₉	—	127	3	no	—
38	C₉	—	127	2	no	—
39	C₉	C₃×#11765919	1	3	yes	—
40	C₃	—	127	9	no	—
41	C₃	(C₁₂₇⋊C₃)⋊C₂₇	1	3	yes	direct product factor
42	C₃	C₃²×#11765919	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₉	#11765919
commutator, hypocenter	C₁₂₇	C₃²×C₂₇
Frattini	C₃	C₃²×#11765919
Fitting	C₃×C₉×C₁₂₇	C₉
socle	C₃²×C₁₂₇	C₃×C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₉
cosocle	#11765917	C₃³
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
1. (C₁₂₇⋊C₃)⋊C₂₇	C₃	direct (N × H)
2. C₃×#16812186	C₃	semidirect
4. #16812186	C₃²	semidirect
12. C₃×C₁₂₇⋊C₃	C₂₇	semidirect
18. C₃×C₁₂₇	C₃×C₂₇	semidirect
20. C₁₂₇⋊C₃	C₃×C₂₇	semidirect
22. C₁₂₇	C₃²×C₂₇	semidirect
41. C₃	(C₁₂₇⋊C₃)⋊C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
(C₁₂₇⋊C₃)⋊C₂₇	3
C₃×#16812186	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃²×C₂₇	127

Subgroups — C3×(C127⋊C3)⋊C27 #44525200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₁₂₇⋊C₃)⋊C₂₇ #44525200