Subgroups — C₃×#23779860 #44525148

Order 30861.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779860	C₃	1	27	yes	maximal, direct product factor
2	C₃×#16812184	C₃	1	2	yes	maximal, complemented
3	C₃×#16812183	C₃	1	3	yes	maximal, complemented
4	C₃×#16812182	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₁₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₂₇⋊C₃	C₃²	1	3	yes	—
9	#16812184	C₃²	1	18	yes	complemented
10	#16812183	C₃²	1	27	yes	complemented
11	#16812182	C₃²	1	27	yes	complemented
12	C₃²⋊(C₁₂₇⋊C₃)	C₃²	1	9	yes	—
13	C₃×#11765917	C₃²	1	6	yes	—
14	C₉×C₁₂₇⋊C₃	C₃²	1	27	yes	complemented
15	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₁₂₇	C₃²	1	9	yes	complemented
20	C₃²×C₁₂₇	—	3	3	no	—
21	C₃²×C₁₂₇	C₃³	1	3	yes	—
22	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
23	C₃×C₁₂₇⋊C₃	—	3	9	no	—
24	C₃×C₁₂₇⋊C₃	C₃³	1	9	yes	—
25	C₉×C₁₂₇	C₃³	1	3	yes	—
26	C₉×C₁₂₇	C₃³	1	3	yes	—
27	C₉×C₁₂₇	C₃³	1	3	yes	—
28	#11765917	C₃³	1	18	yes	—
29	C₃×C₁₂₇	—	3	3	no	—
30	C₃×C₁₂₇	#737	1	3	yes	complemented
31	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
32	C₁₂₇⋊C₃	—	3	9	no	—
33	C₃×#737	—	127	1	no	maximal, Sylow
34	C₁₂₇	C₃×#737	1	1	yes	characteristic, complemented, Sylow
35	#737	—	127	27	no	—
36	C₃×3₋¹⁺²	—	127	2	no	—
37	C₃×3₋¹⁺²	—	127	3	no	—
38	C₃×3₋¹⁺²	—	127	3	no	—
39	C₃×H(3,𝔽₃)	—	127	1	no	—
40	C₃²×C₉	—	127	3	no	—
41	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
42	C₃³	—	127	3	no	—
43	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	127	18	no	—
45	3₋¹⁺²	—	127	27	no	—
46	3₋¹⁺²	—	127	27	no	—
47	H(3,𝔽₃)	—	127	9	no	—
48	C₃×C₉	—	127	6	no	—
49	C₃×C₉	—	127	27	no	—
50	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₁₂₇⋊C₃	1	9	yes	complemented
54	C₃²	—	3	3	no	—
55	C₃²	—	381	9	no	—
56	C₃²	—	127	9	no	—
57	C₃²	C₃²×C₁₂₇⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
59	C₉	—	127	18	no	—
60	C₉	C₃²×C₁₂₇⋊C₃	1	3	yes	—
61	C₉	C₃²×C₁₂₇⋊C₃	1	3	yes	—
62	C₉	C₃²×C₁₂₇⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	381	9	no	—
65	C₃	#23779860	1	3	yes	direct product factor
66	C₃	C₃³×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₁₂₇⋊C₃
commutator, cosocle	C₃×C₁₂₇	C₃⁴
Frattini	C₃	C₃³×C₁₂₇⋊C₃
Fitting	C₃²×C₉×C₁₂₇	C₃
socle	C₃²×C₁₂₇	C₃³
prime radical	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃
hypercenter	C₃²×C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#737
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #23779860	C₃	direct (N × H)
2. C₃×#16812184	C₃	semidirect
3. C₃×#16812183	C₃	semidirect
4. C₃×#16812182	C₃	semidirect
6. C₃×C₉×C₁₂₇⋊C₃	C₃	semidirect
7. C₃²×C₉×C₁₂₇	C₃	semidirect
9. #16812184	C₃²	semidirect
10. #16812183	C₃²	semidirect
11. #16812182	C₃²	semidirect
14. C₉×C₁₂₇⋊C₃	C₃²	semidirect
19. C₃×C₉×C₁₂₇	C₃²	semidirect
30. C₃×C₁₂₇	#737	semidirect
34. C₁₂₇	C₃×#737	semidirect
41. C₃²×C₉	C₁₂₇⋊C₃	semidirect
53. C₃×C₉	C₃×C₁₂₇⋊C₃	semidirect
65. C₃	#23779860	direct (N × H)

Maximal subgroups

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

subgroup	index
#23779860	3
C₃×#16812184	3
C₃×#16812183	3
C₃×#16812182	3
C₃×C₃²⋊(C₁₂₇⋊C₃)	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃²×C₉×C₁₂₇	3
C₃×#737	127

Subgroups — C3×#23779860 #44525148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779860 #44525148