Subgroups — C₃×3₋¹⁺²×C₁₂₇⋊C₃ #44525142

Order 30861.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃²	C₃²×C₁₂₇⋊C₃
commutator, cosocle	C₃×C₁₂₇	C₃⁴
Frattini	C₃	C₃³×C₁₂₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃²×C₁₂₇	C₃³
prime radical	C₃³×C₁₂₇⋊C₃	C₃
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃²×3₋¹⁺²
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. C₃×#16812184	C₃	semidirect
3. C₃×#16812183	C₃	semidirect
4. C₃×#16812182	C₃	semidirect
5. 3₋¹⁺²×C₁₂₇⋊C₃	C₃	direct (N × H)
6. C₃×C₉×C₁₂₇⋊C₃	C₃	semidirect
7. C₃×3₋¹⁺²×C₁₂₇	C₃	semidirect
13. #16812184	C₃²	semidirect
14. #16812183	C₃²	semidirect
15. #16812182	C₃²	semidirect
16. C₃×#11765917	C₃²	semidirect
17. C₉×C₁₂₇⋊C₃	C₃²	semidirect
19. 3₋¹⁺²×C₁₂₇	C₃²	semidirect
20. C₃×C₉×C₁₂₇	C₃²	semidirect
27. C₃×C₁₂₇⋊C₃	3₋¹⁺²	direct (N × H)
31. C₉×C₁₂₇	C₃³	semidirect
32. #11765917	C₃³	semidirect
34. C₃×C₁₂₇	C₃×3₋¹⁺²	semidirect
38. C₁₂₇⋊C₃	C₃×3₋¹⁺²	direct (N × H)
40. C₁₂₇	C₃²×3₋¹⁺²	semidirect
46. C₃×3₋¹⁺²	C₁₂₇⋊C₃	direct (N × H)
57. 3₋¹⁺²	C₃×C₁₂₇⋊C₃	direct (N × H)
60. C₃×C₉	C₃×C₁₂₇⋊C₃	semidirect
72. C₉	C₃²×C₁₂₇⋊C₃	semidirect
77. C₃	3₋¹⁺²×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
C₃×#16812184	3
C₃×#16812183	3
C₃×#16812182	3
3₋¹⁺²×C₁₂₇⋊C₃	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃×3₋¹⁺²×C₁₂₇	3
C₃²×3₋¹⁺²	127

Subgroups — C3×3−1+2×C127⋊C3 #44525142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×3₋¹⁺²×C₁₂₇⋊C₃ #44525142