Subgroups — C₃×#23779861 #44525149

Order 30861.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779861	C₃	1	27	yes	maximal, direct product factor
2	C₃×#16812184	C₃	1	1	yes	maximal, characteristic, 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	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₁₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
8	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃²×C₁₂₇⋊C₃	C₃²	1	3	yes	—
10	#16812184	C₃²	1	9	yes	complemented
11	#16812183	C₃²	1	27	yes	complemented
12	#16812182	C₃²	1	27	yes	complemented
13	C₃²⋊(C₁₂₇⋊C₃)	C₃²	1	9	yes	—
14	C₃×#11765917	C₃²	1	1	yes	characteristic
15	C₃×#11765917	C₃²	1	3	yes	—
16	C₃×#11765917	C₃²	1	1	yes	characteristic
17	C₃×#11765917	C₃²	1	1	yes	characteristic
18	C₃×#11765917	C₃²	1	9	yes	complemented
19	C₉×C₁₂₇⋊C₃	C₃²	1	27	yes	complemented
20	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
21	3₋¹⁺²×C₁₂₇	C₃²	1	9	yes	complemented
22	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
23	C₃²×C₁₂₇	—	3	3	no	—
24	C₃²×C₁₂₇	C₃³	1	3	yes	—
25	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
26	C₃×C₁₂₇⋊C₃	—	3	9	no	—
27	C₃×C₁₂₇⋊C₃	C₃³	1	9	yes	—
28	C₉×C₁₂₇	C₃³	1	9	yes	—
29	#11765917	C₃³	1	3	yes	—
30	#11765917	C₃³	1	9	yes	—
31	#11765917	C₃³	1	3	yes	—
32	#11765917	C₃³	1	3	yes	—
33	C₃×C₁₂₇	—	3	3	no	—
34	C₃×C₁₂₇	#737	1	3	yes	complemented
35	C₃×C₁₂₇	C₃⁴	1	1	yes	characteristic
36	C₁₂₇⋊C₃	—	3	9	no	—
37	C₃×#737	—	127	1	no	maximal, Sylow
38	C₁₂₇	C₃×#737	1	1	yes	characteristic, complemented, Sylow
39	#737	—	127	27	no	—
40	C₃×3₋¹⁺²	—	127	1	no	—
41	C₃×3₋¹⁺²	—	127	3	no	—
42	C₃×3₋¹⁺²	—	127	3	no	—
43	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
44	C₃×H(3,𝔽₃)	—	127	1	no	—
45	C₃²×C₉	—	127	1	no	—
46	C₃²×C₉	—	127	3	no	—
47	C₃³	—	127	3	no	—
48	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
49	3₋¹⁺²	—	127	9	no	—
50	3₋¹⁺²	—	127	27	no	—
51	3₋¹⁺²	—	127	27	no	—
52	3₋¹⁺²	C₃×C₁₂₇⋊C₃	1	9	yes	complemented
53	H(3,𝔽₃)	—	127	9	no	—
54	C₃×C₉	—	127	9	no	—
55	C₃×C₉	—	127	1	no	—
56	C₃×C₉	—	127	3	no	—
57	C₃×C₉	—	127	1	no	—
58	C₃×C₉	—	127	1	no	—
59	C₃×C₉	—	127	27	no	—
60	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
61	C₃²	—	3	3	no	—
62	C₃²	—	381	9	no	—
63	C₃²	—	127	9	no	—
64	C₃²	C₃²×C₁₂₇⋊C₃	1	3	yes	—
65	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
66	C₉	—	127	3	no	—
67	C₉	—	127	3	no	—
68	C₉	—	127	3	no	—
69	C₉	—	127	9	no	—
70	C₉	C₃²×C₁₂₇⋊C₃	1	9	yes	—
71	C₃	—	3	3	no	—
72	C₃	—	381	9	no	—
73	C₃	#23779861	1	3	yes	direct product factor
74	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	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#737
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
1. #23779861	C₃	direct (N × H)
2. C₃×#16812184	C₃	semidirect
3. C₃×#16812183	C₃	semidirect
4. C₃×#16812182	C₃	semidirect
6. C₃²×#11765917	C₃	semidirect
7. C₃×C₉×C₁₂₇⋊C₃	C₃	semidirect
8. C₃×3₋¹⁺²×C₁₂₇	C₃	semidirect
10. #16812184	C₃²	semidirect
11. #16812183	C₃²	semidirect
12. #16812182	C₃²	semidirect
18. C₃×#11765917	C₃²	semidirect
19. C₉×C₁₂₇⋊C₃	C₃²	semidirect
21. 3₋¹⁺²×C₁₂₇	C₃²	semidirect
34. C₃×C₁₂₇	#737	semidirect
38. C₁₂₇	C₃×#737	semidirect
43. C₃×3₋¹⁺²	C₁₂₇⋊C₃	semidirect
52. 3₋¹⁺²	C₃×C₁₂₇⋊C₃	semidirect
73. C₃	#23779861	direct (N × H)

Maximal subgroups

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

subgroup	index
#23779861	3
C₃×#16812184	3
C₃×#16812183	3
C₃×#16812182	3
C₃×C₃²⋊(C₁₂₇⋊C₃)	3
C₃²×#11765917	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃×3₋¹⁺²×C₁₂₇	3
C₃×#737	127

Subgroups — C3×#23779861 #44525149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779861 #44525149