Subgroups — C₃×#23779833 #44525006

Order 30861.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
2	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
3	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic
4	#23779833	C₃	1	9	yes	maximal, direct product factor
5	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11765917	—	3	3	no	—
7	C₃×#11765917	—	3	3	no	—
8	C₃×#11765917	C₉	1	9	yes	complemented
9	C₃×#11765917	C₃²	1	3	yes	—
10	C₃×#11765917	C₃²	1	3	yes	—
11	C₃×#11765917	C₃²	1	3	yes	—
12	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₁₂₇	—	3	3	no	—
14	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
15	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
16	C₃²×C₁₂₇	3₋¹⁺²	1	3	yes	—
17	C₃²×C₁₂₇	3₋¹⁺²	1	3	yes	—
18	C₃²×C₁₂₇	3₋¹⁺²	1	3	yes	—
19	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
20	C₉×C₁₂₇	—	3	3	no	—
21	#11765917	—	3	3	no	—
22	#11765917	—	3	3	no	—
23	#11765917	C₃×C₉	1	9	yes	complemented
24	C₃×C₁₂₇	C₉⋊C₉	1	9	yes	complemented
25	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
26	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₉⋊C₉	—	127	1	no	maximal, Sylow
30	C₁₂₇	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₃²×C₉	—	127	1	no	—
32	C₃²×C₉	—	127	1	no	—
33	C₃²×C₉	—	127	1	no	—
34	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
35	C₉⋊C₉	—	127	9	no	—
36	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	381	3	no	—
39	C₃×C₉	—	381	3	no	—
40	C₃×C₉	—	127	3	no	—
41	C₃×C₉	—	127	3	no	—
42	C₃×C₉	—	127	9	no	—
43	C₃×C₉	—	127	3	no	—
44	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
45	C₃²	C₉×C₁₂₇⋊C₃	1	3	yes	—
46	C₃²	#16812182	1	3	yes	—
47	C₃²	#16812183	1	3	yes	—
48	C₃²	#16812184	1	3	yes	—
49	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	381	3	no	—
52	C₉	—	381	3	no	—
53	C₉	—	127	9	no	—
54	C₃	#23779833	1	9	yes	direct product factor
55	C₃	C₃×C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
56	C₃	C₃×#16812182	1	1	yes	characteristic
57	C₃	C₃×#16812183	1	1	yes	characteristic
58	C₃	C₃×#16812184	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. #23779833	C₃	direct (N × H)
8. C₃×#11765917	C₉	semidirect
23. #11765917	C₃×C₉	semidirect
24. C₃×C₁₂₇	C₉⋊C₉	semidirect
30. C₁₂₇	C₃×C₉⋊C₉	semidirect
54. C₃	#23779833	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11765917	3
#23779833	3
C₃²×C₉×C₁₂₇	3
C₃×C₉⋊C₉	127

Subgroups — C3×#23779833 #44525006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779833 #44525006