Subgroups — C₃×#23779846 #44525096

Order 30861.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812184	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×#11765917	C₃	1	1	yes	maximal, characteristic, complemented
4	#23779846	C₃	1	9	yes	maximal, direct product factor
5	C₃×3₋¹⁺²×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₂₇⋊C₃	—	3	1	no	—
7	#16812184	—	3	2	no	—
8	#16812184	C₃²	1	3	yes	complemented
9	C₃²⋊(C₁₂₇⋊C₃)	—	3	2	no	—
10	C₃²⋊(C₁₂₇⋊C₃)	C₃²	1	3	yes	—
11	C₃×#11765917	—	3	2	no	—
12	C₃×#11765917	—	3	1	no	—
13	C₃×#11765917	—	3	1	no	—
14	C₃×#11765917	C₃²	1	3	yes	complemented
15	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
16	3₋¹⁺²×C₁₂₇	—	3	2	no	—
17	3₋¹⁺²×C₁₂₇	C₃²	1	3	yes	complemented
18	C₃×C₉×C₁₂₇	—	3	1	no	—
19	C₃²×C₁₂₇	—	3	3	no	—
20	C₃²×C₁₂₇	H(3,𝔽₃)	1	2	yes	—
21	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
23	C₃×C₁₂₇⋊C₃	—	3	3	no	—
24	C₃×C₁₂₇⋊C₃	—	9	3	no	—
25	C₉×C₁₂₇	—	3	3	no	—
26	#11765917	—	3	3	no	—
27	#11765917	—	3	3	no	—
28	C₃×C₁₂₇	—	3	2	no	—
29	C₃×C₁₂₇	—	3	1	no	—
30	C₃×C₁₂₇	#731	1	3	yes	complemented
31	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	C₁₂₇⋊C₃	—	9	3	no	—
33	C₃×#731	—	127	1	no	maximal, Sylow
34	C₁₂₇	C₃×#731	1	1	yes	characteristic, complemented, Sylow
35	C₃×3₋¹⁺²	—	127	1	no	—
36	C₃×3₋¹⁺²	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
37	C₃×H(3,𝔽₃)	—	127	1	no	—
38	C₃²×C₉	—	127	1	no	—
39	#731	—	127	9	no	—
40	C₃³	—	381	1	no	—
41	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
42	3₋¹⁺²	—	3	2	no	—
43	3₋¹⁺²	—	381	2	no	—
44	3₋¹⁺²	—	127	3	no	—
45	3₋¹⁺²	C₃×C₁₂₇⋊C₃	1	3	yes	complemented
46	H(3,𝔽₃)	—	381	2	no	—
47	H(3,𝔽₃)	—	127	3	no	—
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	—	381	2	no	—
50	C₃×C₉	—	381	1	no	—
51	C₃×C₉	—	381	1	no	—
52	C₃×C₉	—	127	3	no	—
53	C₃²	—	3	3	no	—
54	C₃²	—	1143	3	no	—
55	C₃²	—	381	3	no	—
56	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	2	yes	—
57	C₃²	C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic
58	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
59	C₉	—	3	3	no	—
60	C₉	—	381	3	no	—
61	C₉	—	381	3	no	—
62	C₃	—	3	2	no	—
63	C₃	—	3	1	no	—
64	C₃	—	1143	3	no	—
65	C₃	#23779846	1	3	yes	direct product factor
66	C₃	C₃×C₃²⋊(C₁₂₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₂₇⋊C₃)
commutator, cosocle	C₃²×C₁₂₇	C₃³
Frattini	C₃²	C₃²×C₁₂₇⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₂₇	C₃
socle	C₃²×C₁₂₇	H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₁₂₇⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×#731
LCS	G ▷ C₃²×C₁₂₇ ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃×#16812184	C₃	semidirect
3. C₃²×#11765917	C₃	semidirect
4. #23779846	C₃	direct (N × H)
5. C₃×3₋¹⁺²×C₁₂₇	C₃	semidirect
8. #16812184	C₃²	semidirect
14. C₃×#11765917	C₃²	semidirect
17. 3₋¹⁺²×C₁₂₇	C₃²	semidirect
30. C₃×C₁₂₇	#731	semidirect
34. C₁₂₇	C₃×#731	semidirect
36. C₃×3₋¹⁺²	C₁₂₇⋊C₃	semidirect
45. 3₋¹⁺²	C₃×C₁₂₇⋊C₃	semidirect
65. C₃	#23779846	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16812184	3
C₃×C₃²⋊(C₁₂₇⋊C₃)	3
C₃²×#11765917	3
#23779846	3
C₃×3₋¹⁺²×C₁₂₇	3
C₃×#731	127

Subgroups — C3×#23779846 #44525096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23779846 #44525096