Group #44525043 — subgroups

Subgroups — #44525043

Order 30861.

124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812182	C₃	1	1	yes	maximal, characteristic
2	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#23779834	C₃	1	1	yes	maximal, characteristic, complemented
4	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
5	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
6	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
7	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
8	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
9	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
10	#23779833	C₃	1	1	yes	maximal, characteristic, complemented
11	#23779831	C₃	1	1	yes	maximal, characteristic
12	#23779831	C₃	1	1	yes	maximal, characteristic
13	C₉⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃²×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
15	#16812182	—	3	3	no	—
16	C₃×#11765917	C₃²	1	1	yes	characteristic
17	C₃×#11765917	C₃²	1	1	yes	characteristic
18	C₃×#11765917	C₃²	1	1	yes	characteristic
19	C₃×#11765917	C₃²	1	1	yes	characteristic
20	C₃×#11765917	C₃²	1	1	yes	characteristic
21	C₃×#11765917	C₃²	1	1	yes	characteristic
22	C₃×#11765917	C₃²	1	1	yes	characteristic
23	C₃×#11765917	C₃²	1	1	yes	characteristic
24	C₉×C₁₂₇⋊C₃	—	3	3	no	—
25	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
26	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
27	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
28	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
29	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
30	C₃×C₁₂₇⋊C₃	—	3	1	no	—
31	C₃×C₁₂₇⋊C₃	—	3	1	no	—
32	C₃×C₁₂₇⋊C₃	—	3	1	no	—
33	C₃×C₁₂₇⋊C₃	3₋¹⁺²	1	3	yes	—
34	C₉×C₁₂₇	—	3	1	no	—
35	C₉×C₁₂₇	—	3	1	no	—
36	C₉×C₁₂₇	—	3	1	no	—
37	C₉×C₁₂₇	—	3	1	no	—
38	#11765917	—	3	1	no	—
39	#11765917	—	3	1	no	—
40	#11765917	—	3	1	no	—
41	#11765917	—	3	1	no	—
42	#11765917	—	3	1	no	—
43	#11765917	—	3	1	no	—
44	#11765917	—	3	1	no	—
45	#11765917	3₋¹⁺²	1	3	yes	complemented
46	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
47	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
48	C₃×C₁₂₇	#737	1	1	yes	characteristic
49	C₃×C₁₂₇	#737	1	1	yes	characteristic
50	C₁₂₇⋊C₃	—	3	3	no	—
51	#6894	—	127	1	no	maximal, Sylow
52	C₁₂₇	#6894	1	1	yes	characteristic, complemented, Sylow
53	C₃×3₋¹⁺²	—	127	1	no	—
54	C₃²×C₉	—	127	1	no	—
55	C₉⋊C₉	—	127	1	no	—
56	C₉⋊C₉	—	127	1	no	—
57	C₉⋊C₉	—	127	1	no	—
58	C₉⋊C₉	—	127	1	no	—
59	C₉⋊C₉	—	127	1	no	—
60	C₉⋊C₉	—	127	1	no	—
61	C₉⋊C₉	—	127	1	no	—
62	C₉⋊C₉	—	127	1	no	—
63	C₉⋊C₉	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
64	C₃²⋊C₉	—	127	1	no	—
65	C₃²⋊C₉	—	127	1	no	—
66	C₃³	—	127	1	no	—
67	3₋¹⁺²	—	381	3	no	—
68	C₃×C₉	—	381	3	no	—
69	C₃×C₉	—	127	1	no	—
70	C₃×C₉	—	127	1	no	—
71	C₃×C₉	—	127	1	no	—
72	C₃×C₉	—	127	1	no	—
73	C₃×C₉	—	127	1	no	—
74	C₃×C₉	—	127	1	no	—
75	C₃×C₉	—	127	1	no	—
76	C₃×C₉	—	127	1	no	—
77	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
78	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
79	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
80	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
81	C₃²	—	381	1	no	—
82	C₃²	—	381	1	no	—
83	C₃²	—	381	1	no	—
84	C₃²	—	127	3	no	—
85	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	3	1	no	—
90	C₉	—	381	1	no	—
91	C₉	—	381	1	no	—
92	C₉	—	381	1	no	—
93	C₉	—	381	1	no	—
94	C₉	—	381	1	no	—
95	C₉	—	381	1	no	—
96	C₉	—	381	1	no	—
97	C₉	—	127	3	no	—
98	C₃	—	381	3	no	—
99	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	1	yes	characteristic
100	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	1	yes	characteristic
101	C₃	#23779860	1	1	yes	characteristic
102	C₃	#23779861	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#16812182

C₃

yes

maximal, characteristic

C₃×C₉×C₁₂₇⋊C₃

C₃

yes

maximal, characteristic

#23779834

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779833

C₃

yes

maximal, characteristic, complemented

#23779831

C₃

yes

maximal, characteristic

#23779831

C₃

yes

maximal, characteristic

C₉⋊C₉×C₁₂₇

C₃

yes

maximal, characteristic, complemented

C₃²×C₁₂₇⋊C₃

C₃²

yes

characteristic

#16812182

—

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₃×#11765917

C₃²

yes

characteristic

C₉×C₁₂₇⋊C₃

—

C₃×C₉×C₁₂₇

C₃²

yes

characteristic

C₃×C₉×C₁₂₇

C₃²

yes

characteristic

C₃×C₉×C₁₂₇

C₃²

yes

characteristic

C₃×C₉×C₁₂₇

C₃²

yes

characteristic

C₃²×C₁₂₇

C₃³

yes

characteristic

C₃×C₁₂₇⋊C₃

—

C₃×C₁₂₇⋊C₃

—

C₃×C₁₂₇⋊C₃

—

C₃×C₁₂₇⋊C₃

3₋¹⁺²

yes

—

C₉×C₁₂₇

—

C₉×C₁₂₇

—

C₉×C₁₂₇

—

C₉×C₁₂₇

—

—

—

—

—

—

—

—

3₋¹⁺²

yes

complemented

C₃×C₁₂₇

C₃×3₋¹⁺²

yes

characteristic

C₃×C₁₂₇

C₃×3₋¹⁺²

yes

C₃×C₁₂₇

yes

C₃×C₁₂₇

yes

C₁₂₇⋊C₃

—

#6894

—

127

maximal, Sylow

C₁₂₇

#6894

yes

characteristic, complemented, Sylow

C₃×3₋¹⁺²

—

127

—

C₃²×C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

—

127

—

C₉⋊C₉

C₁₂₇⋊C₃

yes

characteristic, complemented

C₃²⋊C₉

—

127

—

C₃²⋊C₉

—

127

—

C₃³

—

127

—

3₋¹⁺²

—

381

—

C₃×C₉

—

381

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

—

127

—

C₃×C₉

C₃×C₁₂₇⋊C₃

yes

characteristic

C₃×C₉

C₃×C₁₂₇⋊C₃

yes

characteristic

C₃×C₉

C₃×C₁₂₇⋊C₃

yes

characteristic

C₃×C₉

C₃×C₁₂₇⋊C₃

yes

characteristic

C₃²

—

381

—

C₃²

—

381

—

C₃²

—

381

—

C₃²

—

127

—

C₃²

C₃²×C₁₂₇⋊C₃

yes

characteristic

C₉

—

C₉

—

C₉

—

C₉

—

C₉

—

381

—

C₉

—

381

—

C₉

—

381

—

C₉

—

381

—

C₉

—

381

—

C₉

—

381

—

C₉

—

381

—

C₉

—

127

—

C₃

—

381

—

C₃

3₋¹⁺²×C₁₂₇⋊C₃

yes

characteristic

100

C₃

3₋¹⁺²×C₁₂₇⋊C₃

yes

characteristic

101

C₃

#23779860

yes

characteristic

102

C₃

#23779861

yes

characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₂₇⋊C₃
commutator, socle, cosocle	C₃²×C₁₂₇	C₃³
Fitting	C₉⋊C₉×C₁₂₇	C₃
prime radical	C₃²×C₁₂₇⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₁₂₇⋊C₃
hypocenter	C₁₂₇	#6894
LCS	G ▷ C₃²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

subgroup

G/H

center, Frattini

C₃²

C₃²×C₁₂₇⋊C₃

commutator, socle, cosocle

C₃²×C₁₂₇

C₃³

Fitting

C₉⋊C₉×C₁₂₇

C₃

prime radical

C₃²×C₁₂₇⋊C₃

C₃²

hypercenter

C₉⋊C₉

C₁₂₇⋊C₃

C₁₂₇

G ▷ C₃²×C₁₂₇ ▷ C₁₂₇

C₁ ◁ C₃² ◁ C₉⋊C₉

N	H ≅ G/N	type
3. #23779834	C₃	semidirect
4. #23779833	C₃	semidirect
5. #23779833	C₃	semidirect
6. #23779833	C₃	semidirect
7. #23779833	C₃	semidirect
8. #23779833	C₃	semidirect
9. #23779833	C₃	semidirect
10. #23779833	C₃	semidirect
13. C₉⋊C₉×C₁₂₇	C₃	semidirect
45. #11765917	3₋¹⁺²	semidirect
52. C₁₂₇	#6894	semidirect
63. C₉⋊C₉	C₁₂₇⋊C₃	semidirect

H ≅ G/N

type

3. #23779834

C₃

semidirect

4. #23779833

C₃

semidirect

5. #23779833

C₃

semidirect

6. #23779833

C₃

semidirect

7. #23779833

C₃

semidirect

8. #23779833

C₃

semidirect

9. #23779833

C₃

semidirect

10. #23779833

C₃

semidirect

13. C₉⋊C₉×C₁₂₇

C₃

semidirect

45. #11765917

3₋¹⁺²

semidirect

52. C₁₂₇

#6894

semidirect

63. C₉⋊C₉

C₁₂₇⋊C₃

semidirect

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

subgroup	index
C₃×#16812182	3
C₃×C₉×C₁₂₇⋊C₃	3
#23779834	3
#23779833	3
#23779831	3
C₉⋊C₉×C₁₂₇	3
#6894	127

subgroup

index

C₃×C₉×C₁₂₇⋊C₃

C₉⋊C₉×C₁₂₇

127

Subgroups — #44525043

Conjugacy classes of subgroups

Complements

Maximal subgroups