Group #44525051 — subgroups

Subgroups — #44525051

Order 30861.

114 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 47 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×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#23779835	C₃	1	1	yes	maximal, characteristic, complemented
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	#23779831	C₃	1	1	yes	maximal, characteristic
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	C₃×#11765917	C₃²	1	1	yes	characteristic
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	C₉×C₁₂₇⋊C₃	—	3	3	no	—
24	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
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	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
29	C₃×C₁₂₇⋊C₃	—	3	1	no	—
30	C₃×C₁₂₇⋊C₃	—	3	1	no	—
31	C₃×C₁₂₇⋊C₃	—	3	1	no	—
32	C₃×C₁₂₇⋊C₃	3₋¹⁺²	1	3	yes	—
33	C₉×C₁₂₇	—	3	1	no	—
34	C₉×C₁₂₇	—	3	1	no	—
35	C₉×C₁₂₇	—	3	1	no	—
36	C₉×C₁₂₇	—	3	1	no	—
37	#11765917	—	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	C₃×C₁₂₇	C₃×3₋¹⁺²	1	1	yes	characteristic
46	C₃×C₁₂₇	#737	1	1	yes	characteristic
47	C₃×C₁₂₇	#737	1	1	yes	characteristic
48	C₃×C₁₂₇	#737	1	1	yes	characteristic
49	C₁₂₇⋊C₃	—	3	3	no	—
50	#6895	—	127	1	no	maximal, Sylow
51	C₁₂₇	#6895	1	1	yes	characteristic, complemented, Sylow
52	C₃²×C₉	—	127	1	no	—
53	C₉⋊C₉	—	127	1	no	—
54	C₉⋊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	C₁₂₇⋊C₃	1	1	yes	characteristic, complemented
62	C₃²⋊C₉	—	127	1	no	—
63	C₃²⋊C₉	—	127	1	no	—
64	C₃²⋊C₉	—	127	1	no	—
65	C₃³	—	127	1	no	—
66	C₃×C₉	—	381	3	no	—
67	C₃×C₉	—	127	1	no	—
68	C₃×C₉	—	127	1	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	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
76	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
77	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
78	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
79	C₃²	—	381	1	no	—
80	C₃²	—	381	1	no	—
81	C₃²	—	381	1	no	—
82	C₃²	—	127	3	no	—
83	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	381	1	no	—
89	C₉	—	381	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	C₃	—	381	3	no	—
97	C₃	3₋¹⁺²×C₁₂₇⋊C₃	1	1	yes	characteristic
98	C₃	#23779860	1	1	yes	characteristic
99	C₃	#23779861	1	1	yes	characteristic
100	C₃	#23779861	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₉×C₁₂₇⋊C₃

C₃

yes

maximal, characteristic

#23779835

C₃

yes

maximal, characteristic, complemented

#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

#23779831

C₃

yes

maximal, characteristic

#23779831

C₃

yes

maximal, characteristic

#23779831

C₃

yes

maximal, characteristic

C₉⋊C₉×C₁₂₇

C₃

yes

maximal, characteristic, complemented

C₃²×C₁₂₇⋊C₃

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

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

—

—

—

—

—

—

—

—

—

C₃×C₁₂₇

C₃×3₋¹⁺²

yes

C₃×C₁₂₇

yes

C₃×C₁₂₇

yes

C₃×C₁₂₇

yes

C₁₂₇⋊C₃

—

#6895

—

127

maximal, Sylow

C₁₂₇

#6895

yes

characteristic, complemented, Sylow

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

—

C₃²⋊C₉

—

127

—

C₃³

—

127

—

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

—

381

—

C₃

—

381

—

C₃

3₋¹⁺²×C₁₂₇⋊C₃

yes

C₃

yes

C₃

yes

100

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	#6895
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
2. #23779835	C₃	semidirect
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
13. C₉⋊C₉×C₁₂₇	C₃	semidirect
51. C₁₂₇	#6895	semidirect
61. C₉⋊C₉	C₁₂₇⋊C₃	semidirect

H ≅ G/N

type

2. #23779835

C₃

semidirect

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

13. C₉⋊C₉×C₁₂₇

C₃

semidirect

51. C₁₂₇

#6895

semidirect

61. 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×C₉×C₁₂₇⋊C₃	3
#23779835	3
#23779834	3
#23779833	3
#23779831	3
C₉⋊C₉×C₁₂₇	3
#6895	127

subgroup

index

C₃×C₉×C₁₂₇⋊C₃

C₉⋊C₉×C₁₂₇

127

Subgroups — #44525051

Conjugacy classes of subgroups

Complements

Maximal subgroups