Group #22548412 — subgroups

Subgroups — C₁₁×#10624889 #22548412

Order 8019.

620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 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	C₁₁×#6897	C₃	1	18	yes	maximal, complemented
2	C₁₁×#6896	C₃	1	9	yes	maximal, complemented
3	C₁₁×#6894	C₃	1	6	yes	maximal, complemented
4	C₁₁×#6891	C₃	1	2	yes	maximal
5	C₁₁×#6891	C₃	1	1	yes	maximal, characteristic
6	C₉×C₁₁×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
7	C₃×C₁₁×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
8	C₃⁴×C₁₁	C₃²	1	1	yes	characteristic
9	C₃×C₁₁×3₋¹⁺²	C₃²	1	3	yes	—
10	C₃×C₁₁×3₋¹⁺²	C₃²	1	6	yes	—
11	C₃²×C₉×C₁₁	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₁	C₃²	1	2	yes	—
13	C₁₁×C₉⋊C₉	C₃²	1	18	yes	complemented
14	C₁₁×C₉⋊C₉	C₃²	1	54	yes	complemented
15	C₁₁×C₃²⋊C₉	C₃²	1	3	yes	—
16	C₁₁×C₃²⋊C₉	C₃²	1	6	yes	—
17	C₁₁×C₃²⋊C₉	C₃²	1	6	yes	—
18	C₁₁×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₁₁×C₃²⋊C₉	C₃²	1	6	yes	—
20	C₁₁×C₃²⋊C₉	C₃²	1	12	yes	—
21	C₉²×C₁₁	C₃²	1	9	yes	complemented
22	#10624889	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₃³×C₁₁	—	3	3	no	—
24	C₃³×C₁₁	—	9	1	no	—
25	C₃³×C₁₁	—	9	2	no	—
26	C₃³×C₁₁	C₃³	1	2	yes	—
27	C₃³×C₁₁	C₃³	1	1	yes	characteristic
28	C₃³×C₁₁	C₃³	1	1	yes	characteristic
29	C₁₁×3₋¹⁺²	—	3	9	no	—
30	C₁₁×3₋¹⁺²	—	9	6	no	—
31	C₃×C₉×C₁₁	—	9	1	no	—
32	C₃×C₉×C₁₁	—	9	2	no	—
33	C₃×C₉×C₁₁	C₃³	1	3	yes	—
34	C₃×C₉×C₁₁	C₃³	1	9	yes	—
35	C₃×C₉×C₁₁	C₃³	1	18	yes	—
36	C₃×C₉×C₁₁	C₃³	1	6	yes	—
37	#6897	C₃×C₁₁	1	18	yes	complemented
38	#6896	C₃×C₁₁	1	9	yes	complemented
39	#6894	C₃×C₁₁	1	6	yes	complemented
40	#6891	C₃×C₁₁	1	2	yes	—
41	#6891	C₃×C₁₁	1	1	yes	characteristic
42	C₉×3₋¹⁺²	C₃×C₁₁	1	3	yes	complemented
43	C₃×C₃²⋊C₉	C₃×C₁₁	1	1	yes	characteristic
44	C₃²×C₁₁	—	3	1	no	—
45	C₃²×C₁₁	—	3	2	no	—
46	C₃²×C₁₁	—	3	2	no	—
47	C₃²×C₁₁	—	3	1	no	—
48	C₃²×C₁₁	—	3	2	no	—
49	C₃²×C₁₁	—	3	2	no	—
50	C₃²×C₁₁	—	3	4	no	—
51	C₃²×C₁₁	—	3	1	no	—
52	C₃²×C₁₁	—	9	9	no	—
53	C₃²×C₁₁	#737	1	3	yes	—
54	C₃²×C₁₁	C₃⁴	1	1	yes	characteristic
55	C₉×C₁₁	—	3	9	no	—
56	C₉×C₁₁	—	3	3	no	—
57	C₉×C₁₁	—	3	6	no	—
58	C₉×C₁₁	—	3	18	no	—
59	C₃⁴	C₃²×C₁₁	1	1	yes	characteristic
60	C₃×3₋¹⁺²	C₃²×C₁₁	1	3	yes	—
61	C₃×3₋¹⁺²	C₃²×C₁₁	1	6	yes	—
62	C₃²×C₉	C₃²×C₁₁	1	1	yes	characteristic
63	C₃²×C₉	C₃²×C₁₁	1	2	yes	—
64	C₉⋊C₉	C₃²×C₁₁	1	18	yes	complemented
65	C₉⋊C₉	C₃²×C₁₁	1	54	yes	complemented
66	C₃²⋊C₉	C₃²×C₁₁	1	3	yes	—
67	C₃²⋊C₉	C₃²×C₁₁	1	6	yes	—
68	C₃²⋊C₉	C₃²×C₁₁	1	6	yes	—
69	C₃²⋊C₉	C₃²×C₁₁	1	3	yes	—
70	C₃²⋊C₉	C₃²×C₁₁	1	6	yes	—
71	C₃²⋊C₉	C₃²×C₁₁	1	12	yes	—
72	C₉²	C₃²×C₁₁	1	9	yes	complemented
73	C₃×C₁₁	—	3	3	no	—
74	C₃×C₁₁	—	9	1	no	—
75	C₃×C₁₁	—	9	2	no	—
76	C₃×C₁₁	C₃×#737	1	1	yes	characteristic
77	C₃×C₁₁	3₋¹⁺⁴	1	1	yes	characteristic
78	C₃×C₁₁	3₋¹⁺⁴	1	2	yes	—
79	C₃³	—	3	3	no	—
80	C₃³	—	9	1	no	—
81	C₃³	—	9	2	no	—
82	C₃³	C₃³×C₁₁	1	2	yes	—
83	C₃³	C₃³×C₁₁	1	1	yes	characteristic
84	C₃³	C₃³×C₁₁	1	1	yes	characteristic
85	3₋¹⁺²	—	3	9	no	—
86	3₋¹⁺²	—	9	6	no	—
87	C₃×C₉	—	9	1	no	—
88	C₃×C₉	—	9	2	no	—
89	C₃×C₉	C₃³×C₁₁	1	3	yes	—
90	C₃×C₉	C₃³×C₁₁	1	9	yes	—
91	C₃×C₉	C₃³×C₁₁	1	18	yes	—
92	C₃×C₉	C₃³×C₁₁	1	6	yes	—
93	C₁₁	#10624889	1	1	yes	characteristic, direct product factor, Sylow
94	C₃²	—	3	1	no	—
95	C₃²	—	3	2	no	—
96	C₃²	—	3	2	no	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	2	no	—
99	C₃²	—	3	2	no	—
100	C₃²	—	3	4	no	—
101	C₃²	—	3	1	no	—
102	C₃²	—	9	9	no	—
103	C₃²	C₁₁×#737	1	3	yes	—
104	C₃²	C₃⁴×C₁₁	1	1	yes	characteristic
105	C₉	—	3	9	no	—
106	C₉	—	3	3	no	—
107	C₉	—	3	6	no	—
108	C₉	—	3	18	no	—
109	C₃	—	3	3	no	—
110	C₃	—	9	1	no	—
111	C₃	—	9	2	no	—
112	C₃	C₃×C₁₁×#737	1	1	yes	characteristic
113	C₃	C₁₁×3₋¹⁺⁴	1	1	yes	characteristic
114	C₃	C₁₁×3₋¹⁺⁴	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₁×#6897

C₃

yes

maximal, complemented

C₁₁×#6896

C₃

yes

maximal, complemented

C₁₁×#6894

C₃

yes

maximal, complemented

C₁₁×#6891

C₃

yes

maximal

C₁₁×#6891

C₃

yes

maximal, characteristic

C₉×C₁₁×3₋¹⁺²

C₃

yes

maximal, complemented

C₃×C₁₁×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₃⁴×C₁₁

C₃²

yes

characteristic

C₃×C₁₁×3₋¹⁺²

C₃²

yes

—

C₃×C₁₁×3₋¹⁺²

C₃²

yes

—

C₃²×C₉×C₁₁

C₃²

yes

characteristic

C₃²×C₉×C₁₁

C₃²

yes

—

C₁₁×C₉⋊C₉

C₃²

yes

complemented

C₁₁×C₉⋊C₉

C₃²

yes

complemented

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₁₁×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₁

C₃²

yes

complemented

#10624889

C₁₁

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₁

—

C₃³×C₁₁

—

C₃³×C₁₁

—

C₃³×C₁₁

C₃³

yes

—

C₃³×C₁₁

C₃³

yes

characteristic

C₃³×C₁₁

C₃³

yes

characteristic

C₁₁×3₋¹⁺²

—

C₁₁×3₋¹⁺²

—

C₃×C₉×C₁₁

—

C₃×C₉×C₁₁

—

C₃×C₉×C₁₁

C₃³

yes

—

C₃×C₉×C₁₁

C₃³

yes

—

C₃×C₉×C₁₁

C₃³

yes

—

C₃×C₉×C₁₁

C₃³

yes

—

#6897

C₃×C₁₁

yes

complemented

#6896

C₃×C₁₁

yes

complemented

#6894

C₃×C₁₁

yes

complemented

#6891

C₃×C₁₁

yes

—

#6891

C₃×C₁₁

yes

characteristic

C₉×3₋¹⁺²

C₃×C₁₁

yes

complemented

C₃×C₃²⋊C₉

C₃×C₁₁

yes

characteristic

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

—

C₃²×C₁₁

#737

yes

—

C₃²×C₁₁

C₃⁴

yes

characteristic

C₉×C₁₁

—

C₉×C₁₁

—

C₉×C₁₁

—

C₉×C₁₁

—

C₃⁴

C₃²×C₁₁

yes

characteristic

C₃×3₋¹⁺²

C₃²×C₁₁

yes

—

C₃×3₋¹⁺²

C₃²×C₁₁

yes

—

C₃²×C₉

C₃²×C₁₁

yes

characteristic

C₃²×C₉

C₃²×C₁₁

yes

—

C₉⋊C₉

C₃²×C₁₁

yes

complemented

C₉⋊C₉

C₃²×C₁₁

yes

complemented

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₃²⋊C₉

C₃²×C₁₁

yes

—

C₉²

C₃²×C₁₁

yes

complemented

C₃×C₁₁

—

C₃×C₁₁

—

C₃×C₁₁

—

C₃×C₁₁

C₃×#737

yes

characteristic

C₃×C₁₁

3₋¹⁺⁴

yes

characteristic

C₃×C₁₁

3₋¹⁺⁴

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃³×C₁₁

yes

—

C₃³

C₃³×C₁₁

yes

characteristic

C₃³

C₃³×C₁₁

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₃³×C₁₁

yes

—

C₃×C₉

C₃³×C₁₁

yes

—

C₃×C₉

C₃³×C₁₁

yes

—

C₃×C₉

C₃³×C₁₁

yes

—

C₁₁

#10624889

yes

characteristic, direct product factor, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

100

C₃²

—

101

C₃²

—

102

C₃²

—

103

C₃²

C₁₁×#737

yes

—

104

C₃²

C₃⁴×C₁₁

yes

characteristic

105

C₉

—

106

C₉

—

107

C₉

—

108

C₉

—

109

C₃

—

110

C₃

—

111

C₃

—

112

C₃

C₃×C₁₁×#737

yes

characteristic

113

C₃

C₁₁×3₋¹⁺⁴

yes

characteristic

114

C₃

C₁₁×3₋¹⁺⁴

yes

—

	subgroup	G/H
center, socle	C₃²×C₁₁	C₃⁴
commutator, Frattini	C₃²	C₃⁴×C₁₁
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₁ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₁

C₃⁴

commutator, Frattini

C₃²

C₃⁴×C₁₁

LCS

G ▷ C₃² ▷ C₁

UCS

C₁ ◁ C₃²×C₁₁ ◁ G

N	H ≅ G/N	type
1. C₁₁×#6897	C₃	semidirect
2. C₁₁×#6896	C₃	semidirect
3. C₁₁×#6894	C₃	semidirect
6. C₉×C₁₁×3₋¹⁺²	C₃	semidirect
13. C₁₁×C₉⋊C₉	C₃²	semidirect
14. C₁₁×C₉⋊C₉	C₃²	semidirect
21. C₉²×C₁₁	C₃²	semidirect
22. #10624889	C₁₁	direct (N × H)
37. #6897	C₃×C₁₁	semidirect
38. #6896	C₃×C₁₁	semidirect
39. #6894	C₃×C₁₁	semidirect
42. C₉×3₋¹⁺²	C₃×C₁₁	semidirect
64. C₉⋊C₉	C₃²×C₁₁	semidirect
65. C₉⋊C₉	C₃²×C₁₁	semidirect
72. C₉²	C₃²×C₁₁	semidirect
93. C₁₁	#10624889	direct (N × H)

H ≅ G/N

type

1. C₁₁×#6897

C₃

semidirect

2. C₁₁×#6896

C₃

semidirect

3. C₁₁×#6894

C₃

semidirect

6. C₉×C₁₁×3₋¹⁺²

C₃

semidirect

13. C₁₁×C₉⋊C₉

C₃²

semidirect

14. C₁₁×C₉⋊C₉

C₃²

semidirect

21. C₉²×C₁₁

C₃²

semidirect

22. #10624889

C₁₁

direct (N × H)

37. #6897

C₃×C₁₁

semidirect

38. #6896

C₃×C₁₁

semidirect

39. #6894

C₃×C₁₁

semidirect

42. C₉×3₋¹⁺²

C₃×C₁₁

semidirect

64. C₉⋊C₉

C₃²×C₁₁

semidirect

65. C₉⋊C₉

C₃²×C₁₁

semidirect

72. C₉²

C₃²×C₁₁

semidirect

93. C₁₁

#10624889

direct (N × H)

Subgroups — C₁₁×#10624889 #22548412

Conjugacy classes of subgroups

Complements

Subgroups — C11×#10624889 #22548412

Conjugacy classes of subgroups

Complements

Subgroups — C₁₁×#10624889 #22548412