Group #11766812 — subgroups

Subgroups — C₉×#2091 #11766812

Order 1152.

333 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 120 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	C₉×#430	C₂	1	3	yes	maximal, complemented
2	C₉×#407	C₂	1	3	yes	maximal
3	C₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2091	C₃	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₉×M₁₆	C₂²	1	3	yes	—
7	C₂×C₉×M₁₆	C₂²	1	3	yes	—
8	C₉×#108	—	2	6	no	—
9	C₉×C₂²⋊C₈	—	2	6	no	—
10	C₃×#430	C₂×C₃	1	3	yes	—
11	C₃×#407	C₂×C₃	1	3	yes	—
12	C₃×#338	C₂×C₃	1	1	yes	characteristic
13	C₂⁴×C₉	Q₈	1	1	yes	characteristic
14	C₂²×C₄×C₉	—	2	3	no	—
15	C₂²×C₄×C₉	—	2	3	no	—
16	C₂²×C₄×C₉	Q₈	1	1	yes	characteristic
17	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
18	C₉×M₁₆	—	2	6	no	—
19	C₉×M₁₆	—	2	6	no	—
20	C₂×C₈×C₉	—	2	3	no	—
21	C₂×C₈×C₉	D₄	1	6	yes	—
22	#2091	C₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
24	C₂×C₃×M₁₆	C₂²×C₃	1	3	yes	—
25	C₂×C₃×M₁₆	C₂²×C₃	1	3	yes	—
26	C₃×#108	—	2	6	no	—
27	C₃×C₂²⋊C₈	—	2	6	no	—
28	C₂³×C₉	—	2	3	no	—
29	C₂³×C₉	—	4	2	no	—
30	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₉	—	2	3	no	—
32	C₂×C₄×C₉	—	4	3	no	—
33	C₂×C₄×C₉	—	4	1	no	—
34	C₂×C₄×C₉	C₂×D₄	1	3	yes	—
35	C₂×C₄×C₉	#41	1	3	yes	—
36	C₈×C₉	—	2	6	no	—
37	C₈×C₉	—	4	3	no	—
38	#430	C₂×C₉	1	3	yes	complemented
39	#407	C₂×C₉	1	3	yes	—
40	#338	C₂×C₉	1	1	yes	characteristic, complemented
41	C₂⁴×C₃	C₃×Q₈	1	1	yes	characteristic
42	C₂²×C₃×C₄	—	2	3	no	—
43	C₂²×C₃×C₄	—	2	3	no	—
44	C₂²×C₃×C₄	C₃×Q₈	1	1	yes	characteristic
45	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
46	C₃×M₁₆	—	2	6	no	—
47	C₃×M₁₆	—	2	6	no	—
48	C₂×C₃×C₈	—	2	3	no	—
49	C₂×C₃×C₈	C₃×D₄	1	6	yes	—
50	C₂²×C₉	—	2	6	no	—
51	C₂²×C₉	—	4	1	no	—
52	C₂²×C₉	—	4	3	no	—
53	C₂²×C₉	—	4	1	no	—
54	C₂²×C₉	C₂²⋊Q₈	1	3	yes	—
55	C₄×C₉	—	4	1	no	—
56	C₄×C₉	#123	1	3	yes	—
57	C₄×C₉	#127	1	1	yes	characteristic
58	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
59	C₂×M₁₆	C₂²×C₉	1	3	yes	—
60	C₂×M₁₆	C₂²×C₉	1	3	yes	—
61	#108	—	2	6	no	—
62	C₂²⋊C₈	—	2	6	no	—
63	C₂³×C₃	—	2	3	no	—
64	C₂³×C₃	—	4	2	no	—
65	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
66	C₂×C₃×C₄	—	2	3	no	—
67	C₂×C₃×C₄	—	4	3	no	—
68	C₂×C₃×C₄	—	4	1	no	—
69	C₂×C₃×C₄	C₂×C₃×D₄	1	3	yes	—
70	C₂×C₃×C₄	C₃×#41	1	3	yes	—
71	C₃×C₈	—	2	6	no	—
72	C₃×C₈	—	4	3	no	—
73	C₂×C₉	—	2	3	no	—
74	C₂×C₉	—	4	2	no	—
75	C₂×C₉	#399	1	1	yes	characteristic
76	C₂⁴	Q₈×C₉	1	1	yes	characteristic
77	C₂²×C₄	—	2	3	no	—
78	C₂²×C₄	—	2	3	no	—
79	C₂²×C₄	Q₈×C₉	1	1	yes	characteristic
80	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
81	M₁₆	—	2	6	no	—
82	M₁₆	—	2	6	no	—
83	C₂×C₈	—	2	3	no	—
84	C₂×C₈	D₄×C₉	1	6	yes	—
85	C₂²×C₃	—	2	6	no	—
86	C₂²×C₃	—	4	1	no	—
87	C₂²×C₃	—	4	3	no	—
88	C₂²×C₃	—	4	1	no	—
89	C₂²×C₃	C₃×C₂²⋊Q₈	1	3	yes	—
90	C₃×C₄	—	4	1	no	—
91	C₃×C₄	C₃×#123	1	3	yes	—
92	C₃×C₄	C₃×#127	1	1	yes	characteristic
93	C₉	#2091	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³	—	2	3	no	—
95	C₂³	—	4	2	no	—
96	C₂³	C₂×Q₈×C₉	1	1	yes	characteristic
97	C₂×C₄	—	2	3	no	—
98	C₂×C₄	—	4	3	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	C₂×D₄×C₉	1	3	yes	—
101	C₂×C₄	C₉×#41	1	3	yes	—
102	C₈	—	2	6	no	—
103	C₈	—	4	3	no	—
104	C₂×C₃	—	2	3	no	—
105	C₂×C₃	—	4	2	no	—
106	C₂×C₃	C₃×#399	1	1	yes	characteristic
107	C₂²	—	2	6	no	—
108	C₂²	—	4	1	no	—
109	C₂²	—	4	3	no	—
110	C₂²	—	4	1	no	—
111	C₂²	C₉×C₂²⋊Q₈	1	3	yes	—
112	C₄	—	4	1	no	—
113	C₄	C₉×#123	1	3	yes	—
114	C₄	C₉×#127	1	1	yes	characteristic
115	C₃	C₃×#2091	1	1	yes	characteristic
116	C₂	—	2	3	no	—
117	C₂	—	4	2	no	—
118	C₂	C₉×#399	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#430

C₂

yes

maximal, complemented

C₉×#407

C₂

yes

maximal

C₉×#338

C₂

yes

maximal, characteristic, complemented

C₃×#2091

C₃

yes

maximal, characteristic

C₂³×C₄×C₉

C₂²

yes

characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂×C₉×M₁₆

C₂²

yes

—

C₉×#108

—

C₉×C₂²⋊C₈

—

C₃×#430

C₂×C₃

yes

—

C₃×#407

C₂×C₃

yes

—

C₃×#338

C₂×C₃

yes

characteristic

C₂⁴×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

Q₈

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

#2091

C₉

yes

characteristic, direct product factor, Sylow

C₂³×C₃×C₄

C₂²×C₃

yes

characteristic

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₃×#108

—

C₃×C₂²⋊C₈

—

C₂³×C₉

—

C₂³×C₉

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

#41

yes

—

C₈×C₉

—

C₈×C₉

—

#430

C₂×C₉

yes

complemented

#407

C₂×C₉

yes

—

#338

C₂×C₉

yes

characteristic, complemented

C₂⁴×C₃

C₃×Q₈

yes

characteristic

C₂²×C₃×C₄

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₃×Q₈

yes

characteristic

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₃×D₄

yes

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊Q₈

yes

—

C₄×C₉

—

C₄×C₉

#123

yes

—

C₄×C₉

#127

yes

characteristic

C₂³×C₄

C₂²×C₉

yes

characteristic

C₂×M₁₆

C₂²×C₉

yes

—

C₂×M₁₆

C₂²×C₉

yes

—

#108

—

C₂²⋊C₈

—

C₂³×C₃

—

C₂³×C₃

—

C₂³×C₃

C₂×C₃×Q₈

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

—

C₂×C₃×C₄

C₃×#41

yes

—

C₃×C₈

—

C₃×C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#399

yes

characteristic

C₂⁴

Q₈×C₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Q₈×C₉

yes

characteristic

C₂²×C₄

C₂³×C₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₉

yes

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

—

C₂²×C₃

C₃×C₂²⋊Q₈

yes

—

C₃×C₄

—

C₃×C₄

C₃×#123

yes

—

C₃×C₄

C₃×#127

yes

characteristic

C₉

#2091

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

C₂×Q₈×C₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₄×C₉

yes

—

101

C₂×C₄

C₉×#41

yes

—

102

C₈

—

103

C₈

—

104

C₂×C₃

—

105

C₂×C₃

—

106

C₂×C₃

C₃×#399

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₉×C₂²⋊Q₈

yes

—

112

C₄

—

113

C₄

C₉×#123

yes

—

114

C₄

C₉×#127

yes

characteristic

115

C₃

C₃×#2091

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

C₉×#399

yes

characteristic

	subgroup	G/H
center	C₄×C₉	#127
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#399
prime radical	C₂⁴×C₃	C₃×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₄×C₉

#127

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂×C₃

C₃×#399

prime radical

C₂⁴×C₃

C₃×Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
1. C₉×#430	C₂	semidirect
3. C₉×#338	C₂	semidirect
22. #2091	C₉	direct (N × H)
38. #430	C₂×C₉	semidirect
40. #338	C₂×C₉	semidirect
93. C₉	#2091	direct (N × H)

H ≅ G/N

type

1. C₉×#430

C₂

semidirect

3. C₉×#338

C₂

semidirect

22. #2091

C₉

direct (N × H)

38. #430

C₂×C₉

semidirect

40. #338

C₂×C₉

semidirect

93. C₉

#2091

direct (N × H)

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

subgroup	index
C₉×#430	2
C₉×#407	2
C₉×#338	2
C₃×#2091	3

subgroup

index

Subgroups — C₉×#2091 #11766812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2091 #11766812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2091 #11766812