Group #11766824 — subgroups

Subgroups — C₉×#2103 #11766824

Order 1152.

222 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 108 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	1	yes	maximal, characteristic
2	C₉×#424	C₂	1	1	yes	maximal, characteristic
3	C₉×#344	C₂	1	2	yes	maximal
4	C₉×#341	C₂	1	2	yes	maximal
5	C₉×#338	C₂	1	1	yes	maximal, characteristic
6	C₃×#2103	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×M₁₆	C₂²	1	2	yes	—
8	C₂×C₉×M₁₆	C₂²	1	2	yes	—
9	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₉×#117	C₂²	1	1	yes	characteristic
12	C₉×#108	—	2	2	no	—
13	C₉×C₄⋊C₈	—	2	2	no	—
14	C₃×#430	C₂×C₃	1	1	yes	characteristic
15	C₃×#424	C₂×C₃	1	1	yes	characteristic
16	C₃×#344	C₂×C₃	1	2	yes	—
17	C₃×#341	C₂×C₃	1	2	yes	—
18	C₃×#338	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
20	C₉×M₁₆	—	2	2	no	—
21	C₉×M₁₆	—	2	2	no	—
22	C₉×M₁₆	—	2	2	no	—
23	C₉×M₁₆	—	2	2	no	—
24	C₉×M₁₆	—	2	2	no	—
25	C₂×C₈×C₉	—	2	1	no	—
26	C₂×C₈×C₉	—	2	2	no	—
27	C₂×C₈×C₉	—	2	2	no	—
28	C₂×C₈×C₉	—	2	2	no	—
29	C₂×C₈×C₉	D₄	1	2	yes	—
30	C₉×C₄⋊C₄	—	2	1	no	—
31	C₉×C₂²⋊C₄	Q₈	1	2	yes	—
32	C₄²×C₉	—	2	1	no	—
33	#2103	C₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
35	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
36	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
38	C₃×#117	C₂²×C₃	1	1	yes	characteristic
39	C₃×#108	—	2	2	no	—
40	C₃×C₄⋊C₈	—	2	2	no	—
41	C₂³×C₉	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₉	—	2	2	no	—
43	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₉	#41	1	2	yes	—
45	C₂×C₄×C₉	#41	1	2	yes	—
46	C₂×C₄×C₉	#41	1	1	yes	characteristic
47	C₈×C₉	—	2	2	no	—
48	C₈×C₉	—	4	1	no	—
49	C₈×C₉	—	4	2	no	—
50	C₈×C₉	—	4	2	no	—
51	#430	C₂×C₉	1	1	yes	characteristic
52	#424	C₂×C₉	1	1	yes	characteristic
53	#344	C₂×C₉	1	2	yes	—
54	#341	C₂×C₉	1	2	yes	—
55	#338	C₂×C₉	1	1	yes	characteristic
56	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
57	C₃×M₁₆	—	2	2	no	—
58	C₃×M₁₆	—	2	2	no	—
59	C₃×M₁₆	—	2	2	no	—
60	C₃×M₁₆	—	2	2	no	—
61	C₃×M₁₆	—	2	2	no	—
62	C₂×C₃×C₈	—	2	1	no	—
63	C₂×C₃×C₈	—	2	2	no	—
64	C₂×C₃×C₈	—	2	2	no	—
65	C₂×C₃×C₈	—	2	2	no	—
66	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
67	C₃×C₄⋊C₄	—	2	1	no	—
68	C₃×C₂²⋊C₄	C₃×Q₈	1	2	yes	—
69	C₃×C₄²	—	2	1	no	—
70	C₂²×C₉	—	4	1	no	—
71	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
72	C₂²×C₉	#125	1	2	yes	—
73	C₄×C₉	—	4	2	no	—
74	C₄×C₉	#123	1	1	yes	characteristic
75	C₄×C₉	#124	1	1	yes	characteristic
76	C₄×C₉	#126	1	2	yes	—
77	C₂×M₁₆	C₂²×C₉	1	2	yes	—
78	C₂×M₁₆	C₂²×C₉	1	2	yes	—
79	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
80	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
81	#117	C₂²×C₉	1	1	yes	characteristic
82	#108	—	2	2	no	—
83	C₄⋊C₈	—	2	2	no	—
84	C₂³×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
85	C₂×C₃×C₄	—	2	2	no	—
86	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄	C₃×#41	1	2	yes	—
88	C₂×C₃×C₄	C₃×#41	1	2	yes	—
89	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
90	C₃×C₈	—	2	2	no	—
91	C₃×C₈	—	4	1	no	—
92	C₃×C₈	—	4	2	no	—
93	C₃×C₈	—	4	2	no	—
94	C₂×C₉	—	2	1	no	—
95	C₂×C₉	—	2	2	no	—
96	C₂×C₉	#400	1	1	yes	characteristic
97	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
98	M₁₆	—	2	2	no	—
99	M₁₆	—	2	2	no	—
100	M₁₆	—	2	2	no	—
101	M₁₆	—	2	2	no	—
102	M₁₆	—	2	2	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	D₄×C₉	1	2	yes	—
108	C₄⋊C₄	—	2	1	no	—
109	C₂²⋊C₄	Q₈×C₉	1	2	yes	—
110	C₄²	—	2	1	no	—
111	C₂²×C₃	—	4	1	no	—
112	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
113	C₂²×C₃	C₃×#125	1	2	yes	—
114	C₃×C₄	—	4	2	no	—
115	C₃×C₄	C₃×#123	1	1	yes	characteristic
116	C₃×C₄	C₃×#124	1	1	yes	characteristic
117	C₃×C₄	C₃×#126	1	2	yes	—
118	C₉	#2103	1	1	yes	characteristic, direct product factor, Sylow
119	C₂³	C₂×Q₈×C₉	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
122	C₂×C₄	C₉×#41	1	2	yes	—
123	C₂×C₄	C₉×#41	1	2	yes	—
124	C₂×C₄	C₉×#41	1	1	yes	characteristic
125	C₈	—	2	2	no	—
126	C₈	—	4	1	no	—
127	C₈	—	4	2	no	—
128	C₈	—	4	2	no	—
129	C₂×C₃	—	2	1	no	—
130	C₂×C₃	—	2	2	no	—
131	C₂×C₃	C₃×#400	1	1	yes	characteristic
132	C₂²	—	4	1	no	—
133	C₂²	C₉×C₂²⋊Q₈	1	1	yes	characteristic
134	C₂²	C₉×#125	1	2	yes	—
135	C₄	—	4	2	no	—
136	C₄	C₉×#123	1	1	yes	characteristic
137	C₄	C₉×#124	1	1	yes	characteristic
138	C₄	C₉×#126	1	2	yes	—
139	C₃	C₃×#2103	1	1	yes	characteristic
140	C₂	—	2	1	no	—
141	C₂	—	2	2	no	—
142	C₂	C₉×#400	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#430

C₂

yes

maximal, characteristic

C₉×#424

C₂

yes

maximal, characteristic

C₉×#344

C₂

yes

maximal

C₉×#341

C₂

yes

maximal

C₉×#338

C₂

yes

maximal, characteristic

C₃×#2103

C₃

yes

maximal, characteristic

C₂×C₉×M₁₆

C₂²

yes

—

C₂×C₉×M₁₆

C₂²

yes

—

C₂×C₉×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₉

C₂²

yes

characteristic

C₉×#117

C₂²

yes

characteristic

C₉×#108

—

C₉×C₄⋊C₈

—

C₃×#430

C₂×C₃

yes

characteristic

C₃×#424

C₂×C₃

yes

characteristic

C₃×#344

C₂×C₃

yes

—

C₃×#341

C₂×C₃

yes

—

C₃×#338

C₂×C₃

yes

characteristic

C₂²×C₄×C₉

C₂³

yes

characteristic

C₉×M₁₆

—

C₉×M₁₆

—

C₉×M₁₆

—

C₉×M₁₆

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₂²⋊C₄

Q₈

yes

—

C₄²×C₉

—

#2103

C₉

yes

characteristic, direct product factor, Sylow

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₂×C₃×M₁₆

C₂²×C₃

yes

—

C₂×C₃×M₁₆

C₂²×C₃

yes

characteristic

C₂²×C₃×C₈

C₂²×C₃

yes

characteristic

C₃×#117

C₂²×C₃

yes

characteristic

C₃×#108

—

C₃×C₄⋊C₈

—

C₂³×C₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×C₄×C₉

#41

yes

characteristic

C₈×C₉

—

C₈×C₉

—

C₈×C₉

—

C₈×C₉

—

#430

C₂×C₉

yes

characteristic

#424

C₂×C₉

yes

characteristic

#344

C₂×C₉

yes

—

#341

C₂×C₉

yes

—

#338

C₂×C₉

yes

characteristic

C₂²×C₃×C₄

C₂³×C₃

yes

characteristic

C₃×M₁₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₃×D₄

yes

—

C₃×C₄⋊C₄

—

C₃×C₂²⋊C₄

C₃×Q₈

yes

—

C₃×C₄²

—

C₂²×C₉

—

C₂²×C₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₉

#125

yes

—

C₄×C₉

—

C₄×C₉

yes

C₄×C₉

yes

C₄×C₉

yes

—

C₂×M₁₆

C₂²×C₉

yes

—

C₂×M₁₆

C₂²×C₉

yes

—

C₂×M₁₆

C₂²×C₉

yes

characteristic

C₂²×C₈

C₂²×C₉

yes

characteristic

#117

C₂²×C₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₂³×C₃

C₂×C₃×Q₈

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×C₃×D₄

yes

characteristic

C₂×C₃×C₄

C₃×#41

yes

—

C₂×C₃×C₄

C₃×#41

yes

—

C₂×C₃×C₄

C₃×#41

yes

characteristic

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₃×C₈

—

C₂×C₉

—

C₂×C₉

—

C₂×C₉

#400

yes

characteristic

C₂²×C₄

C₂³×C₉

yes

characteristic

M₁₆

—

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

D₄×C₉

yes

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

Q₈×C₉

yes

—

110

C₄²

—

111

C₂²×C₃

—

112

C₂²×C₃

C₃×C₂²⋊Q₈

yes

characteristic

113

C₂²×C₃

C₃×#125

yes

—

114

C₃×C₄

—

115

C₃×C₄

C₃×#123

yes

characteristic

116

C₃×C₄

C₃×#124

yes

characteristic

117

C₃×C₄

C₃×#126

yes

—

118

C₉

#2103

yes

characteristic, direct product factor, Sylow

119

C₂³

C₂×Q₈×C₉

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

C₂×D₄×C₉

yes

characteristic

122

C₂×C₄

C₉×#41

yes

—

123

C₂×C₄

C₉×#41

yes

—

124

C₂×C₄

C₉×#41

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₂×C₃

—

130

C₂×C₃

—

131

C₂×C₃

C₃×#400

yes

characteristic

132

C₂²

—

133

C₂²

C₉×C₂²⋊Q₈

yes

characteristic

134

C₂²

C₉×#125

yes

—

135

C₄

—

136

C₄

C₉×#123

yes

characteristic

137

C₄

C₉×#124

yes

characteristic

138

C₄

C₉×#126

yes

—

139

C₃

C₃×#2103

yes

characteristic

140

C₂

—

141

C₂

—

142

C₂

C₉×#400

yes

characteristic

	subgroup	G/H
center	C₄×C₉	#124
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#400
prime radical	C₂³×C₃	C₂×C₃×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

subgroup

G/H

center

C₄×C₉

#124

commutator

C₂²×C₄

C₂³×C₉

Frattini, cosocle

C₂²×C₃×C₄

C₂³×C₃

socle

C₂×C₃

C₃×#400

prime radical

C₂³×C₃

C₂×C₃×Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

N	H ≅ G/N	type
33. #2103	C₉	direct (N × H)
118. C₉	#2103	direct (N × H)

H ≅ G/N

type

33. #2103

C₉

direct (N × H)

118. C₉

#2103

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×#424	2
C₉×#344	2
C₉×#341	2
C₉×#338	2
C₃×#2103	3

subgroup

index

Subgroups — C₉×#2103 #11766824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#2103 #11766824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2103 #11766824