Group #11797353 — subgroups

Subgroups — #11797353

Order 1152.

207 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 207 conjugacy classes of subgroups — too many to draw. Only its 90 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	#10588371	C₂	1	1	yes	maximal, characteristic
2	C₉×#346	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₉)⋊C₁₆	C₂	1	2	yes	maximal
4	Dic₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#69074	—	3	1	no	maximal
7	C₂×#3663	C₄	1	1	yes	characteristic
8	C₂×C₈×D₉	C₂²	1	1	yes	characteristic
9	#63434	C₄	1	1	yes	characteristic
10	C₂×C₉×C₁₆	C₂²	1	2	yes	—
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	#63375	C₄	1	1	yes	characteristic
13	C₈×Dic₉	C₂²	1	1	yes	characteristic
14	C₂×C₉⋊C₁₆	C₂²	1	2	yes	—
15	#63362	C₄	1	1	yes	characteristic
16	#4689	—	3	1	no	—
17	C₃×#346	D₃	1	1	yes	characteristic
18	(C₂×D₃)⋊C₁₆	—	3	2	no	—
19	Dic₃⋊C₁₆	—	3	2	no	—
20	C₄×C₃⋊C₁₆	—	3	1	no	—
21	C₂×C₄×D₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
24	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
25	(C₂×D₉)⋊C₄	C₈	1	2	yes	—
26	Dic₉⋊C₄	C₈	1	2	yes	—
27	C₄×Dic₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₉⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×C₉⋊C₈	C₂×C₄	1	1	yes	characteristic
30	#3663	—	2	2	no	—
31	C₈×D₉	—	2	2	no	—
32	C₉×C₁₆	—	2	2	no	—
33	C₉⋊C₁₆	—	2	2	no	—
34	#2164	—	9	1	no	Sylow
35	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
36	C₂×D₃×C₈	—	3	1	no	—
37	#872	—	3	1	no	—
38	C₂×C₃×C₁₆	C₂×D₃	1	2	yes	—
39	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
40	#815	—	3	1	no	—
41	C₈×Dic₃	—	3	1	no	—
42	C₂×C₃⋊C₁₆	—	3	2	no	—
43	#803	—	3	1	no	—
44	C₂²×D₉	C₂×C₈	1	1	yes	characteristic
45	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
46	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×Dic₉	C₂×C₈	1	2	yes	—
48	C₂×Dic₉	C₂×C₈	1	1	yes	characteristic
49	C₄×D₉	—	2	1	no	—
50	C₄×D₉	—	2	1	no	—
51	C₈×C₉	M₁₆	1	2	yes	—
52	C₈×C₉	#41	1	2	yes	—
53	C₉⋊C₈	—	2	1	no	—
54	C₉⋊C₈	—	2	1	no	—
55	#405	—	9	1	no	—
56	C₄⋊C₁₆	—	9	2	no	—
57	C₂²⋊C₁₆	—	9	2	no	—
58	#346	D₉	1	1	yes	characteristic, complemented
59	C₄×C₁₆	—	9	1	no	—
60	C₂×C₄×D₃	—	3	1	no	—
61	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
62	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
63	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
64	(C₂×D₃)⋊C₄	—	3	2	no	—
65	Dic₃⋊C₄	—	3	2	no	—
66	C₄×Dic₃	—	3	1	no	—
67	C₂×C₃⋊C₈	—	3	1	no	—
68	C₂×C₃⋊C₈	—	3	1	no	—
69	ΓL(1,𝔽₂₅)	—	6	2	no	—
70	D₃×C₈	—	6	2	no	—
71	C₃×C₁₆	—	2	2	no	—
72	C₃⋊C₁₆	—	6	2	no	—
73	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×D₉	—	2	1	no	—
75	C₂×D₉	—	2	2	no	—
76	C₄×C₉	—	2	2	no	—
77	C₄×C₉	#117	1	1	yes	characteristic
78	C₄×C₉	C₂×M₁₆	1	1	yes	characteristic
79	Dic₉	—	2	1	no	—
80	Dic₉	—	2	2	no	—
81	C₂×M₁₆	—	9	1	no	—
82	C₂²×C₈	—	9	1	no	—
83	#117	—	9	1	no	—
84	C₂×C₁₆	—	9	2	no	—
85	C₂×C₁₆	C₂×D₉	1	2	yes	—
86	#97	—	9	1	no	—
87	#97	—	9	1	no	—
88	C₄×C₈	—	9	1	no	—
89	C₄×C₈	C₂×D₉	1	1	yes	characteristic
90	C₂²×D₃	—	3	1	no	—
91	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
92	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
93	C₂×Dic₃	—	3	2	no	—
94	C₂×Dic₃	—	3	1	no	—
95	C₄×D₃	—	6	1	no	—
96	C₄×D₃	—	6	1	no	—
97	C₃×C₈	ΓL(1,𝔽₂₅)	1	2	yes	—
98	C₃×C₈	#235	1	2	yes	—
99	C₃⋊C₈	—	6	1	no	—
100	C₃⋊C₈	—	6	1	no	—
101	C₂×C₉	#431	1	1	yes	characteristic
102	C₂×C₉	#504	1	2	yes	—
103	D₉	—	4	1	no	—
104	C₂²×C₄	—	9	1	no	—
105	M₁₆	—	18	2	no	—
106	C₂×C₈	—	9	1	no	—
107	C₂×C₈	—	9	1	no	—
108	C₂×C₈	—	18	2	no	—
109	C₂×C₈	C₄×D₉	1	1	yes	characteristic
110	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
111	C₄⋊C₄	—	9	2	no	—
112	C₂²⋊C₄	—	9	2	no	—
113	C₄²	—	9	1	no	—
114	C₄²	C₄×D₉	1	1	yes	characteristic
115	C₁₆	—	2	2	no	—
116	C₁₆	—	18	2	no	—
117	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
118	C₂×D₃	—	6	2	no	—
119	C₂×D₃	—	6	1	no	—
120	C₃×C₄	—	2	2	no	—
121	C₃×C₄	#872	1	1	yes	characteristic
122	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
123	Dic₃	—	6	2	no	—
124	Dic₃	—	6	1	no	—
125	C₉	#2164	1	1	yes	characteristic, complemented, Sylow
126	C₂³	—	9	1	no	—
127	C₂×C₄	—	9	2	no	—
128	C₂×C₄	—	9	1	no	—
129	C₂×C₄	—	18	1	no	—
130	C₂×C₄	—	18	1	no	—
131	C₂×C₄	C₈×D₉	1	2	yes	—
132	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
133	C₈	—	18	1	no	—
134	C₈	—	18	1	no	—
135	C₈	#3663	1	2	yes	—
136	C₈	#3697	1	2	yes	—
137	C₂×C₃	#4685	1	1	yes	characteristic
138	C₂×C₃	#4907	1	2	yes	—
139	D₃	—	12	1	no	—
140	C₂²	—	18	2	no	—
141	C₂²	—	18	1	no	—
142	C₂²	C₂×C₈×D₉	1	1	yes	characteristic
143	C₄	—	2	2	no	—
144	C₄	—	18	2	no	—
145	C₄	—	18	1	no	—
146	C₄	#63434	1	1	yes	characteristic
147	C₄	C₂×#3663	1	1	yes	characteristic
148	C₃	#69074	1	1	yes	characteristic
149	C₂	—	36	1	no	—
150	C₂	#10588367	1	1	yes	characteristic
151	C₂	#10588587	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10588371

C₂

yes

maximal, characteristic

C₉×#346

C₂

yes

maximal, characteristic, complemented

(C₂×D₉)⋊C₁₆

C₂

yes

maximal

Dic₉⋊C₁₆

C₂

yes

maximal, complemented

C₄×C₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#69074

—

maximal

C₂×#3663

C₄

yes

characteristic

C₂×C₈×D₉

C₂²

yes

characteristic

#63434

C₄

yes

characteristic

C₂×C₉×C₁₆

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63375

C₄

yes

characteristic

C₈×Dic₉

C₂²

yes

characteristic

C₂×C₉⋊C₁₆

C₂²

yes

—

#63362

C₄

yes

characteristic

#4689

—

C₃×#346

D₃

yes

characteristic

(C₂×D₃)⋊C₁₆

—

Dic₃⋊C₁₆

—

C₄×C₃⋊C₁₆

—

C₂×C₄×D₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

C₂×C₄

yes

characteristic

C₂×C₈×C₉

C₂³

yes

characteristic

C₄²×C₉

C₂×C₄

yes

characteristic

(C₂×D₉)⋊C₄

C₈

yes

—

Dic₉⋊C₄

C₈

yes

—

C₄×Dic₉

C₂×C₄

yes

characteristic

C₂×C₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₉⋊C₈

C₂×C₄

yes

characteristic

#3663

—

C₈×D₉

—

C₉×C₁₆

—

C₉⋊C₁₆

—

#2164

—

Sylow

C₂×ΓL(1,𝔽₂₅)

—

C₂×D₃×C₈

—

#872

—

C₂×C₃×C₁₆

C₂×D₃

yes

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#815

—

C₈×Dic₃

—

C₂×C₃⋊C₁₆

—

#803

—

C₂²×D₉

C₂×C₈

yes

characteristic

C₂×C₄×C₉

C₂×C₈

yes

—

C₂×C₄×C₉

C₂²×C₄

yes

characteristic

C₂×Dic₉

C₂×C₈

yes

—

C₂×Dic₉

C₂×C₈

yes

characteristic

C₄×D₉

—

C₄×D₉

—

C₈×C₉

M₁₆

yes

—

C₈×C₉

#41

yes

—

C₉⋊C₈

—

C₉⋊C₈

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

D₉

yes

characteristic, complemented

C₄×C₁₆

—

C₂×C₄×D₃

—

C₂×C₃×C₈

C₄×D₃

yes

characteristic

C₂×C₃×C₈

C₂²×D₃

yes

characteristic

C₃×C₄²

C₄×D₃

yes

characteristic

(C₂×D₃)⋊C₄

—

Dic₃⋊C₄

—

C₄×Dic₃

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

ΓL(1,𝔽₂₅)

—

D₃×C₈

—

C₃×C₁₆

—

C₃⋊C₁₆

—

C₂²×C₉

C₂²×C₈

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

#117

yes

characteristic

C₄×C₉

C₂×M₁₆

yes

characteristic

Dic₉

—

Dic₉

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₉

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂²×D₃

—

C₂×C₃×C₄

D₃×C₈

yes

—

C₂×C₃×C₄

C₂×C₄×D₃

yes

characteristic

C₂×Dic₃

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

ΓL(1,𝔽₂₅)

yes

—

C₃×C₈

#235

yes

—

C₃⋊C₈

—

100

C₃⋊C₈

—

101

C₂×C₉

#431

yes

characteristic

102

C₂×C₉

#504

yes

—

103

D₉

—

104

C₂²×C₄

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₄×D₉

yes

characteristic

110

C₂×C₈

C₂²×D₉

yes

characteristic

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

C₄×D₉

yes

characteristic

115

C₁₆

—

116

C₁₆

—

117

C₂²×C₃

C₂×D₃×C₈

yes

characteristic

118

C₂×D₃

—

119

C₂×D₃

—

120

C₃×C₄

—

121

C₃×C₄

#872

yes

characteristic

122

C₃×C₄

C₂×ΓL(1,𝔽₂₅)

yes

characteristic

123

Dic₃

—

124

Dic₃

—

125

C₉

#2164

yes

characteristic, complemented, Sylow

126

C₂³

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

C₈×D₉

yes

—

132

C₂×C₄

C₂×C₄×D₉

yes

characteristic

133

C₈

—

134

C₈

—

135

C₈

#3663

yes

—

136

C₈

#3697

yes

—

137

C₂×C₃

#4685

yes

characteristic

138

C₂×C₃

#4907

yes

—

139

D₃

—

140

C₂²

—

141

C₂²

—

142

C₂²

C₂×C₈×D₉

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

#63434

yes

characteristic

147

C₄

C₂×#3663

yes

characteristic

148

C₃

#69074

yes

characteristic

149

C₂

—

150

C₂

#10588367

yes

characteristic

151

C₂

#10588587

yes

—

	subgroup	G/H
center	C₂×C₈	C₂²×D₉
commutator	C₂²×C₉	C₂²×C₈
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₉×#346	C₂
socle	C₂²×C₃	C₂×D₃×C₈
prime radical	C₂²×D₉	C₂×C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	#346	D₉
hypocenter	C₉	#2164
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center

C₂×C₈

C₂²×D₉

commutator

C₂²×C₉

C₂²×C₈

Frattini

C₂×C₃×C₈

C₂²×D₃

Fitting

C₉×#346

C₂

socle

C₂²×C₃

C₂×D₃×C₈

prime radical

C₂²×D₉

C₂×C₈

cosocle

C₂×C₈×C₉

C₂³

D₉

C₉

G ▷ C₂²×C₉ ▷ C₉

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
2. C₉×#346	C₂	semidirect
4. Dic₉⋊C₁₆	C₂	semidirect
5. C₄×C₉⋊C₁₆	C₂	semidirect
58. #346	D₉	semidirect
125. C₉	#2164	semidirect

H ≅ G/N

type

2. C₉×#346

C₂

semidirect

4. Dic₉⋊C₁₆

C₂

semidirect

5. C₄×C₉⋊C₁₆

C₂

semidirect

58. #346

D₉

semidirect

125. C₉

#2164

semidirect

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

subgroup	index
#10588371	2
C₉×#346	2
(C₂×D₉)⋊C₁₆	2
Dic₉⋊C₁₆	2
C₄×C₉⋊C₁₆	2
#69074	3

subgroup

index

#10588371

C₉×#346

(C₂×D₉)⋊C₁₆

Dic₉⋊C₁₆

C₄×C₉⋊C₁₆

#69074

Subgroups — #11797353

Conjugacy classes of subgroups

Complements

Maximal subgroups