Group #11795327 — subgroups

Subgroups — #11795327

Order 1152.

264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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	C₂×C₉×#106	C₂	1	1	yes	maximal, characteristic
2	#10588783	C₂	1	1	yes	maximal, characteristic
3	#10588644	C₂	1	2	yes	maximal
4	#10588227	C₂	1	1	yes	maximal, characteristic
5	#10588207	C₂	1	2	yes	maximal
6	#70573	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
9	#63488	C₂²	1	1	yes	characteristic
10	C₂×#3667	C₂²	1	1	yes	characteristic
11	C₂×#3667	C₂²	1	2	yes	—
12	C₉×#106	—	2	2	no	—
13	Dic₉⋊C₈	—	2	2	no	—
14	#63367	—	2	2	no	—
15	#63366	—	2	2	no	—
16	C₂×C₃×#106	D₃	1	1	yes	characteristic
17	#5102	—	3	1	no	—
18	#4964	—	3	2	no	—
19	#4552	—	3	1	no	—
20	#4530	—	3	2	no	—
21	C₂²×C₄×C₉	—	2	2	no	—
22	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂×C₈×C₉	—	2	2	no	—
24	C₂×C₈×C₉	D₄	1	2	yes	—
25	C₉×C₄⋊C₄	—	2	2	no	—
26	C₉×C₄⋊C₄	—	2	2	no	—
27	#3676	—	2	1	no	—
28	C₄⋊Dic₉	D₄	1	2	yes	—
29	C₄×Dic₉	—	2	1	no	—
30	#3667	—	2	2	no	—
31	#3667	—	2	2	no	—
32	#3667	Q₈	1	4	yes	—
33	C₂×C₉⋊C₈	—	2	2	no	—
34	C₂×C₉⋊C₈	—	2	1	no	—
35	#2090	—	9	1	no	Sylow
36	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
38	#926	—	3	1	no	—
39	C₂×#208	—	3	2	no	—
40	C₂×#208	—	3	1	no	—
41	C₃×#106	—	2	2	no	—
42	Dic₃⋊C₈	—	6	2	no	—
43	#808	—	6	2	no	—
44	#807	—	6	2	no	—
45	C₂³×C₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₉	—	4	2	no	—
47	C₂×C₄×C₉	—	8	2	no	—
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
51	C₂×C₄×C₉	#41	1	2	yes	—
52	C₂×Dic₉	—	2	2	no	—
53	C₈×C₉	—	2	2	no	—
54	C₉⋊C₈	—	2	4	no	—
55	C₉⋊C₈	—	4	1	no	—
56	#428	—	9	2	no	—
57	C₂×#106	D₉	1	1	yes	characteristic
58	#424	—	9	1	no	—
59	#343	—	9	2	no	—
60	#341	—	9	1	no	—
61	C₂²×C₃×C₄	—	2	2	no	—
62	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
63	C₂×C₃×C₈	—	2	2	no	—
64	C₂×C₃×C₈	#67	1	2	yes	—
65	C₃×C₄⋊C₄	—	2	2	no	—
66	C₃×C₄⋊C₄	—	2	2	no	—
67	#217	—	6	1	no	—
68	C₄⋊Dic₃	—	3	2	no	—
69	C₄×Dic₃	—	6	1	no	—
70	#208	—	3	4	no	—
71	#208	—	6	2	no	—
72	#208	—	6	2	no	—
73	C₂×C₃⋊C₈	—	6	2	no	—
74	C₂×C₃⋊C₈	—	6	1	no	—
75	C₂²×C₉	—	2	2	no	—
76	C₂²×C₉	#121	1	1	yes	characteristic
77	C₂²×C₉	#125	1	2	yes	—
78	C₄×C₉	—	8	2	no	—
79	C₄×C₉	C₂²⋊Q₈	1	2	yes	—
80	C₄×C₉	#123	1	1	yes	characteristic
81	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
82	Dic₉	—	4	2	no	—
83	C₂×M₁₆	—	9	2	no	—
84	C₂×M₁₆	—	9	1	no	—
85	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
86	#117	—	9	1	no	—
87	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
88	#107	—	18	2	no	—
89	#106	—	2	2	no	—
90	#106	—	18	2	no	—
91	C₄⋊C₈	—	18	2	no	—
92	C₂³×C₃	#237	1	1	yes	characteristic
93	C₂×C₃×C₄	—	4	2	no	—
94	C₂×C₃×C₄	—	8	2	no	—
95	C₂×C₃×C₄	#235	1	2	yes	—
96	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
98	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
99	C₂×Dic₃	—	6	2	no	—
100	C₃×C₈	—	2	2	no	—
101	C₃⋊C₈	—	6	4	no	—
102	C₃⋊C₈	—	12	1	no	—
103	C₂×C₉	—	2	2	no	—
104	C₂×C₉	#398	1	1	yes	characteristic
105	C₂×C₉	#471	1	2	yes	—
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
108	M₁₆	—	9	4	no	—
109	M₁₆	—	18	2	no	—
110	M₁₆	—	18	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	18	2	no	—
113	C₂×C₈	—	18	1	no	—
114	C₂×C₈	#611	1	2	yes	—
115	C₄⋊C₄	—	2	2	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	9	2	no	—
118	C₂²⋊C₄	—	18	1	no	—
119	C₄²	—	18	1	no	—
120	C₂²×C₃	—	2	2	no	—
121	C₂²×C₃	#889	1	2	yes	—
122	C₂²×C₃	#938	1	1	yes	characteristic
123	C₃×C₄	—	8	2	no	—
124	C₃×C₄	#896	1	2	yes	—
125	C₃×C₄	#929	1	1	yes	characteristic
126	C₃×C₄	#944	1	1	yes	characteristic
127	Dic₃	—	12	2	no	—
128	C₉	#2090	1	1	yes	characteristic, complemented, Sylow
129	C₂³	#3699	1	1	yes	characteristic
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	—	8	2	no	—
132	C₂×C₄	—	18	2	no	—
133	C₂×C₄	#3697	1	2	yes	—
134	C₂×C₄	D₄×D₉	1	1	yes	characteristic
135	C₂×C₄	Q₈×D₉	1	2	yes	—
136	C₂×C₄	C₂×#611	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	18	4	no	—
139	C₈	—	36	1	no	—
140	C₂×C₃	—	2	2	no	—
141	C₂×C₃	#4983	1	1	yes	characteristic
142	C₂×C₃	#5177	1	2	yes	—
143	C₂²	—	2	2	no	—
144	C₂²	#63451	1	2	yes	—
145	C₂²	#63500	1	1	yes	characteristic
146	C₄	—	8	2	no	—
147	C₄	—	36	2	no	—
148	C₄	#63458	1	2	yes	—
149	C₄	#63491	1	1	yes	characteristic
150	C₄	#63506	1	1	yes	characteristic
151	C₃	#70573	1	1	yes	characteristic
152	C₂	—	2	2	no	—
153	C₂	#10588663	1	1	yes	characteristic
154	C₂	#10588857	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₉×#106

C₂

yes

maximal, characteristic

#10588783

C₂

yes

maximal, characteristic

#10588644

C₂

yes

maximal

#10588227

C₂

yes

maximal, characteristic

#10588207

C₂

yes

maximal

#70573

—

maximal

C₂²×C₈×C₉

C₂²

yes

characteristic

C₂×C₉×C₄⋊C₄

C₂²

yes

—

#63488

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

characteristic

C₂×#3667

C₂²

yes

—

C₉×#106

—

Dic₉⋊C₈

—

#63367

—

#63366

—

C₂×C₃×#106

D₃

yes

—

—

—

—

C₂²×C₄×C₉

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

#3676

—

C₄⋊Dic₉

D₄

yes

—

C₄×Dic₉

—

#3667

—

#3667

—

#3667

Q₈

yes

—

C₂×C₉⋊C₈

—

C₂×C₉⋊C₈

—

#2090

—

Sylow

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₂×C₃×C₄⋊C₄

C₂×D₃

yes

—

—

—

—

—

Dic₃⋊C₈

—

#808

—

#807

—

C₂³×C₉

#41

yes

characteristic

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×Q₈

yes

—

C₂×C₄×C₉

#41

yes

—

C₂×Dic₉

—

C₈×C₉

—

C₉⋊C₈

—

C₉⋊C₈

—

#428

—

C₂×#106

D₉

yes

—

—

—

C₂²×C₃×C₄

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×C₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

#217

—

C₄⋊Dic₃

—

C₄×Dic₃

—

#208

—

#208

—

#208

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂²×C₉

—

C₂²×C₉

#121

yes

characteristic

C₂²×C₉

#125

yes

—

C₄×C₉

—

C₄×C₉

C₂²⋊Q₈

yes

—

C₄×C₉

#123

yes

characteristic

C₄×C₉

C₄⋊Q₈

yes

characteristic

Dic₉

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

C₂×D₉

yes

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂³×C₃

#237

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

#235

yes

—

C₂×C₃×C₄

D₃×D₄

yes

characteristic

C₂×C₃×C₄

D₃×Q₈

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

100

C₃×C₈

—

101

C₃⋊C₈

—

102

C₃⋊C₈

—

103

C₂×C₉

—

104

C₂×C₉

#398

yes

characteristic

105

C₂×C₉

#471

yes

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₉

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

#611

yes

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂²×C₃

—

121

C₂²×C₃

#889

yes

—

122

C₂²×C₃

#938

yes

characteristic

123

C₃×C₄

—

124

C₃×C₄

#896

yes

—

125

C₃×C₄

#929

yes

characteristic

126

C₃×C₄

#944

yes

characteristic

127

Dic₃

—

128

C₉

#2090

yes

characteristic, complemented, Sylow

129

C₂³

#3699

yes

characteristic

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

#3697

yes

—

134

C₂×C₄

D₄×D₉

yes

characteristic

135

C₂×C₄

Q₈×D₉

yes

—

136

C₂×C₄

C₂×#611

yes

characteristic

137

C₈

—

138

C₈

—

139

C₈

—

140

C₂×C₃

—

141

C₂×C₃

#4983

yes

characteristic

142

C₂×C₃

#5177

yes

—

143

C₂²

—

144

C₂²

#63451

yes

—

145

C₂²

#63500

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

#63458

yes

—

149

C₄

#63491

yes

characteristic

150

C₄

#63506

yes

characteristic

151

C₃

#70573

yes

characteristic

152

C₂

—

153

C₂

#10588663

yes

characteristic

154

C₂

#10588857

yes

—

	subgroup	G/H
center	C₂²	#63500
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂×C₉×#106	C₂
socle	C₂²×C₃	#938
prime radical	C₂³×C₃	#237
hypercenter	C₂×#106	D₉
hypocenter	C₉	#2090
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂²

#63500

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

Fitting

C₂×C₉×#106

C₂

C₂²×C₃

C₂³×C₃

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
128. C₉	#2090	semidirect

H ≅ G/N

type

128. C₉

#2090

semidirect

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

subgroup	index
C₂×C₉×#106	2
#10588783	2
#10588644	2
#10588227	2
#10588207	2
#70573	3

subgroup

index

C₂×C₉×#106

Subgroups — #11795327

Conjugacy classes of subgroups

Complements

Maximal subgroups