Group #11795324 — subgroups

Subgroups — #11795324

Order 1152.

264 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 96 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×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×#63377	C₂	1	1	yes	maximal, characteristic
3	#10588679	C₂	1	2	yes	maximal
4	#10588234	C₂	1	2	yes	maximal
5	#10588227	C₂	1	1	yes	maximal, characteristic
6	#70533	—	3	1	no	maximal
7	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×#3667	C₂²	1	2	yes	—
12	C₉×C₄⋊C₈	—	2	2	no	—
13	#63377	—	2	2	no	—
14	#63367	—	2	2	no	—
15	#63366	—	2	2	no	—
16	C₃×#424	D₃	1	1	yes	characteristic
17	C₂×#817	—	3	1	no	—
18	#4995	—	3	2	no	—
19	#4554	—	3	2	no	—
20	#4552	—	3	1	no	—
21	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₉	—	2	2	no	—
23	C₉×M₁₆	—	2	2	no	—
24	C₂×C₈×C₉	—	2	2	no	—
25	C₂×C₈×C₉	—	2	1	no	—
26	C₂×C₈×C₉	D₄	1	2	yes	—
27	C₉×C₄⋊C₄	D₄	1	2	yes	—
28	C₉×C₂²⋊C₄	—	2	1	no	—
29	C₄²×C₉	—	2	1	no	—
30	C₄⋊Dic₉	—	2	2	no	—
31	C₄⋊Dic₉	—	2	2	no	—
32	#3667	—	2	2	no	—
33	#3667	Q₈	1	4	yes	—
34	C₂×C₉⋊C₈	—	2	2	no	—
35	#2090	—	9	1	no	Sylow
36	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
37	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
38	C₃×#117	C₂×D₃	1	1	yes	characteristic
39	C₂×C₄⋊Dic₃	—	3	2	no	—
40	C₂×#208	—	3	2	no	—
41	C₃×C₄⋊C₈	—	2	2	no	—
42	#817	—	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	—	2	2	no	—
47	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
50	C₂×C₄×C₉	#41	1	2	yes	—
51	C₂×Dic₉	—	4	2	no	—
52	C₂×Dic₉	—	8	2	no	—
53	C₈×C₉	—	2	2	no	—
54	C₈×C₉	—	4	1	no	—
55	C₉⋊C₈	—	2	4	no	—
56	#428	—	9	2	no	—
57	C₂×#106	—	9	1	no	—
58	#424	D₉	1	1	yes	characteristic
59	#343	—	9	2	no	—
60	#341	—	9	1	no	—
61	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
62	C₂²×Dic₃	—	6	2	no	—
63	C₃×M₁₆	—	2	2	no	—
64	C₂×C₃×C₈	—	2	2	no	—
65	C₂×C₃×C₈	—	2	1	no	—
66	C₂×C₃×C₈	#67	1	2	yes	—
67	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
68	C₃×C₂²⋊C₄	—	2	1	no	—
69	C₃×C₄²	—	2	1	no	—
70	C₄⋊Dic₃	—	6	2	no	—
71	C₄⋊Dic₃	—	6	2	no	—
72	#208	—	3	4	no	—
73	#208	—	6	2	no	—
74	C₂×C₃⋊C₈	—	6	2	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	—	4	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	—	8	2	no	—
83	C₂×M₁₆	—	9	2	no	—
84	C₂×M₁₆	C₂×D₉	1	1	yes	characteristic
85	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
86	#117	C₂×D₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	9	2	no	—
88	#107	—	18	2	no	—
89	#106	—	18	2	no	—
90	#106	—	18	2	no	—
91	C₄⋊C₈	—	2	2	no	—
92	C₂³×C₃	#235	1	1	yes	characteristic
93	C₂×C₃×C₄	—	2	2	no	—
94	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
95	C₂×C₃×C₄	#237	1	2	yes	—
96	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
97	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
98	C₂×Dic₃	—	12	2	no	—
99	C₂×Dic₃	—	24	2	no	—
100	C₃×C₈	—	2	2	no	—
101	C₃×C₈	—	4	1	no	—
102	C₃⋊C₈	—	6	4	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	—	18	2	no	—
107	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
108	M₁₆	—	2	2	no	—
109	M₁₆	—	9	4	no	—
110	M₁₆	—	18	2	no	—
111	C₂×C₈	—	2	2	no	—
112	C₂×C₈	—	2	1	no	—
113	C₂×C₈	—	18	2	no	—
114	C₂×C₈	#611	1	2	yes	—
115	C₄⋊C₄	—	18	2	no	—
116	C₄⋊C₄	—	18	2	no	—
117	C₄⋊C₄	D₃₆	1	2	yes	—
118	C₂²⋊C₄	—	2	1	no	—
119	C₄²	—	2	1	no	—
120	C₂²×C₃	—	2	2	no	—
121	C₂²×C₃	#889	1	2	yes	—
122	C₂²×C₃	#930	1	1	yes	characteristic
123	C₃×C₄	—	4	2	no	—
124	C₃×C₄	#897	1	2	yes	—
125	C₃×C₄	#935	1	1	yes	characteristic
126	C₃×C₄	#944	1	1	yes	characteristic
127	Dic₃	—	24	2	no	—
128	C₉	#2090	1	1	yes	characteristic, complemented, Sylow
129	C₂³	#3697	1	1	yes	characteristic
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	36	2	no	—
132	C₂×C₄	—	72	2	no	—
133	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
134	C₂×C₄	#3699	1	2	yes	—
135	C₂×C₄	Q₈×D₉	1	2	yes	—
136	C₂×C₄	C₂×#611	1	1	yes	characteristic
137	C₈	—	2	2	no	—
138	C₈	—	4	1	no	—
139	C₈	—	18	4	no	—
140	C₂×C₃	—	2	2	no	—
141	C₂×C₃	#4981	1	1	yes	characteristic
142	C₂×C₃	#5141	1	2	yes	—
143	C₂²	—	2	2	no	—
144	C₂²	#63451	1	2	yes	—
145	C₂²	#63492	1	1	yes	characteristic
146	C₄	—	4	2	no	—
147	C₄	—	72	2	no	—
148	C₄	#63459	1	2	yes	—
149	C₄	#63497	1	1	yes	characteristic
150	C₄	#63506	1	1	yes	characteristic
151	C₃	#70533	1	1	yes	characteristic
152	C₂	—	2	2	no	—
153	C₂	#10588661	1	1	yes	characteristic
154	C₂	#10588822	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#424

C₂

yes

maximal, characteristic

C₂×#63377

C₂

yes

maximal, characteristic

#10588679

C₂

yes

maximal

#10588234

C₂

yes

maximal

#10588227

C₂

yes

maximal, characteristic

#70533

—

maximal

C₂×C₉×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₉

C₂²

yes

characteristic

C₉×#117

C₂²

yes

characteristic

C₂×C₄⋊Dic₉

C₂²

yes

—

C₂×#3667

C₂²

yes

—

C₉×C₄⋊C₈

—

—

—

—

D₃

yes

—

—

—

—

C₂²×C₄×C₉

C₂³

yes

characteristic

C₂²×Dic₉

—

C₉×M₁₆

—

C₂×C₈×C₉

—

C₂×C₈×C₉

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

D₄

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄⋊Dic₉

—

C₄⋊Dic₉

—

#3667

—

#3667

Q₈

yes

—

C₂×C₉⋊C₈

—

#2090

—

Sylow

C₂×C₃×M₁₆

C₂×D₃

yes

characteristic

C₂²×C₃×C₈

C₂×D₃

yes

characteristic

C₃×#117

C₂×D₃

yes

characteristic

C₂×C₄⋊Dic₃

—

C₂×#208

—

C₃×C₄⋊C₈

—

#817

—

#808

—

#807

—

C₂³×C₉

#41

yes

characteristic

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

—

C₂×Dic₉

—

C₈×C₉

—

C₈×C₉

—

C₉⋊C₈

—

#428

—

C₂×#106

—

#424

D₉

yes

characteristic

#343

—

#341

—

C₂²×C₃×C₄

C₂²×D₃

yes

characteristic

C₂²×Dic₃

—

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

D₁₂

yes

—

C₃×C₂²⋊C₄

—

C₃×C₄²

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

#208

—

#208

—

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

C₂×D₉

yes

characteristic

C₂²×C₈

C₂×D₉

yes

characteristic

#117

C₂×D₉

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂³×C₃

#235

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

#237

yes

—

C₂×C₃×C₄

D₃×Q₈

yes

—

C₂×C₃×C₄

C₂×#67

yes

characteristic

C₂×Dic₃

—

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

D₃₆

yes

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂²×C₃

—

121

C₂²×C₃

#889

yes

—

122

C₂²×C₃

#930

yes

characteristic

123

C₃×C₄

—

124

C₃×C₄

#897

yes

—

125

C₃×C₄

#935

yes

characteristic

126

C₃×C₄

#944

yes

characteristic

127

Dic₃

—

128

C₉

#2090

yes

characteristic, complemented, Sylow

129

C₂³

#3697

yes

characteristic

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

C₂×D₃₆

yes

characteristic

134

C₂×C₄

#3699

yes

—

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

#4981

yes

characteristic

142

C₂×C₃

#5141

yes

—

143

C₂²

—

144

C₂²

#63451

yes

—

145

C₂²

#63492

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

#63459

yes

—

149

C₄

#63497

yes

characteristic

150

C₄

#63506

yes

characteristic

151

C₃

#70533

yes

characteristic

152

C₂

—

153

C₂

#10588661

yes

characteristic

154

C₂

#10588822

yes

—

	subgroup	G/H
center	C₂²	#63492
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#424	C₂
socle	C₂²×C₃	#930
prime radical	C₂³×C₃	#235
hypercenter	#424	D₉
hypocenter	C₉	#2090
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#63492

commutator, cosocle

C₂²×C₄×C₉

C₂³

Frattini

C₂²×C₃×C₄

C₂²×D₃

C₂

C₂²×C₃

C₂³×C₃

D₉

C₉

G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

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
C₉×#424	2
C₂×#63377	2
#10588679	2
#10588234	2
#10588227	2
#70533	3

subgroup

index

Subgroups — #11795324

Conjugacy classes of subgroups

Complements

Maximal subgroups