Group #11782899 — subgroups

Subgroups — #11782899

Order 1152.

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

normal subgroups only

This group has 363 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	C₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588773	C₂	1	2	yes	maximal, complemented
3	#10588755	C₂	1	2	yes	maximal, complemented
4	#10588377	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588132	C₂	1	1	yes	maximal, characteristic, complemented
6	#71262	—	3	1	no	maximal
7	C₂×C₉×SD₁₆	—	2	2	no	—
8	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₉×#127	C₂²	1	1	yes	characteristic
10	C₂×#3673	—	2	4	no	—
11	C₂×D₇₂	—	2	2	no	—
12	#63436	C₂²	1	2	yes	—
13	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
14	#63369	—	2	4	no	—
15	C₄×C₉⋊C₈	C₂²	1	2	yes	—
16	C₃×#492	D₃	1	1	yes	characteristic
17	#5088	—	3	2	no	—
18	#5073	—	3	2	no	—
19	#4695	—	3	1	no	—
20	#4455	—	3	1	no	—
21	C₂×Q₈×C₉	—	2	1	no	—
22	C₂×D₄×C₉	—	2	2	no	—
23	C₂×D₄×C₉	—	2	1	no	—
24	C₂×D₃₆	—	2	2	no	—
25	C₂×D₃₆	—	2	2	no	—
26	C₂×D₃₆	—	2	2	no	—
27	C₉×SD₁₆	—	4	4	no	—
28	C₂×C₈×C₉	D₄	1	2	yes	—
29	C₉×C₄⋊C₄	—	2	2	no	—
30	C₄²×C₉	C₂³	1	1	yes	characteristic
31	#3673	—	4	8	no	—
32	C₂×C₉⋊C₈	D₄	1	4	yes	—
33	D₇₂	—	4	4	no	—
34	#1721	—	9	1	no	Sylow
35	C₂×C₃×SD₁₆	—	2	2	no	—
36	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
37	C₃×#127	C₂×D₃	1	1	yes	characteristic
38	C₂×#213	—	6	4	no	—
39	C₂×D₂₄	—	6	2	no	—
40	#874	—	3	2	no	—
41	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
42	#809	—	6	4	no	—
43	C₄×C₃⋊C₈	—	3	2	no	—
44	C₂³×C₉	—	4	1	no	—
45	C₂²×D₉	—	4	2	no	—
46	Q₈×C₉	—	4	2	no	—
47	D₄×C₉	—	4	2	no	—
48	D₄×C₉	—	4	4	no	—
49	C₂×C₄×C₉	—	4	1	no	—
50	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
52	D₃₆	—	4	4	no	—
53	D₃₆	—	4	4	no	—
54	D₃₆	—	4	4	no	—
55	C₈×C₉	D₈	1	4	yes	complemented
56	C₉⋊C₈	—	2	4	no	—
57	#493	—	9	2	no	—
58	#493	—	9	1	no	—
59	#492	D₉	1	1	yes	characteristic, complemented
60	#486	—	9	2	no	—
61	#322	—	9	1	no	—
62	C₂×C₃×Q₈	—	2	1	no	—
63	C₂×C₃×D₄	—	2	2	no	—
64	C₂×C₃×D₄	—	2	1	no	—
65	C₂×D₁₂	—	6	2	no	—
66	C₂×D₁₂	—	6	2	no	—
67	C₂×D₁₂	—	6	2	no	—
68	C₃×SD₁₆	—	4	4	no	—
69	C₂×C₃×C₈	#67	1	2	yes	—
70	C₃×C₄⋊C₄	—	2	2	no	—
71	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
72	#213	—	12	8	no	—
73	C₂×C₃⋊C₈	—	3	4	no	—
74	D₂₄	—	12	4	no	—
75	C₂²×C₉	—	8	1	no	—
76	C₂²×C₉	—	8	2	no	—
77	C₂²×C₉	#127	1	1	yes	characteristic
78	C₂×D₉	—	8	2	no	—
79	C₂×D₉	—	8	2	no	—
80	C₂×D₉	—	8	2	no	—
81	C₄×C₉	—	8	1	no	—
82	C₄×C₉	C₂×D₈	1	2	yes	—
83	C₄×C₉	AGL(1,ℤ/8)	1	4	yes	—
84	C₂×SD₁₆	—	2	2	no	—
85	C₂×D₈	—	18	4	no	—
86	C₂×D₈	—	18	2	no	—
87	C₄⋊Q₈	C₂×D₉	1	1	yes	characteristic
88	#127	—	9	2	no	—
89	#127	C₂×D₉	1	1	yes	characteristic
90	#102	—	18	4	no	—
91	C₄×C₈	—	9	2	no	—
92	C₄×C₈	C₂×D₉	1	1	yes	characteristic
93	C₂³×C₃	—	4	1	no	—
94	C₂²×D₃	—	12	2	no	—
95	C₃×Q₈	—	4	2	no	—
96	C₃×D₄	—	4	4	no	—
97	C₃×D₄	—	4	2	no	—
98	C₂×C₃×C₄	—	4	1	no	—
99	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
100	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
101	D₁₂	—	12	4	no	—
102	D₁₂	—	12	4	no	—
103	D₁₂	—	12	4	no	—
104	C₃×C₈	#213	1	4	yes	—
105	C₃⋊C₈	—	6	4	no	—
106	C₂×C₉	—	16	1	no	—
107	C₂×C₉	#493	1	1	yes	characteristic
108	C₂×C₉	#496	1	2	yes	—
109	D₉	—	16	2	no	—
110	C₂×Q₈	—	2	1	no	—
111	C₂×D₄	—	2	2	no	—
112	C₂×D₄	—	2	1	no	—
113	C₂×D₄	—	18	2	no	—
114	C₂×D₄	—	18	2	no	—
115	C₂×D₄	—	18	2	no	—
116	SD₁₆	—	4	4	no	—
117	D₈	—	36	8	no	—
118	D₈	—	36	4	no	—
119	C₂×C₈	—	9	4	no	—
120	C₂×C₈	#611	1	2	yes	—
121	C₄⋊C₄	—	2	2	no	—
122	C₄²	C₂²×D₉	1	1	yes	characteristic
123	C₂²×C₃	—	8	2	no	—
124	C₂²×C₃	—	8	1	no	—
125	C₂²×C₃	#940	1	1	yes	characteristic
126	C₂×D₃	—	24	2	no	—
127	C₂×D₃	—	24	2	no	—
128	C₂×D₃	—	24	2	no	—
129	C₃×C₄	—	8	1	no	—
130	C₃×C₄	#914	1	4	yes	—
131	C₃×C₄	C₂×#213	1	2	yes	—
132	C₉	#1721	1	1	yes	characteristic, complemented, Sylow
133	C₂³	—	4	1	no	—
134	C₂³	—	36	2	no	—
135	Q₈	—	4	2	no	—
136	D₄	—	4	2	no	—
137	D₄	—	4	4	no	—
138	D₄	—	36	4	no	—
139	D₄	—	36	4	no	—
140	D₄	—	36	4	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	D₄×D₉	1	2	yes	—
143	C₂×C₄	C₂×#611	1	1	yes	characteristic
144	C₈	—	18	4	no	—
145	C₈	#3673	1	4	yes	complemented
146	C₂×C₃	—	16	1	no	—
147	C₂×C₃	#5073	1	1	yes	characteristic
148	C₂×C₃	#5176	1	2	yes	—
149	D₃	—	48	2	no	—
150	C₂²	—	8	1	no	—
151	C₂²	—	8	2	no	—
152	C₂²	—	72	2	no	—
153	C₂²	—	72	2	no	—
154	C₂²	—	72	2	no	—
155	C₂²	#63502	1	1	yes	characteristic
156	C₄	—	8	1	no	—
157	C₄	#63476	1	4	yes	—
158	C₄	C₂×#3673	1	2	yes	—
159	C₃	#71262	1	1	yes	characteristic
160	C₂	—	16	1	no	—
161	C₂	—	144	2	no	—
162	C₂	#10588755	1	1	yes	characteristic
163	C₂	#10588856	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₉×#492

C₂

yes

maximal, characteristic, complemented

#10588773

C₂

yes

maximal, complemented

#10588755

C₂

yes

maximal, complemented

#10588377

C₂

yes

maximal, characteristic, complemented

#10588132

C₂

yes

maximal, characteristic, complemented

#71262

—

maximal

C₂×C₉×SD₁₆

—

C₉×C₄⋊Q₈

C₂²

yes

characteristic

C₉×#127

C₂²

yes

characteristic

C₂×#3673

—

C₂×D₇₂

—

#63436

C₂²

yes

—

C₄×C₈×C₉

C₂²

yes

characteristic

#63369

—

C₄×C₉⋊C₈

C₂²

yes

—

C₃×#492

D₃

yes

—

—

—

—

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₉×SD₁₆

—

C₂×C₈×C₉

D₄

yes

—

C₉×C₄⋊C₄

—

C₄²×C₉

C₂³

yes

characteristic

#3673

—

C₂×C₉⋊C₈

D₄

yes

—

D₇₂

—

#1721

—

Sylow

C₂×C₃×SD₁₆

—

C₃×C₄⋊Q₈

C₂×D₃

yes

characteristic

C₃×#127

C₂×D₃

yes

characteristic

C₂×#213

—

C₂×D₂₄

—

#874

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

#809

—

C₄×C₃⋊C₈

—

C₂³×C₉

—

C₂²×D₉

—

Q₈×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

D₃₆

—

D₃₆

—

D₃₆

—

C₈×C₉

D₈

yes

complemented

C₉⋊C₈

—

#493

—

#493

—

#492

D₉

yes

characteristic, complemented

#486

—

#322

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×C₃×D₄

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₃×SD₁₆

—

C₂×C₃×C₈

#67

yes

—

C₃×C₄⋊C₄

—

C₃×C₄²

C₂²×D₃

yes

characteristic

#213

—

C₂×C₃⋊C₈

—

D₂₄

—

C₂²×C₉

—

C₂²×C₉

—

C₂²×C₉

#127

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

—

C₄×C₉

C₂×D₈

yes

—

C₄×C₉

AGL(1,ℤ/8)

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₉

yes

characteristic

#127

—

#127

C₂×D₉

yes

characteristic

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂³×C₃

—

C₂²×D₃

—

C₃×Q₈

—

C₃×D₄

—

C₃×D₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

D₃×D₄

yes

—

100

C₂×C₃×C₄

C₂×#67

yes

characteristic

101

D₁₂

—

102

D₁₂

—

103

D₁₂

—

104

C₃×C₈

#213

yes

—

105

C₃⋊C₈

—

106

C₂×C₉

—

107

C₂×C₉

#493

yes

characteristic

108

C₂×C₉

#496

yes

—

109

D₉

—

110

C₂×Q₈

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

SD₁₆

—

117

D₈

—

118

D₈

—

119

C₂×C₈

—

120

C₂×C₈

#611

yes

—

121

C₄⋊C₄

—

122

C₄²

C₂²×D₉

yes

characteristic

123

C₂²×C₃

—

124

C₂²×C₃

—

125

C₂²×C₃

#940

yes

characteristic

126

C₂×D₃

—

127

C₂×D₃

—

128

C₂×D₃

—

129

C₃×C₄

—

130

C₃×C₄

#914

yes

—

131

C₃×C₄

C₂×#213

yes

—

132

C₉

#1721

yes

characteristic, complemented, Sylow

133

C₂³

—

134

C₂³

—

135

Q₈

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

D₄×D₉

yes

—

143

C₂×C₄

C₂×#611

yes

characteristic

144

C₈

—

145

C₈

#3673

yes

complemented

146

C₂×C₃

—

147

C₂×C₃

#5073

yes

characteristic

148

C₂×C₃

#5176

yes

—

149

D₃

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

#63502

yes

characteristic

156

C₄

—

157

C₄

#63476

yes

—

158

C₄

C₂×#3673

yes

—

159

C₃

#71262

yes

characteristic

160

C₂

—

161

C₂

—

144

—

162

C₂

#10588755

yes

characteristic

163

C₂

#10588856

yes

—

	subgroup	G/H
center	C₂²	#63502
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#492	C₂
socle	C₂²×C₃	#940
hypercenter	#492	D₉
hypocenter	C₉	#1721
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#63502

commutator, cosocle

C₄²×C₉

C₂³

Frattini

C₃×C₄²

C₂²×D₃

C₂

C₂²×C₃

D₉

C₉

G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. C₉×#492	C₂	semidirect
2. #10588773	C₂	semidirect
3. #10588755	C₂	semidirect
4. #10588377	C₂	semidirect
5. #10588132	C₂	semidirect
55. C₈×C₉	D₈	semidirect
59. #492	D₉	semidirect
132. C₉	#1721	semidirect
145. C₈	#3673	semidirect

H ≅ G/N

type

1. C₉×#492

C₂

semidirect

2. #10588773

C₂

semidirect

3. #10588755

C₂

semidirect

4. #10588377

C₂

semidirect

5. #10588132

C₂

semidirect

55. C₈×C₉

D₈

semidirect

59. #492

D₉

semidirect

132. C₉

#1721

semidirect

145. C₈

#3673

semidirect

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

subgroup	index
C₉×#492	2
#10588773	2
#10588755	2
#10588377	2
#10588132	2
#71262	3

subgroup

index

Subgroups — #11782899

Conjugacy classes of subgroups

Complements

Maximal subgroups