Group #11782905 — subgroups

Subgroups — #11782905

Order 1152.

363 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 98 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	#10588377	C₂	1	1	yes	maximal, characteristic, complemented
2	#10588377	C₂	1	2	yes	maximal, complemented
3	#10588376	C₂	1	2	yes	maximal, complemented
4	#10588375	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	#68094	—	3	1	no	maximal
7	C₂×D₇₂	—	2	4	no	—
8	C₂×D₇₂	—	2	2	no	—
9	C₂×#3664	—	2	2	no	—
10	#63436	C₂²	1	1	yes	characteristic
11	#63436	C₂²	1	2	yes	—
12	#63431	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₉	C₂²	1	2	yes	—
15	#63380	—	2	4	no	—
16	#4695	—	3	1	no	—
17	#4695	—	3	2	no	—
18	#4694	—	3	2	no	—
19	#4693	—	3	1	no	—
20	C₃×#322	D₃	1	1	yes	characteristic
21	C₂×D₃₆	—	2	2	no	—
22	C₂×D₃₆	—	2	1	no	—
23	C₂×D₃₆	—	2	2	no	—
24	C₂×D₃₆	—	2	2	no	—
25	C₂×D₃₆	—	2	2	no	—
26	C₂×Dic₁₈	—	2	1	no	—
27	C₂×C₈×C₉	D₄	1	4	yes	—
28	C₂×C₈×C₉	D₄	1	2	yes	—
29	C₄²×C₉	C₂³	1	1	yes	characteristic
30	C₄⋊Dic₉	—	2	2	no	—
31	D₇₂	—	4	8	no	—
32	D₇₂	—	4	4	no	—
33	#3664	—	4	4	no	—
34	#1721	—	9	1	no	Sylow
35	C₂×D₂₄	—	6	4	no	—
36	C₂×D₂₄	—	6	2	no	—
37	C₂×#204	—	6	2	no	—
38	#874	—	3	1	no	—
39	#874	—	3	2	no	—
40	#869	—	3	1	no	—
41	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
42	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
43	#821	—	6	4	no	—
44	C₂²×D₉	—	4	2	no	—
45	C₂²×D₉	—	4	1	no	—
46	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
48	C₂×Dic₉	—	4	1	no	—
49	D₃₆	—	4	2	no	—
50	D₃₆	—	4	4	no	—
51	D₃₆	—	4	4	no	—
52	D₃₆	—	4	4	no	—
53	D₃₆	—	4	4	no	—
54	Dic₁₈	—	4	2	no	—
55	C₈×C₉	—	2	4	no	—
56	C₈×C₉	D₈	1	4	yes	complemented
57	#493	—	9	2	no	—
58	#493	—	9	1	no	—
59	#492	—	9	1	no	—
60	#486	—	9	2	no	—
61	#322	D₉	1	1	yes	characteristic, complemented
62	C₂×D₁₂	—	6	2	no	—
63	C₂×D₁₂	—	6	1	no	—
64	C₂×D₁₂	—	6	2	no	—
65	C₂×D₁₂	—	6	2	no	—
66	C₂×D₁₂	—	6	2	no	—
67	C₂×Dic₆	—	6	1	no	—
68	C₂×C₃×C₈	D₁₂	1	4	yes	—
69	C₂×C₃×C₈	D₁₂	1	2	yes	—
70	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
71	C₄⋊Dic₃	—	6	2	no	—
72	D₂₄	—	12	8	no	—
73	D₂₄	—	12	4	no	—
74	#204	—	12	4	no	—
75	C₂²×C₉	#127	1	1	yes	characteristic
76	C₂×D₉	—	8	1	no	—
77	C₂×D₉	—	8	2	no	—
78	C₂×D₉	—	8	2	no	—
79	C₂×D₉	—	8	2	no	—
80	C₂×D₉	—	8	2	no	—
81	C₄×C₉	C₂×D₈	1	2	yes	—
82	C₄×C₉	AGL(1,ℤ/8)	1	4	yes	—
83	Dic₉	—	8	1	no	—
84	C₂×SD₁₆	—	18	2	no	—
85	C₂×D₈	—	18	4	no	—
86	C₂×D₈	—	18	2	no	—
87	C₄⋊Q₈	—	9	1	no	—
88	#127	—	9	2	no	—
89	#127	—	9	1	no	—
90	#102	—	18	4	no	—
91	C₄×C₈	C₂×D₉	1	2	yes	—
92	C₄×C₈	C₂×D₉	1	1	yes	characteristic
93	C₂²×D₃	—	12	2	no	—
94	C₂²×D₃	—	12	1	no	—
95	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
96	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
97	C₂×Dic₃	—	12	1	no	—
98	D₁₂	—	12	2	no	—
99	D₁₂	—	12	4	no	—
100	D₁₂	—	12	4	no	—
101	D₁₂	—	12	4	no	—
102	D₁₂	—	12	4	no	—
103	Dic₆	—	12	2	no	—
104	C₃×C₈	—	2	4	no	—
105	C₃×C₈	D₂₄	1	4	yes	—
106	C₂×C₉	#493	1	1	yes	characteristic
107	C₂×C₉	#496	1	2	yes	—
108	D₉	—	16	1	no	—
109	D₉	—	16	2	no	—
110	C₂×Q₈	—	18	1	no	—
111	C₂×D₄	—	18	2	no	—
112	C₂×D₄	—	18	2	no	—
113	C₂×D₄	—	18	2	no	—
114	C₂×D₄	—	18	2	no	—
115	C₂×D₄	—	18	1	no	—
116	SD₁₆	—	36	4	no	—
117	D₈	—	36	8	no	—
118	D₈	—	36	4	no	—
119	C₂×C₈	D₃₆	1	4	yes	—
120	C₂×C₈	D₃₆	1	2	yes	—
121	C₄⋊C₄	—	18	2	no	—
122	C₄²	C₂²×D₉	1	1	yes	characteristic
123	C₂²×C₃	#874	1	1	yes	characteristic
124	C₂×D₃	—	24	1	no	—
125	C₂×D₃	—	24	2	no	—
126	C₂×D₃	—	24	2	no	—
127	C₂×D₃	—	24	2	no	—
128	C₂×D₃	—	24	2	no	—
129	C₃×C₄	C₂×D₂₄	1	2	yes	—
130	C₃×C₄	#908	1	4	yes	—
131	Dic₃	—	24	1	no	—
132	C₉	#1721	1	1	yes	characteristic, complemented, Sylow
133	C₂³	—	36	2	no	—
134	C₂³	—	36	1	no	—
135	Q₈	—	36	2	no	—
136	D₄	—	36	4	no	—
137	D₄	—	36	2	no	—
138	D₄	—	36	4	no	—
139	D₄	—	36	4	no	—
140	D₄	—	36	4	no	—
141	C₂×C₄	—	36	1	no	—
142	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
143	C₂×C₄	C₂×D₃₆	1	2	yes	—
144	C₈	—	2	4	no	—
145	C₈	D₇₂	1	4	yes	complemented
146	C₂×C₃	#4695	1	1	yes	characteristic
147	C₂×C₃	#4712	1	2	yes	—
148	D₃	—	48	1	no	—
149	D₃	—	48	2	no	—
150	C₂²	—	72	2	no	—
151	C₂²	—	72	1	no	—
152	C₂²	—	72	2	no	—
153	C₂²	—	72	2	no	—
154	C₂²	—	72	2	no	—
155	C₂²	#63436	1	1	yes	characteristic
156	C₄	—	72	1	no	—
157	C₄	C₂×D₇₂	1	2	yes	—
158	C₄	#63470	1	4	yes	—
159	C₃	#68094	1	1	yes	characteristic
160	C₂	—	144	2	no	—
161	C₂	—	144	1	no	—
162	C₂	#10588377	1	1	yes	characteristic
163	C₂	#10588393	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#10588377

C₂

yes

maximal, characteristic, complemented

#10588377

C₂

yes

maximal, complemented

#10588376

C₂

yes

maximal, complemented

#10588375

C₂

yes

maximal, characteristic, complemented

C₉×#322

C₂

yes

maximal, characteristic, complemented

#68094

—

maximal

C₂×D₇₂

—

C₂×D₇₂

—

C₂×#3664

—

#63436

C₂²

yes

characteristic

#63436

C₂²

yes

—

#63431

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

characteristic

C₄×C₈×C₉

C₂²

yes

—

—

—

—

—

—

D₃

yes

characteristic

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×D₃₆

—

C₂×Dic₁₈

—

C₂×C₈×C₉

D₄

yes

—

C₂×C₈×C₉

D₄

yes

—

C₄²×C₉

C₂³

yes

characteristic

C₄⋊Dic₉

—

D₇₂

—

D₇₂

—

#3664

—

#1721

—

Sylow

C₂×D₂₄

—

C₂×D₂₄

—

—

—

—

—

C₃×C₄×C₈

C₂×D₃

yes

characteristic

C₃×C₄×C₈

C₂×D₃

yes

—

#821

—

C₂²×D₉

—

C₂²×D₉

—

C₂×C₄×C₉

C₂×D₄

yes

characteristic

C₂×C₄×C₉

C₂×D₄

yes

—

C₂×Dic₉

—

D₃₆

—

D₃₆

—

D₃₆

—

D₃₆

—

D₃₆

—

Dic₁₈

—

C₈×C₉

—

C₈×C₉

D₈

yes

—

—

—

—

D₉

yes

characteristic, complemented

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×D₁₂

—

C₂×Dic₆

—

C₂×C₃×C₈

D₁₂

yes

—

C₂×C₃×C₈

D₁₂

yes

—

C₃×C₄²

C₂²×D₃

yes

characteristic

C₄⋊Dic₃

—

D₂₄

—

D₂₄

—

#204

—

C₂²×C₉

#127

yes

characteristic

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₂×D₉

—

C₄×C₉

C₂×D₈

yes

—

C₄×C₉

AGL(1,ℤ/8)

yes

—

Dic₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

#127

—

#102

—

C₄×C₈

C₂×D₉

yes

—

C₄×C₈

C₂×D₉

yes

characteristic

C₂²×D₃

—

C₂²×D₃

—

C₂×C₃×C₄

C₂×D₁₂

yes

characteristic

C₂×C₃×C₄

C₂×D₁₂

yes

—

C₂×Dic₃

—

D₁₂

—

D₁₂

—

100

D₁₂

—

101

D₁₂

—

102

D₁₂

—

103

Dic₆

—

104

C₃×C₈

—

105

C₃×C₈

D₂₄

yes

—

106

C₂×C₉

#493

yes

characteristic

107

C₂×C₉

#496

yes

—

108

D₉

—

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

D₃₆

yes

—

120

C₂×C₈

D₃₆

yes

—

121

C₄⋊C₄

—

122

C₄²

C₂²×D₉

yes

characteristic

123

C₂²×C₃

#874

yes

characteristic

124

C₂×D₃

—

125

C₂×D₃

—

126

C₂×D₃

—

127

C₂×D₃

—

128

C₂×D₃

—

129

C₃×C₄

C₂×D₂₄

yes

—

130

C₃×C₄

#908

yes

—

131

Dic₃

—

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

C₂×D₃₆

yes

characteristic

143

C₂×C₄

C₂×D₃₆

yes

—

144

C₈

—

145

C₈

D₇₂

yes

complemented

146

C₂×C₃

#4695

yes

characteristic

147

C₂×C₃

#4712

yes

—

148

D₃

—

149

D₃

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

#63436

yes

characteristic

156

C₄

—

157

C₄

C₂×D₇₂

yes

—

158

C₄

#63470

yes

—

159

C₃

#68094

yes

characteristic

160

C₂

—

144

—

161

C₂

—

144

—

162

C₂

#10588377

yes

characteristic

163

C₂

#10588393

yes

—

	subgroup	G/H
center	C₂²	#63436
commutator, cosocle	C₄²×C₉	C₂³
Frattini	C₃×C₄²	C₂²×D₃
Fitting	C₉×#322	C₂
socle	C₂²×C₃	#874
hypercenter	#322	D₉
hypocenter	C₉	#1721
LCS	G ▷ C₄²×C₉ ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322

subgroup

G/H

center

C₂²

#63436

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 ◁ #322

N	H ≅ G/N	type
1. #10588377	C₂	semidirect
2. #10588377	C₂	semidirect
3. #10588376	C₂	semidirect
4. #10588375	C₂	semidirect
5. C₉×#322	C₂	semidirect
56. C₈×C₉	D₈	semidirect
61. #322	D₉	semidirect
132. C₉	#1721	semidirect
145. C₈	D₇₂	semidirect

H ≅ G/N

type

1. #10588377

C₂

semidirect

2. #10588377

C₂

semidirect

3. #10588376

C₂

semidirect

4. #10588375

C₂

semidirect

5. C₉×#322

C₂

semidirect

56. C₈×C₉

D₈

semidirect

61. #322

D₉

semidirect

132. C₉

#1721

semidirect

145. C₈

D₇₂

semidirect

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

subgroup	index
#10588377	2
#10588376	2
#10588375	2
C₉×#322	2
#68094	3

subgroup

index

Subgroups — #11782905

Conjugacy classes of subgroups

Complements

Maximal subgroups