Group #25014660 — subgroups

Subgroups — #25014660

Order 11008.

274 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14582729	C₂	1	1	yes	maximal, characteristic
2	#19136191	C₂	1	1	yes	maximal, characteristic
3	#19135378	C₂	1	2	yes	maximal
4	#19132703	C₂	1	2	yes	maximal
5	C₂×C₄₃×#367	C₂	1	1	yes	maximal, characteristic
6	C₂×#13063265	C₂²	1	1	yes	characteristic
7	C₂×#13063261	C₂²	1	2	yes	—
8	#14582939	—	2	2	no	—
9	#14582854	C₂²	1	1	yes	characteristic
10	#14582729	C₄	1	4	yes	complemented
11	#14582674	—	2	1	no	—
12	C₁₆×Dic₄₃	—	2	1	no	—
13	#14582668	—	2	2	no	—
14	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#107×C₄₃	C₂²	1	2	yes	—
16	C₄₃×#367	—	2	1	no	—
17	C₄₃×#367	—	2	1	no	—
18	C₂×#10621877	—	2	2	no	—
19	C₂×#10621877	D₄	1	1	yes	characteristic
20	#13063284	D₄	1	1	yes	characteristic
21	#13063265	—	2	1	no	—
22	#13063265	Q₈	1	2	yes	—
23	C₂×C₄₃⋊C₁₆	—	2	1	no	—
24	#13063261	—	2	2	no	—
25	#13063261	C₂×C₄	1	4	yes	—
26	#13063258	—	4	2	no	—
27	#13063256	—	4	2	no	—
28	#13063235	—	2	1	no	—
29	C₈×Dic₄₃	—	2	1	no	—
30	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
32	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
33	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
34	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₄₃	Q₈	1	2	yes	—
36	#107×C₄₃	—	2	2	no	—
37	#107×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	4	2	no	—
39	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
45	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
46	C₄⋊C₄×C₄₃	—	4	2	no	—
47	C₄⋊C₄×C₄₃	—	4	2	no	—
48	C₂²⋊Dic₄₃	—	2	1	no	—
49	C₄⋊Dic₄₃	D₈	1	2	yes	—
50	C₄×Dic₄₃	—	2	1	no	—
51	#10621877	—	2	1	no	—
52	#10621877	—	2	4	no	—
53	#10621877	—	4	2	no	—
54	#10621877	Q₁₆	1	2	yes	—
55	C₂×C₄₃⋊C₈	—	2	1	no	—
56	C₂×C₄₃⋊C₈	—	4	2	no	—
57	C₁₆×C₄₃	C₄⋊C₄	1	2	yes	—
58	C₁₆×C₄₃	C₄⋊C₄	1	2	yes	—
59	C₄₃⋊C₁₆	—	2	2	no	—
60	C₂³×C₄₃	#135	1	1	yes	characteristic
61	C₂×C₄×C₄₃	—	8	2	no	—
62	C₂×C₄×C₄₃	—	16	2	no	—
63	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
64	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
65	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
66	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
67	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
68	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
69	C₂×Dic₄₃	—	2	2	no	—
70	C₈×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₈×C₄₃	C₄×Q₈	1	1	yes	characteristic
72	C₈×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
73	C₈×C₄₃	#125	1	1	yes	characteristic
74	C₄₃⋊C₈	—	2	2	no	—
75	C₄₃⋊C₈	—	4	4	no	—
76	#13172	—	43	1	no	maximal, Sylow
77	C₂²×C₄₃	—	2	2	no	—
78	C₂²×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
79	C₂²×C₄₃	#466	1	1	yes	characteristic
80	C₂²×C₄₃	#499	1	1	yes	characteristic
81	C₄×C₄₃	—	16	2	no	—
82	C₄×C₄₃	#389	1	1	yes	characteristic
83	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
84	C₄×C₄₃	#467	1	1	yes	characteristic
85	C₄×C₄₃	#500	1	1	yes	characteristic
86	Dic₄₃	—	4	2	no	—
87	C₂×#368	—	43	1	no	—
88	C₂×#367	D₄₃	1	1	yes	characteristic
89	#2108	—	43	1	no	—
90	#1952	—	43	2	no	—
91	#1387	—	43	2	no	—
92	C₂×C₄₃	—	2	1	no	—
93	C₂×C₄₃	—	2	1	no	—
94	C₂×C₄₃	#1942	1	1	yes	characteristic
95	C₂×C₄₃	#2223	1	2	yes	—
96	C₂×M₃₂	—	43	1	no	—
97	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
98	C₂×#108	—	43	2	no	—
99	#428	—	86	2	no	—
100	C₂×#107	C₂×D₄₃	1	2	yes	—
101	#405	—	43	1	no	—
102	#368	—	43	4	no	—
103	#367	—	2	1	no	—
104	#367	—	2	1	no	—
105	#346	—	86	1	no	—
106	C₄×C₁₆	—	86	1	no	—
107	#343	—	86	2	no	—
108	C₄₃	#13172	1	1	yes	characteristic, complemented, Sylow
109	C₂×M₁₆	—	43	1	no	—
110	C₂×M₁₆	—	86	2	no	—
111	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
112	#117	—	43	1	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	M₃₂	—	43	2	no	—
115	M₃₂	—	86	1	no	—
116	C₂×C₁₆	—	86	1	no	—
117	C₂×C₁₆	Dic₈₆	1	2	yes	—
118	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
119	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
120	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
121	#108	—	43	4	no	—
122	#108	—	86	2	no	—
123	#107	—	2	2	no	—
124	#107	—	2	2	no	—
125	#107	—	172	2	no	—
126	#106	—	172	2	no	—
127	#97	—	86	1	no	—
128	C₄×C₈	—	86	1	no	—
129	C₂²×C₄	—	4	2	no	—
130	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
131	M₁₆	—	43	2	no	—
132	M₁₆	—	86	1	no	—
133	M₁₆	—	86	4	no	—
134	M₁₆	—	172	2	no	—
135	C₂×C₈	—	86	1	no	—
136	C₂×C₈	—	172	2	no	—
137	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
138	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
139	C₂×C₈	#10621900	1	1	yes	characteristic
140	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
141	C₂×C₈	#10621902	1	1	yes	characteristic
142	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
143	C₄⋊C₄	—	4	2	no	—
144	C₄⋊C₄	—	4	2	no	—
145	C₄⋊C₄	—	43	2	no	—
146	C₂²⋊C₄	—	86	1	no	—
147	C₄²	—	86	1	no	—
148	C₁₆	—	86	2	no	—
149	C₁₆	Dic₄₃⋊C₄	1	2	yes	—
150	C₁₆	Dic₄₃⋊C₄	1	2	yes	—
151	C₂³	#13063344	1	1	yes	characteristic
152	C₂×C₄	—	8	2	no	—
153	C₂×C₄	—	16	2	no	—
154	C₂×C₄	—	86	2	no	—
155	C₂×C₄	#13063287	1	1	yes	characteristic
156	C₂×C₄	#13063296	1	1	yes	characteristic
157	C₂×C₄	#13063324	1	1	yes	characteristic
158	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
159	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
160	C₂×C₄	#13063348	1	1	yes	characteristic
161	C₈	—	86	2	no	—
162	C₈	—	172	4	no	—
163	C₈	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
164	C₈	#13063290	1	1	yes	characteristic
165	C₈	#13063301	1	1	yes	characteristic
166	C₈	#13063316	1	1	yes	characteristic
167	C₂²	—	2	2	no	—
168	C₂²	#14582993	1	1	yes	characteristic
169	C₂²	#14583132	1	1	yes	characteristic
170	C₂²	#14583300	1	1	yes	characteristic
171	C₄	—	16	2	no	—
172	C₄	—	172	2	no	—
173	C₄	#14582795	1	1	yes	characteristic
174	C₄	#14582981	1	1	yes	characteristic
175	C₄	#14583137	1	1	yes	characteristic
176	C₄	#14583303	1	1	yes	characteristic
177	C₂	—	2	1	no	—
178	C₂	—	2	1	no	—
179	C₂	#19135326	1	1	yes	characteristic
180	C₂	#19136722	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14582729

C₂

yes

maximal, characteristic

#19136191

C₂

yes

maximal, characteristic

#19135378

C₂

yes

maximal

#19132703

C₂

yes

maximal

C₂×C₄₃×#367

C₂

yes

maximal, characteristic

C₂×#13063265

C₂²

yes

characteristic

C₂×#13063261

C₂²

yes

—

#14582939

—

#14582854

C₂²

yes

characteristic

#14582729

C₄

yes

complemented

#14582674

—

C₁₆×Dic₄₃

—

#14582668

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#107×C₄₃

C₂²

yes

—

C₄₃×#367

—

C₄₃×#367

—

C₂×#10621877

—

C₂×#10621877

D₄

yes

characteristic

#13063284

D₄

yes

characteristic

#13063265

—

#13063265

Q₈

yes

—

C₂×C₄₃⋊C₁₆

—

#13063261

—

#13063261

C₂×C₄

yes

—

#13063258

—

#13063256

—

#13063235

—

C₈×Dic₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

Q₈

yes

—

#107×C₄₃

—

#107×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₄₃

C₂×Q₈

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

D₈

yes

—

C₄×Dic₄₃

—

—

—

—

Q₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

C₄⋊C₄

yes

—

C₁₆×C₄₃

C₄⋊C₄

yes

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#135

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

characteristic

C₂×C₄×C₄₃

#121

yes

characteristic

C₂×C₄×C₄₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₄₃

#135

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₄×Q₈

yes

characteristic

C₈×C₄₃

C₂²⋊Q₈

yes

characteristic

C₈×C₄₃

#125

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

#13172

—

maximal, Sylow

C₂²×C₄₃

—

C₂²×C₄₃

C₄×Q₁₆

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

#389

yes

characteristic

C₄×C₄₃

C₄×D₈

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

C₂×#368

—

C₂×#367

D₄₃

yes

—

—

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#1942

yes

characteristic

C₂×C₄₃

#2223

yes

—

C₂×M₃₂

—

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

C₂×#108

—

#428

—

100

C₂×#107

C₂×D₄₃

yes

—

101

#405

—

102

#368

—

103

#367

—

104

#367

—

105

#346

—

106

C₄×C₁₆

—

107

#343

—

108

C₄₃

#13172

yes

characteristic, complemented, Sylow

109

C₂×M₁₆

—

110

C₂×M₁₆

—

111

C₂²×C₈

C₂²×D₄₃

yes

characteristic

112

#117

—

113

C₂×C₄⋊C₄

—

114

M₃₂

—

115

M₃₂

—

116

C₂×C₁₆

—

117

C₂×C₁₆

Dic₈₆

yes

—

118

C₂×C₁₆

C₄×D₄₃

yes

—

119

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

120

C₂×C₁₆

C₂²⋊D₄₃

yes

characteristic

121

#108

—

122

#108

—

123

#107

—

124

#107

—

125

#107

—

172

—

126

#106

—

172

—

127

#97

—

128

C₄×C₈

—

129

C₂²×C₄

—

130

C₂²×C₄

D₄×D₄₃

yes

characteristic

131

M₁₆

—

132

M₁₆

—

133

M₁₆

—

134

M₁₆

—

172

—

135

C₂×C₈

—

136

C₂×C₈

—

172

—

137

C₂×C₈

C₂×Dic₈₆

yes

characteristic

138

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

139

C₂×C₈

#10621900

yes

characteristic

140

C₂×C₈

Q₈×D₄₃

yes

characteristic

141

C₂×C₈

#10621902

yes

characteristic

142

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₂²⋊C₄

—

147

C₄²

—

148

C₁₆

—

149

C₁₆

Dic₄₃⋊C₄

yes

—

150

C₁₆

Dic₄₃⋊C₄

yes

—

151

C₂³

#13063344

yes

characteristic

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

#13063287

yes

characteristic

156

C₂×C₄

#13063296

yes

characteristic

157

C₂×C₄

#13063324

yes

characteristic

158

C₂×C₄

D₈×D₄₃

yes

characteristic

159

C₂×C₄

Q₁₆×D₄₃

yes

characteristic

160

C₂×C₄

#13063348

yes

characteristic

161

C₈

—

162

C₈

—

172

—

163

C₈

C₂×Dic₄₃⋊C₄

yes

characteristic

164

C₈

#13063290

yes

characteristic

165

C₈

#13063301

yes

characteristic

166

C₈

#13063316

yes

characteristic

167

C₂²

—

168

C₂²

#14582993

yes

characteristic

169

C₂²

#14583132

yes

characteristic

170

C₂²

#14583300

yes

characteristic

171

C₄

—

172

C₄

—

172

—

173

C₄

#14582795

yes

characteristic

174

C₄

#14582981

yes

characteristic

175

C₄

#14583137

yes

characteristic

176

C₄

#14583303

yes

characteristic

177

C₂

—

178

C₂

—

179

C₂

#19135326

yes

characteristic

180

C₂

#19136722

yes

—

	subgroup	G/H
center	C₂²	#14583132
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#367	C₂
socle	C₂²×C₄₃	#466
prime radical	C₂³×C₄₃	#135
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#367	D₄₃
hypocenter	C₄₃	#13172
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

subgroup

G/H

center

C₂²

#14583132

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#367

C₂

C₂²×C₄₃

C₂³×C₄₃

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

N	H ≅ G/N	type
10. #14582729	C₄	semidirect
108. C₄₃	#13172	semidirect

H ≅ G/N

type

10. #14582729

C₄

semidirect

108. C₄₃

#13172

semidirect

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

subgroup	index
C₂×#14582729	2
#19136191	2
#19135378	2
#19132703	2
C₂×C₄₃×#367	2
#13172	43

subgroup

index

C₂×C₄₃×#367

Subgroups — #25014660

Conjugacy classes of subgroups

Complements

Maximal subgroups