Group #26033162 — subgroups

Subgroups — #26033162

Order 11392.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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	Q₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152008	C₂	1	2	yes	maximal, complemented
3	#19152001	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151902	C₂	1	2	yes	maximal, complemented
5	#19151890	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151888	C₂	1	1	yes	maximal, characteristic
7	#19151878	C₂	1	2	yes	maximal
8	#19151729	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151698	C₂	1	2	yes	maximal
10	C₄×#13083562	C₂	1	1	yes	maximal, characteristic
11	#554×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#13083562	C₂²	1	1	yes	characteristic
13	#15668012	C₂²	1	2	yes	—
14	#15668012	C₂²	1	1	yes	characteristic
15	#15668011	—	2	1	no	—
16	#15668011	—	2	2	no	—
17	Q₈×Dic₈₉	—	2	1	no	—
18	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
19	C₄×Dic₁₇₈	C₂²	1	2	yes	—
20	#15667945	C₂²	1	2	yes	—
21	#15667945	C₂²	1	2	yes	—
22	#15667945	C₂²	1	2	yes	—
23	#15667943	C₂²	1	2	yes	—
24	#15667943	C₂²	1	1	yes	characteristic
25	C₄⋊#10623494	C₂²	1	2	yes	—
26	C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	#15667935	C₂²	1	2	yes	—
28	#15667935	C₂²	1	1	yes	characteristic
29	#15667933	C₂²	1	1	yes	characteristic
30	#15667933	C₂²	1	2	yes	—
31	#15667923	C₂²	1	2	yes	—
32	C₄×#10623494	C₂²	1	1	yes	characteristic
33	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	#125×C₈₉	C₂²	1	2	yes	—
35	C₂²⋊Q₈×C₈₉	—	2	1	no	—
36	C₂²⋊Q₈×C₈₉	—	2	2	no	—
37	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₈₉	C₂²	1	2	yes	—
39	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
41	C₂×Dic₁₇₈	—	2	1	no	—
42	C₂×Dic₁₇₈	—	2	2	no	—
43	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
44	#13083562	Q₈	1	4	yes	complemented
45	C₂×#10623494	C₂³	1	1	yes	characteristic
46	C₂×#10623494	C₂³	1	2	yes	—
47	C₂×#10623494	C₂³	1	1	yes	characteristic
48	C₄⋊Dic₈₉	—	2	2	no	—
49	C₄⋊Dic₈₉	—	2	1	no	—
50	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
51	C₄⋊Dic₈₉	C₂³	1	2	yes	—
52	#13083553	—	2	1	no	—
53	#13083553	—	2	2	no	—
54	C₄×Dic₈₉	—	2	2	no	—
55	C₄×Dic₈₉	—	2	1	no	—
56	C₂×Q₈×C₈₉	—	2	1	no	—
57	C₂×Q₈×C₈₉	D₄	1	1	yes	characteristic
58	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₈₉	—	2	1	no	—
60	C₂²×C₄×C₈₉	—	2	2	no	—
61	C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₄⋊C₄×C₈₉	D₄	1	2	yes	—
66	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
68	C₂²⋊C₄×C₈₉	—	2	1	no	—
69	C₂²⋊C₄×C₈₉	—	2	2	no	—
70	C₄²×C₈₉	C₂³	1	2	yes	—
71	C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	C₂³×C₈₉	—	2	1	no	—
73	Q₈×C₈₉	—	2	2	no	—
74	Q₈×C₈₉	—	8	1	no	—
75	D₄×C₈₉	—	2	1	no	—
76	D₄×C₈₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	2	no	—
79	C₂×C₄×C₈₉	—	4	2	no	—
80	C₂×C₄×C₈₉	—	8	2	no	—
81	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
86	C₂×Dic₈₉	—	2	1	no	—
87	C₂×Dic₈₉	—	2	2	no	—
88	C₂×Dic₈₉	—	2	1	no	—
89	Dic₁₇₈	—	2	1	no	—
90	Dic₁₇₈	—	8	2	no	—
91	Dic₁₇₈	—	8	1	no	—
92	Dic₁₇₈	C₂×Q₈	1	2	yes	—
93	#10623494	—	2	1	no	—
94	#10623494	—	2	2	no	—
95	#10623494	C₂×Q₈	1	2	yes	—
96	C₂²×C₈₉	—	2	2	no	—
97	C₂²×C₈₉	—	4	1	no	—
98	C₂²×C₈₉	—	4	1	no	—
99	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₈₉	—	2	2	no	—
101	C₄×C₈₉	—	2	2	no	—
102	C₄×C₈₉	—	2	1	no	—
103	C₄×C₈₉	—	4	1	no	—
104	C₄×C₈₉	—	4	2	no	—
105	C₄×C₈₉	#137	1	2	yes	—
106	C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
108	Dic₈₉	—	2	2	no	—
109	Dic₈₉	—	4	1	no	—
110	Dic₈₉	—	4	2	no	—
111	C₂×C₈₉	—	4	2	no	—
112	C₂×C₈₉	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
114	C₂×C₈₉	#576	1	1	yes	characteristic
115	#3385	—	89	1	no	maximal, Sylow
116	C₈₉	#3385	1	1	yes	characteristic, complemented, Sylow
117	Q₈²	—	89	1	no	—
118	#554	D₈₉	1	1	yes	characteristic
119	#501	—	89	2	no	—
120	#500	—	89	1	no	—
121	#479	—	89	2	no	—
122	#477	—	89	1	no	—
123	#476	—	89	1	no	—
124	#474	—	89	2	no	—
125	#446	—	89	1	no	—
126	#440	—	89	2	no	—
127	C₄×SD₁₆	—	89	1	no	—
128	C₂×SD₁₆	—	89	1	no	—
129	C₄⋊Q₈	—	89	2	no	—
130	C₄⋊Q₈	—	89	1	no	—
131	C₄⋊Q₈	—	178	1	no	—
132	C₄⋊Q₈	—	178	2	no	—
133	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
134	#125	C₂×D₈₉	1	2	yes	—
135	C₂²⋊Q₈	—	2	1	no	—
136	C₂²⋊Q₈	—	2	2	no	—
137	C₄×Q₈	—	89	1	no	—
138	C₄×Q₈	—	89	2	no	—
139	C₄×Q₈	—	178	1	no	—
140	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
141	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
142	C₄×D₄	C₂×D₈₉	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	#107	—	89	2	no	—
145	#107	—	89	2	no	—
146	#107	—	89	2	no	—
147	#106	—	89	1	no	—
148	#106	—	89	2	no	—
149	C₄⋊C₈	—	89	2	no	—
150	C₄⋊C₈	—	89	1	no	—
151	#103	—	89	1	no	—
152	#103	—	89	2	no	—
153	#102	—	89	1	no	—
154	#102	—	89	2	no	—
155	#97	—	89	2	no	—
156	C₄×C₈	—	89	1	no	—
157	C₂×Q₈	—	2	1	no	—
158	C₂×Q₈	—	89	1	no	—
159	C₂×Q₈	—	178	1	no	—
160	C₂×Q₈	—	178	2	no	—
161	C₂×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	2	2	no	—
165	SD₁₆	—	89	4	no	—
166	C₂×C₈	—	89	1	no	—
167	C₂×C₈	—	89	1	no	—
168	C₂×C₈	—	89	2	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	89	1	no	—
173	C₄⋊C₄	—	89	2	no	—
174	C₄⋊C₄	—	178	1	no	—
175	C₄⋊C₄	—	178	2	no	—
176	C₄⋊C₄	—	178	2	no	—
177	C₄⋊C₄	—	178	1	no	—
178	C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
179	C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
181	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
182	C₂²⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₄²	—	178	2	no	—
185	C₄²	—	178	1	no	—
186	C₄²	C₂²×D₈₉	1	1	yes	characteristic
187	C₄²	C₂²×D₈₉	1	2	yes	—
188	C₂³	—	2	1	no	—
189	Q₈	—	2	2	no	—
190	Q₈	—	8	1	no	—
191	Q₈	—	89	2	no	—
192	Q₈	—	178	1	no	—
193	Q₈	—	712	2	no	—
194	Q₈	—	712	1	no	—
195	D₄	—	2	1	no	—
196	D₄	Q₈×D₈₉	1	2	yes	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	8	2	no	—
201	C₂×C₄	—	178	2	no	—
202	C₂×C₄	—	178	1	no	—
203	C₂×C₄	—	178	1	no	—
204	C₂×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
205	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
206	C₂×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
209	C₈	—	89	2	no	—
210	C₈	—	178	1	no	—
211	C₈	—	178	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	4	2	no	—
221	C₄	—	356	1	no	—
222	C₄	—	356	2	no	—
223	C₄	—	178	2	no	—
224	C₄	#15668042	1	2	yes	—
225	C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
226	C₄	#15668060	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
229	C₂	C₂×#15668042	1	1	yes	characteristic
230	C₂	#19152401	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₇₈

C₂

yes

maximal, characteristic, complemented

#19152008

C₂

yes

maximal, complemented

#19152001

C₂

yes

maximal, characteristic, complemented

#19151902

C₂

yes

maximal, complemented

#19151890

C₂

yes

maximal, characteristic, complemented

#19151888

C₂

yes

maximal, characteristic

#19151878

C₂

yes

maximal

#19151729

C₂

yes

maximal, characteristic, complemented

#19151698

C₂

yes

maximal

C₄×#13083562

C₂

yes

maximal, characteristic

#554×C₈₉

C₂

yes

maximal, characteristic

C₂×#13083562

C₂²

yes

characteristic

#15668012

C₂²

yes

—

#15668012

C₂²

yes

characteristic

#15668011

—

#15668011

—

Q₈×Dic₈₉

—

C₄×Dic₁₇₈

C₂²

yes

characteristic

C₄×Dic₁₇₈

C₂²

yes

—

#15667945

C₂²

yes

—

#15667945

C₂²

yes

—

#15667945

C₂²

yes

—

#15667943

C₂²

yes

—

#15667943

C₂²

yes

characteristic

C₄⋊#10623494

C₂²

yes

—

C₄⋊#10623494

C₂²

yes

characteristic

#15667935

C₂²

yes

—

#15667935

C₂²

yes

characteristic

#15667933

C₂²

yes

characteristic

#15667933

C₂²

yes

—

#15667923

C₂²

yes

—

C₄×#10623494

C₂²

yes

characteristic

C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#125×C₈₉

C₂²

yes

—

C₂²⋊Q₈×C₈₉

—

C₂²⋊Q₈×C₈₉

—

C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₄×D₄×C₈₉

C₂²

yes

—

C₄×D₄×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

C₂³

yes

characteristic

#13083562

Q₈

yes

complemented

C₂×#10623494

C₂³

yes

characteristic

C₂×#10623494

C₂³

yes

—

C₂×#10623494

C₂³

yes

characteristic

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

C₂³

yes

characteristic

C₄⋊Dic₈₉

C₂³

yes

—

#13083553

—

#13083553

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

D₄

yes

characteristic

C₂×D₄×C₈₉

C₂³

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₄⋊C₄×C₈₉

D₄

yes

—

C₄⋊C₄×C₈₉

C₂³

yes

characteristic

C₄⋊C₄×C₈₉

C₂³

yes

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₂³

yes

—

C₄²×C₈₉

C₂³

yes

characteristic

C₂³×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

C₂×Q₈

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

C₂⁴

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

C₂×Q₈

yes

—

#10623494

—

#10623494

—

#10623494

C₂×Q₈

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂²×D₄

yes

characteristic

100

C₄×C₈₉

—

101

C₄×C₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

#137

yes

—

106

C₄×C₈₉

C₂²×Q₈

yes

characteristic

107

C₄×C₈₉

2₋¹⁺⁴

yes

characteristic

108

Dic₈₉

—

109

Dic₈₉

—

110

Dic₈₉

—

111

C₂×C₈₉

—

112

C₂×C₈₉

D₄×Q₈

yes

characteristic

113

C₂×C₈₉

C₂×#137

yes

characteristic

114

C₂×C₈₉

yes

115

—

116

C₈₉

#3385

yes

characteristic, complemented, Sylow

117

Q₈²

—

118

#554

D₈₉

yes

characteristic

119

#501

—

120

#500

—

121

#479

—

122

#477

—

123

#476

—

124

#474

—

125

#446

—

126

#440

—

127

C₄×SD₁₆

—

128

C₂×SD₁₆

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

178

—

132

C₄⋊Q₈

—

178

—

133

C₄⋊Q₈

C₂×D₈₉

yes

characteristic

134

#125

C₂×D₈₉

yes

—

135

C₂²⋊Q₈

—

136

C₂²⋊Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

178

—

140

C₄×Q₈

C₂×D₈₉

yes

characteristic

141

C₄×D₄

C₂×D₈₉

yes

characteristic

142

C₄×D₄

C₂×D₈₉

yes

—

143

C₂×C₄⋊C₄

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#103

—

153

#102

—

154

#102

—

155

#97

—

156

C₄×C₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

178

—

160

C₂×Q₈

—

178

—

161

C₂×Q₈

C₂²⋊D₈₉

yes

characteristic

162

C₂×D₄

C₂²×D₈₉

yes

characteristic

163

C₂²×C₄

—

164

C₂²×C₄

—

165

SD₁₆

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

178

—

175

C₄⋊C₄

—

178

—

176

C₄⋊C₄

—

178

—

177

C₄⋊C₄

—

178

—

178

C₄⋊C₄

C₂²⋊D₈₉

yes

characteristic

179

C₄⋊C₄

C₂²⋊D₈₉

yes

—

180

C₄⋊C₄

C₂²×D₈₉

yes

characteristic

181

C₄⋊C₄

C₂²×D₈₉

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

178

—

185

C₄²

—

178

—

186

C₄²

C₂²×D₈₉

yes

characteristic

187

C₄²

C₂²×D₈₉

yes

—

188

C₂³

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

178

—

193

Q₈

—

712

—

194

Q₈

—

712

—

195

D₄

—

196

D₄

Q₈×D₈₉

yes

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

178

—

202

C₂×C₄

—

178

—

203

C₂×C₄

—

178

—

204

C₂×C₄

C₂×C₂²⋊D₈₉

yes

—

205

C₂×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

206

C₂×C₄

C₂×C₂²⋊D₈₉

yes

—

207

C₂×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

208

C₂×C₄

C₂³×D₈₉

yes

characteristic

209

C₈

—

210

C₈

—

178

—

211

C₈

—

178

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂²×C₂²⋊D₈₉

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

356

—

222

C₄

—

356

—

223

C₄

—

178

—

224

C₄

#15668042

yes

—

225

C₄

C₂×Q₈×D₈₉

yes

characteristic

226

C₄

#15668060

yes

characteristic

227

C₂

—

228

C₂

Q₈×C₂²⋊D₈₉

yes

characteristic

229

C₂

C₂×#15668042

yes

characteristic

230

C₂

#19152401

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#554×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×D₄×C₈₉	C₂³
hypercenter	#554	D₈₉
hypocenter	C₈₉	#3385
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₈₉

commutator, cosocle

C₂×C₄×C₈₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₈₉

Fitting

#554×C₈₉

C₂

socle

C₂²×C₈₉

C₂²×D₄

prime radical

C₂×D₄×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

N	H ≅ G/N	type
1. Q₈×Dic₁₇₈	C₂	semidirect
2. #19152008	C₂	semidirect
3. #19152001	C₂	semidirect
4. #19151902	C₂	semidirect
5. #19151890	C₂	semidirect
8. #19151729	C₂	semidirect
44. #13083562	Q₈	semidirect
116. C₈₉	#3385	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₇₈

C₂

semidirect

2. #19152008

C₂

semidirect

3. #19152001

C₂

semidirect

4. #19151902

C₂

semidirect

5. #19151890

C₂

semidirect

8. #19151729

C₂

semidirect

44. #13083562

Q₈

semidirect

116. C₈₉

#3385

semidirect

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

subgroup	index
Q₈×Dic₁₇₈	2
#19152008	2
#19152001	2
#19151902	2
#19151890	2
#19151888	2
#19151878	2
#19151729	2
#19151698	2
C₄×#13083562	2
#554×C₈₉	2
#3385	89

subgroup

index

Q₈×Dic₁₇₈

#554×C₈₉

Subgroups — #26033162

Conjugacy classes of subgroups

Complements

Maximal subgroups