Group #28378321 — subgroups

Subgroups — D₁₀₉⋊(Q₈⋊C₈) #28378321

Order 13952.

280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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	D₁₀₉⋊(C₄⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₀₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20295876	C₂	1	2	yes	maximal, complemented
4	Q₈⋊#11724786	C₂	1	2	yes	maximal, complemented
5	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂×D₁₀₉⋊C₈	—	2	1	no	—
7	C₂×D₁₀₉⋊C₈	—	2	1	no	—
8	#16812766	—	2	1	no	—
9	C₄⋊#11724786	C₂²	1	2	yes	—
10	C₄×#11724786	—	2	1	no	—
11	C₄×#11724786	C₂²	1	2	yes	—
12	C₂×Q₈×D₁₀₉	C₄	1	1	yes	characteristic
13	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic
14	C₄×Dic₂₁₈	—	2	1	no	—
15	C₄×Dic₂₁₈	C₄	1	1	yes	characteristic
16	#16812664	—	2	1	no	—
17	#16812664	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×D₁₀₉	—	2	1	no	—
19	C₄⋊C₄×D₁₀₉	C₄	1	1	yes	characteristic
20	C₄²×D₁₀₉	—	2	1	no	—
21	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₁₀₉	C₄	1	1	yes	characteristic
23	D₁₀₉⋊C₈	—	2	4	no	—
24	D₁₀₉⋊C₈	—	4	2	no	—
25	C₂×#11724786	—	2	2	no	—
26	C₂×#11724786	—	2	2	no	—
27	C₂×Dic₂₁₈	—	2	1	no	—
28	C₂×Dic₂₁₈	C₂×C₄	1	1	yes	characteristic
29	Q₈×D₁₀₉	—	2	2	no	—
30	Q₈×D₁₀₉	C₈	1	4	yes	complemented
31	C₂×C₄×D₁₀₉	—	2	1	no	—
32	C₂×C₄×D₁₀₉	—	2	1	no	—
33	C₂×C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
35	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
36	C₄⋊Dic₁₀₉	—	2	1	no	—
37	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
38	#13182008	—	2	1	no	—
39	#13182008	—	2	1	no	—
40	#13182008	—	2	1	no	—
41	C₄×Dic₁₀₉	—	2	1	no	—
42	C₄×Dic₁₀₉	—	2	1	no	—
43	C₄×Dic₁₀₉	—	2	1	no	—
44	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
45	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
46	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
47	C₂×Q₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
48	C₄⋊C₄×C₁₀₉	—	2	1	no	—
49	C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×C₁₀₉	—	2	1	no	—
51	C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
53	Q₈×C₁₀₉	—	2	1	no	—
54	Q₈×C₁₀₉	C₂×C₈	1	2	yes	complemented
55	C₂×C₄×C₁₀₉	—	2	1	no	—
56	C₂×C₄×C₁₀₉	—	2	1	no	—
57	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×Dic₁₀₉	—	2	1	no	—
61	C₂×Dic₁₀₉	—	2	1	no	—
62	C₂×Dic₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
64	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
65	C₄×D₁₀₉	—	2	4	no	—
66	C₄×D₁₀₉	—	2	2	no	—
67	C₄×D₁₀₉	—	4	2	no	—
68	C₄×D₁₀₉	C₂×C₈	1	2	yes	—
69	C₄×D₁₀₉	M₁₆	1	2	yes	—
70	C₄×D₁₀₉	SD₁₆	1	2	yes	—
71	C₄×D₁₀₉	Q₁₆	1	2	yes	—
72	Dic₂₁₈	—	2	1	no	—
73	Dic₂₁₈	—	2	4	no	—
74	Dic₂₁₈	C₂×C₈	1	2	yes	complemented
75	#11724786	—	2	4	no	—
76	#11724786	—	4	2	no	—
77	C₂²×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
78	C₂×D₁₀₉	C₂²⋊C₈	1	2	yes	—
79	C₂×D₁₀₉	#103	1	2	yes	—
80	C₂×D₁₀₉	#104	1	2	yes	—
81	C₄×C₁₀₉	—	2	2	no	—
82	C₄×C₁₀₉	—	2	1	no	—
83	C₄×C₁₀₉	—	4	1	no	—
84	C₄×C₁₀₉	#103	1	2	yes	—
85	C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
86	C₄×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
87	Dic₁₀₉	—	2	2	no	—
88	Dic₁₀₉	—	2	1	no	—
89	Dic₁₀₉	—	4	1	no	—
90	Dic₁₀₉	C₂²⋊C₈	1	2	yes	—
91	Dic₁₀₉	C₂×SD₁₆	1	1	yes	characteristic
92	Dic₁₀₉	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₁₀₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
94	C₂×C₁₀₉	C₂×#103	1	1	yes	characteristic
95	C₂×C₁₀₉	C₂×#104	1	1	yes	characteristic
96	D₁₀₉	Q₈⋊C₈	1	4	yes	complemented
97	C₂×Q₈⋊C₈	—	109	1	no	maximal, Sylow
98	C₁₀₉	C₂×Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
99	C₂×C₄×Q₈	—	109	1	no	—
100	C₂×C₄⋊C₈	—	109	1	no	—
101	C₂×C₄×C₈	—	109	1	no	—
102	Q₈⋊C₈	—	109	2	no	—
103	Q₈⋊C₈	—	109	2	no	—
104	C₂²×Q₈	—	109	1	no	—
105	C₂²×C₈	—	218	1	no	—
106	C₂²×C₈	—	218	1	no	—
107	C₄×Q₈	—	109	1	no	—
108	C₄×Q₈	—	109	1	no	—
109	C₄×Q₈	—	109	1	no	—
110	C₄×Q₈	—	218	1	no	—
111	C₄×Q₈	—	218	1	no	—
112	C₄×Q₈	#89137	1	1	yes	characteristic
113	C₂×C₄⋊C₄	—	109	1	no	—
114	C₂×C₄⋊C₄	—	218	1	no	—
115	C₂×C₄²	—	109	1	no	—
116	C₂×C₄²	—	218	1	no	—
117	C₄⋊C₈	—	109	2	no	—
118	C₄⋊C₈	—	218	1	no	—
119	C₄×C₈	—	109	2	no	—
120	C₄×C₈	—	218	1	no	—
121	C₂×Q₈	—	109	4	no	—
122	C₂×Q₈	—	109	1	no	—
123	C₂×Q₈	—	218	1	no	—
124	C₂×Q₈	—	218	2	no	—
125	C₂×Q₈	C₂×#89137	1	1	yes	characteristic
126	C₂²×C₄	—	109	1	no	—
127	C₂²×C₄	—	109	1	no	—
128	C₂²×C₄	—	109	1	no	—
129	C₂²×C₄	—	218	1	no	—
130	C₂²×C₄	—	218	1	no	—
131	C₂×C₈	—	436	2	no	—
132	C₂×C₈	—	218	2	no	—
133	C₂×C₈	—	218	2	no	—
134	C₂×C₈	—	218	4	no	—
135	C₄⋊C₄	—	2	1	no	—
136	C₄⋊C₄	—	109	1	no	—
137	C₄⋊C₄	—	218	1	no	—
138	C₄⋊C₄	—	218	1	no	—
139	C₄⋊C₄	—	218	1	no	—
140	C₄⋊C₄	—	218	1	no	—
141	C₄⋊C₄	C₂×#89137	1	1	yes	characteristic
142	C₄²	—	2	1	no	—
143	C₄²	—	109	1	no	—
144	C₄²	—	109	1	no	—
145	C₄²	—	109	1	no	—
146	C₄²	—	218	1	no	—
147	C₄²	—	218	1	no	—
148	C₄²	—	218	1	no	—
149	C₄²	C₂×#89137	1	1	yes	characteristic
150	C₂³	—	109	1	no	—
151	Q₈	—	2	1	no	—
152	Q₈	—	109	2	no	—
153	Q₈	—	218	4	no	—
154	Q₈	—	218	1	no	—
155	Q₈	D₁₀₉⋊C₈	1	2	yes	complemented
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	109	1	no	—
159	C₂×C₄	—	109	1	no	—
160	C₂×C₄	—	109	2	no	—
161	C₂×C₄	—	109	2	no	—
162	C₂×C₄	—	109	2	no	—
163	C₂×C₄	—	109	2	no	—
164	C₂×C₄	—	109	1	no	—
165	C₂×C₄	—	436	2	no	—
166	C₂×C₄	—	218	2	no	—
167	C₂×C₄	—	218	4	no	—
168	C₂×C₄	—	218	1	no	—
169	C₂×C₄	—	218	1	no	—
170	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
171	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
172	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
173	C₈	—	436	2	no	—
174	C₈	—	218	4	no	—
175	C₂²	—	109	2	no	—
176	C₂²	—	109	2	no	—
177	C₂²	—	109	2	no	—
178	C₂²	C₂×C₂²⋊#89137	1	1	yes	characteristic
179	C₄	—	2	2	no	—
180	C₄	—	2	1	no	—
181	C₄	—	4	1	no	—
182	C₄	—	109	2	no	—
183	C₄	—	109	1	no	—
184	C₄	—	109	1	no	—
185	C₄	—	436	1	no	—
186	C₄	—	218	2	no	—
187	C₄	—	218	1	no	—
188	C₄	#16812762	1	2	yes	—
189	C₄	C₂×D₁₀₉⋊C₈	1	1	yes	characteristic
190	C₄	D₁₀₉⋊M₁₆	1	1	yes	characteristic
191	C₂	—	109	4	no	—
192	C₂	D₁₀₉⋊(C₂²⋊C₈)	1	1	yes	characteristic
193	C₂	C₂×#16812762	1	1	yes	characteristic
194	C₂	D₁₀₉⋊#104	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₀₉⋊(C₄⋊C₈)

C₂

yes

maximal, characteristic

C₄×D₁₀₉⋊C₈

C₂

yes

maximal, characteristic

#20295876

C₂

yes

maximal, complemented

Q₈⋊#11724786

C₂

yes

maximal, complemented

C₄×Q₈×D₁₀₉

C₂

yes

maximal, characteristic

C₂×D₁₀₉⋊C₈

—

C₂×D₁₀₉⋊C₈

—

#16812766

—

C₄⋊#11724786

C₂²

yes

—

C₄×#11724786

—

C₄×#11724786

C₂²

yes

—

C₂×Q₈×D₁₀₉

C₄

yes

characteristic

Q₈×Dic₁₀₉

C₂²

yes

characteristic

C₄×Dic₂₁₈

—

C₄×Dic₂₁₈

C₄

yes

characteristic

#16812664

—

#16812664

C₂²

yes

characteristic

C₄⋊C₄×D₁₀₉

—

C₄⋊C₄×D₁₀₉

C₄

yes

characteristic

C₄²×D₁₀₉

—

C₄²×D₁₀₉

C₂²

yes

characteristic

C₄×Q₈×C₁₀₉

C₄

yes

characteristic

D₁₀₉⋊C₈

—

D₁₀₉⋊C₈

—

C₂×#11724786

—

C₂×#11724786

—

C₂×Dic₂₁₈

—

C₂×Dic₂₁₈

C₂×C₄

yes

characteristic

Q₈×D₁₀₉

—

Q₈×D₁₀₉

C₈

yes

complemented

C₂×C₄×D₁₀₉

—

C₂×C₄×D₁₀₉

—

C₂×C₄×D₁₀₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₀₉

D₄

yes

characteristic

C₂×C₄×D₁₀₉

D₄

yes

characteristic

C₄⋊Dic₁₀₉

—

C₄⋊Dic₁₀₉

C₂×C₄

yes

—

—

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

—

C₄×Dic₁₀₉

D₄

yes

characteristic

C₄×Dic₁₀₉

D₄

yes

characteristic

C₄×Dic₁₀₉

C₂³

yes

characteristic

C₂×Q₈×C₁₀₉

C₂×C₄

yes

characteristic

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

C₂×C₄

yes

characteristic

C₄²×C₁₀₉

—

C₄²×C₁₀₉

C₂×C₄

yes

characteristic

C₂²×D₁₀₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₀₉

—

Q₈×C₁₀₉

C₂×C₈

yes

complemented

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₀₉

C₂×D₄

yes

characteristic

C₂×Dic₁₀₉

C₂×D₄

yes

characteristic

C₄×D₁₀₉

—

C₄×D₁₀₉

—

C₄×D₁₀₉

—

C₄×D₁₀₉

C₂×C₈

yes

—

C₄×D₁₀₉

M₁₆

yes

—

C₄×D₁₀₉

SD₁₆

yes

—

C₄×D₁₀₉

Q₁₆

yes

—

Dic₂₁₈

—

Dic₂₁₈

—

Dic₂₁₈

C₂×C₈

yes

complemented

#11724786

—

#11724786

—

C₂²×C₁₀₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₀₉

C₂²⋊C₈

yes

—

C₂×D₁₀₉

#103

yes

—

C₂×D₁₀₉

#104

yes

—

C₄×C₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

—

C₄×C₁₀₉

#103

yes

—

C₄×C₁₀₉

C₂²×C₈

yes

characteristic

C₄×C₁₀₉

C₂×M₁₆

yes

characteristic

Dic₁₀₉

—

Dic₁₀₉

—

Dic₁₀₉

—

Dic₁₀₉

C₂²⋊C₈

yes

—

Dic₁₀₉

C₂×SD₁₆

yes

characteristic

Dic₁₀₉

C₂×Q₁₆

yes

characteristic

C₂×C₁₀₉

C₂×C₂²⋊C₈

yes

C₂×C₁₀₉

yes

C₂×C₁₀₉

yes

D₁₀₉

Q₈⋊C₈

yes

complemented

C₂×Q₈⋊C₈

—

109

maximal, Sylow

C₁₀₉

C₂×Q₈⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

—

109

—

100

C₂×C₄⋊C₈

—

109

—

101

C₂×C₄×C₈

—

109

—

102

Q₈⋊C₈

—

109

—

103

Q₈⋊C₈

—

109

—

104

C₂²×Q₈

—

109

—

105

C₂²×C₈

—

218

—

106

C₂²×C₈

—

218

—

107

C₄×Q₈

—

109

—

108

C₄×Q₈

—

109

—

109

C₄×Q₈

—

109

—

110

C₄×Q₈

—

218

—

111

C₄×Q₈

—

218

—

112

C₄×Q₈

#89137

yes

characteristic

113

C₂×C₄⋊C₄

—

109

—

114

C₂×C₄⋊C₄

—

218

—

115

C₂×C₄²

—

109

—

116

C₂×C₄²

—

218

—

117

C₄⋊C₈

—

109

—

118

C₄⋊C₈

—

218

—

119

C₄×C₈

—

109

—

120

C₄×C₈

—

218

—

121

C₂×Q₈

—

109

—

122

C₂×Q₈

—

109

—

123

C₂×Q₈

—

218

—

124

C₂×Q₈

—

218

—

125

C₂×Q₈

C₂×#89137

yes

characteristic

126

C₂²×C₄

—

109

—

127

C₂²×C₄

—

109

—

128

C₂²×C₄

—

109

—

129

C₂²×C₄

—

218

—

130

C₂²×C₄

—

218

—

131

C₂×C₈

—

436

—

132

C₂×C₈

—

218

—

133

C₂×C₈

—

218

—

134

C₂×C₈

—

218

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

109

—

137

C₄⋊C₄

—

218

—

138

C₄⋊C₄

—

218

—

139

C₄⋊C₄

—

218

—

140

C₄⋊C₄

—

218

—

141

C₄⋊C₄

C₂×#89137

yes

characteristic

142

C₄²

—

143

C₄²

—

109

—

144

C₄²

—

109

—

145

C₄²

—

109

—

146

C₄²

—

218

—

147

C₄²

—

218

—

148

C₄²

—

218

—

149

C₄²

C₂×#89137

yes

characteristic

150

C₂³

—

109

—

151

Q₈

—

152

Q₈

—

109

—

153

Q₈

—

218

—

154

Q₈

—

218

—

155

Q₈

D₁₀₉⋊C₈

yes

complemented

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

109

—

159

C₂×C₄

—

109

—

160

C₂×C₄

—

109

—

161

C₂×C₄

—

109

—

162

C₂×C₄

—

109

—

163

C₂×C₄

—

109

—

164

C₂×C₄

—

109

—

165

C₂×C₄

—

436

—

166

C₂×C₄

—

218

—

167

C₂×C₄

—

218

—

168

C₂×C₄

—

218

—

169

C₂×C₄

—

218

—

170

C₂×C₄

C₂²⋊#89137

yes

characteristic

171

C₂×C₄

C₂²⋊#89137

yes

characteristic

172

C₂×C₄

C₂²×#89137

yes

characteristic

173

C₈

—

436

—

174

C₈

—

218

—

175

C₂²

—

109

—

176

C₂²

—

109

—

177

C₂²

—

109

—

178

C₂²

C₂×C₂²⋊#89137

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

109

—

183

C₄

—

109

—

184

C₄

—

109

—

185

C₄

—

436

—

186

C₄

—

218

—

187

C₄

—

218

—

188

C₄

#16812762

yes

—

189

C₄

C₂×D₁₀₉⋊C₈

yes

characteristic

190

C₄

D₁₀₉⋊M₁₆

yes

characteristic

191

C₂

—

109

—

192

C₂

D₁₀₉⋊(C₂²⋊C₈)

yes

characteristic

193

C₂

C₂×#16812762

yes

characteristic

194

C₂

D₁₀₉⋊#104

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#89137
commutator	C₄×C₁₀₉	C₂²×C₈
Frattini	C₂×C₄	C₂²×#89137
Fitting	C₄×Q₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₀₉	C₂²⋊C₄
cosocle	C₄×Dic₁₀₉	C₂³
hypercenter	C₄×Q₈	#89137
hypocenter	C₁₀₉	C₂×Q₈⋊C₈
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#89137

commutator

C₄×C₁₀₉

C₂²×C₈

Frattini

C₂×C₄

C₂²×#89137

Fitting

C₄×Q₈×C₁₀₉

C₄

socle

C₂²×C₁₀₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₁₀₉

C₂²⋊C₄

cosocle

C₄×Dic₁₀₉

C₂³

hypercenter

C₄×Q₈

#89137

hypocenter

C₁₀₉

C₂×Q₈⋊C₈

LCS

G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

N	H ≅ G/N	type
3. #20295876	C₂	semidirect
4. Q₈⋊#11724786	C₂	semidirect
30. Q₈×D₁₀₉	C₈	semidirect
54. Q₈×C₁₀₉	C₂×C₈	semidirect
74. Dic₂₁₈	C₂×C₈	semidirect
96. D₁₀₉	Q₈⋊C₈	semidirect
98. C₁₀₉	C₂×Q₈⋊C₈	semidirect
155. Q₈	D₁₀₉⋊C₈	semidirect

H ≅ G/N

type

3. #20295876

C₂

semidirect

4. Q₈⋊#11724786

C₂

semidirect

30. Q₈×D₁₀₉

C₈

semidirect

54. Q₈×C₁₀₉

C₂×C₈

semidirect

74. Dic₂₁₈

C₂×C₈

semidirect

96. D₁₀₉

Q₈⋊C₈

semidirect

98. C₁₀₉

C₂×Q₈⋊C₈

semidirect

155. Q₈

D₁₀₉⋊C₈

semidirect

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

subgroup	index
D₁₀₉⋊(C₄⋊C₈)	2
C₄×D₁₀₉⋊C₈	2
#20295876	2
Q₈⋊#11724786	2
C₄×Q₈×D₁₀₉	2
C₂×Q₈⋊C₈	109

subgroup

index

D₁₀₉⋊(C₄⋊C₈)

C₄×D₁₀₉⋊C₈

#20295876

Q₈⋊#11724786

C₄×Q₈×D₁₀₉

C₂×Q₈⋊C₈

109

Subgroups — D₁₀₉⋊(Q₈⋊C₈) #28378321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D109⋊(Q8⋊C8) #28378321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₀₉⋊(Q₈⋊C₈) #28378321