Group #28373427 — subgroups

Subgroups — #28373427

Order 13952.

424 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 125 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	#20295577	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295387	C₂	1	4	yes	maximal, complemented
4	#20295376	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295374	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295373	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295026	C₂	1	4	yes	maximal, complemented
8	C₄×#13182012	C₂	1	1	yes	maximal, characteristic, complemented
9	#487×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13182030	C₂²	1	2	yes	—
11	C₂×Q₈×D₁₀₉	—	2	1	no	—
12	C₂×#13182012	C₂²	1	2	yes	—
13	#16812699	C₂²	1	1	yes	characteristic
14	#16812698	—	2	1	no	—
15	#16812698	C₂²	1	2	yes	—
16	#16812697	—	2	1	no	—
17	#16812696	C₂²	1	1	yes	characteristic
18	#16812688	C₂²	1	2	yes	—
19	#16812674	—	2	1	no	—
20	#16812674	—	2	1	no	—
21	#16812661	—	2	1	no	—
22	#16812661	—	2	1	no	—
23	C₄⋊C₄×D₁₀₉	—	2	1	no	—
24	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
25	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
26	#16812623	C₂²	1	4	yes	—
27	#16812621	C₂²	1	4	yes	—
28	#16812619	C₂²	1	4	yes	—
29	#16812609	C₂²	1	2	yes	—
30	C₄×#11724784	C₂²	1	1	yes	characteristic
31	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
33	#103×C₁₀₉	C₂²	1	4	yes	—
34	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
35	#13182030	—	2	8	no	—
36	C₂×Dic₂₁₈	—	2	1	no	—
37	C₂×Dic₂₁₈	—	2	2	no	—
38	Q₈×D₁₀₉	—	4	4	no	—
39	C₂×D₄₃₆	—	2	2	no	—
40	C₂×D₄₃₆	—	2	1	no	—
41	C₂×D₄₃₆	—	2	1	no	—
42	C₂×D₄₃₆	C₂³	1	2	yes	—
43	C₂×C₄×D₁₀₉	—	2	2	no	—
44	C₂×C₄×D₁₀₉	—	2	2	no	—
45	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
46	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
47	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
48	#13182012	—	2	4	no	—
49	C₂×#11724784	C₂³	1	2	yes	—
50	C₄⋊Dic₁₀₉	—	2	1	no	—
51	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
52	#13182008	—	2	2	no	—
53	#13182008	—	2	2	no	—
54	#13182006	—	2	2	no	—
55	#13182006	—	2	2	no	—
56	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
57	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
58	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
59	C₂×Q₈×C₁₀₉	—	2	1	no	—
60	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
61	C₂×C₈×C₁₀₉	C₂³	1	2	yes	—
62	C₄⋊C₄×C₁₀₉	—	2	1	no	—
63	C₄⋊C₄×C₁₀₉	—	2	1	no	—
64	C₄⋊C₄×C₁₀₉	—	2	1	no	—
65	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
66	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
67	C₂²×D₁₀₉	—	2	2	no	—
68	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
69	Q₈×C₁₀₉	—	2	4	no	—
70	Q₈×C₁₀₉	—	4	2	no	—
71	C₂×C₄×C₁₀₉	—	2	2	no	—
72	C₂×C₄×C₁₀₉	—	2	2	no	—
73	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
76	C₂×Dic₁₀₉	—	2	2	no	—
77	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
78	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
80	D₄₃₆	—	2	4	no	—
81	D₄₃₆	—	4	4	no	—
82	D₄₃₆	—	4	2	no	—
83	D₄₃₆	—	4	2	no	—
84	C₄×D₁₀₉	—	2	2	no	—
85	C₄×D₁₀₉	—	2	2	no	—
86	C₄×D₁₀₉	—	4	4	no	—
87	C₄×D₁₀₉	—	4	4	no	—
88	C₄×D₁₀₉	#41	1	4	yes	—
89	Dic₂₁₈	—	4	4	no	—
90	Dic₂₁₈	—	4	2	no	—
91	C₈×C₁₀₉	—	2	2	no	—
92	#11724784	—	2	2	no	—
93	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
94	C₂×D₁₀₉	—	2	1	no	—
95	C₂×D₁₀₉	—	2	1	no	—
96	C₂×D₁₀₉	—	4	2	no	—
97	C₂×D₁₀₉	—	4	2	no	—
98	C₂×D₁₀₉	—	4	2	no	—
99	C₂×D₁₀₉	#124	1	2	yes	—
100	C₄×C₁₀₉	—	4	2	no	—
101	C₄×C₁₀₉	—	4	2	no	—
102	C₄×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
103	C₄×C₁₀₉	#137	1	2	yes	—
104	C₄×C₁₀₉	C₂×#41	1	2	yes	—
105	Dic₁₀₉	—	2	1	no	—
106	Dic₁₀₉	—	2	1	no	—
107	Dic₁₀₉	—	4	2	no	—
108	Dic₁₀₉	#124	1	2	yes	—
109	C₂×C₁₀₉	C₂×#124	1	1	yes	characteristic
110	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
111	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
112	D₁₀₉	—	2	2	no	—
113	D₁₀₉	—	8	2	no	—
114	#3141	—	109	1	no	maximal, Sylow
115	C₁₀₉	#3141	1	1	yes	characteristic, complemented, Sylow
116	#532	—	109	1	no	—
117	C₂×C₄⋊Q₈	—	109	1	no	—
118	#489	—	109	4	no	—
119	#487	—	109	1	no	—
120	#487	D₁₀₉	1	1	yes	characteristic, complemented
121	#486	—	109	1	no	—
122	#486	—	109	1	no	—
123	#417	—	109	4	no	—
124	C₄×M₁₆	—	109	1	no	—
125	C₂×#41	—	109	2	no	—
126	C₂²×Q₈	—	218	1	no	—
127	C₂×M₁₆	—	109	2	no	—
128	C₄⋊Q₈	—	109	2	no	—
129	C₄⋊Q₈	—	109	1	no	—
130	C₄⋊Q₈	—	218	1	no	—
131	C₄⋊Q₈	—	218	1	no	—
132	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic
133	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic
134	#127	—	109	1	no	—
135	#124	—	109	2	no	—
136	#121	—	218	1	no	—
137	#121	—	218	1	no	—
138	C₄×D₄	—	218	1	no	—
139	C₄×D₄	—	218	1	no	—
140	C₂×C₄⋊C₄	—	109	2	no	—
141	C₂×C₄⋊C₄	—	218	1	no	—
142	C₂×C₄²	—	109	1	no	—
143	#103	—	109	4	no	—
144	#103	C₂×D₁₀₉	1	4	yes	—
145	#102	—	109	4	no	—
146	#102	—	109	4	no	—
147	#97	—	109	2	no	—
148	C₄×C₈	—	109	1	no	—
149	C₄×C₈	C₂×D₁₀₉	1	1	yes	characteristic
150	#41	—	218	8	no	—
151	C₂×Q₈	—	2	1	no	—
152	C₂×Q₈	—	436	4	no	—
153	C₂×Q₈	—	218	2	no	—
154	C₂×Q₈	—	218	1	no	—
155	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
156	C₂×D₄	—	109	2	no	—
157	C₂×D₄	—	218	2	no	—
158	C₂×D₄	—	218	1	no	—
159	C₂×D₄	—	218	1	no	—
160	C₂²×C₄	—	109	1	no	—
161	C₂²×C₄	—	109	1	no	—
162	C₂²×C₄	—	109	1	no	—
163	C₂²×C₄	—	218	2	no	—
164	C₂²×C₄	—	218	2	no	—
165	M₁₆	—	218	4	no	—
166	C₂×C₈	—	109	2	no	—
167	C₂×C₈	C₂²×D₁₀₉	1	2	yes	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	109	2	no	—
172	C₄⋊C₄	—	218	2	no	—
173	C₄⋊C₄	—	218	2	no	—
174	C₄⋊C₄	—	218	1	no	—
175	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
176	C₂²⋊C₄	—	218	2	no	—
177	C₂²⋊C₄	—	218	2	no	—
178	C₄²	—	109	1	no	—
179	C₄²	—	109	1	no	—
180	C₄²	—	109	1	no	—
181	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
182	C₂³	—	109	1	no	—
183	C₂³	—	218	2	no	—
184	Q₈	—	2	4	no	—
185	Q₈	—	4	2	no	—
186	Q₈	—	436	4	no	—
187	Q₈	—	436	2	no	—
188	D₄	—	436	4	no	—
189	D₄	—	436	2	no	—
190	D₄	—	436	2	no	—
191	D₄	—	218	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	109	1	no	—
195	C₂×C₄	—	109	4	no	—
196	C₂×C₄	—	109	1	no	—
197	C₂×C₄	—	109	1	no	—
198	C₂×C₄	—	436	4	no	—
199	C₂×C₄	—	436	4	no	—
200	C₂×C₄	—	218	2	no	—
201	C₂×C₄	—	218	2	no	—
202	C₂×C₄	—	218	2	no	—
203	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
204	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
205	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
206	C₈	—	2	2	no	—
207	C₈	—	218	2	no	—
208	C₂²	—	109	2	no	—
209	C₂²	—	436	2	no	—
210	C₂²	—	436	2	no	—
211	C₂²	—	436	2	no	—
212	C₂²	—	218	1	no	—
213	C₂²	—	218	1	no	—
214	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
215	C₄	—	4	2	no	—
216	C₄	—	4	2	no	—
217	C₄	—	109	2	no	—
218	C₄	—	436	2	no	—
219	C₄	—	218	1	no	—
220	C₄	—	218	1	no	—
221	C₄	#16812726	1	2	yes	—
222	C₄	#16812731	1	2	yes	—
223	C₄	#41×D₁₀₉	1	2	yes	—
224	C₂	—	872	2	no	—
225	C₂	—	218	2	no	—
226	C₂	#124×D₁₀₉	1	1	yes	characteristic
227	C₂	C₂×#16812726	1	1	yes	characteristic
228	C₂	C₂×#16812731	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20295577

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₁₀₉

C₂

yes

maximal, characteristic, complemented

#20295387

C₂

yes

maximal, complemented

#20295376

C₂

yes

maximal, characteristic, complemented

#20295374

C₂

yes

maximal, characteristic, complemented

#20295373

C₂

yes

maximal, characteristic, complemented

#20295026

C₂

yes

maximal, complemented

C₄×#13182012

C₂

yes

maximal, characteristic, complemented

#487×C₁₀₉

C₂

yes

maximal, characteristic, complemented

C₂×#13182030

C₂²

yes

—

C₂×Q₈×D₁₀₉

—

C₂×#13182012

C₂²

yes

—

#16812699

C₂²

yes

characteristic

#16812698

—

#16812698

C₂²

yes

—

#16812697

—

#16812696

C₂²

yes

characteristic

#16812688

C₂²

yes

—

—

—

—

—

C₄⋊C₄×D₁₀₉

—

C₄⋊C₄×D₁₀₉

C₂²

yes

—

C₄²×D₁₀₉

C₂²

yes

characteristic

#16812623

C₂²

yes

—

#16812621

C₂²

yes

—

#16812619

C₂²

yes

—

#16812609

C₂²

yes

—

C₄×#11724784

C₂²

yes

characteristic

C₄⋊Q₈×C₁₀₉

C₂²

yes

characteristic

C₄⋊Q₈×C₁₀₉

C₂²

yes

characteristic

#103×C₁₀₉

C₂²

yes

—

C₄×C₈×C₁₀₉

C₂²

yes

characteristic

#13182030

—

C₂×Dic₂₁₈

—

C₂×Dic₂₁₈

—

Q₈×D₁₀₉

—

C₂×D₄₃₆

—

C₂×D₄₃₆

—

C₂×D₄₃₆

—

C₂×D₄₃₆

C₂³

yes

—

C₂×C₄×D₁₀₉

—

C₂×C₄×D₁₀₉

—

C₂×C₄×D₁₀₉

D₄

yes

characteristic

C₂×C₄×D₁₀₉

D₄

yes

characteristic

C₂×C₄×D₁₀₉

C₂³

yes

characteristic

#13182012

—

C₂×#11724784

C₂³

yes

—

C₄⋊Dic₁₀₉

—

C₄⋊Dic₁₀₉

C₂³

yes

—

—

—

—

—

C₄×Dic₁₀₉

D₄

yes

characteristic

C₄×Dic₁₀₉

D₄

yes

characteristic

C₄×Dic₁₀₉

C₂³

yes

characteristic

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

C₂³

yes

—

C₂×C₈×C₁₀₉

C₂³

yes

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

C₂³

yes

—

C₄²×C₁₀₉

C₂³

yes

characteristic

C₂²×D₁₀₉

—

C₂²×D₁₀₉

C₂×D₄

yes

characteristic

Q₈×C₁₀₉

—

Q₈×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₀₉

C₂⁴

yes

characteristic

C₂×Dic₁₀₉

—

C₂×Dic₁₀₉

C₂×D₄

yes

characteristic

C₂×Dic₁₀₉

C₂×D₄

yes

characteristic

C₂×Dic₁₀₉

C₂×D₄

yes

characteristic

D₄₃₆

—

D₄₃₆

—

D₄₃₆

—

D₄₃₆

—

C₄×D₁₀₉

—

C₄×D₁₀₉

—

C₄×D₁₀₉

—

C₄×D₁₀₉

—

C₄×D₁₀₉

#41

yes

—

Dic₂₁₈

—

Dic₂₁₈

—

C₈×C₁₀₉

—

#11724784

—

C₂²×C₁₀₉

C₂²×D₄

yes

characteristic

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

—

C₂×D₁₀₉

#124

yes

—

100

C₄×C₁₀₉

—

101

C₄×C₁₀₉

—

102

C₄×C₁₀₉

AGL(1,ℤ/8)

yes

—

103

C₄×C₁₀₉

#137

yes

—

104

C₄×C₁₀₉

C₂×#41

yes

—

105

Dic₁₀₉

—

106

Dic₁₀₉

—

107

Dic₁₀₉

—

108

Dic₁₀₉

#124

yes

—

109

C₂×C₁₀₉

C₂×#124

yes

characteristic

110

C₂×C₁₀₉

C₂×AGL(1,ℤ/8)

yes

characteristic

111

C₂×C₁₀₉

C₂×#137

yes

characteristic

112

D₁₀₉

—

113

D₁₀₉

—

114

#3141

—

109

maximal, Sylow

115

C₁₀₉

#3141

yes

characteristic, complemented, Sylow

116

#532

—

109

—

117

C₂×C₄⋊Q₈

—

109

—

118

#489

—

109

—

119

#487

—

109

—

120

#487

D₁₀₉

yes

characteristic, complemented

121

#486

—

109

—

122

#486

—

109

—

123

#417

—

109

—

124

C₄×M₁₆

—

109

—

125

C₂×#41

—

109

—

126

C₂²×Q₈

—

218

—

127

C₂×M₁₆

—

109

—

128

C₄⋊Q₈

—

109

—

129

C₄⋊Q₈

—

109

—

130

C₄⋊Q₈

—

218

—

131

C₄⋊Q₈

—

218

—

132

C₄⋊Q₈

C₂×D₁₀₉

yes

characteristic

133

C₄⋊Q₈

C₂×D₁₀₉

yes

characteristic

134

#127

—

109

—

135

#124

—

109

—

136

#121

—

218

—

137

#121

—

218

—

138

C₄×D₄

—

218

—

139

C₄×D₄

—

218

—

140

C₂×C₄⋊C₄

—

109

—

141

C₂×C₄⋊C₄

—

218

—

142

C₂×C₄²

—

109

—

143

#103

—

109

—

144

#103

C₂×D₁₀₉

yes

—

145

#102

—

109

—

146

#102

—

109

—

147

#97

—

109

—

148

C₄×C₈

—

109

—

149

C₄×C₈

C₂×D₁₀₉

yes

characteristic

150

#41

—

218

—

151

C₂×Q₈

—

152

C₂×Q₈

—

436

—

153

C₂×Q₈

—

218

—

154

C₂×Q₈

—

218

—

155

C₂×Q₈

C₂²×D₁₀₉

yes

—

156

C₂×D₄

—

109

—

157

C₂×D₄

—

218

—

158

C₂×D₄

—

218

—

159

C₂×D₄

—

218

—

160

C₂²×C₄

—

109

—

161

C₂²×C₄

—

109

—

162

C₂²×C₄

—

109

—

163

C₂²×C₄

—

218

—

164

C₂²×C₄

—

218

—

165

M₁₆

—

218

—

166

C₂×C₈

—

109

—

167

C₂×C₈

C₂²×D₁₀₉

yes

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

109

—

172

C₄⋊C₄

—

218

—

173

C₄⋊C₄

—

218

—

174

C₄⋊C₄

—

218

—

175

C₄⋊C₄

C₂²×D₁₀₉

yes

—

176

C₂²⋊C₄

—

218

—

177

C₂²⋊C₄

—

218

—

178

C₄²

—

109

—

179

C₄²

—

109

—

180

C₄²

—

109

—

181

C₄²

C₂²×D₁₀₉

yes

characteristic

182

C₂³

—

109

—

183

C₂³

—

218

—

184

Q₈

—

185

Q₈

—

186

Q₈

—

436

—

187

Q₈

—

436

—

188

D₄

—

436

—

189

D₄

—

436

—

190

D₄

—

436

—

191

D₄

—

218

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

109

—

195

C₂×C₄

—

109

—

196

C₂×C₄

—

109

—

197

C₂×C₄

—

109

—

198

C₂×C₄

—

436

—

199

C₂×C₄

—

436

—

200

C₂×C₄

—

218

—

201

C₂×C₄

—

218

—

202

C₂×C₄

—

218

—

203

C₂×C₄

D₄×D₁₀₉

yes

characteristic

204

C₂×C₄

D₄×D₁₀₉

yes

characteristic

205

C₂×C₄

C₂³×D₁₀₉

yes

characteristic

206

C₈

—

207

C₈

—

218

—

208

C₂²

—

109

—

209

C₂²

—

436

—

210

C₂²

—

436

—

211

C₂²

—

436

—

212

C₂²

—

218

—

213

C₂²

—

218

—

214

C₂²

C₂×D₄×D₁₀₉

yes

characteristic

215

C₄

—

216

C₄

—

217

C₄

—

109

—

218

C₄

—

436

—

219

C₄

—

218

—

220

C₄

—

218

—

221

C₄

#16812726

yes

—

222

C₄

#16812731

yes

—

223

C₄

#41×D₁₀₉

yes

—

224

C₂

—

872

—

225

C₂

—

218

—

226

C₂

#124×D₁₀₉

yes

characteristic

227

C₂

C₂×#16812726

yes

characteristic

228

C₂

C₂×#16812731

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#487×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	#20295577	C₂
hypercenter	#487	D₁₀₉
hypocenter	C₁₀₉	#3141
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

C₂×D₄×D₁₀₉

commutator, cosocle

C₂×C₄×C₁₀₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₀₉

Fitting

#487×C₁₀₉

C₂

socle

C₂²×C₁₀₉

C₂²×D₄

C₂

D₁₀₉

C₁₀₉

G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
2. C₄⋊Q₈×D₁₀₉	C₂	semidirect
3. #20295387	C₂	semidirect
4. #20295376	C₂	semidirect
5. #20295374	C₂	semidirect
6. #20295373	C₂	semidirect
7. #20295026	C₂	semidirect
8. C₄×#13182012	C₂	semidirect
9. #487×C₁₀₉	C₂	semidirect
115. C₁₀₉	#3141	semidirect
120. #487	D₁₀₉	semidirect

H ≅ G/N

type

2. C₄⋊Q₈×D₁₀₉

C₂

semidirect

3. #20295387

C₂

semidirect

4. #20295376

C₂

semidirect

5. #20295374

C₂

semidirect

6. #20295373

C₂

semidirect

7. #20295026

C₂

semidirect

8. C₄×#13182012

C₂

semidirect

9. #487×C₁₀₉

C₂

semidirect

115. C₁₀₉

#3141

semidirect

120. #487

D₁₀₉

semidirect

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

subgroup	index
#20295577	2
C₄⋊Q₈×D₁₀₉	2
#20295387	2
#20295376	2
#20295374	2
#20295373	2
#20295026	2
C₄×#13182012	2
#487×C₁₀₉	2
#3141	109

subgroup

index

C₄⋊Q₈×D₁₀₉

#487×C₁₀₉

109

Subgroups — #28373427

Conjugacy classes of subgroups

Complements

Maximal subgroups