Group #37582910 — subgroups

Subgroups — #37582910

Order 24448.

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	#27133211	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Q₈×D₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#27133021	C₂	1	4	yes	maximal, complemented
4	#27133015	C₂	1	1	yes	maximal, characteristic, complemented
5	#27133014	C₂	1	1	yes	maximal, characteristic, complemented
6	#27133009	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132661	C₂	1	4	yes	maximal, complemented
8	C₄×#15690270	C₂	1	1	yes	maximal, characteristic, complemented
9	#486×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15690286	C₂²	1	2	yes	—
11	C₂×Q₈×D₁₉₁	—	2	1	no	—
12	C₂×#15690270	C₂²	1	2	yes	—
13	#20259322	C₂²	1	1	yes	characteristic
14	#20259322	C₂²	1	1	yes	characteristic
15	#20259321	—	2	1	no	—
16	#20259321	C₂²	1	2	yes	—
17	#20259320	—	2	1	no	—
18	#20259309	C₂²	1	2	yes	—
19	#20259293	—	2	1	no	—
20	#20259293	—	2	1	no	—
21	D₄×Dic₁₉₁	—	2	1	no	—
22	D₄×Dic₁₉₁	—	2	1	no	—
23	C₄⋊C₄×D₁₉₁	—	2	1	no	—
24	C₄⋊C₄×D₁₉₁	C₂²	1	2	yes	—
25	C₄²×D₁₉₁	C₂²	1	1	yes	characteristic
26	#20259247	C₂²	1	4	yes	—
27	#20259245	C₂²	1	4	yes	—
28	#20259243	C₂²	1	4	yes	—
29	#20259232	C₂²	1	2	yes	—
30	C₄×C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
31	C₄⋊Q₈×C₁₉₁	C₂²	1	1	yes	characteristic
32	#127×C₁₉₁	C₂²	1	1	yes	characteristic
33	#102×C₁₉₁	C₂²	1	4	yes	—
34	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
35	#15690286	—	2	8	no	—
36	C₂×Dic₃₈₂	—	2	2	no	—
37	C₂×Dic₃₈₂	—	2	1	no	—
38	C₂×Dic₃₈₂	C₂³	1	2	yes	—
39	Q₈×D₁₉₁	—	4	4	no	—
40	C₂×C₂²⋊D₁₉₁	—	2	2	no	—
41	C₂²×Dic₁₉₁	—	2	2	no	—
42	C₂×C₄×D₁₉₁	—	2	2	no	—
43	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
44	C₂×C₄×D₁₉₁	D₄	1	1	yes	characteristic
45	C₂×C₄×D₁₉₁	C₂³	1	1	yes	characteristic
46	#15690270	—	2	4	no	—
47	C₂×C₁₉₁⋊C₈	C₂³	1	2	yes	—
48	C₄⋊Dic₁₉₁	—	2	1	no	—
49	C₄⋊Dic₁₉₁	—	2	1	no	—
50	C₄⋊Dic₁₉₁	—	2	1	no	—
51	C₄⋊Dic₁₉₁	C₂³	1	2	yes	—
52	Dic₁₉₁⋊C₄	—	2	2	no	—
53	Dic₁₉₁⋊C₄	—	2	2	no	—
54	C₂²⋊Dic₁₉₁	—	2	2	no	—
55	C₂²⋊Dic₁₉₁	—	2	2	no	—
56	C₄×Dic₁₉₁	D₄	1	1	yes	characteristic
57	C₄×Dic₁₉₁	D₄	1	1	yes	characteristic
58	C₄×Dic₁₉₁	C₂³	1	1	yes	characteristic
59	C₂×Q₈×C₁₉₁	—	2	1	no	—
60	C₂×D₄×C₁₉₁	—	2	1	no	—
61	C₂×D₄×C₁₉₁	—	2	1	no	—
62	C₂×D₄×C₁₉₁	C₂³	1	2	yes	—
63	C₂×C₈×C₁₉₁	C₂³	1	2	yes	—
64	C₄⋊C₄×C₁₉₁	—	2	1	no	—
65	C₄⋊C₄×C₁₉₁	C₂³	1	2	yes	—
66	C₄²×C₁₉₁	C₂³	1	1	yes	characteristic
67	C₂²×D₁₉₁	C₂×D₄	1	1	yes	characteristic
68	Dic₃₈₂	—	2	4	no	—
69	Dic₃₈₂	—	4	4	no	—
70	Dic₃₈₂	—	4	2	no	—
71	C₂²⋊D₁₉₁	—	4	4	no	—
72	C₂×Dic₁₉₁	—	2	2	no	—
73	C₂×Dic₁₉₁	—	2	2	no	—
74	C₂×Dic₁₉₁	—	4	4	no	—
75	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
76	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
77	C₂×Dic₁₉₁	C₂×D₄	1	1	yes	characteristic
78	C₄×D₁₉₁	—	2	2	no	—
79	C₄×D₁₉₁	—	2	2	no	—
80	C₄×D₁₉₁	—	4	4	no	—
81	C₄×D₁₉₁	#41	1	4	yes	—
82	C₁₉₁⋊C₈	—	2	2	no	—
83	C₂³×C₁₉₁	—	2	2	no	—
84	Q₈×C₁₉₁	—	4	2	no	—
85	D₄×C₁₉₁	—	2	4	no	—
86	D₄×C₁₉₁	—	4	2	no	—
87	D₄×C₁₉₁	—	4	2	no	—
88	C₂×C₄×C₁₉₁	—	2	2	no	—
89	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
92	C₈×C₁₉₁	—	2	2	no	—
93	C₂²×C₁₉₁	—	4	2	no	—
94	C₂²×C₁₉₁	—	4	2	no	—
95	C₂²×C₁₉₁	—	4	2	no	—
96	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
97	C₂×D₁₉₁	—	2	1	no	—
98	C₂×D₁₉₁	—	2	1	no	—
99	C₂×D₁₉₁	#124	1	2	yes	—
100	C₄×C₁₉₁	—	4	2	no	—
101	C₄×C₁₉₁	AGL(1,ℤ/8)	1	2	yes	—
102	C₄×C₁₉₁	#137	1	2	yes	—
103	C₄×C₁₉₁	C₂×#41	1	2	yes	—
104	Dic₁₉₁	—	2	1	no	—
105	Dic₁₉₁	—	2	1	no	—
106	Dic₁₉₁	—	4	2	no	—
107	Dic₁₉₁	—	4	2	no	—
108	Dic₁₉₁	#124	1	2	yes	—
109	C₂×C₁₉₁	—	8	2	no	—
110	C₂×C₁₉₁	C₂×#124	1	1	yes	characteristic
111	C₂×C₁₉₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
112	C₂×C₁₉₁	C₂×#137	1	1	yes	characteristic
113	D₁₉₁	—	2	2	no	—
114	C₁₉₁	#3141	1	1	yes	characteristic, complemented, Sylow
115	#3141	—	191	1	no	maximal, Sylow
116	#532	—	191	1	no	—
117	C₂×C₄⋊Q₈	—	191	1	no	—
118	#489	—	191	4	no	—
119	#487	—	191	1	no	—
120	#487	—	191	1	no	—
121	#486	—	191	1	no	—
122	#486	D₁₉₁	1	1	yes	characteristic, complemented
123	#417	—	191	4	no	—
124	C₄×M₁₆	—	191	1	no	—
125	C₂×#41	—	191	2	no	—
126	C₂²×Q₈	—	382	1	no	—
127	C₂×M₁₆	—	191	2	no	—
128	C₄⋊Q₈	—	382	1	no	—
129	C₄⋊Q₈	—	382	1	no	—
130	C₄⋊Q₈	—	191	2	no	—
131	C₄⋊Q₈	—	191	1	no	—
132	C₄⋊Q₈	—	191	1	no	—
133	C₄⋊Q₈	C₂×D₁₉₁	1	1	yes	characteristic
134	#127	C₂×D₁₉₁	1	1	yes	characteristic
135	#124	—	191	2	no	—
136	#121	—	382	1	no	—
137	#121	—	382	1	no	—
138	C₄×D₄	—	382	1	no	—
139	C₄×D₄	—	382	1	no	—
140	C₂×C₄⋊C₄	—	382	1	no	—
141	C₂×C₄⋊C₄	—	191	2	no	—
142	C₂×C₄²	—	191	1	no	—
143	#103	—	191	4	no	—
144	#103	—	191	4	no	—
145	#102	—	191	4	no	—
146	#102	C₂×D₁₉₁	1	4	yes	—
147	#97	—	191	2	no	—
148	C₄×C₈	—	191	1	no	—
149	C₄×C₈	C₂×D₁₉₁	1	1	yes	characteristic
150	#41	—	382	8	no	—
151	C₂×Q₈	—	2	1	no	—
152	C₂×Q₈	—	382	2	no	—
153	C₂×Q₈	—	382	1	no	—
154	C₂×Q₈	—	191	2	no	—
155	C₂×Q₈	—	764	4	no	—
156	C₂×D₄	—	2	1	no	—
157	C₂×D₄	—	2	1	no	—
158	C₂×D₄	—	382	2	no	—
159	C₂×D₄	C₂²×D₁₉₁	1	2	yes	—
160	C₂²×C₄	—	382	2	no	—
161	C₂²×C₄	—	382	2	no	—
162	C₂²×C₄	—	191	1	no	—
163	C₂²×C₄	—	191	1	no	—
164	C₂²×C₄	—	191	1	no	—
165	M₁₆	—	382	4	no	—
166	C₂×C₈	—	191	2	no	—
167	C₂×C₈	C₂²×D₁₉₁	1	2	yes	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	382	2	no	—
170	C₄⋊C₄	—	382	2	no	—
171	C₄⋊C₄	—	382	1	no	—
172	C₄⋊C₄	—	382	1	no	—
173	C₄⋊C₄	—	382	1	no	—
174	C₄⋊C₄	—	191	2	no	—
175	C₄⋊C₄	C₂²×D₁₉₁	1	2	yes	—
176	C₂²⋊C₄	—	382	2	no	—
177	C₂²⋊C₄	—	382	2	no	—
178	C₄²	—	191	1	no	—
179	C₄²	—	191	1	no	—
180	C₄²	—	191	1	no	—
181	C₄²	C₂²×D₁₉₁	1	1	yes	characteristic
182	C₂³	—	2	2	no	—
183	C₂³	—	191	1	no	—
184	Q₈	—	4	2	no	—
185	Q₈	—	382	4	no	—
186	Q₈	—	764	4	no	—
187	Q₈	—	764	2	no	—
188	D₄	—	2	4	no	—
189	D₄	—	4	2	no	—
190	D₄	—	4	2	no	—
191	D₄	—	764	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	382	2	no	—
194	C₂×C₄	—	382	2	no	—
195	C₂×C₄	—	382	2	no	—
196	C₂×C₄	—	382	2	no	—
197	C₂×C₄	—	191	1	no	—
198	C₂×C₄	—	191	1	no	—
199	C₂×C₄	—	191	1	no	—
200	C₂×C₄	—	191	4	no	—
201	C₂×C₄	—	764	4	no	—
202	C₂×C₄	—	764	4	no	—
203	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
204	C₂×C₄	D₄×D₁₉₁	1	1	yes	characteristic
205	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
206	C₈	—	2	2	no	—
207	C₈	—	382	2	no	—
208	C₂²	—	4	2	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	382	1	no	—
212	C₂²	—	382	1	no	—
213	C₂²	—	191	2	no	—
214	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
215	C₄	—	4	2	no	—
216	C₄	—	382	1	no	—
217	C₄	—	382	1	no	—
218	C₄	—	191	2	no	—
219	C₄	—	764	2	no	—
220	C₄	—	764	2	no	—
221	C₄	#20259346	1	2	yes	—
222	C₄	#20259351	1	2	yes	—
223	C₄	#41×D₁₉₁	1	2	yes	—
224	C₂	—	8	2	no	—
225	C₂	—	382	2	no	—
226	C₂	#124×D₁₉₁	1	1	yes	characteristic
227	C₂	C₂×#20259346	1	1	yes	characteristic
228	C₂	C₂×#20259351	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#27133211

C₂

yes

maximal, characteristic

C₄⋊Q₈×D₁₉₁

C₂

yes

maximal, characteristic, complemented

#27133021

C₂

yes

maximal, complemented

#27133015

C₂

yes

maximal, characteristic, complemented

#27133014

C₂

yes

maximal, characteristic, complemented

#27133009

C₂

yes

maximal, characteristic, complemented

#27132661

C₂

yes

maximal, complemented

C₄×#15690270

C₂

yes

maximal, characteristic, complemented

#486×C₁₉₁

C₂

yes

maximal, characteristic, complemented

C₂×#15690286

C₂²

yes

—

C₂×Q₈×D₁₉₁

—

C₂×#15690270

C₂²

yes

—

#20259322

C₂²

yes

characteristic

#20259322

C₂²

yes

characteristic

#20259321

—

#20259321

C₂²

yes

—

#20259320

—

#20259309

C₂²

yes

—

#20259293

—

#20259293

—

D₄×Dic₁₉₁

—

D₄×Dic₁₉₁

—

C₄⋊C₄×D₁₉₁

—

C₄⋊C₄×D₁₉₁

C₂²

yes

—

C₄²×D₁₉₁

C₂²

yes

characteristic

#20259247

C₂²

yes

—

#20259245

C₂²

yes

—

#20259243

C₂²

yes

—

#20259232

C₂²

yes

—

C₄×C₁₉₁⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₁₉₁

C₂²

yes

characteristic

#127×C₁₉₁

C₂²

yes

characteristic

#102×C₁₉₁

C₂²

yes

—

C₄×C₈×C₁₉₁

C₂²

yes

characteristic

#15690286

—

C₂×Dic₃₈₂

—

C₂×Dic₃₈₂

—

C₂×Dic₃₈₂

C₂³

yes

—

Q₈×D₁₉₁

—

C₂×C₂²⋊D₁₉₁

—

C₂²×Dic₁₉₁

—

C₂×C₄×D₁₉₁

—

C₂×C₄×D₁₉₁

D₄

yes

characteristic

C₂×C₄×D₁₉₁

D₄

yes

characteristic

C₂×C₄×D₁₉₁

C₂³

yes

characteristic

#15690270

—

C₂×C₁₉₁⋊C₈

C₂³

yes

—

C₄⋊Dic₁₉₁

—

C₄⋊Dic₁₉₁

—

C₄⋊Dic₁₉₁

—

C₄⋊Dic₁₉₁

C₂³

yes

—

Dic₁₉₁⋊C₄

—

Dic₁₉₁⋊C₄

—

C₂²⋊Dic₁₉₁

—

C₂²⋊Dic₁₉₁

—

C₄×Dic₁₉₁

D₄

yes

characteristic

C₄×Dic₁₉₁

D₄

yes

characteristic

C₄×Dic₁₉₁

C₂³

yes

characteristic

C₂×Q₈×C₁₉₁

—

C₂×D₄×C₁₉₁

—

C₂×D₄×C₁₉₁

—

C₂×D₄×C₁₉₁

C₂³

yes

—

C₂×C₈×C₁₉₁

C₂³

yes

—

C₄⋊C₄×C₁₉₁

—

C₄⋊C₄×C₁₉₁

C₂³

yes

—

C₄²×C₁₉₁

C₂³

yes

characteristic

C₂²×D₁₉₁

C₂×D₄

yes

characteristic

Dic₃₈₂

—

Dic₃₈₂

—

Dic₃₈₂

—

C₂²⋊D₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

C₂×D₄

yes

characteristic

C₂×Dic₁₉₁

C₂×D₄

yes

characteristic

C₂×Dic₁₉₁

C₂×D₄

yes

characteristic

C₄×D₁₉₁

—

C₄×D₁₉₁

—

C₄×D₁₉₁

—

C₄×D₁₉₁

#41

yes

—

C₁₉₁⋊C₈

—

C₂³×C₁₉₁

—

Q₈×C₁₉₁

—

D₄×C₁₉₁

—

D₄×C₁₉₁

—

D₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₁

C₂⁴

yes

characteristic

C₈×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

C₂²×C₁₉₁

C₂²×D₄

yes

characteristic

C₂×D₁₉₁

—

C₂×D₁₉₁

—

C₂×D₁₉₁

#124

yes

—

100

C₄×C₁₉₁

—

101

C₄×C₁₉₁

AGL(1,ℤ/8)

yes

—

102

C₄×C₁₉₁

#137

yes

—

103

C₄×C₁₉₁

C₂×#41

yes

—

104

Dic₁₉₁

—

105

Dic₁₉₁

—

106

Dic₁₉₁

—

107

Dic₁₉₁

—

108

Dic₁₉₁

#124

yes

—

109

C₂×C₁₉₁

—

110

C₂×C₁₉₁

C₂×#124

yes

characteristic

111

C₂×C₁₉₁

C₂×AGL(1,ℤ/8)

yes

characteristic

112

C₂×C₁₉₁

C₂×#137

yes

characteristic

113

D₁₉₁

—

114

C₁₉₁

#3141

yes

characteristic, complemented, Sylow

115

#3141

—

191

maximal, Sylow

116

#532

—

191

—

117

C₂×C₄⋊Q₈

—

191

—

118

#489

—

191

—

119

#487

—

191

—

120

#487

—

191

—

121

#486

—

191

—

122

#486

D₁₉₁

yes

characteristic, complemented

123

#417

—

191

—

124

C₄×M₁₆

—

191

—

125

C₂×#41

—

191

—

126

C₂²×Q₈

—

382

—

127

C₂×M₁₆

—

191

—

128

C₄⋊Q₈

—

382

—

129

C₄⋊Q₈

—

382

—

130

C₄⋊Q₈

—

191

—

131

C₄⋊Q₈

—

191

—

132

C₄⋊Q₈

—

191

—

133

C₄⋊Q₈

C₂×D₁₉₁

yes

characteristic

134

#127

C₂×D₁₉₁

yes

characteristic

135

#124

—

191

—

136

#121

—

382

—

137

#121

—

382

—

138

C₄×D₄

—

382

—

139

C₄×D₄

—

382

—

140

C₂×C₄⋊C₄

—

382

—

141

C₂×C₄⋊C₄

—

191

—

142

C₂×C₄²

—

191

—

143

#103

—

191

—

144

#103

—

191

—

145

#102

—

191

—

146

#102

C₂×D₁₉₁

yes

—

147

#97

—

191

—

148

C₄×C₈

—

191

—

149

C₄×C₈

C₂×D₁₉₁

yes

characteristic

150

#41

—

382

—

151

C₂×Q₈

—

152

C₂×Q₈

—

382

—

153

C₂×Q₈

—

382

—

154

C₂×Q₈

—

191

—

155

C₂×Q₈

—

764

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

382

—

159

C₂×D₄

C₂²×D₁₉₁

yes

—

160

C₂²×C₄

—

382

—

161

C₂²×C₄

—

382

—

162

C₂²×C₄

—

191

—

163

C₂²×C₄

—

191

—

164

C₂²×C₄

—

191

—

165

M₁₆

—

382

—

166

C₂×C₈

—

191

—

167

C₂×C₈

C₂²×D₁₉₁

yes

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

382

—

170

C₄⋊C₄

—

382

—

171

C₄⋊C₄

—

382

—

172

C₄⋊C₄

—

382

—

173

C₄⋊C₄

—

382

—

174

C₄⋊C₄

—

191

—

175

C₄⋊C₄

C₂²×D₁₉₁

yes

—

176

C₂²⋊C₄

—

382

—

177

C₂²⋊C₄

—

382

—

178

C₄²

—

191

—

179

C₄²

—

191

—

180

C₄²

—

191

—

181

C₄²

C₂²×D₁₉₁

yes

characteristic

182

C₂³

—

183

C₂³

—

191

—

184

Q₈

—

185

Q₈

—

382

—

186

Q₈

—

764

—

187

Q₈

—

764

—

188

D₄

—

189

D₄

—

190

D₄

—

191

D₄

—

764

—

192

C₂×C₄

—

193

C₂×C₄

—

382

—

194

C₂×C₄

—

382

—

195

C₂×C₄

—

382

—

196

C₂×C₄

—

382

—

197

C₂×C₄

—

191

—

198

C₂×C₄

—

191

—

199

C₂×C₄

—

191

—

200

C₂×C₄

—

191

—

201

C₂×C₄

—

764

—

202

C₂×C₄

—

764

—

203

C₂×C₄

D₄×D₁₉₁

yes

characteristic

204

C₂×C₄

D₄×D₁₉₁

yes

characteristic

205

C₂×C₄

C₂³×D₁₉₁

yes

characteristic

206

C₈

—

207

C₈

—

382

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

382

—

212

C₂²

—

382

—

213

C₂²

—

191

—

214

C₂²

C₂×D₄×D₁₉₁

yes

characteristic

215

C₄

—

216

C₄

—

382

—

217

C₄

—

382

—

218

C₄

—

191

—

219

C₄

—

764

—

220

C₄

—

764

—

221

C₄

#20259346

yes

—

222

C₄

#20259351

yes

—

223

C₄

#41×D₁₉₁

yes

—

224

C₂

—

225

C₂

—

382

—

226

C₂

#124×D₁₉₁

yes

characteristic

227

C₂

C₂×#20259346

yes

characteristic

228

C₂

C₂×#20259351

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	#486×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
prime radical	#27133211	C₂
hypercenter	#486	D₁₉₁
hypocenter	C₁₉₁	#3141
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉₁

commutator, cosocle

C₂×C₄×C₁₉₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉₁

Fitting

#486×C₁₉₁

C₂

socle

C₂²×C₁₉₁

C₂²×D₄

C₂

D₁₉₁

C₁₉₁

G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
2. C₄⋊Q₈×D₁₉₁	C₂	semidirect
3. #27133021	C₂	semidirect
4. #27133015	C₂	semidirect
5. #27133014	C₂	semidirect
6. #27133009	C₂	semidirect
7. #27132661	C₂	semidirect
8. C₄×#15690270	C₂	semidirect
9. #486×C₁₉₁	C₂	semidirect
114. C₁₉₁	#3141	semidirect
122. #486	D₁₉₁	semidirect

H ≅ G/N

type

2. C₄⋊Q₈×D₁₉₁

C₂

semidirect

3. #27133021

C₂

semidirect

4. #27133015

C₂

semidirect

5. #27133014

C₂

semidirect

6. #27133009

C₂

semidirect

7. #27132661

C₂

semidirect

8. C₄×#15690270

C₂

semidirect

9. #486×C₁₉₁

C₂

semidirect

114. C₁₉₁

#3141

semidirect

122. #486

D₁₉₁

semidirect

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

subgroup	index
#27133211	2
C₄⋊Q₈×D₁₉₁	2
#27133021	2
#27133015	2
#27133014	2
#27133009	2
#27132661	2
C₄×#15690270	2
#486×C₁₉₁	2
#3141	191

subgroup

index

C₄⋊Q₈×D₁₉₁

#486×C₁₉₁

191

Subgroups — #37582910

Conjugacy classes of subgroups

Complements

Maximal subgroups