Group #37582172 — subgroups

Subgroups — #37582172

Order 24448.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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	C₂²×#15690277	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#20259329	C₂	1	1	yes	maximal, characteristic
3	#27133234	C₂	1	1	yes	maximal, characteristic
4	#27132919	C₂	1	4	yes	maximal, complemented
5	#27132902	C₂	1	4	yes	maximal, complemented
6	#27132699	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132672	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132671	C₂	1	1	yes	maximal, characteristic, complemented
9	#536×C₁₉₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
11	C₂×#15690277	—	2	4	no	—
12	C₂×#15690277	C₂²	1	2	yes	—
13	C₂×#15690277	C₂²	1	2	yes	—
14	#20259329	—	2	4	no	—
15	C₂×#15690271	C₂²	1	1	yes	characteristic
16	C₂×#15690271	C₂²	1	2	yes	—
17	C₂²×C₁₉₁⋊C₈	C₂²	1	2	yes	—
18	C₂²×C₁₉₁⋊C₈	C₂²	1	1	yes	characteristic
19	#20259320	—	2	1	no	—
20	#20259309	—	2	1	no	—
21	#20259303	—	2	2	no	—
22	#20259301	C₂²	1	4	yes	—
23	#20259281	C₂²	1	1	yes	characteristic
24	#20259255	C₂²	1	2	yes	—
25	#20259253	C₂²	1	2	yes	—
26	#20259246	C₂²	1	4	yes	—
27	#20259245	C₂²	1	4	yes	—
28	C₂×#41×C₁₉₁	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉₁	C₂²	1	1	yes	characteristic
30	C₄⋊Q₈×C₁₉₁	—	2	1	no	—
31	#124×C₁₉₁	—	2	1	no	—
32	#123×C₁₉₁	—	2	2	no	—
33	C₂²⋊Q₈×C₁₉₁	C₂²	1	4	yes	—
34	#117×C₁₉₁	C₂²	1	1	yes	characteristic
35	C₂×Dic₃₈₂	—	2	1	no	—
36	C₂×Dic₃₈₂	—	2	2	no	—
37	C₂×Dic₃₈₂	—	2	2	no	—
38	C₂×Dic₃₈₂	C₂³	1	2	yes	—
39	C₂²×Dic₁₉₁	—	2	1	no	—
40	#15690277	—	2	4	no	—
41	#15690277	—	2	4	no	—
42	#15690271	—	2	4	no	—
43	#15690271	—	2	2	no	—
44	C₂×C₁₉₁⋊C₈	—	2	4	no	—
45	C₂×C₁₉₁⋊C₈	D₄	1	4	yes	—
46	C₂×C₁₉₁⋊C₈	C₂³	1	2	yes	—
47	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₁₉₁⋊C₈	C₂³	1	1	yes	characteristic
49	C₄⋊Dic₁₉₁	C₂³	1	2	yes	—
50	Dic₁₉₁⋊C₄	—	2	4	no	—
51	C₂²⋊Dic₁₉₁	—	2	1	no	—
52	C₂²⋊Dic₁₉₁	—	2	4	no	—
53	C₄×Dic₁₉₁	—	2	1	no	—
54	#41×C₁₉₁	—	2	2	no	—
55	#41×C₁₉₁	—	2	2	no	—
56	C₂×Q₈×C₁₉₁	—	2	1	no	—
57	C₂×Q₈×C₁₉₁	—	2	2	no	—
58	C₂×Q₈×C₁₉₁	—	2	2	no	—
59	C₂×Q₈×C₁₉₁	D₄	1	1	yes	characteristic
60	C₂×Q₈×C₁₉₁	C₂³	1	2	yes	—
61	C₂×D₄×C₁₉₁	D₄	1	2	yes	—
62	C₂×D₄×C₁₉₁	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉₁	—	2	1	no	—
64	C₂²×C₄×C₁₉₁	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₁₉₁	—	2	4	no	—
67	C₄⋊C₄×C₁₉₁	C₂³	1	2	yes	—
68	C₂²⋊C₄×C₁₉₁	—	2	1	no	—
69	C₂²⋊C₄×C₁₉₁	—	2	4	no	—
70	C₄²×C₁₉₁	—	2	1	no	—
71	Dic₃₈₂	—	2	2	no	—
72	Dic₃₈₂	—	2	2	no	—
73	Dic₃₈₂	—	4	2	no	—
74	C₂×Dic₁₉₁	—	2	2	no	—
75	C₂×Dic₁₉₁	—	2	2	no	—
76	C₂×Dic₁₉₁	—	4	2	no	—
77	C₁₉₁⋊C₈	—	2	2	no	—
78	C₁₉₁⋊C₈	C₂×D₄	1	2	yes	—
79	C₁₉₁⋊C₈	C₂×D₄	1	2	yes	—
80	C₂³×C₁₉₁	C₂×D₄	1	2	yes	—
81	C₂³×C₁₉₁	C₂×D₄	1	1	yes	characteristic
82	Q₈×C₁₉₁	—	2	2	no	—
83	Q₈×C₁₉₁	—	2	2	no	—
84	Q₈×C₁₉₁	—	2	2	no	—
85	Q₈×C₁₉₁	—	4	2	no	—
86	D₄×C₁₉₁	—	2	4	no	—
87	D₄×C₁₉₁	—	2	2	no	—
88	C₂×C₄×C₁₉₁	—	2	2	no	—
89	C₂×C₄×C₁₉₁	—	2	2	no	—
90	C₂×C₄×C₁₉₁	—	2	2	no	—
91	C₂×C₄×C₁₉₁	—	2	2	no	—
92	C₂×C₄×C₁₉₁	—	4	2	no	—
93	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
94	C₂×C₄×C₁₉₁	C₂×D₄	1	2	yes	—
95	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉₁	#41	1	2	yes	—
97	C₂×C₄×C₁₉₁	C₂⁴	1	1	yes	characteristic
98	C₂²×C₁₉₁	—	2	2	no	—
99	C₂²×C₁₉₁	—	2	2	no	—
100	C₂²×C₁₉₁	—	2	4	no	—
101	C₂²×C₁₉₁	#121	1	2	yes	—
102	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
103	C₄×C₁₉₁	—	2	2	no	—
104	C₄×C₁₉₁	—	4	2	no	—
105	C₄×C₁₉₁	—	4	2	no	—
106	C₄×C₁₉₁	#121	1	2	yes	—
107	C₄×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₁₉₁	C₂×#41	1	1	yes	characteristic
109	Dic₁₉₁	—	4	2	no	—
110	Dic₁₉₁	—	4	2	no	—
111	C₂×C₁₉₁	—	2	2	no	—
112	C₂×C₁₉₁	—	4	2	no	—
113	C₂×C₁₉₁	C₂×#121	1	1	yes	characteristic
114	C₂×C₁₉₁	#578	1	2	yes	—
115	C₁₉₁	#3059	1	1	yes	characteristic, complemented, Sylow
116	#3059	—	191	1	no	maximal, Sylow
117	C₂²×Q₁₆	—	191	1	no	—
118	C₂×#131	—	191	1	no	—
119	#536	—	191	1	no	—
120	#536	D₁₉₁	1	1	yes	characteristic
121	#470	—	191	4	no	—
122	#467	—	191	4	no	—
123	#427	—	191	1	no	—
124	#419	—	191	1	no	—
125	#419	—	191	1	no	—
126	C₂×#41	C₂×D₁₉₁	1	1	yes	characteristic
127	C₂²×Q₈	—	191	1	no	—
128	C₂²×Q₈	C₂×D₁₉₁	1	1	yes	characteristic
129	C₂×Q₁₆	—	382	4	no	—
130	C₂×Q₁₆	—	191	2	no	—
131	C₂×Q₁₆	—	191	2	no	—
132	#131	—	382	4	no	—
133	C₂×M₁₆	—	191	1	no	—
134	C₂×M₁₆	—	191	2	no	—
135	C₂²×C₈	—	191	2	no	—
136	C₂²×C₈	—	191	1	no	—
137	C₄⋊Q₈	—	2	1	no	—
138	C₄⋊Q₈	—	382	1	no	—
139	#124	—	2	1	no	—
140	#124	—	382	1	no	—
141	#123	—	2	2	no	—
142	#123	—	382	2	no	—
143	C₂²⋊Q₈	—	191	4	no	—
144	C₂²⋊Q₈	C₂×D₁₉₁	1	4	yes	—
145	#117	—	191	1	no	—
146	#117	C₂×D₁₉₁	1	1	yes	characteristic
147	#107	—	191	2	no	—
148	#106	—	191	2	no	—
149	#103	—	191	4	no	—
150	#103	—	191	4	no	—
151	#41	—	2	2	no	—
152	#41	—	2	2	no	—
153	C₂×Q₈	—	2	1	no	—
154	C₂×Q₈	—	2	2	no	—
155	C₂×Q₈	—	2	2	no	—
156	C₂×Q₈	—	382	1	no	—
157	C₂×Q₈	—	382	2	no	—
158	C₂×Q₈	—	382	2	no	—
159	C₂×Q₈	—	191	2	no	—
160	C₂×Q₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
161	C₂×Q₈	C₂²×D₁₉₁	1	2	yes	—
162	C₂×D₄	C₂²⋊D₁₉₁	1	2	yes	—
163	C₂×D₄	C₂²⋊D₁₉₁	1	1	yes	characteristic
164	C₂²×C₄	—	2	1	no	—
165	C₂²×C₄	—	382	1	no	—
166	C₂²×C₄	C₂²×D₁₉₁	1	2	yes	—
167	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
168	Q₁₆	—	382	4	no	—
169	Q₁₆	—	382	4	no	—
170	M₁₆	—	382	2	no	—
171	M₁₆	—	382	4	no	—
172	C₂×C₈	—	382	4	no	—
173	C₂×C₈	—	191	2	no	—
174	C₂×C₈	—	191	4	no	—
175	C₂×C₈	—	191	1	no	—
176	C₂×C₈	—	191	1	no	—
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	382	4	no	—
179	C₄⋊C₄	—	191	2	no	—
180	C₄⋊C₄	C₂²×D₁₉₁	1	2	yes	—
181	C₂²⋊C₄	—	2	1	no	—
182	C₂²⋊C₄	—	2	4	no	—
183	C₂²⋊C₄	—	382	1	no	—
184	C₂²⋊C₄	—	382	4	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	382	1	no	—
187	C₂³	C₂×C₂²⋊D₁₉₁	1	2	yes	—
188	C₂³	C₂×C₂²⋊D₁₉₁	1	1	yes	characteristic
189	Q₈	—	2	2	no	—
190	Q₈	—	2	2	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	4	2	no	—
193	Q₈	—	382	2	no	—
194	Q₈	—	382	2	no	—
195	Q₈	—	764	2	no	—
196	D₄	—	2	4	no	—
197	D₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	382	2	no	—
204	C₂×C₄	—	382	2	no	—
205	C₂×C₄	—	764	2	no	—
206	C₂×C₄	D₄×D₁₉₁	1	2	yes	—
207	C₂×C₄	C₂×C₂²⋊D₁₉₁	1	2	yes	—
208	C₂×C₄	C₂×C₂²⋊D₁₉₁	1	1	yes	characteristic
209	C₂×C₄	#15690286	1	2	yes	—
210	C₂×C₄	C₂³×D₁₉₁	1	1	yes	characteristic
211	C₈	—	382	2	no	—
212	C₈	—	191	2	no	—
213	C₈	—	191	2	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	2	4	no	—
216	C₂²	—	2	2	no	—
217	C₂²	#20259294	1	2	yes	—
218	C₂²	C₂²×C₂²⋊D₁₉₁	1	1	yes	characteristic
219	C₄	—	2	2	no	—
220	C₄	—	4	2	no	—
221	C₄	—	4	2	no	—
222	C₄	—	764	2	no	—
223	C₄	—	764	2	no	—
224	C₄	#20259294	1	2	yes	—
225	C₄	C₂×D₄×D₁₉₁	1	1	yes	characteristic
226	C₄	C₂×#15690286	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	—	4	2	no	—
229	C₂	C₂×#20259294	1	1	yes	characteristic
230	C₂	#27133478	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#15690277

C₂

yes

maximal, characteristic, complemented

C₂×#20259329

C₂

yes

maximal, characteristic

#27133234

C₂

yes

maximal, characteristic

#27132919

C₂

yes

maximal, complemented

#27132902

C₂

yes

maximal, complemented

#27132699

C₂

yes

maximal, characteristic, complemented

#27132672

C₂

yes

maximal, characteristic, complemented

#27132671

C₂

yes

maximal, characteristic, complemented

#536×C₁₉₁

C₂

yes

maximal, characteristic

C₂²×Dic₃₈₂

C₂²

yes

characteristic

C₂×#15690277

—

C₂×#15690277

C₂²

yes

—

C₂×#15690277

C₂²

yes

—

#20259329

—

C₂×#15690271

C₂²

yes

characteristic

C₂×#15690271

C₂²

yes

—

C₂²×C₁₉₁⋊C₈

C₂²

yes

—

C₂²×C₁₉₁⋊C₈

C₂²

yes

—

—

—

C₂²

yes

—

#20259281

C₂²

yes

characteristic

#20259255

C₂²

yes

—

#20259253

C₂²

yes

—

#20259246

C₂²

yes

—

#20259245

C₂²

yes

—

C₂×#41×C₁₉₁

C₂²

yes

characteristic

C₂²×Q₈×C₁₉₁

C₂²

yes

characteristic

C₄⋊Q₈×C₁₉₁

—

#124×C₁₉₁

—

#123×C₁₉₁

—

C₂²⋊Q₈×C₁₉₁

C₂²

yes

—

#117×C₁₉₁

C₂²

yes

characteristic

C₂×Dic₃₈₂

—

C₂×Dic₃₈₂

—

C₂×Dic₃₈₂

—

C₂×Dic₃₈₂

C₂³

yes

—

C₂²×Dic₁₉₁

—

—

—

—

—

C₂×C₁₉₁⋊C₈

—

C₂×C₁₉₁⋊C₈

D₄

yes

—

C₂×C₁₉₁⋊C₈

C₂³

yes

—

C₂×C₁₉₁⋊C₈

C₂³

yes

characteristic

C₂×C₁₉₁⋊C₈

C₂³

yes

characteristic

C₄⋊Dic₁₉₁

C₂³

yes

—

Dic₁₉₁⋊C₄

—

C₂²⋊Dic₁₉₁

—

C₂²⋊Dic₁₉₁

—

C₄×Dic₁₉₁

—

#41×C₁₉₁

—

#41×C₁₉₁

—

C₂×Q₈×C₁₉₁

—

C₂×Q₈×C₁₉₁

—

C₂×Q₈×C₁₉₁

—

C₂×Q₈×C₁₉₁

D₄

yes

characteristic

C₂×Q₈×C₁₉₁

C₂³

yes

—

C₂×D₄×C₁₉₁

D₄

yes

—

C₂×D₄×C₁₉₁

D₄

yes

characteristic

C₂²×C₄×C₁₉₁

—

C₂²×C₄×C₁₉₁

C₂³

yes

—

C₂²×C₄×C₁₉₁

C₂³

yes

characteristic

C₄⋊C₄×C₁₉₁

—

C₄⋊C₄×C₁₉₁

C₂³

yes

—

C₂²⋊C₄×C₁₉₁

—

C₂²⋊C₄×C₁₉₁

—

C₄²×C₁₉₁

—

Dic₃₈₂

—

Dic₃₈₂

—

Dic₃₈₂

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₂×Dic₁₉₁

—

C₁₉₁⋊C₈

—

C₁₉₁⋊C₈

C₂×D₄

yes

—

C₁₉₁⋊C₈

C₂×D₄

yes

—

C₂³×C₁₉₁

C₂×D₄

yes

—

C₂³×C₁₉₁

C₂×D₄

yes

characteristic

Q₈×C₁₉₁

—

Q₈×C₁₉₁

—

Q₈×C₁₉₁

—

Q₈×C₁₉₁

—

D₄×C₁₉₁

—

D₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

—

C₂×C₄×C₁₉₁

C₂×D₄

yes

—

C₂×C₄×C₁₉₁

C₂×D₄

yes

—

C₂×C₄×C₁₉₁

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉₁

#41

yes

—

C₂×C₄×C₁₉₁

C₂⁴

yes

characteristic

C₂²×C₁₉₁

—

C₂²×C₁₉₁

—

100

C₂²×C₁₉₁

—

101

C₂²×C₁₉₁

#121

yes

—

102

C₂²×C₁₉₁

C₂²×D₄

yes

characteristic

103

C₄×C₁₉₁

—

104

C₄×C₁₉₁

—

105

C₄×C₁₉₁

—

106

C₄×C₁₉₁

#121

yes

—

107

C₄×C₁₉₁

C₂²×D₄

yes

characteristic

108

C₄×C₁₉₁

C₂×#41

yes

characteristic

109

Dic₁₉₁

—

110

Dic₁₉₁

—

111

C₂×C₁₉₁

—

112

C₂×C₁₉₁

—

113

C₂×C₁₉₁

C₂×#121

yes

characteristic

114

C₂×C₁₉₁

#578

yes

—

115

C₁₉₁

#3059

yes

characteristic, complemented, Sylow

116

#3059

—

191

maximal, Sylow

117

C₂²×Q₁₆

—

191

—

118

C₂×#131

—

191

—

119

#536

—

191

—

120

#536

D₁₉₁

yes

characteristic

121

#470

—

191

—

122

#467

—

191

—

123

#427

—

191

—

124

#419

—

191

—

125

#419

—

191

—

126

C₂×#41

C₂×D₁₉₁

yes

characteristic

127

C₂²×Q₈

—

191

—

128

C₂²×Q₈

C₂×D₁₉₁

yes

characteristic

129

C₂×Q₁₆

—

382

—

130

C₂×Q₁₆

—

191

—

131

C₂×Q₁₆

—

191

—

132

#131

—

382

—

133

C₂×M₁₆

—

191

—

134

C₂×M₁₆

—

191

—

135

C₂²×C₈

—

191

—

136

C₂²×C₈

—

191

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

382

—

139

#124

—

140

#124

—

382

—

141

#123

—

142

#123

—

382

—

143

C₂²⋊Q₈

—

191

—

144

C₂²⋊Q₈

C₂×D₁₉₁

yes

—

145

#117

—

191

—

146

#117

C₂×D₁₉₁

yes

characteristic

147

#107

—

191

—

148

#106

—

191

—

149

#103

—

191

—

150

#103

—

191

—

151

#41

—

152

#41

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

382

—

157

C₂×Q₈

—

382

—

158

C₂×Q₈

—

382

—

159

C₂×Q₈

—

191

—

160

C₂×Q₈

C₂²⋊D₁₉₁

yes

characteristic

161

C₂×Q₈

C₂²×D₁₉₁

yes

—

162

C₂×D₄

C₂²⋊D₁₉₁

yes

—

163

C₂×D₄

C₂²⋊D₁₉₁

yes

characteristic

164

C₂²×C₄

—

165

C₂²×C₄

—

382

—

166

C₂²×C₄

C₂²×D₁₉₁

yes

—

167

C₂²×C₄

C₂²×D₁₉₁

yes

characteristic

168

Q₁₆

—

382

—

169

Q₁₆

—

382

—

170

M₁₆

—

382

—

171

M₁₆

—

382

—

172

C₂×C₈

—

382

—

173

C₂×C₈

—

191

—

174

C₂×C₈

—

191

—

175

C₂×C₈

—

191

—

176

C₂×C₈

—

191

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

382

—

179

C₄⋊C₄

—

191

—

180

C₄⋊C₄

C₂²×D₁₉₁

yes

—

181

C₂²⋊C₄

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

382

—

184

C₂²⋊C₄

—

382

—

185

C₄²

—

186

C₄²

—

382

—

187

C₂³

C₂×C₂²⋊D₁₉₁

yes

—

188

C₂³

C₂×C₂²⋊D₁₉₁

yes

characteristic

189

Q₈

—

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

382

—

194

Q₈

—

382

—

195

Q₈

—

764

—

196

D₄

—

197

D₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

382

—

204

C₂×C₄

—

382

—

205

C₂×C₄

—

764

—

206

C₂×C₄

D₄×D₁₉₁

yes

—

207

C₂×C₄

C₂×C₂²⋊D₁₉₁

yes

—

208

C₂×C₄

C₂×C₂²⋊D₁₉₁

yes

characteristic

209

C₂×C₄

#15690286

yes

—

210

C₂×C₄

C₂³×D₁₉₁

yes

characteristic

211

C₈

—

382

—

212

C₈

—

191

—

213

C₈

—

191

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

#20259294

yes

—

218

C₂²

C₂²×C₂²⋊D₁₉₁

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

764

—

223

C₄

—

764

—

224

C₄

#20259294

yes

—

225

C₄

C₂×D₄×D₁₉₁

yes

characteristic

226

C₄

C₂×#15690286

yes

characteristic

227

C₂

—

228

C₂

—

229

C₂

C₂×#20259294

yes

characteristic

230

C₂

#27133478

yes

—

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉₁
commutator, cosocle	C₂×C₄×C₁₉₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉₁
Fitting	#536×C₁₉₁	C₂
socle	C₂²×C₁₉₁	C₂²×D₄
prime radical	C₂×#41×C₁₉₁	C₂²
hypercenter	#536	D₁₉₁
hypocenter	C₁₉₁	#3059
LCS	G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ #536

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₁₉₁

commutator, cosocle

C₂×C₄×C₁₉₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉₁

Fitting

#536×C₁₉₁

C₂

socle

C₂²×C₁₉₁

C₂²×D₄

prime radical

C₂×#41×C₁₉₁

C₂²

D₁₉₁

C₁₉₁

G ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁

UCS

C₁ ◁ C₂² ◁ C₂×#41 ◁ #536

N	H ≅ G/N	type
1. C₂²×#15690277	C₂	semidirect
4. #27132919	C₂	semidirect
5. #27132902	C₂	semidirect
6. #27132699	C₂	semidirect
7. #27132672	C₂	semidirect
8. #27132671	C₂	semidirect
115. C₁₉₁	#3059	semidirect

H ≅ G/N

type

1. C₂²×#15690277

C₂

semidirect

4. #27132919

C₂

semidirect

5. #27132902

C₂

semidirect

6. #27132699

C₂

semidirect

7. #27132672

C₂

semidirect

8. #27132671

C₂

semidirect

115. C₁₉₁

#3059

semidirect

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

subgroup	index
C₂²×#15690277	2
C₂×#20259329	2
#27133234	2
#27132919	2
#27132902	2
#27132699	2
#27132672	2
#27132671	2
#536×C₁₉₁	2
#3059	191

subgroup

index

#536×C₁₉₁

191

Subgroups — #37582172

Conjugacy classes of subgroups

Complements

Maximal subgroups