Group #36447425 — subgroups

Subgroups — #36447425

Order 22784.

388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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	#26028965	C₂	1	1	yes	maximal, characteristic
2	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
3	#26018886	C₂	1	2	yes	maximal
4	#26018162	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15668018	C₄	1	2	yes	—
7	#19152148	C₂²	1	1	yes	characteristic
8	#19151677	—	2	1	no	—
9	#19151677	—	2	1	no	—
10	C₈×D₃₅₆	—	2	1	no	—
11	C₈×D₃₅₆	—	2	1	no	—
12	#19151655	C₂²	1	2	yes	—
13	#19151622	C₂²	1	1	yes	characteristic
14	#19151564	C₄	1	2	yes	—
15	#19151351	—	2	1	no	—
16	#19151349	—	2	1	no	—
17	#19151337	—	2	4	no	—
18	#432×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	#335×C₈₉	—	2	1	no	—
21	#334×C₈₉	—	2	1	no	—
22	C₂×#13083574	C₂×C₄	1	2	yes	—
23	#15668018	—	4	4	no	—
24	C₂×#13083558	C₂×C₄	1	2	yes	—
25	C₂×#13083557	—	2	2	no	—
26	C₂×C₈×D₈₉	—	2	2	no	—
27	#15668012	Q₈	1	1	yes	characteristic
28	#15668009	Q₈	1	1	yes	characteristic
29	#15668000	D₄	1	2	yes	—
30	#15667986	—	2	1	no	—
31	#15667986	—	2	1	no	—
32	C₄×D₃₅₆	—	2	1	no	—
33	C₄×D₃₅₆	—	2	1	no	—
34	C₄⋊#10623494	—	2	1	no	—
35	C₄⋊#10623494	—	2	1	no	—
36	C₄⋊#10623494	—	2	2	no	—
37	C₂²⋊#10623494	—	2	2	no	—
38	#15667924	—	2	2	no	—
39	#15667924	—	2	2	no	—
40	#15667923	—	2	2	no	—
41	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
44	C₄⋊C₈×C₈₉	—	2	2	no	—
45	C₂²⋊C₈×C₈₉	—	2	2	no	—
46	#97×C₈₉	—	2	2	no	—
47	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
50	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
51	#13083574	—	4	2	no	—
52	#13083574	—	4	2	no	—
53	C₂×Dic₁₇₈	C₄⋊C₄	1	2	yes	—
54	C₂×D₃₅₆	—	2	1	no	—
55	C₂×D₃₅₆	—	2	1	no	—
56	C₂×D₃₅₆	C₄⋊C₄	1	2	yes	—
57	C₂×C₂²⋊D₈₉	—	2	2	no	—
58	C₂×C₄×D₈₉	—	2	2	no	—
59	#13083558	—	4	2	no	—
60	#13083557	—	4	4	no	—
61	C₂×#10623494	—	2	2	no	—
62	C₂×#10623494	—	4	2	no	—
63	C₈×D₈₉	—	4	4	no	—
64	C₄⋊Dic₈₉	—	2	1	no	—
65	C₄⋊Dic₈₉	—	2	1	no	—
66	#13083551	—	2	2	no	—
67	#13083551	—	2	2	no	—
68	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
70	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
71	C₂×C₈×C₈₉	—	2	2	no	—
72	C₂×C₈×C₈₉	—	4	1	no	—
73	C₂×C₈×C₈₉	—	4	2	no	—
74	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
82	C₂³×C₈₉	#117	1	1	yes	characteristic
83	C₂²×D₈₉	—	2	2	no	—
84	C₂×C₄×C₈₉	—	2	1	no	—
85	C₂×C₄×C₈₉	—	2	1	no	—
86	C₂×C₄×C₈₉	—	4	1	no	—
87	C₂×C₄×C₈₉	—	4	1	no	—
88	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂²⋊D₈₉	—	4	4	no	—
95	C₂×Dic₈₉	—	2	2	no	—
96	D₃₅₆	—	4	2	no	—
97	D₃₅₆	—	4	2	no	—
98	D₃₅₆	—	4	2	no	—
99	C₄×D₈₉	—	4	2	no	—
100	C₄×D₈₉	—	4	2	no	—
101	Dic₁₇₈	—	4	2	no	—
102	C₈×C₈₉	—	2	1	no	—
103	C₈×C₈₉	—	2	1	no	—
104	C₈×C₈₉	—	2	1	no	—
105	C₈×C₈₉	—	8	2	no	—
106	C₈×C₈₉	#100	1	2	yes	—
107	#10623494	—	4	2	no	—
108	#10623494	—	8	2	no	—
109	C₂²×C₈₉	—	2	1	no	—
110	C₂²×C₈₉	—	2	1	no	—
111	C₂²×C₈₉	—	2	1	no	—
112	C₂²×C₈₉	#380	1	1	yes	characteristic
113	C₂×D₈₉	—	4	2	no	—
114	C₂×D₈₉	—	4	2	no	—
115	C₂×D₈₉	—	4	2	no	—
116	C₄×C₈₉	—	2	1	no	—
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	2	1	no	—
119	C₄×C₈₉	—	2	1	no	—
120	C₄×C₈₉	—	2	1	no	—
121	C₄×C₈₉	C₂×#100	1	1	yes	characteristic
122	C₄×C₈₉	#413	1	1	yes	characteristic
123	Dic₈₉	—	4	2	no	—
124	#8632	—	89	1	no	maximal, Sylow
125	C₂×C₈₉	—	4	1	no	—
126	C₂×C₈₉	#1800	1	1	yes	characteristic
127	C₂×C₈₉	#1814	1	1	yes	characteristic
128	C₂×C₈₉	#1814	1	1	yes	characteristic
129	D₈₉	—	8	2	no	—
130	#2931	—	89	1	no	—
131	#1568	—	89	1	no	—
132	#1568	D₈₉	1	1	yes	characteristic, complemented
133	#1536	—	89	2	no	—
134	#1307	—	89	2	no	—
135	C₈₉	#8632	1	1	yes	characteristic, complemented, Sylow
136	C₂×#131	—	89	2	no	—
137	#532	—	89	1	no	—
138	#436	—	178	1	no	—
139	#436	—	178	1	no	—
140	C₈×D₄	—	178	1	no	—
141	C₈×D₄	—	178	1	no	—
142	#432	—	89	2	no	—
143	#432	C₂×D₈₉	1	2	yes	—
144	#423	—	89	1	no	—
145	#408	—	89	2	no	—
146	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
147	#335	—	2	1	no	—
148	#335	—	178	1	no	—
149	#334	—	2	1	no	—
150	#334	—	178	1	no	—
151	#329	—	178	4	no	—
152	C₂×#41	—	89	2	no	—
153	#131	—	356	4	no	—
154	C₂×M₁₆	—	89	2	no	—
155	C₂×M₁₆	—	178	2	no	—
156	C₂²×C₈	—	178	2	no	—
157	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
158	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
159	C₄⋊Q₈	—	89	1	no	—
160	#127	—	89	1	no	—
161	#124	—	89	2	no	—
162	#121	—	178	1	no	—
163	#121	—	178	1	no	—
164	C₄×D₄	—	178	1	no	—
165	C₄×D₄	—	178	1	no	—
166	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	178	1	no	—
169	C₄⋊C₈	—	178	2	no	—
170	C₄⋊C₈	—	178	1	no	—
171	C₂²⋊C₈	—	2	2	no	—
172	C₂²⋊C₈	—	178	2	no	—
173	C₂²⋊C₈	—	178	2	no	—
174	C₂²⋊C₈	—	178	2	no	—
175	#97	—	2	2	no	—
176	#97	—	178	2	no	—
177	C₄×C₈	D₃₅₆	1	1	yes	characteristic
178	C₄×C₈	D₃₅₆	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
181	#41	—	356	2	no	—
182	#41	—	356	2	no	—
183	C₂×Q₈	—	89	2	no	—
184	C₂×D₄	—	89	2	no	—
185	C₂×D₄	—	178	2	no	—
186	C₂×D₄	—	178	1	no	—
187	C₂×D₄	—	178	1	no	—
188	C₂²×C₄	—	178	2	no	—
189	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
190	C₂²×C₄	#13083573	1	1	yes	characteristic
191	C₂²×C₄	#13083575	1	1	yes	characteristic
192	M₁₆	—	356	4	no	—
193	M₁₆	—	356	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	356	4	no	—
198	C₂×C₈	—	356	2	no	—
199	C₂×C₈	—	178	2	no	—
200	C₂×C₈	#13083551	1	1	yes	characteristic
201	C₂×C₈	#13083551	1	1	yes	characteristic
202	C₂×C₈	#13083551	1	1	yes	characteristic
203	C₂×C₈	#13083551	1	1	yes	characteristic
204	C₄⋊C₄	—	178	1	no	—
205	C₄⋊C₄	—	178	1	no	—
206	C₂²⋊C₄	—	178	2	no	—
207	C₂²⋊C₄	—	178	2	no	—
208	C₄²	D₄×D₈₉	1	1	yes	characteristic
209	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
210	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
211	C₄²	Q₈×D₈₉	1	1	yes	characteristic
212	C₂³	—	178	2	no	—
213	C₂³	#15667970	1	1	yes	characteristic
214	Q₈	—	356	2	no	—
215	D₄	—	356	2	no	—
216	D₄	—	356	2	no	—
217	D₄	—	356	2	no	—
218	D₄	—	356	4	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	4	1	no	—
222	C₂×C₄	—	4	1	no	—
223	C₂×C₄	—	356	2	no	—
224	C₂×C₄	—	356	2	no	—
225	C₂×C₄	—	178	2	no	—
226	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
227	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
228	C₂×C₄	#15667983	1	1	yes	characteristic
229	C₂×C₄	#15667987	1	1	yes	characteristic
230	C₂×C₄	#15667988	1	1	yes	characteristic
231	C₂×C₄	#15667992	1	1	yes	characteristic
232	C₈	—	2	1	no	—
233	C₈	—	2	1	no	—
234	C₈	—	2	1	no	—
235	C₈	—	8	2	no	—
236	C₈	—	356	2	no	—
237	C₈	—	712	2	no	—
238	C₈	#15667928	1	2	yes	—
239	C₂²	—	2	1	no	—
240	C₂²	—	2	1	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	356	2	no	—
243	C₂²	—	356	2	no	—
244	C₂²	—	356	2	no	—
245	C₂²	#19151455	1	1	yes	characteristic
246	C₄	—	2	1	no	—
247	C₄	—	2	1	no	—
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	356	2	no	—
252	C₄	C₂×#15667928	1	1	yes	characteristic
253	C₄	#19151580	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	712	2	no	—
256	C₂	#26020241	1	1	yes	characteristic
257	C₂	#26020303	1	1	yes	characteristic
258	C₂	#26020307	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26028965

C₂

yes

maximal, characteristic

#26019015

C₂

yes

maximal, characteristic, complemented

#26018886

C₂

yes

maximal

#26018162

C₂

yes

maximal, complemented

C₈₉×#1568

C₂

yes

maximal, characteristic, complemented

C₂×#15668018

C₄

yes

—

#19152148

C₂²

yes

characteristic

#19151677

—

#19151677

—

C₈×D₃₅₆

—

C₈×D₃₅₆

—

#19151655

C₂²

yes

—

#19151622

C₂²

yes

characteristic

#19151564

C₄

yes

—

#19151351

—

#19151349

—

#19151337

—

#432×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

#334×C₈₉

—

C₂×#13083574

C₂×C₄

yes

—

#15668018

—

C₂×#13083558

C₂×C₄

yes

—

C₂×#13083557

—

C₂×C₈×D₈₉

—

#15668012

Q₈

yes

characteristic

#15668009

Q₈

yes

characteristic

#15668000

D₄

yes

—

#15667986

—

#15667986

—

C₄×D₃₅₆

—

C₄×D₃₅₆

—

—

—

—

—

—

—

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

#97×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

#13083574

—

#13083574

—

C₂×Dic₁₇₈

C₄⋊C₄

yes

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

C₄⋊C₄

yes

—

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

—

—

—

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083551

—

#13083551

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

C₂²×C₄×C₈₉

yes

C₂²×C₄×C₈₉

yes

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₂³×C₈₉

#117

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

100

C₄×D₈₉

—

101

Dic₁₇₈

—

102

C₈×C₈₉

—

103

C₈×C₈₉

—

104

C₈×C₈₉

—

105

C₈×C₈₉

—

106

C₈×C₈₉

#100

yes

—

107

#10623494

—

108

#10623494

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

#380

yes

characteristic

113

C₂×D₈₉

—

114

C₂×D₈₉

—

115

C₂×D₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

C₂×#100

yes

characteristic

122

C₄×C₈₉

#413

yes

characteristic

123

Dic₈₉

—

124

#8632

—

maximal, Sylow

125

C₂×C₈₉

—

126

C₂×C₈₉

#1800

yes

characteristic

127

C₂×C₈₉

#1814

yes

characteristic

128

C₂×C₈₉

#1814

yes

characteristic

129

D₈₉

—

130

#2931

—

131

#1568

—

132

#1568

D₈₉

yes

characteristic, complemented

133

#1536

—

134

#1307

—

135

C₈₉

#8632

yes

characteristic, complemented, Sylow

136

C₂×#131

—

137

#532

—

138

#436

—

178

—

139

#436

—

178

—

140

C₈×D₄

—

178

—

141

C₈×D₄

—

178

—

142

#432

—

143

#432

C₂×D₈₉

yes

—

144

#423

—

145

#408

—

146

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

147

#335

—

148

#335

—

178

—

149

#334

—

150

#334

—

178

—

151

#329

—

178

—

152

C₂×#41

—

153

#131

—

356

—

154

C₂×M₁₆

—

155

C₂×M₁₆

—

178

—

156

C₂²×C₈

—

178

—

157

C₂²×C₈

C₄×D₈₉

yes

characteristic

158

C₂²×C₈

C₄×D₈₉

yes

characteristic

159

C₄⋊Q₈

—

160

#127

—

161

#124

—

162

#121

—

178

—

163

#121

—

178

—

164

C₄×D₄

—

178

—

165

C₄×D₄

—

178

—

166

C₂×C₄²

C₂²×D₈₉

yes

characteristic

167

C₄⋊C₈

—

168

C₄⋊C₈

—

178

—

169

C₄⋊C₈

—

178

—

170

C₄⋊C₈

—

178

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

178

—

173

C₂²⋊C₈

—

178

—

174

C₂²⋊C₈

—

178

—

175

#97

—

176

#97

—

178

—

177

C₄×C₈

D₃₅₆

yes

characteristic

178

C₄×C₈

D₃₅₆

yes

characteristic

179

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

180

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

181

#41

—

356

—

182

#41

—

356

—

183

C₂×Q₈

—

184

C₂×D₄

—

185

C₂×D₄

—

178

—

186

C₂×D₄

—

178

—

187

C₂×D₄

—

178

—

188

C₂²×C₄

—

178

—

189

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

190

C₂²×C₄

#13083573

yes

characteristic

191

C₂²×C₄

#13083575

yes

characteristic

192

M₁₆

—

356

—

193

M₁₆

—

356

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

356

—

198

C₂×C₈

—

356

—

199

C₂×C₈

—

178

—

200

C₂×C₈

#13083551

yes

characteristic

201

C₂×C₈

#13083551

yes

characteristic

202

C₂×C₈

#13083551

yes

characteristic

203

C₂×C₈

#13083551

yes

characteristic

204

C₄⋊C₄

—

178

—

205

C₄⋊C₄

—

178

—

206

C₂²⋊C₄

—

178

—

207

C₂²⋊C₄

—

178

—

208

C₄²

D₄×D₈₉

yes

characteristic

209

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

210

C₄²

C₂×D₃₅₆

yes

characteristic

211

C₄²

Q₈×D₈₉

yes

characteristic

212

C₂³

—

178

—

213

C₂³

#15667970

yes

characteristic

214

Q₈

—

356

—

215

D₄

—

356

—

216

D₄

—

356

—

217

D₄

—

356

—

218

D₄

—

356

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

356

—

224

C₂×C₄

—

356

—

225

C₂×C₄

—

178

—

226

C₂×C₄

C₂×#13083551

yes

characteristic

227

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

228

C₂×C₄

#15667983

yes

characteristic

229

C₂×C₄

#15667987

yes

characteristic

230

C₂×C₄

#15667988

yes

characteristic

231

C₂×C₄

#15667992

yes

characteristic

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

236

C₈

—

356

—

237

C₈

—

712

—

238

C₈

#15667928

yes

—

239

C₂²

—

240

C₂²

—

241

C₂²

—

242

C₂²

—

356

—

243

C₂²

—

356

—

244

C₂²

—

356

—

245

C₂²

#19151455

yes

characteristic

246

C₄

—

247

C₄

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

356

—

252

C₄

C₂×#15667928

yes

characteristic

253

C₄

#19151580

yes

characteristic

254

C₂

—

255

C₂

—

712

—

256

C₂

#26020241

yes

characteristic

257

C₂

#26020303

yes

characteristic

258

C₂

#26020307

yes

characteristic

	subgroup	G/H
center	C₂²	#19151455
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1568	C₂
socle	C₂²×C₈₉	#380
prime radical	#19152148	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1568	D₈₉
hypocenter	C₈₉	#8632
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#19151455

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1568

C₂

C₂²×C₈₉

C₂²

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
2. #26019015	C₂	semidirect
4. #26018162	C₂	semidirect
5. C₈₉×#1568	C₂	semidirect
132. #1568	D₈₉	semidirect
135. C₈₉	#8632	semidirect

H ≅ G/N

type

2. #26019015

C₂

semidirect

4. #26018162

C₂

semidirect

5. C₈₉×#1568

C₂

semidirect

132. #1568

D₈₉

semidirect

135. C₈₉

#8632

semidirect

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

subgroup	index
#26028965	2
#26019015	2
#26018886	2
#26018162	2
C₈₉×#1568	2
#8632	89

subgroup

index

C₈₉×#1568

Subgroups — #36447425

Conjugacy classes of subgroups

Complements

Maximal subgroups