Group #36472391 — subgroups

Subgroups — #36472391

Order 22784.

314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂×#19151413	C₂	1	1	yes	maximal, characteristic
2	#26021973	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151375	C₂	1	1	yes	maximal, characteristic
4	#26021121	C₂	1	1	yes	maximal, characteristic
5	#26021003	C₂	1	1	yes	maximal, characteristic
6	#26018359	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1383	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
9	C₂×#15667952	C₂²	1	1	yes	characteristic
10	#19151636	C₂²	1	1	yes	characteristic
11	#19151626	—	2	1	no	—
12	C₂×#15667935	—	2	1	no	—
13	C₂×#15667922	C₂²	1	1	yes	characteristic
14	#19151503	—	2	1	no	—
15	#19151413	—	2	2	no	—
16	#19151403	C₄	1	4	yes	complemented
17	#19151375	—	2	2	no	—
18	#19151359	—	2	1	no	—
19	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₇₈	—	2	1	no	—
23	C₂×Dic₃₅₆	—	2	1	no	—
24	C₂×Dic₃₅₆	—	2	1	no	—
25	C₂×Dic₃₅₆	—	2	1	no	—
26	C₂×Dic₃₅₆	—	2	1	no	—
27	C₂×Dic₃₅₆	—	2	1	no	—
28	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
29	C₂²×#10623494	D₄	1	1	yes	characteristic
30	#15667971	—	2	1	no	—
31	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
32	#15667952	—	2	1	no	—
33	#15667952	D₄	1	2	yes	—
34	C₂×#13083549	—	2	1	no	—
35	#15667946	C₂×C₄	1	2	yes	—
36	#15667944	—	2	1	no	—
37	#15667941	—	4	2	no	—
38	#15667935	—	4	2	no	—
39	#15667922	—	2	1	no	—
40	#15667922	—	2	1	no	—
41	#15667919	—	4	2	no	—
42	C₂×M₁₆×C₈₉	—	2	1	no	—
43	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
45	M₃₂×C₈₉	—	2	1	no	—
46	M₃₂×C₈₉	—	2	1	no	—
47	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
48	#108×C₈₉	—	2	1	no	—
49	#108×C₈₉	—	2	1	no	—
50	#106×C₈₉	—	2	1	no	—
51	#106×C₈₉	—	2	1	no	—
52	C₂×Dic₁₇₈	—	2	2	no	—
53	C₂×Dic₁₇₈	—	4	1	no	—
54	C₂×Dic₁₇₈	—	4	1	no	—
55	C₂×Dic₁₇₈	—	4	1	no	—
56	C₂×Dic₁₇₈	—	4	1	no	—
57	C₂×Dic₁₇₈	—	4	1	no	—
58	C₂²×Dic₈₉	—	2	1	no	—
59	C₂²×Dic₈₉	—	4	1	no	—
60	Dic₃₅₆	—	2	2	no	—
61	Dic₃₅₆	—	2	2	no	—
62	Dic₃₅₆	—	4	1	no	—
63	Dic₃₅₆	—	4	1	no	—
64	C₂×#10623494	—	2	1	no	—
65	C₂×#10623494	—	2	1	no	—
66	C₂×#10623494	—	2	1	no	—
67	C₄⋊Dic₈₉	—	2	2	no	—
68	C₂²⋊Dic₈₉	—	4	1	no	—
69	C₄×Dic₈₉	—	2	1	no	—
70	C₄×Dic₈₉	—	2	1	no	—
71	C₄×Dic₈₉	—	4	1	no	—
72	#13083549	—	2	2	no	—
73	C₂²×C₄×C₈₉	—	4	1	no	—
74	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
75	M₁₆×C₈₉	—	4	1	no	—
76	M₁₆×C₈₉	—	4	1	no	—
77	C₂×C₈×C₈₉	—	4	1	no	—
78	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
81	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
82	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
83	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
84	C₄⋊C₄×C₈₉	—	4	1	no	—
85	C₄⋊C₄×C₈₉	—	4	1	no	—
86	C₁₆×C₈₉	—	2	2	no	—
87	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₈₉	—	8	2	no	—
89	C₂×C₄×C₈₉	—	8	1	no	—
90	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
91	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
92	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
93	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
96	C₂×Dic₈₉	—	4	2	no	—
97	C₂×Dic₈₉	—	4	2	no	—
98	C₂×Dic₈₉	—	4	2	no	—
99	C₂×Dic₈₉	—	4	1	no	—
100	C₂×Dic₈₉	—	8	1	no	—
101	C₂×Dic₈₉	—	8	1	no	—
102	Dic₁₇₈	—	4	2	no	—
103	Dic₁₇₈	—	4	2	no	—
104	Dic₁₇₈	—	8	1	no	—
105	Dic₁₇₈	—	8	1	no	—
106	C₈×C₈₉	—	8	1	no	—
107	C₈×C₈₉	#117	1	1	yes	characteristic
108	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
109	C₈×C₈₉	#123	1	1	yes	characteristic
110	C₈×C₈₉	#126	1	1	yes	characteristic
111	#10623494	—	4	1	no	—
112	C₂²×C₈₉	—	2	2	no	—
113	C₂²×C₈₉	#442	1	1	yes	characteristic
114	C₂²×C₈₉	#468	1	1	yes	characteristic
115	C₂²×C₈₉	#490	1	1	yes	characteristic
116	C₄×C₈₉	—	16	1	no	—
117	C₄×C₈₉	#388	1	1	yes	characteristic
118	C₄×C₈₉	#440	1	1	yes	characteristic
119	C₄×C₈₉	#469	1	1	yes	characteristic
120	C₄×C₈₉	#489	1	1	yes	characteristic
121	Dic₈₉	—	8	1	no	—
122	Dic₈₉	—	8	2	no	—
123	Dic₈₉	—	8	2	no	—
124	#13154	—	89	1	no	maximal, Sylow
125	C₂×C₈₉	—	2	1	no	—
126	C₂×C₈₉	—	2	1	no	—
127	C₂×C₈₉	#1936	1	1	yes	characteristic
128	C₂×C₈₉	#2180	1	2	yes	—
129	C₂×#362	—	89	1	no	—
130	#2141	—	89	1	no	—
131	C₂×#347	—	89	1	no	—
132	#1971	—	89	1	no	—
133	#1946	—	89	1	no	—
134	#1386	—	89	1	no	—
135	#1383	D₈₉	1	1	yes	characteristic
136	C₈₉	#13154	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₁₆	—	89	1	no	—
138	C₂×M₃₂	—	89	1	no	—
139	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
140	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
141	#427	—	89	1	no	—
142	C₂×#106	C₂×D₈₉	1	1	yes	characteristic
143	#424	—	178	1	no	—
144	C₂×#103	—	178	1	no	—
145	C₂×#97	—	89	1	no	—
146	#391	—	178	1	no	—
147	#362	—	178	2	no	—
148	#358	—	89	4	no	—
149	#347	—	178	2	no	—
150	#339	—	178	1	no	—
151	C₂²×Q₈	—	178	1	no	—
152	C₂×Q₁₆	—	89	2	no	—
153	C₂×Q₁₆	—	178	1	no	—
154	C₂×Q₁₆	—	178	1	no	—
155	C₂×Q₁₆	—	178	1	no	—
156	C₂×Q₁₆	—	178	1	no	—
157	C₂×Q₁₆	—	178	1	no	—
158	C₂×M₁₆	—	2	1	no	—
159	C₂²×C₈	—	89	1	no	—
160	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
161	#117	—	178	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄²	—	89	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	—	2	1	no	—
166	M₃₂	—	89	2	no	—
167	M₃₂	—	178	1	no	—
168	C₂×C₁₆	—	178	1	no	—
169	C₂×C₁₆	C₄×D₈₉	1	2	yes	—
170	#108	—	2	1	no	—
171	#108	—	2	1	no	—
172	#107	—	89	2	no	—
173	#106	—	2	1	no	—
174	#106	—	2	1	no	—
175	#106	—	178	1	no	—
176	C₄⋊C₈	—	356	2	no	—
177	#103	—	356	2	no	—
178	#97	—	178	1	no	—
179	#97	—	178	1	no	—
180	#95	—	356	2	no	—
181	C₂×Q₈	—	356	1	no	—
182	C₂×Q₈	—	356	1	no	—
183	C₂×Q₈	—	356	1	no	—
184	C₂×Q₈	—	356	1	no	—
185	C₂×Q₈	—	356	1	no	—
186	C₂×Q₈	—	178	2	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	356	1	no	—
189	C₂²×C₄	—	178	1	no	—
190	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
191	Q₁₆	—	356	1	no	—
192	Q₁₆	—	356	1	no	—
193	Q₁₆	—	178	2	no	—
194	Q₁₆	—	178	2	no	—
195	M₁₆	—	4	1	no	—
196	M₁₆	—	4	1	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	178	1	no	—
199	C₂×C₈	—	178	1	no	—
200	C₂×C₈	—	178	1	no	—
201	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
202	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
203	C₂×C₈	#13083573	1	1	yes	characteristic
204	C₂×C₈	#13083574	1	1	yes	characteristic
205	C₂×C₈	#13083574	1	1	yes	characteristic
206	C₂×C₈	#13083575	1	1	yes	characteristic
207	C₄⋊C₄	—	4	1	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	178	2	no	—
210	C₂²⋊C₄	—	356	1	no	—
211	C₄²	—	356	1	no	—
212	C₄²	—	178	1	no	—
213	C₄²	—	178	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	178	2	no	—
216	C₂³	#15668039	1	1	yes	characteristic
217	Q₈	—	356	2	no	—
218	Q₈	—	356	2	no	—
219	Q₈	—	712	1	no	—
220	Q₈	—	712	1	no	—
221	C₂×C₄	—	8	2	no	—
222	C₂×C₄	—	8	1	no	—
223	C₂×C₄	—	356	2	no	—
224	C₂×C₄	—	356	2	no	—
225	C₂×C₄	—	356	2	no	—
226	C₂×C₄	—	356	1	no	—
227	C₂×C₄	—	712	1	no	—
228	C₂×C₄	—	712	1	no	—
229	C₂×C₄	#15667974	1	1	yes	characteristic
230	C₂×C₄	#15667985	1	1	yes	characteristic
231	C₂×C₄	#15667998	1	1	yes	characteristic
232	C₂×C₄	#15668036	1	1	yes	characteristic
233	C₂×C₄	#15668039	1	1	yes	characteristic
234	C₂×C₄	#15668044	1	1	yes	characteristic
235	C₈	—	8	1	no	—
236	C₈	—	356	1	no	—
237	C₈	#15667969	1	1	yes	characteristic
238	C₈	#15667972	1	1	yes	characteristic
239	C₈	#15667997	1	1	yes	characteristic
240	C₈	#15668007	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#19151709	1	1	yes	characteristic
243	C₂²	#19151847	1	1	yes	characteristic
244	C₂²	#19151961	1	1	yes	characteristic
245	C₄	—	16	1	no	—
246	C₄	—	712	1	no	—
247	C₄	—	712	2	no	—
248	C₄	—	712	2	no	—
249	C₄	#19151487	1	1	yes	characteristic
250	C₄	#19151697	1	1	yes	characteristic
251	C₄	#19151850	1	1	yes	characteristic
252	C₄	#19151959	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#26020947	1	1	yes	characteristic
256	C₂	#26022142	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151413

C₂

yes

maximal, characteristic

#26021973

C₂

yes

maximal, characteristic

C₂×#19151375

C₂

yes

maximal, characteristic

#26021121

C₂

yes

maximal, characteristic

#26021003

C₂

yes

maximal, characteristic

#26018359

C₂

yes

maximal, characteristic

C₈₉×#1383

C₂

yes

maximal, characteristic

C₂²×Dic₃₅₆

C₂²

yes

characteristic

C₂×#15667952

C₂²

yes

characteristic

#19151636

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#19151375

—

#19151359

—

C₂×M₃₂×C₈₉

C₂²

yes

characteristic

C₂×#108×C₈₉

C₂²

yes

characteristic

C₂×#106×C₈₉

C₂²

yes

characteristic

C₂²×Dic₁₇₈

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

C₂×C₄

yes

—

C₂²×#10623494

D₄

yes

characteristic

#15667971

—

C₂×C₄×Dic₈₉

D₄

yes

characteristic

#15667952

—

#15667952

D₄

yes

—

C₂×#13083549

—

#15667946

C₂×C₄

yes

—

—

—

—

—

—

—

C₂×M₁₆×C₈₉

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₈₉

—

M₃₂×C₈₉

—

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

#108×C₈₉

—

#108×C₈₉

—

#106×C₈₉

—

#106×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

#13083549

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×D₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

100

C₂×Dic₈₉

—

101

C₂×Dic₈₉

—

102

Dic₁₇₈

—

103

Dic₁₇₈

—

104

Dic₁₇₈

—

105

Dic₁₇₈

—

106

C₈×C₈₉

—

107

C₈×C₈₉

#117

yes

characteristic

108

C₈×C₈₉

C₄×D₄

yes

characteristic

109

C₈×C₈₉

#123

yes

characteristic

110

C₈×C₈₉

#126

yes

characteristic

111

#10623494

—

112

C₂²×C₈₉

—

113

C₂²×C₈₉

#442

yes

characteristic

114

C₂²×C₈₉

#468

yes

characteristic

115

C₂²×C₈₉

#490

yes

characteristic

116

C₄×C₈₉

—

117

C₄×C₈₉

#388

yes

characteristic

118

C₄×C₈₉

#440

yes

characteristic

119

C₄×C₈₉

#469

yes

characteristic

120

C₄×C₈₉

#489

yes

characteristic

121

Dic₈₉

—

122

Dic₈₉

—

123

Dic₈₉

—

124

#13154

—

maximal, Sylow

125

C₂×C₈₉

—

126

C₂×C₈₉

—

127

C₂×C₈₉

#1936

yes

characteristic

128

C₂×C₈₉

#2180

yes

—

129

C₂×#362

—

130

#2141

—

131

C₂×#347

—

132

#1971

—

133

#1946

—

134

#1386

—

135

#1383

D₈₉

yes

characteristic

136

C₈₉

#13154

yes

characteristic, complemented, Sylow

137

C₂²×Q₁₆

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₈₉

yes

characteristic

140

C₂×#108

C₂×D₈₉

yes

characteristic

141

#427

—

142

C₂×#106

C₂×D₈₉

yes

characteristic

143

#424

—

178

—

144

C₂×#103

—

178

—

145

C₂×#97

—

146

#391

—

178

—

147

#362

—

178

—

148

#358

—

149

#347

—

178

—

150

#339

—

178

—

151

C₂²×Q₈

—

178

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

178

—

154

C₂×Q₁₆

—

178

—

155

C₂×Q₁₆

—

178

—

156

C₂×Q₁₆

—

178

—

157

C₂×Q₁₆

—

178

—

158

C₂×M₁₆

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₈₉

yes

characteristic

161

#117

—

178

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

178

—

168

C₂×C₁₆

—

178

—

169

C₂×C₁₆

C₄×D₈₉

yes

—

170

#108

—

171

#108

—

172

#107

—

173

#106

—

174

#106

—

175

#106

—

178

—

176

C₄⋊C₈

—

356

—

177

#103

—

356

—

178

#97

—

178

—

179

#97

—

178

—

180

#95

—

356

—

181

C₂×Q₈

—

356

—

182

C₂×Q₈

—

356

—

183

C₂×Q₈

—

356

—

184

C₂×Q₈

—

356

—

185

C₂×Q₈

—

356

—

186

C₂×Q₈

—

178

—

187

C₂²×C₄

—

188

C₂²×C₄

—

356

—

189

C₂²×C₄

—

178

—

190

C₂²×C₄

D₄×D₈₉

yes

characteristic

191

Q₁₆

—

356

—

192

Q₁₆

—

356

—

193

Q₁₆

—

178

—

194

Q₁₆

—

178

—

195

M₁₆

—

196

M₁₆

—

197

C₂×C₈

—

198

C₂×C₈

—

178

—

199

C₂×C₈

—

178

—

200

C₂×C₈

—

178

—

201

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

202

C₂×C₈

D₄×D₈₉

yes

characteristic

203

C₂×C₈

#13083573

yes

characteristic

204

C₂×C₈

#13083574

yes

characteristic

205

C₂×C₈

#13083574

yes

characteristic

206

C₂×C₈

#13083575

yes

characteristic

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

178

—

210

C₂²⋊C₄

—

356

—

211

C₄²

—

356

—

212

C₄²

—

178

—

213

C₄²

—

178

—

214

C₁₆

—

215

C₁₆

—

178

—

216

C₂³

#15668039

yes

characteristic

217

Q₈

—

356

—

218

Q₈

—

356

—

219

Q₈

—

712

—

220

Q₈

—

712

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

356

—

224

C₂×C₄

—

356

—

225

C₂×C₄

—

356

—

226

C₂×C₄

—

356

—

227

C₂×C₄

—

712

—

228

C₂×C₄

—

712

—

229

C₂×C₄

#15667974

yes

characteristic

230

C₂×C₄

#15667985

yes

characteristic

231

C₂×C₄

#15667998

yes

characteristic

232

C₂×C₄

#15668036

yes

characteristic

233

C₂×C₄

#15668039

yes

characteristic

234

C₂×C₄

#15668044

yes

characteristic

235

C₈

—

236

C₈

—

356

—

237

C₈

#15667969

yes

characteristic

238

C₈

#15667972

yes

characteristic

239

C₈

#15667997

yes

characteristic

240

C₈

#15668007

yes

characteristic

241

C₂²

—

242

C₂²

#19151709

yes

characteristic

243

C₂²

#19151847

yes

characteristic

244

C₂²

#19151961

yes

characteristic

245

C₄

—

246

C₄

—

712

—

247

C₄

—

712

—

248

C₄

—

712

—

249

C₄

#19151487

yes

characteristic

250

C₄

#19151697

yes

characteristic

251

C₄

#19151850

yes

characteristic

252

C₄

#19151959

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#26020947

yes

characteristic

256

C₂

#26022142

yes

—

	subgroup	G/H
center	C₂²	#19151709
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1383	C₂
socle	C₂²×C₈₉	#442
prime radical	C₂³×C₈₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1383	D₈₉
hypocenter	C₈₉	#13154
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1383

subgroup

G/H

center

C₂²

#19151709

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₈₉×#1383

C₂

C₂²×C₈₉

C₂³×C₈₉

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1383

N	H ≅ G/N	type
16. #19151403	C₄	semidirect
136. C₈₉	#13154	semidirect

H ≅ G/N

type

16. #19151403

C₄

semidirect

136. C₈₉

#13154

semidirect

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

subgroup	index
C₂×#19151413	2
#26021973	2
C₂×#19151375	2
#26021121	2
#26021003	2
#26018359	2
C₈₉×#1383	2
#13154	89

subgroup

index

C₈₉×#1383

Subgroups — #36472391

Conjugacy classes of subgroups

Complements

Maximal subgroups