Group #36472801 — subgroups

Subgroups — #36472801

Order 22784.

438 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic₇₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151401	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic
4	#26021111	C₂	1	2	yes	maximal
5	C₂×#366×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₅₆	C₂²	1	2	yes	—
7	C₂×Dic₇₁₂	—	2	2	no	—
8	C₂×Dic₇₁₂	—	2	2	no	—
9	C₂×Dic₇₁₂	C₄	1	4	yes	complemented
10	C₂²×#13083549	C₂²	1	1	yes	characteristic
11	C₂×#15667935	—	2	2	no	—
12	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
13	#19151503	—	2	2	no	—
14	#19151401	—	2	4	no	—
15	C₁₆×Dic₈₉	—	2	2	no	—
16	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#107×C₈₉	C₂²	1	2	yes	—
18	#366×C₈₉	—	2	2	no	—
19	C₂²×Dic₁₇₈	—	2	2	no	—
20	C₂×Dic₃₅₆	—	2	2	no	—
21	C₂×Dic₃₅₆	—	2	2	no	—
22	C₂×Dic₃₅₆	—	2	2	no	—
23	C₂×Dic₃₅₆	—	2	2	no	—
24	C₂×Dic₃₅₆	—	2	2	no	—
25	C₂×Dic₃₅₆	C₂×C₄	1	4	yes	—
26	C₂²×#10623494	D₄	1	1	yes	characteristic
27	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
28	Dic₇₁₂	—	2	8	no	—
29	C₂×#13083549	—	2	1	no	—
30	C₂×#13083549	—	2	1	no	—
31	C₂×#13083549	D₄	1	2	yes	—
32	#15667935	—	4	4	no	—
33	C₈×Dic₈₉	—	2	1	no	—
34	C₈×Dic₈₉	—	2	1	no	—
35	#15667919	—	4	4	no	—
36	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
38	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
39	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
40	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
41	#107×C₈₉	—	2	2	no	—
42	#107×C₈₉	—	2	2	no	—
43	C₂×Dic₁₇₈	—	2	4	no	—
44	C₂×Dic₁₇₈	—	4	2	no	—
45	C₂×Dic₁₇₈	—	4	2	no	—
46	C₂×Dic₁₇₈	—	4	2	no	—
47	C₂×Dic₁₇₈	—	4	2	no	—
48	C₂×Dic₁₇₈	—	4	2	no	—
49	C₂²×Dic₈₉	—	4	2	no	—
50	C₂²×Dic₈₉	D₈	1	2	yes	—
51	Dic₃₅₆	—	2	4	no	—
52	Dic₃₅₆	—	2	4	no	—
53	Dic₃₅₆	—	4	2	no	—
54	Dic₃₅₆	—	4	2	no	—
55	C₂×#10623494	—	2	1	no	—
56	C₂×#10623494	—	2	1	no	—
57	C₂×#10623494	D₈	1	2	yes	—
58	C₄×Dic₈₉	—	2	1	no	—
59	C₄×Dic₈₉	—	2	1	no	—
60	#13083549	—	2	2	no	—
61	C₂²×C₄×C₈₉	—	4	2	no	—
62	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
68	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
69	C₄⋊C₄×C₈₉	—	4	2	no	—
70	C₄⋊C₄×C₈₉	—	4	2	no	—
71	C₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₈₉	—	8	2	no	—
74	C₂×C₄×C₈₉	—	8	4	no	—
75	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
77	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
78	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
80	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
81	C₂×Dic₈₉	—	2	2	no	—
82	C₂×Dic₈₉	—	2	2	no	—
83	C₂×Dic₈₉	—	4	4	no	—
84	C₂×Dic₈₉	—	8	2	no	—
85	C₂×Dic₈₉	—	8	2	no	—
86	C₂×Dic₈₉	Q₃₂	1	4	yes	complemented
87	Dic₁₇₈	—	4	4	no	—
88	Dic₁₇₈	—	4	4	no	—
89	Dic₁₇₈	—	8	2	no	—
90	Dic₁₇₈	—	8	2	no	—
91	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
93	C₈×C₈₉	#121	1	1	yes	characteristic
94	C₈×C₈₉	#124	1	1	yes	characteristic
95	#10623494	—	2	2	no	—
96	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₈₉	#466	1	1	yes	characteristic
98	C₂²×C₈₉	#493	1	1	yes	characteristic
99	C₂²×C₈₉	C₂×Q₃₂	1	2	yes	—
100	C₂²×C₈₉	#508	1	2	yes	—
101	C₄×C₈₉	—	16	2	no	—
102	C₄×C₈₉	#390	1	1	yes	characteristic
103	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
104	C₄×C₈₉	#466	1	1	yes	characteristic
105	C₄×C₈₉	#495	1	1	yes	characteristic
106	Dic₈₉	—	2	4	no	—
107	Dic₈₉	—	8	4	no	—
108	#13236	—	89	1	no	maximal, Sylow
109	C₂×C₈₉	#1970	1	1	yes	characteristic
110	C₂×C₈₉	C₄×Q₃₂	1	2	yes	—
111	C₂×C₈₉	#2216	1	2	yes	—
112	C₂×C₈₉	#2247	1	1	yes	characteristic
113	C₂×C₈₉	#2249	1	1	yes	characteristic
114	C₂²×Q₃₂	—	89	1	no	—
115	C₂×#366	D₈₉	1	1	yes	characteristic
116	C₂×#358	—	89	2	no	—
117	C₂×C₄×C₁₆	—	89	1	no	—
118	#1969	—	89	2	no	—
119	C₈₉	#13236	1	1	yes	characteristic, complemented, Sylow
120	C₂²×Q₁₆	—	89	2	no	—
121	C₂×Q₃₂	—	89	4	no	—
122	C₂×Q₃₂	—	178	2	no	—
123	C₂×Q₃₂	—	178	2	no	—
124	C₂²×C₁₆	—	89	1	no	—
125	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
126	C₂×#107	C₂×D₈₉	1	2	yes	—
127	C₂×#103	—	178	2	no	—
128	C₂×C₄×C₈	—	89	1	no	—
129	#391	—	178	2	no	—
130	#366	—	2	2	no	—
131	#358	—	178	4	no	—
132	C₄×C₁₆	—	178	2	no	—
133	C₂²×Q₈	—	178	2	no	—
134	C₂×Q₁₆	—	89	4	no	—
135	C₂×Q₁₆	—	178	2	no	—
136	C₂×Q₁₆	—	178	2	no	—
137	C₂×Q₁₆	—	178	2	no	—
138	C₂×Q₁₆	—	178	2	no	—
139	C₂×Q₁₆	—	178	2	no	—
140	C₂²×C₈	—	89	1	no	—
141	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄²	—	89	1	no	—
144	Q₃₂	—	178	8	no	—
145	C₂×C₁₆	—	89	2	no	—
146	C₂×C₁₆	—	178	1	no	—
147	C₂×C₁₆	—	178	1	no	—
148	C₂×C₁₆	C₄×D₈₉	1	2	yes	—
149	C₂×C₁₆	D₃₅₆	1	2	yes	—
150	C₂×C₁₆	C₂²⋊D₈₉	1	2	yes	—
151	#107	—	2	2	no	—
152	#107	—	2	2	no	—
153	#103	—	356	4	no	—
154	C₄×C₈	—	178	1	no	—
155	C₄×C₈	—	178	1	no	—
156	#95	—	356	4	no	—
157	C₂×Q₈	—	356	2	no	—
158	C₂×Q₈	—	356	2	no	—
159	C₂×Q₈	—	356	2	no	—
160	C₂×Q₈	—	356	2	no	—
161	C₂×Q₈	—	356	2	no	—
162	C₂×Q₈	—	178	4	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	—	89	2	no	—
165	C₂²×C₄	—	356	2	no	—
166	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
167	Q₁₆	—	356	2	no	—
168	Q₁₆	—	356	2	no	—
169	Q₁₆	—	178	4	no	—
170	Q₁₆	—	178	4	no	—
171	C₂×C₈	—	89	2	no	—
172	C₂×C₈	—	178	1	no	—
173	C₂×C₈	—	178	1	no	—
174	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
175	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
176	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
177	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
178	C₂×C₈	#13083575	1	1	yes	characteristic
179	C₂×C₈	#13083575	1	1	yes	characteristic
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄²	—	178	1	no	—
183	C₄²	—	178	1	no	—
184	C₁₆	—	178	2	no	—
185	C₁₆	#13083551	1	4	yes	—
186	C₂³	D₈×D₈₉	1	1	yes	characteristic
187	Q₈	—	356	4	no	—
188	Q₈	—	356	4	no	—
189	Q₈	—	712	2	no	—
190	Q₈	—	712	2	no	—
191	C₂×C₄	—	8	2	no	—
192	C₂×C₄	—	8	4	no	—
193	C₂×C₄	—	89	4	no	—
194	C₂×C₄	—	356	4	no	—
195	C₂×C₄	—	178	2	no	—
196	C₂×C₄	—	178	2	no	—
197	C₂×C₄	—	712	2	no	—
198	C₂×C₄	—	712	2	no	—
199	C₂×C₄	#15667974	1	1	yes	characteristic
200	C₂×C₄	#15667987	1	1	yes	characteristic
201	C₂×C₄	#15668008	1	1	yes	characteristic
202	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
203	C₂×C₄	#15668035	1	1	yes	characteristic
204	C₂×C₄	#15668035	1	1	yes	characteristic
205	C₈	—	178	2	no	—
206	C₈	C₂×#13083551	1	1	yes	characteristic
207	C₈	#15667974	1	1	yes	characteristic
208	C₈	#15667987	1	1	yes	characteristic
209	C₈	#15668001	1	1	yes	characteristic
210	C₂²	#19151680	1	1	yes	characteristic
211	C₂²	#19151835	1	1	yes	characteristic
212	C₂²	#19151973	1	1	yes	characteristic
213	C₂²	Q₃₂×D₈₉	1	2	yes	—
214	C₂²	#19152027	1	2	yes	—
215	C₄	—	16	2	no	—
216	C₄	—	178	4	no	—
217	C₄	—	712	4	no	—
218	C₄	#19151499	1	1	yes	characteristic
219	C₄	#19151680	1	1	yes	characteristic
220	C₄	#19151835	1	1	yes	characteristic
221	C₄	#19151983	1	1	yes	characteristic
222	C₂	#26021116	1	1	yes	characteristic
223	C₂	#26022110	1	2	yes	—
224	C₂	#26022344	1	2	yes	—
225	C₂	#26022503	1	1	yes	characteristic
226	C₂	#26022510	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₁₂

C₂

yes

maximal, characteristic

C₂×#19151401

C₂

yes

maximal

C₂×C₁₆×Dic₈₉

C₂

yes

maximal, characteristic

#26021111

C₂

yes

maximal

C₂×#366×C₈₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₅₆

C₂²

yes

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

C₄

yes

complemented

C₂²×#13083549

C₂²

yes

characteristic

C₂×#15667935

—

C₂×C₈×Dic₈₉

C₂²

yes

characteristic

#19151503

—

#19151401

—

C₁₆×Dic₈₉

—

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#107×C₈₉

C₂²

yes

—

#366×C₈₉

—

C₂²×Dic₁₇₈

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

C₂×C₄

yes

—

C₂²×#10623494

D₄

yes

characteristic

C₂×C₄×Dic₈₉

D₄

yes

characteristic

Dic₇₁₂

—

C₂×#13083549

—

C₂×#13083549

—

C₂×#13083549

D₄

yes

—

#15667935

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

#15667919

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₂×C₁₆×C₈₉

D₄

yes

—

#107×C₈₉

—

#107×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

D₈

yes

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

D₈

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

#13083549

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₁₆×C₈₉

C₂²⋊C₄

yes

—

C₂³×C₈₉

C₂×D₈

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

C₂×D₈

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

Q₃₂

yes

complemented

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₉

C₄×D₄

yes

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

C₄×D₈

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

C₂×Q₃₂

yes

—

100

C₂²×C₈₉

#508

yes

—

101

C₄×C₈₉

—

102

C₄×C₈₉

#390

yes

characteristic

103

C₄×C₈₉

C₄×D₈

yes

characteristic

104

C₄×C₈₉

#466

yes

characteristic

105

C₄×C₈₉

#495

yes

characteristic

106

Dic₈₉

—

107

Dic₈₉

—

108

#13236

—

maximal, Sylow

109

C₂×C₈₉

#1970

yes

characteristic

110

C₂×C₈₉

C₄×Q₃₂

yes

—

111

C₂×C₈₉

#2216

yes

—

112

C₂×C₈₉

#2247

yes

characteristic

113

C₂×C₈₉

#2249

yes

characteristic

114

C₂²×Q₃₂

—

115

C₂×#366

D₈₉

yes

characteristic

116

C₂×#358

—

117

C₂×C₄×C₁₆

—

118

#1969

—

119

C₈₉

#13236

yes

characteristic, complemented, Sylow

120

C₂²×Q₁₆

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

—

178

—

123

C₂×Q₃₂

—

178

—

124

C₂²×C₁₆

—

125

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

126

C₂×#107

C₂×D₈₉

yes

—

127

C₂×#103

—

178

—

128

C₂×C₄×C₈

—

129

#391

—

178

—

130

#366

—

131

#358

—

178

—

132

C₄×C₁₆

—

178

—

133

C₂²×Q₈

—

178

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

178

—

136

C₂×Q₁₆

—

178

—

137

C₂×Q₁₆

—

178

—

138

C₂×Q₁₆

—

178

—

139

C₂×Q₁₆

—

178

—

140

C₂²×C₈

—

141

C₂²×C₈

C₂²×D₈₉

yes

characteristic

142

C₂×C₄⋊C₄

—

143

C₂×C₄²

—

144

Q₃₂

—

178

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

178

—

147

C₂×C₁₆

—

178

—

148

C₂×C₁₆

C₄×D₈₉

yes

—

149

C₂×C₁₆

D₃₅₆

yes

—

150

C₂×C₁₆

C₂²⋊D₈₉

yes

—

151

#107

—

152

#107

—

153

#103

—

356

—

154

C₄×C₈

—

178

—

155

C₄×C₈

—

178

—

156

#95

—

356

—

157

C₂×Q₈

—

356

—

158

C₂×Q₈

—

356

—

159

C₂×Q₈

—

356

—

160

C₂×Q₈

—

356

—

161

C₂×Q₈

—

356

—

162

C₂×Q₈

—

178

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

356

—

166

C₂²×C₄

D₄×D₈₉

yes

characteristic

167

Q₁₆

—

356

—

168

Q₁₆

—

356

—

169

Q₁₆

—

178

—

170

Q₁₆

—

178

—

171

C₂×C₈

—

172

C₂×C₈

—

178

—

173

C₂×C₈

—

178

—

174

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

175

C₂×C₈

D₄×D₈₉

yes

characteristic

176

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

177

C₂×C₈

C₂×D₃₅₆

yes

characteristic

178

C₂×C₈

#13083575

yes

characteristic

179

C₂×C₈

#13083575

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄²

—

178

—

183

C₄²

—

178

—

184

C₁₆

—

178

—

185

C₁₆

#13083551

yes

—

186

C₂³

D₈×D₈₉

yes

characteristic

187

Q₈

—

356

—

188

Q₈

—

356

—

189

Q₈

—

712

—

190

Q₈

—

712

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

356

—

195

C₂×C₄

—

178

—

196

C₂×C₄

—

178

—

197

C₂×C₄

—

712

—

198

C₂×C₄

—

712

—

199

C₂×C₄

#15667974

yes

characteristic

200

C₂×C₄

#15667987

yes

characteristic

201

C₂×C₄

#15668008

yes

characteristic

202

C₂×C₄

D₈×D₈₉

yes

characteristic

203

C₂×C₄

#15668035

yes

characteristic

204

C₂×C₄

#15668035

yes

characteristic

205

C₈

—

178

—

206

C₈

C₂×#13083551

yes

characteristic

207

C₈

#15667974

yes

characteristic

208

C₈

#15667987

yes

characteristic

209

C₈

#15668001

yes

characteristic

210

C₂²

#19151680

yes

characteristic

211

C₂²

#19151835

yes

characteristic

212

C₂²

#19151973

yes

characteristic

213

C₂²

Q₃₂×D₈₉

yes

—

214

C₂²

#19152027

yes

—

215

C₄

—

216

C₄

—

178

—

217

C₄

—

712

—

218

C₄

#19151499

yes

characteristic

219

C₄

#19151680

yes

characteristic

220

C₄

#19151835

yes

characteristic

221

C₄

#19151983

yes

characteristic

222

C₂

#26021116

yes

characteristic

223

C₂

#26022110

yes

—

224

C₂

#26022344

yes

—

225

C₂

#26022503

yes

characteristic

226

C₂

#26022510

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₈₉
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×#366×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#366	D₈₉
hypocenter	C₈₉	#13236
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₈₉

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×#366×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

C₂×D₈

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
9. C₂×Dic₇₁₂	C₄	semidirect
86. C₂×Dic₈₉	Q₃₂	semidirect
119. C₈₉	#13236	semidirect

H ≅ G/N

type

9. C₂×Dic₇₁₂

C₄

semidirect

86. C₂×Dic₈₉

Q₃₂

semidirect

119. C₈₉

#13236

semidirect

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

subgroup	index
C₂²×Dic₇₁₂	2
C₂×#19151401	2
C₂×C₁₆×Dic₈₉	2
#26021111	2
C₂×#366×C₈₉	2
#13236	89

subgroup

index

C₂²×Dic₇₁₂

C₂×#19151401

C₂×C₁₆×Dic₈₉

#26021111

C₂×#366×C₈₉

#13236

Subgroups — #36472801

Conjugacy classes of subgroups

Complements

Maximal subgroups