Group #36469658 — subgroups

Subgroups — #36469658

Order 22784.

442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 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	C₄×#15668034	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151406	C₂	1	2	yes	maximal
3	C₄×#15667948	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018348	C₂	1	2	yes	maximal, complemented
5	C₂×#346×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15668034	C₂²	1	1	yes	characteristic
7	C₄×#13083574	—	2	1	no	—
8	C₄×Dic₃₅₆	C₄	1	2	yes	—
9	C₄×#13083563	—	2	2	no	—
10	C₄×D₇₁₂	C₄	1	2	yes	—
11	C₂×#15667948	C₂²	1	2	yes	—
12	#19151636	C₂²	1	1	yes	characteristic
13	#19151595	—	2	1	no	—
14	C₄×#13083558	—	2	1	no	—
15	#19151406	C₄	1	8	yes	complemented
16	#19151363	—	2	1	no	—
17	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
19	#346×C₈₉	—	2	2	no	—
20	C₂×#13083574	—	2	1	no	—
21	#15668034	—	2	2	no	—
22	#15668034	C₂×C₄	1	4	yes	—
23	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
24	C₂×#13083563	—	2	1	no	—
25	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
26	C₂×#13083558	—	2	2	no	—
27	C₄×Dic₁₇₈	—	2	2	no	—
28	C₄×D₃₅₆	—	2	2	no	—
29	C₄×C₂²⋊D₈₉	—	4	2	no	—
30	#15667971	—	2	1	no	—
31	#15667969	—	4	1	no	—
32	C₄²×D₈₉	—	4	1	no	—
33	#15667948	—	2	2	no	—
34	#15667948	C₂×C₄	1	4	yes	complemented
35	#15667946	C₂×C₄	1	2	yes	—
36	#15667944	—	2	1	no	—
37	#15667937	—	2	2	no	—
38	#15667934	—	2	2	no	—
39	#15667923	—	4	1	no	—
40	C₄×#10623494	—	4	1	no	—
41	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₈₉	—	2	2	no	—
45	C₂×C₁₆×C₈₉	—	2	2	no	—
46	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
47	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₈₉	D₄	1	2	yes	—
49	#13083574	—	2	4	no	—
50	#13083574	—	4	2	no	—
51	C₂×Dic₁₇₈	—	2	1	no	—
52	C₂×D₃₅₆	—	2	1	no	—
53	C₂×C₂²⋊D₈₉	—	4	1	no	—
54	C₂×C₄×D₈₉	—	4	1	no	—
55	C₂×C₄×D₈₉	—	4	2	no	—
56	Dic₃₅₆	—	2	1	no	—
57	Dic₃₅₆	C₄²	1	2	yes	—
58	#13083563	—	2	4	no	—
59	D₇₁₂	—	2	1	no	—
60	D₇₁₂	C₄²	1	2	yes	—
61	#13083558	—	2	4	no	—
62	#13083558	—	4	2	no	—
63	C₂×#10623494	—	4	2	no	—
64	C₄⋊Dic₈₉	—	2	2	no	—
65	#13083553	—	4	2	no	—
66	C₂²⋊Dic₈₉	—	4	1	no	—
67	#13083551	—	4	2	no	—
68	C₄×Dic₈₉	—	4	2	no	—
69	C₄×Dic₈₉	—	4	1	no	—
70	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	—	2	2	no	—
73	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
76	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	#41	1	2	yes	—
78	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
79	C₄²×C₈₉	D₈	1	1	yes	characteristic
80	C₄²×C₈₉	D₈	1	1	yes	characteristic
81	C₁₆×C₈₉	—	2	4	no	—
82	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
83	C₂²×D₈₉	—	4	1	no	—
84	C₂×C₄×C₈₉	—	4	2	no	—
85	C₂×C₄×C₈₉	#102	1	2	yes	—
86	C₂×C₄×C₈₉	#102	1	2	yes	—
87	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
89	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#135	1	2	yes	—
91	C₂²⋊D₈₉	—	4	4	no	—
92	C₂×Dic₈₉	—	4	1	no	—
93	C₂×Dic₈₉	—	4	2	no	—
94	D₃₅₆	—	2	2	no	—
95	D₃₅₆	—	4	1	no	—
96	C₄×D₈₉	—	4	4	no	—
97	C₄×D₈₉	—	8	4	no	—
98	Dic₁₇₈	—	2	2	no	—
99	Dic₁₇₈	—	4	1	no	—
100	C₈×C₈₉	—	2	2	no	—
101	C₈×C₈₉	C₂×C₄²	1	1	yes	characteristic
102	C₈×C₈₉	#117	1	1	yes	characteristic
103	C₈×C₈₉	C₄×D₄	1	2	yes	—
104	#10623494	—	4	4	no	—
105	C₂²×C₈₉	—	2	2	no	—
106	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
107	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
108	C₂×D₈₉	—	4	2	no	—
109	C₂×D₈₉	—	8	2	no	—
110	C₄×C₈₉	—	2	2	no	—
111	C₄×C₈₉	—	2	2	no	—
112	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
113	C₄×C₈₉	#416	1	1	yes	characteristic
114	C₄×C₈₉	C₄×D₈	1	2	yes	—
115	Dic₈₉	—	4	2	no	—
116	Dic₈₉	—	8	2	no	—
117	#12640	—	89	1	no	maximal, Sylow
118	C₂×C₈₉	—	2	2	no	—
119	C₂×C₈₉	C₄×#102	1	1	yes	characteristic
120	C₂×C₈₉	#2143	1	2	yes	—
121	D₈₉	—	8	2	no	—
122	C₄×#135	—	89	1	no	—
123	C₂×#359	—	89	2	no	—
124	C₂×#346	D₈₉	1	1	yes	characteristic, complemented
125	C₄×#108	—	89	1	no	—
126	#1382	—	89	2	no	—
127	C₈₉	#12640	1	1	yes	characteristic, complemented, Sylow
128	C₂×#135	—	89	1	no	—
129	C₄×#41	—	178	1	no	—
130	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
131	C₄×Q₁₆	—	89	2	no	—
132	C₄×SD₁₆	—	178	2	no	—
133	C₄×D₈	—	89	2	no	—
134	C₂×#108	—	89	2	no	—
135	#427	—	89	1	no	—
136	#416	—	178	1	no	—
137	C₄×M₁₆	—	178	1	no	—
138	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
139	#359	—	89	8	no	—
140	#346	—	2	2	no	—
141	#341	—	178	1	no	—
142	C₂×#41	—	178	1	no	—
143	#135	—	89	4	no	—
144	#135	—	178	2	no	—
145	C₂×Q₁₆	—	89	1	no	—
146	C₂×SD₁₆	—	178	1	no	—
147	C₂×D₈	—	89	1	no	—
148	C₂×M₁₆	—	178	2	no	—
149	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
150	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
151	C₄×Q₈	—	178	2	no	—
152	C₄×D₄	—	356	2	no	—
153	C₄×D₄	—	178	2	no	—
154	#117	—	356	1	no	—
155	#117	—	178	1	no	—
156	C₂×C₄²	—	356	1	no	—
157	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
158	C₂×C₁₆	—	2	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	C₄×D₈₉	1	4	yes	complemented
161	#108	—	89	4	no	—
162	#108	—	178	2	no	—
163	#107	—	89	2	no	—
164	#106	—	178	1	no	—
165	#103	—	178	2	no	—
166	#102	—	178	2	no	—
167	#97	—	356	1	no	—
168	C₄×C₈	—	356	1	no	—
169	C₄×C₈	C₄×D₈₉	1	2	yes	—
170	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
171	#41	—	356	2	no	—
172	#41	—	178	4	no	—
173	C₂×Q₈	—	178	1	no	—
174	C₂×D₄	—	356	1	no	—
175	C₂×D₄	—	178	1	no	—
176	C₂²×C₄	—	356	1	no	—
177	C₂²×C₄	—	356	2	no	—
178	C₂²×C₄	#13083563	1	2	yes	—
179	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
180	Q₁₆	—	89	2	no	—
181	Q₁₆	—	178	1	no	—
182	SD₁₆	—	178	4	no	—
183	D₈	—	89	2	no	—
184	D₈	—	178	1	no	—
185	M₁₆	—	356	2	no	—
186	M₁₆	—	178	4	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	356	2	no	—
189	C₂×C₈	#13083551	1	2	yes	—
190	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
191	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
192	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
193	C₂×C₈	#13083574	1	2	yes	—
194	C₄⋊C₄	—	356	2	no	—
195	C₄⋊C₄	—	178	2	no	—
196	C₂²⋊C₄	—	356	1	no	—
197	C₂²⋊C₄	—	356	2	no	—
198	C₄²	—	356	1	no	—
199	C₄²	—	356	2	no	—
200	C₄²	#13083551	1	2	yes	—
201	C₄²	D₇₁₂	1	1	yes	characteristic
202	C₄²	D₇₁₂	1	1	yes	characteristic
203	C₁₆	—	2	4	no	—
204	C₂³	—	356	1	no	—
205	C₂³	C₂×#13083563	1	1	yes	characteristic
206	Q₈	—	356	1	no	—
207	Q₈	—	178	2	no	—
208	D₄	—	356	4	no	—
209	D₄	—	356	1	no	—
210	D₄	—	178	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	356	1	no	—
213	C₂×C₄	—	356	4	no	—
214	C₂×C₄	—	356	2	no	—
215	C₂×C₄	—	712	4	no	—
216	C₂×C₄	#15667934	1	2	yes	—
217	C₂×C₄	#15667934	1	2	yes	—
218	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
219	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
220	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
221	C₂×C₄	#15668034	1	2	yes	—
222	C₈	—	2	2	no	—
223	C₈	—	356	4	no	—
224	C₈	C₄²×D₈₉	1	1	yes	characteristic
225	C₈	#15667969	1	1	yes	characteristic
226	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
227	C₂²	—	2	2	no	—
228	C₂²	—	356	2	no	—
229	C₂²	—	712	2	no	—
230	C₂²	C₂×#15667934	1	1	yes	characteristic
231	C₂²	C₄×#13083563	1	2	yes	—
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	356	2	no	—
235	C₄	—	712	2	no	—
236	C₄	C₄×#13083551	1	1	yes	characteristic
237	C₄	#19151595	1	1	yes	characteristic
238	C₄	C₄×D₇₁₂	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	—	712	2	no	—
241	C₂	C₄×#15667934	1	1	yes	characteristic
242	C₂	#26021981	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#15668034

C₂

yes

maximal, characteristic

C₂×#19151406

C₂

yes

maximal

C₄×#15667948

C₂

yes

maximal, characteristic, complemented

#26018348

C₂

yes

maximal, complemented

C₂×#346×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#15668034

C₂²

yes

characteristic

C₄×#13083574

—

C₄×Dic₃₅₆

C₄

yes

—

C₄×#13083563

—

C₄×D₇₁₂

C₄

yes

—

C₂×#15667948

C₂²

yes

—

#19151636

C₂²

yes

—

—

C₄

yes

complemented

#19151363

—

C₂²×C₁₆×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#346×C₈₉

—

C₂×#13083574

—

#15668034

—

#15668034

C₂×C₄

yes

—

C₂×Dic₃₅₆

C₂×C₄

yes

characteristic

C₂×#13083563

—

C₂×D₇₁₂

C₂×C₄

yes

characteristic

C₂×#13083558

—

C₄×Dic₁₇₈

—

C₄×D₃₅₆

—

C₄×C₂²⋊D₈₉

—

#15667971

—

#15667969

—

C₄²×D₈₉

—

#15667948

—

#15667948

C₂×C₄

yes

complemented

#15667946

C₂×C₄

yes

—

—

—

—

—

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

complemented

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

D₄

yes

—

#13083574

—

#13083574

—

C₂×Dic₁₇₈

—

C₂×D₃₅₆

—

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

Dic₃₅₆

—

Dic₃₅₆

C₄²

yes

—

#13083563

—

D₇₁₂

—

D₇₁₂

C₄²

yes

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

#13083553

—

C₂²⋊Dic₈₉

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

SD₁₆

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₄²×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

D₈

yes

characteristic

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

—

C₂³×C₈₉

C₂×SD₁₆

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

—

C₂×C₄×C₈₉

#102

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

100

C₈×C₈₉

—

101

C₈×C₈₉

C₂×C₄²

yes

characteristic

102

C₈×C₈₉

#117

yes

characteristic

103

C₈×C₈₉

C₄×D₄

yes

—

104

#10623494

—

105

C₂²×C₈₉

—

106

C₂²×C₈₉

C₂×#102

yes

characteristic

107

C₂²×C₈₉

C₄×SD₁₆

yes

—

108

C₂×D₈₉

—

109

C₂×D₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

—

112

C₄×C₈₉

C₄×C₂²⋊C₄

yes

characteristic

113

C₄×C₈₉

#416

yes

characteristic

114

C₄×C₈₉

C₄×D₈

yes

—

115

Dic₈₉

—

116

Dic₈₉

—

117

#12640

—

maximal, Sylow

118

C₂×C₈₉

—

119

C₂×C₈₉

C₄×#102

yes

characteristic

120

C₂×C₈₉

#2143

yes

—

121

D₈₉

—

122

C₄×#135

—

123

C₂×#359

—

124

C₂×#346

D₈₉

yes

characteristic, complemented

125

C₄×#108

—

126

#1382

—

127

C₈₉

#12640

yes

characteristic, complemented, Sylow

128

C₂×#135

—

129

C₄×#41

—

178

—

130

C₂²×C₁₆

C₂×D₈₉

yes

—

131

C₄×Q₁₆

—

132

C₄×SD₁₆

—

178

—

133

C₄×D₈

—

134

C₂×#108

—

135

#427

—

136

#416

—

178

—

137

C₄×M₁₆

—

178

—

138

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

139

#359

—

140

#346

—

141

#341

—

178

—

142

C₂×#41

—

178

—

143

#135

—

144

#135

—

178

—

145

C₂×Q₁₆

—

146

C₂×SD₁₆

—

178

—

147

C₂×D₈

—

148

C₂×M₁₆

—

178

—

149

C₂²×C₈

D₃₅₆

yes

characteristic

150

C₂²×C₈

C₂²×D₈₉

yes

characteristic

151

C₄×Q₈

—

178

—

152

C₄×D₄

—

356

—

153

C₄×D₄

—

178

—

154

#117

—

356

—

155

#117

—

178

—

156

C₂×C₄²

—

356

—

157

C₂×C₄²

D₃₅₆

yes

characteristic

158

C₂×C₁₆

—

159

C₂×C₁₆

—

160

C₂×C₁₆

C₄×D₈₉

yes

complemented

161

#108

—

162

#108

—

178

—

163

#107

—

164

#106

—

178

—

165

#103

—

178

—

166

#102

—

178

—

167

#97

—

356

—

168

C₄×C₈

—

356

—

169

C₄×C₈

C₄×D₈₉

yes

—

170

C₄×C₈

C₂²⋊D₈₉

yes

—

171

#41

—

356

—

172

#41

—

178

—

173

C₂×Q₈

—

178

—

174

C₂×D₄

—

356

—

175

C₂×D₄

—

178

—

176

C₂²×C₄

—

356

—

177

C₂²×C₄

—

356

—

178

C₂²×C₄

#13083563

yes

—

179

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

180

Q₁₆

—

181

Q₁₆

—

178

—

182

SD₁₆

—

178

—

183

D₈

—

184

D₈

—

178

—

185

M₁₆

—

356

—

186

M₁₆

—

178

—

187

C₂×C₈

—

188

C₂×C₈

—

356

—

189

C₂×C₈

#13083551

yes

—

190

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

191

C₂×C₈

C₂×C₄×D₈₉

yes

—

192

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

193

C₂×C₈

#13083574

yes

—

194

C₄⋊C₄

—

356

—

195

C₄⋊C₄

—

178

—

196

C₂²⋊C₄

—

356

—

197

C₂²⋊C₄

—

356

—

198

C₄²

—

356

—

199

C₄²

—

356

—

200

C₄²

#13083551

yes

—

201

C₄²

D₇₁₂

yes

characteristic

202

C₄²

D₇₁₂

yes

characteristic

203

C₁₆

—

204

C₂³

—

356

—

205

C₂³

C₂×#13083563

yes

characteristic

206

Q₈

—

356

—

207

Q₈

—

178

—

208

D₄

—

356

—

209

D₄

—

356

—

210

D₄

—

178

—

211

C₂×C₄

—

212

C₂×C₄

—

356

—

213

C₂×C₄

—

356

—

214

C₂×C₄

—

356

—

215

C₂×C₄

—

712

—

216

C₂×C₄

#15667934

yes

—

217

C₂×C₄

#15667934

yes

—

218

C₂×C₄

C₂×#13083551

yes

characteristic

219

C₂×C₄

C₄×D₃₅₆

yes

—

220

C₂×C₄

C₂×D₇₁₂

yes

characteristic

221

C₂×C₄

#15668034

yes

—

222

C₈

—

223

C₈

—

356

—

224

C₈

C₄²×D₈₉

yes

characteristic

225

C₈

#15667969

yes

characteristic

226

C₈

C₄×C₂²⋊D₈₉

yes

—

227

C₂²

—

228

C₂²

—

356

—

229

C₂²

—

712

—

230

C₂²

C₂×#15667934

yes

characteristic

231

C₂²

C₄×#13083563

yes

—

232

C₄

—

233

C₄

—

234

C₄

—

356

—

235

C₄

—

712

—

236

C₄

C₄×#13083551

yes

characteristic

237

C₄

#19151595

yes

characteristic

238

C₄

C₄×D₇₁₂

yes

—

239

C₂

—

240

C₂

—

712

—

241

C₂

C₄×#15667934

yes

characteristic

242

C₂

#26021981

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₇₁₂
commutator	C₈×C₈₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×#346×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#102
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#346	D₈₉
hypocenter	C₈₉	#12640
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂×C₄

C₂×D₇₁₂

commutator

C₈×C₈₉

C₂×C₄²

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×#346×C₈₉

C₂

C₂²×C₈₉

C₂²

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
3. C₄×#15667948	C₂	semidirect
4. #26018348	C₂	semidirect
5. C₂×#346×C₈₉	C₂	semidirect
15. #19151406	C₄	semidirect
34. #15667948	C₂×C₄	semidirect
46. C₂×C₁₆×C₈₉	C₂×C₄	semidirect
124. C₂×#346	D₈₉	semidirect
127. C₈₉	#12640	semidirect
160. C₂×C₁₆	C₄×D₈₉	semidirect

H ≅ G/N

type

3. C₄×#15667948

C₂

semidirect

4. #26018348

C₂

semidirect

5. C₂×#346×C₈₉

C₂

semidirect

15. #19151406

C₄

semidirect

34. #15667948

C₂×C₄

semidirect

46. C₂×C₁₆×C₈₉

C₂×C₄

semidirect

124. C₂×#346

D₈₉

semidirect

127. C₈₉

#12640

semidirect

160. C₂×C₁₆

C₄×D₈₉

semidirect

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

subgroup	index
C₄×#15668034	2
C₂×#19151406	2
C₄×#15667948	2
#26018348	2
C₂×#346×C₈₉	2
#12640	89

subgroup

index

C₂×#346×C₈₉

Subgroups — #36469658

Conjugacy classes of subgroups

Complements

Maximal subgroups