Group #36445101 — subgroups

Subgroups — #36445101

Order 22784.

530 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 195 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×#15668018	C₂	1	1	yes	maximal, characteristic
2	#26018635	C₂	1	2	yes	maximal
3	#26018535	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018089	C₂	1	2	yes	maximal, complemented
5	C₂×C₈²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15668018	C₄	1	2	yes	—
7	C₄×#13083574	C₂²	1	1	yes	characteristic
8	#19151651	C₂²	1	2	yes	—
9	#19151553	C₄	1	2	yes	—
10	#19151552	—	2	2	no	—
11	C₄×#13083558	C₂²	1	1	yes	characteristic
12	C₄×#13083557	—	2	1	no	—
13	C₄×C₈×D₈₉	—	2	1	no	—
14	#19151330	C₄	1	4	yes	—
15	#19151327	C₄	1	4	yes	—
16	#19151319	—	2	1	no	—
17	C₈×#10623494	—	2	1	no	—
18	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₈²×C₈₉	—	2	2	no	—
21	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
22	#15668018	—	2	4	no	—
23	#15668018	C₈	1	8	yes	complemented
24	C₂×#13083558	C₂×C₄	1	2	yes	—
25	C₂×#13083557	—	2	2	no	—
26	C₂×C₈×D₈₉	—	2	2	no	—
27	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
28	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
29	C₄×C₂²⋊D₈₉	—	2	2	no	—
30	#15667971	C₂×C₄	1	1	yes	characteristic
31	#15667969	—	2	1	no	—
32	C₄²×D₈₉	—	2	1	no	—
33	C₄⋊#10623494	C₂×C₄	1	4	yes	—
34	C₂²⋊#10623494	—	2	2	no	—
35	#15667923	—	2	1	no	—
36	#15667922	—	2	2	no	—
37	C₄×#10623494	—	2	2	no	—
38	C₄×#10623494	—	2	1	no	—
39	C₈×Dic₈₉	—	2	2	no	—
40	C₂²×C₈×C₈₉	—	2	2	no	—
41	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
43	C₄×C₈×C₈₉	—	2	2	no	—
44	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
45	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₈₉	D₄	1	2	yes	—
48	#13083574	—	2	2	no	—
49	#13083574	C₂×C₈	1	4	yes	—
50	C₂×Dic₁₇₈	C₄²	1	1	yes	characteristic
51	C₂×D₃₅₆	C₄²	1	1	yes	characteristic
52	C₂×C₂²⋊D₈₉	—	2	1	no	—
53	C₂×C₄×D₈₉	—	2	1	no	—
54	C₂×C₄×D₈₉	—	2	2	no	—
55	#13083558	—	2	2	no	—
56	#13083558	C₂×C₈	1	4	yes	—
57	#13083557	—	2	8	no	—
58	C₂×#10623494	—	2	2	no	—
59	C₂×#10623494	—	2	4	no	—
60	C₈×D₈₉	—	2	8	no	—
61	C₄⋊Dic₈₉	C₄²	1	2	yes	—
62	#13083553	—	2	2	no	—
63	C₂²⋊Dic₈₉	—	2	1	no	—
64	#13083551	—	2	2	no	—
65	C₄×Dic₈₉	—	2	1	no	—
66	C₄×Dic₈₉	—	2	2	no	—
67	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₈₉	#41	1	2	yes	—
69	C₂×C₈×C₈₉	—	2	8	no	—
70	C₂×C₈×C₈₉	—	2	4	no	—
71	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
72	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₉	C₂×C₈	1	4	yes	—
74	C₂×C₈×C₈₉	M₁₆	1	4	yes	—
75	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
76	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
78	C₂³×C₈₉	#117	1	1	yes	characteristic
79	C₂²×D₈₉	—	2	1	no	—
80	C₂×C₄×C₈₉	—	2	4	no	—
81	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
85	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
86	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
87	C₂²⋊D₈₉	—	2	4	no	—
88	C₂×Dic₈₉	—	2	1	no	—
89	C₂×Dic₈₉	—	2	2	no	—
90	D₃₅₆	—	2	1	no	—
91	D₃₅₆	C₄×C₈	1	2	yes	—
92	C₄×D₈₉	—	2	4	no	—
93	C₄×D₈₉	—	4	4	no	—
94	Dic₁₇₈	—	2	1	no	—
95	Dic₁₇₈	C₄×C₈	1	2	yes	—
96	C₈×C₈₉	—	2	8	no	—
97	C₈×C₈₉	C₂²⋊C₈	1	4	yes	—
98	C₈×C₈₉	C₂²⋊C₈	1	4	yes	—
99	#10623494	—	2	4	no	—
100	#10623494	—	4	4	no	—
101	C₂²×C₈₉	—	2	2	no	—
102	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₈₉	#431	1	2	yes	—
104	C₂×D₈₉	—	2	2	no	—
105	C₂×D₈₉	—	4	2	no	—
106	C₄×C₈₉	—	2	2	no	—
107	C₄×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
108	C₄×C₈₉	C₄×M₁₆	1	1	yes	characteristic
109	C₄×C₈₉	C₂×C₂²⋊C₈	1	2	yes	—
110	C₄×C₈₉	#443	1	4	yes	—
111	Dic₈₉	—	2	2	no	—
112	Dic₈₉	—	4	2	no	—
113	#8184	—	89	1	no	maximal, Sylow
114	C₂×C₈₉	—	2	2	no	—
115	C₂×C₈₉	C₄×C₂²⋊C₈	1	1	yes	characteristic
116	C₂×C₈₉	#1764	1	2	yes	—
117	D₈₉	—	4	2	no	—
118	C₄×#131	—	89	1	no	—
119	#1476	—	89	2	no	—
120	#1450	—	89	1	no	—
121	C₂×C₈²	D₈₉	1	1	yes	characteristic, complemented
122	#1278	—	89	2	no	—
123	C₈₉	#8184	1	1	yes	characteristic, complemented, Sylow
124	C₂×#131	—	89	2	no	—
125	C₄×#41	—	89	1	no	—
126	#431	—	89	2	no	—
127	#405	—	89	2	no	—
128	#405	—	178	2	no	—
129	C₄×M₁₆	—	89	1	no	—
130	C₄×M₁₆	—	178	1	no	—
131	C₂×C₄×C₈	—	178	1	no	—
132	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
133	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
134	Q₈⋊C₈	—	89	4	no	—
135	D₄⋊C₈	—	89	4	no	—
136	#322	—	178	1	no	—
137	C₈²	—	2	2	no	—
138	C₈²	—	178	1	no	—
139	C₂×#41	—	89	1	no	—
140	#131	—	89	8	no	—
141	#131	—	178	4	no	—
142	C₂×M₁₆	—	89	2	no	—
143	C₂×M₁₆	—	178	2	no	—
144	C₂²×C₈	—	2	2	no	—
145	C₂²×C₈	—	178	2	no	—
146	C₂²×C₈	C₄×D₈₉	1	2	yes	—
147	C₄×Q₈	—	89	2	no	—
148	C₄×D₄	—	89	2	no	—
149	C₄×D₄	—	178	2	no	—
150	#117	—	89	1	no	—
151	#117	—	178	1	no	—
152	C₂×C₄²	—	178	1	no	—
153	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
154	C₄⋊C₈	—	89	4	no	—
155	C₂²⋊C₈	—	178	2	no	—
156	#97	—	178	2	no	—
157	#97	—	178	1	no	—
158	C₄×C₈	—	2	2	no	—
159	C₄×C₈	—	178	2	no	—
160	C₄×C₈	—	178	2	no	—
161	C₄×C₈	—	178	1	no	—
162	C₄×C₈	C₄×D₈₉	1	4	yes	—
163	C₄×C₈	D₃₅₆	1	1	yes	characteristic
164	C₄×C₈	D₃₅₆	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
166	#41	—	89	4	no	—
167	#41	—	178	2	no	—
168	C₂×Q₈	—	89	1	no	—
169	C₂×D₄	—	89	1	no	—
170	C₂×D₄	—	178	1	no	—
171	C₂²×C₄	—	178	2	no	—
172	C₂²×C₄	—	178	1	no	—
173	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
174	C₂²×C₄	#13083574	1	2	yes	—
175	M₁₆	—	89	4	no	—
176	M₁₆	—	178	2	no	—
177	M₁₆	—	178	8	no	—
178	C₂×C₈	—	2	8	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	178	4	no	—
181	C₂×C₈	—	178	2	no	—
182	C₂×C₈	—	178	8	no	—
183	C₂×C₈	#13083551	1	2	yes	—
184	C₂×C₈	#13083551	1	2	yes	—
185	C₂×C₈	C₈×D₈₉	1	4	yes	—
186	C₂×C₈	#13083557	1	4	yes	—
187	C₄⋊C₄	—	89	2	no	—
188	C₄⋊C₄	—	178	2	no	—
189	C₂²⋊C₄	—	178	1	no	—
190	C₂²⋊C₄	—	178	2	no	—
191	C₄²	—	178	2	no	—
192	C₄²	—	178	1	no	—
193	C₄²	C₂×C₄×D₈₉	1	2	yes	—
194	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
195	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
196	C₂³	—	178	1	no	—
197	C₂³	#15667969	1	1	yes	characteristic
198	Q₈	—	89	2	no	—
199	Q₈	—	178	1	no	—
200	D₄	—	89	2	no	—
201	D₄	—	178	4	no	—
202	D₄	—	178	1	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	356	4	no	—
205	C₂×C₄	—	178	2	no	—
206	C₂×C₄	—	178	1	no	—
207	C₂×C₄	—	178	4	no	—
208	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
209	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
210	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
211	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
212	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
213	C₂×C₄	C₂×#13083557	1	2	yes	—
214	C₈	—	2	8	no	—
215	C₈	—	356	4	no	—
216	C₈	—	178	4	no	—
217	C₈	#15667924	1	4	yes	—
218	C₈	#15667924	1	4	yes	—
219	C₂²	—	2	2	no	—
220	C₂²	—	356	2	no	—
221	C₂²	—	178	2	no	—
222	C₂²	C₄×#13083551	1	1	yes	characteristic
223	C₂²	#19151649	1	2	yes	—
224	C₄	—	2	2	no	—
225	C₄	—	356	2	no	—
226	C₄	—	178	2	no	—
227	C₄	C₄×C₈×D₈₉	1	1	yes	characteristic
228	C₄	C₄×#13083557	1	1	yes	characteristic
229	C₄	C₂×#15667924	1	2	yes	—
230	C₄	#19151716	1	4	yes	—
231	C₂	—	2	2	no	—
232	C₂	—	356	2	no	—
233	C₂	C₄×#15667924	1	1	yes	characteristic
234	C₂	#26020089	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#15668018

C₂

yes

maximal, characteristic

#26018635

C₂

yes

maximal

#26018535

C₂

yes

maximal, characteristic, complemented

#26018089

C₂

yes

maximal, complemented

C₂×C₈²×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂×#15668018

C₄

yes

—

C₄×#13083574

C₂²

yes

characteristic

#19151651

C₂²

yes

—

#19151553

C₄

yes

—

#19151552

—

C₄×#13083558

C₂²

yes

characteristic

C₄×#13083557

—

C₄×C₈×D₈₉

—

#19151330

C₄

yes

—

#19151327

C₄

yes

—

#19151319

—

C₈×#10623494

—

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₈²×C₈₉

—

C₂×#13083574

C₂×C₄

yes

characteristic

#15668018

—

#15668018

C₈

yes

complemented

C₂×#13083558

C₂×C₄

yes

—

C₂×#13083557

—

C₂×C₈×D₈₉

—

C₄×Dic₁₇₈

C₂×C₄

yes

—

C₄×D₃₅₆

C₂×C₄

yes

—

C₄×C₂²⋊D₈₉

—

#15667971

C₂×C₄

yes

characteristic

#15667969

—

C₄²×D₈₉

—

C₄⋊#10623494

C₂×C₄

yes

—

—

—

—

—

—

C₈×Dic₈₉

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

—

#13083574

—

#13083574

C₂×C₈

yes

—

C₂×Dic₁₇₈

C₄²

yes

characteristic

C₂×D₃₅₆

C₄²

yes

characteristic

C₂×C₂²⋊D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

#13083558

—

#13083558

C₂×C₈

yes

—

#13083557

—

C₂×#10623494

—

C₂×#10623494

—

C₈×D₈₉

—

C₄⋊Dic₈₉

C₄²

yes

—

#13083553

—

C₂²⋊Dic₈₉

—

#13083551

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂×C₈

yes

—

C₂×C₈×C₈₉

M₁₆

yes

—

C₄²×C₈₉

C₂²×C₄

yes

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₂³×C₈₉

#117

yes

characteristic

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂²×C₈

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂²⋊D₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

D₃₅₆

C₄×C₈

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

Dic₁₇₈

—

Dic₁₇₈

C₄×C₈

yes

—

C₈×C₈₉

—

C₈×C₈₉

C₂²⋊C₈

yes

—

C₈×C₈₉

C₂²⋊C₈

yes

—

#10623494

—

100

#10623494

—

101

C₂²×C₈₉

—

102

C₂²×C₈₉

C₄×C₂²⋊C₄

yes

characteristic

103

C₂²×C₈₉

#431

yes

—

104

C₂×D₈₉

—

105

C₂×D₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

C₂×C₄×C₈

yes

characteristic

108

C₄×C₈₉

C₄×M₁₆

yes

characteristic

109

C₄×C₈₉

C₂×C₂²⋊C₈

yes

—

110

C₄×C₈₉

#443

yes

—

111

Dic₈₉

—

112

Dic₈₉

—

113

#8184

—

maximal, Sylow

114

C₂×C₈₉

—

115

C₂×C₈₉

C₄×C₂²⋊C₈

yes

characteristic

116

C₂×C₈₉

#1764

yes

—

117

D₈₉

—

118

C₄×#131

—

119

#1476

—

120

#1450

—

121

C₂×C₈²

D₈₉

yes

characteristic, complemented

122

#1278

—

123

C₈₉

#8184

yes

characteristic, complemented, Sylow

124

C₂×#131

—

125

C₄×#41

—

126

#431

—

127

#405

—

128

#405

—

178

—

129

C₄×M₁₆

—

130

C₄×M₁₆

—

178

—

131

C₂×C₄×C₈

—

178

—

132

C₂×C₄×C₈

C₂×D₈₉

yes

—

133

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

134

Q₈⋊C₈

—

135

D₄⋊C₈

—

136

#322

—

178

—

137

C₈²

—

138

C₈²

—

178

—

139

C₂×#41

—

140

#131

—

141

#131

—

178

—

142

C₂×M₁₆

—

143

C₂×M₁₆

—

178

—

144

C₂²×C₈

—

145

C₂²×C₈

—

178

—

146

C₂²×C₈

C₄×D₈₉

yes

—

147

C₄×Q₈

—

148

C₄×D₄

—

149

C₄×D₄

—

178

—

150

#117

—

151

#117

—

178

—

152

C₂×C₄²

—

178

—

153

C₂×C₄²

C₂²×D₈₉

yes

characteristic

154

C₄⋊C₈

—

155

C₂²⋊C₈

—

178

—

156

#97

—

178

—

157

#97

—

178

—

158

C₄×C₈

—

159

C₄×C₈

—

178

—

160

C₄×C₈

—

178

—

161

C₄×C₈

—

178

—

162

C₄×C₈

C₄×D₈₉

yes

—

163

C₄×C₈

D₃₅₆

yes

characteristic

164

C₄×C₈

D₃₅₆

yes

characteristic

165

C₄×C₈

C₂²⋊D₈₉

yes

—

166

#41

—

167

#41

—

178

—

168

C₂×Q₈

—

169

C₂×D₄

—

170

C₂×D₄

—

178

—

171

C₂²×C₄

—

178

—

172

C₂²×C₄

—

178

—

173

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

174

C₂²×C₄

#13083574

yes

—

175

M₁₆

—

176

M₁₆

—

178

—

177

M₁₆

—

178

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

178

—

181

C₂×C₈

—

178

—

182

C₂×C₈

—

178

—

183

C₂×C₈

#13083551

yes

—

184

C₂×C₈

#13083551

yes

—

185

C₂×C₈

C₈×D₈₉

yes

—

186

C₂×C₈

#13083557

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

178

—

189

C₂²⋊C₄

—

178

—

190

C₂²⋊C₄

—

178

—

191

C₄²

—

178

—

192

C₄²

—

178

—

193

C₄²

C₂×C₄×D₈₉

yes

—

194

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

195

C₄²

C₂×D₃₅₆

yes

characteristic

196

C₂³

—

178

—

197

C₂³

#15667969

yes

characteristic

198

Q₈

—

199

Q₈

—

178

—

200

D₄

—

201

D₄

—

178

—

202

D₄

—

178

—

203

C₂×C₄

—

204

C₂×C₄

—

356

—

205

C₂×C₄

—

178

—

206

C₂×C₄

—

178

—

207

C₂×C₄

—

178

—

208

C₂×C₄

C₄²×D₈₉

yes

characteristic

209

C₂×C₄

C₂×#13083551

yes

characteristic

210

C₂×C₄

C₄×C₂²⋊D₈₉

yes

—

211

C₂×C₄

C₄×D₃₅₆

yes

—

212

C₂×C₄

C₂×C₈×D₈₉

yes

—

213

C₂×C₄

C₂×#13083557

yes

—

214

C₈

—

215

C₈

—

356

—

216

C₈

—

178

—

217

C₈

#15667924

yes

—

218

C₈

#15667924

yes

—

219

C₂²

—

220

C₂²

—

356

—

221

C₂²

—

178

—

222

C₂²

C₄×#13083551

yes

characteristic

223

C₂²

#19151649

yes

—

224

C₄

—

225

C₄

—

356

—

226

C₄

—

178

—

227

C₄

C₄×C₈×D₈₉

yes

characteristic

228

C₄

C₄×#13083557

yes

characteristic

229

C₄

C₂×#15667924

yes

—

230

C₄

#19151716

yes

—

231

C₂

—

232

C₂

—

356

—

233

C₂

C₄×#15667924

yes

characteristic

234

C₂

#26020089

yes

—

	subgroup	G/H
center	C₄×C₈	D₃₅₆
commutator	C₄×C₈₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×C₈²×C₈₉	C₂
socle	C₂²×C₈₉	C₄×C₂²⋊C₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×C₈²	D₈₉
hypocenter	C₈₉	#8184
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

subgroup

G/H

center

C₄×C₈

D₃₅₆

commutator

C₄×C₈₉

C₂×C₄×C₈

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₂×C₈²×C₈₉

C₂

socle

C₂²×C₈₉

C₄×C₂²⋊C₄

prime radical

C₂×#13083574

C₂×C₄

cosocle

C₂×C₄²×C₈₉

C₂³

hypercenter

C₂×C₈²

D₈₉

hypocenter

C₈₉

#8184

LCS

G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

N	H ≅ G/N	type
3. #26018535	C₂	semidirect
4. #26018089	C₂	semidirect
5. C₂×C₈²×C₈₉	C₂	semidirect
23. #15668018	C₈	semidirect
121. C₂×C₈²	D₈₉	semidirect
123. C₈₉	#8184	semidirect

H ≅ G/N

type

3. #26018535

C₂

semidirect

4. #26018089

C₂

semidirect

5. C₂×C₈²×C₈₉

C₂

semidirect

23. #15668018

C₈

semidirect

121. C₂×C₈²

D₈₉

semidirect

123. C₈₉

#8184

semidirect

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

subgroup	index
C₄×#15668018	2
#26018635	2
#26018535	2
#26018089	2
C₂×C₈²×C₈₉	2
#8184	89

subgroup

index

C₂×C₈²×C₈₉

Subgroups — #36445101

Conjugacy classes of subgroups

Complements

Maximal subgroups