Group #36472586 — subgroups

Subgroups — #36472586

Order 22784.

522 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 155 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×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151377	C₂	1	4	yes	maximal, complemented
3	C₂×#19151374	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄⋊C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₈×D₈₉	C₂²	1	2	yes	—
6	C₂×C₄×D₃₅₆	C₄	1	1	yes	characteristic
7	C₂²×#13083549	C₂²	1	2	yes	—
8	C₈×D₃₅₆	—	2	2	no	—
9	C₈×D₃₅₆	—	2	2	no	—
10	C₂×C₄⋊#10623494	C₄	1	1	yes	characteristic
11	C₂×#15667924	C₄	1	2	yes	—
12	#19151377	—	2	8	no	—
13	#19151374	—	2	2	no	—
14	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₁₆×C₈₉	—	2	2	no	—
17	C₂²×D₃₅₆	C₈	1	1	yes	characteristic
18	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
19	C₂²×#10623494	C₂×C₄	1	2	yes	—
20	C₂×C₈×D₈₉	—	2	4	no	—
21	C₂×C₈×D₈₉	—	2	2	no	—
22	C₂×C₈×D₈₉	—	2	2	no	—
23	C₂×C₈×D₈₉	—	2	4	no	—
24	C₄×D₃₅₆	—	2	2	no	—
25	C₄×D₃₅₆	—	2	2	no	—
26	C₂×C₄⋊Dic₈₉	C₈	1	1	yes	characteristic
27	C₂×#13083551	C₈	1	2	yes	—
28	C₂×#13083549	—	2	2	no	—
29	C₂×#13083549	—	2	2	no	—
30	C₂×#13083549	D₄	1	4	yes	complemented
31	C₄⋊#10623494	—	2	2	no	—
32	#15667924	—	2	4	no	—
33	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₁₆×C₈₉	—	2	4	no	—
37	C₂×C₁₆×C₈₉	—	2	2	no	—
38	C₄×C₈×C₈₉	D₄	1	2	yes	—
39	C₄×C₈×C₈₉	D₄	1	2	yes	—
40	C₂³×D₈₉	C₂×C₈	1	2	yes	—
41	C₂×D₃₅₆	—	2	4	no	—
42	C₂×D₃₅₆	—	2	2	no	—
43	C₂²×Dic₈₉	C₂×C₈	1	2	yes	—
44	C₂×C₄×D₈₉	—	2	2	no	—
45	C₂×C₄×D₈₉	—	2	4	no	—
46	C₂×C₄×D₈₉	—	2	2	no	—
47	C₂×C₄×D₈₉	—	2	4	no	—
48	C₂×#10623494	—	2	2	no	—
49	C₂×#10623494	—	2	4	no	—
50	C₈×D₈₉	—	4	4	no	—
51	C₈×D₈₉	—	4	2	no	—
52	C₈×D₈₉	—	4	2	no	—
53	C₄⋊Dic₈₉	—	2	2	no	—
54	#13083551	—	2	4	no	—
55	#13083549	—	2	4	no	—
56	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
57	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
58	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₈₉	—	2	2	no	—
60	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₈₉	#41	1	2	yes	—
65	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₈₉	M₁₆	1	2	yes	—
67	C₁₆×C₈₉	—	4	2	no	—
68	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
69	C₂²×D₈₉	—	2	2	no	—
70	C₂²×D₈₉	—	2	4	no	—
71	C₂²×D₈₉	—	2	2	no	—
72	C₂²×D₈₉	—	2	4	no	—
73	C₂²×D₈₉	M₃₂	1	4	yes	—
74	C₂×C₄×C₈₉	—	2	2	no	—
75	C₂×C₄×C₈₉	—	2	2	no	—
76	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
77	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
78	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
80	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₈₉	#131	1	2	yes	—
82	C₂×Dic₈₉	—	2	2	no	—
83	C₂×Dic₈₉	—	2	4	no	—
84	D₃₅₆	—	2	8	no	—
85	C₄×D₈₉	—	4	2	no	—
86	C₄×D₈₉	—	4	2	no	—
87	C₄×D₈₉	—	4	4	no	—
88	C₈×C₈₉	—	2	2	no	—
89	C₈×C₈₉	#121	1	2	yes	—
90	C₈×C₈₉	#124	1	1	yes	characteristic
91	C₈×C₈₉	#127	1	1	yes	characteristic
92	#10623494	—	4	2	no	—
93	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
94	C₂²×C₈₉	C₈×D₄	1	2	yes	—
95	C₂²×C₈₉	C₂×M₃₂	1	2	yes	—
96	C₂²×C₈₉	#504	1	2	yes	—
97	C₂×D₈₉	—	2	4	no	—
98	C₂×D₈₉	—	2	8	no	—
99	C₂×D₈₉	—	4	2	no	—
100	C₂×D₈₉	—	4	4	no	—
101	C₂×D₈₉	—	4	2	no	—
102	C₄×C₈₉	—	2	2	no	—
103	C₄×C₈₉	—	2	2	no	—
104	C₄×C₈₉	#390	1	1	yes	characteristic
105	C₄×C₈₉	#408	1	1	yes	characteristic
106	C₄×C₈₉	#436	1	2	yes	—
107	Dic₈₉	—	4	2	no	—
108	#13190	—	89	1	no	maximal, Sylow
109	C₂×C₈₉	#1954	1	1	yes	characteristic
110	C₂×C₈₉	#2112	1	1	yes	characteristic
111	C₂×C₈₉	#2113	1	1	yes	characteristic
112	C₂×C₈₉	#2168	1	4	yes	—
113	D₈₉	—	4	4	no	—
114	C₂×C₈×D₄	—	89	1	no	—
115	C₂×C₄⋊C₁₆	D₈₉	1	1	yes	characteristic, complemented
116	C₂×C₂²⋊C₁₆	—	89	4	no	—
117	C₂×#346	—	89	1	no	—
118	C₈₉	#13190	1	1	yes	characteristic, complemented, Sylow
119	C₂³×C₈	—	89	2	no	—
120	C₂×C₄×D₄	—	89	1	no	—
121	C₂²×C₁₆	—	89	2	no	—
122	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
123	C₈×D₄	—	178	2	no	—
124	C₈×D₄	—	178	2	no	—
125	C₂×C₄⋊C₈	—	89	1	no	—
126	C₂×C₂²⋊C₈	—	89	2	no	—
127	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
128	C₄⋊C₁₆	—	2	2	no	—
129	C₂²⋊C₁₆	—	178	8	no	—
130	#346	—	178	2	no	—
131	C₂²×D₄	—	89	1	no	—
132	C₂³×C₄	—	89	2	no	—
133	C₂²×C₈	—	89	2	no	—
134	C₂²×C₈	—	178	4	no	—
135	C₂²×C₈	—	178	2	no	—
136	C₂²×C₈	—	178	2	no	—
137	C₂²×C₈	—	178	4	no	—
138	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
139	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
140	C₄×D₄	—	178	2	no	—
141	C₄×D₄	—	178	2	no	—
142	C₂×C₄⋊C₄	—	89	1	no	—
143	C₂×C₂²⋊C₄	—	89	2	no	—
144	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
145	C₂×C₁₆	—	2	4	no	—
146	C₂×C₁₆	—	2	2	no	—
147	C₂×C₁₆	—	89	4	no	—
148	C₂×C₁₆	—	178	2	no	—
149	C₂×C₁₆	—	178	2	no	—
150	C₄⋊C₈	—	178	2	no	—
151	C₂²⋊C₈	—	178	4	no	—
152	C₄×C₈	D₃₅₆	1	2	yes	—
153	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
154	C₂⁴	—	89	2	no	—
155	C₂×D₄	—	178	4	no	—
156	C₂×D₄	—	178	2	no	—
157	C₂²×C₄	—	89	2	no	—
158	C₂²×C₄	—	178	4	no	—
159	C₂²×C₄	—	178	2	no	—
160	C₂²×C₄	—	178	4	no	—
161	C₂²×C₄	—	178	2	no	—
162	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
163	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	356	4	no	—
167	C₂×C₈	—	356	2	no	—
168	C₂×C₈	—	356	2	no	—
169	C₂×C₈	—	178	4	no	—
170	C₂×C₈	—	178	2	no	—
171	C₂×C₈	#13083551	1	2	yes	—
172	C₂×C₈	D₄×D₈₉	1	2	yes	—
173	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
174	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
175	C₂×C₈	#13083575	1	2	yes	—
176	C₄⋊C₄	—	178	2	no	—
177	C₂²⋊C₄	—	178	4	no	—
178	C₄²	#13083551	1	2	yes	—
179	C₄²	#13083557	1	2	yes	—
180	C₁₆	—	4	2	no	—
181	C₁₆	—	178	4	no	—
182	C₂³	—	89	4	no	—
183	C₂³	—	178	4	no	—
184	C₂³	—	178	2	no	—
185	C₂³	—	178	4	no	—
186	C₂³	—	178	2	no	—
187	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
188	D₄	—	178	8	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	356	4	no	—
192	C₂×C₄	—	356	2	no	—
193	C₂×C₄	—	356	2	no	—
194	C₂×C₄	—	178	4	no	—
195	C₂×C₄	—	178	2	no	—
196	C₂×C₄	#15667924	1	2	yes	—
197	C₂×C₄	#15667924	1	2	yes	—
198	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
199	C₂×C₄	#15667974	1	2	yes	—
200	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
201	C₂×C₄	#15668020	1	2	yes	—
202	C₈	—	2	2	no	—
203	C₈	—	356	2	no	—
204	C₈	#15667987	1	2	yes	—
205	C₈	#15668001	1	1	yes	characteristic
206	C₈	#15668008	1	1	yes	characteristic
207	C₂²	—	356	2	no	—
208	C₂²	—	356	4	no	—
209	C₂²	—	356	2	no	—
210	C₂²	—	178	8	no	—
211	C₂²	—	178	4	no	—
212	C₂²	C₂×#15667924	1	1	yes	characteristic
213	C₂²	#19151663	1	2	yes	—
214	C₂²	M₃₂×D₈₉	1	2	yes	—
215	C₂²	#19152014	1	2	yes	—
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	356	2	no	—
219	C₄	#19151499	1	1	yes	characteristic
220	C₄	#19151566	1	1	yes	characteristic
221	C₄	#19151675	1	2	yes	—
222	C₂	—	356	4	no	—
223	C₂	#26021045	1	1	yes	characteristic
224	C₂	#26021862	1	1	yes	characteristic
225	C₂	#26021865	1	1	yes	characteristic
226	C₂	#26022076	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×D₃₅₆

C₂

yes

maximal, characteristic

C₂×#19151377

C₂

yes

maximal, complemented

C₂×#19151374

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊C₁₆×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₉

C₂²

yes

—

C₂×C₄×D₃₅₆

C₄

yes

characteristic

C₂²×#13083549

C₂²

yes

—

C₈×D₃₅₆

—

C₈×D₃₅₆

—

C₂×C₄⋊#10623494

C₄

yes

characteristic

C₂×#15667924

C₄

yes

—

#19151377

—

#19151374

—

C₂²×C₁₆×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₉

—

C₂²×D₃₅₆

C₈

yes

characteristic

C₂²×C₄×D₈₉

C₂×C₄

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₄×D₃₅₆

—

C₄×D₃₅₆

—

C₂×C₄⋊Dic₈₉

C₈

yes

characteristic

C₂×#13083551

C₈

yes

—

C₂×#13083549

—

C₂×#13083549

—

C₂×#13083549

D₄

yes

complemented

C₄⋊#10623494

—

#15667924

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

—

C₄×C₈×C₈₉

D₄

yes

—

C₂³×D₈₉

C₂×C₈

yes

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂²×Dic₈₉

C₂×C₈

yes

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

C₄⋊Dic₈₉

—

#13083551

—

#13083549

—

C₂²×C₄×C₈₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₈₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₄²×C₈₉

C₂²⋊C₄

yes

—

C₄²×C₈₉

M₁₆

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂²×C₈

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

M₃₂

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

—

C₂×C₄×C₈₉

C₂²⋊C₈

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₉

#131

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

D₃₅₆

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

C₈×C₈₉

#121

yes

—

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

C₂×C₂²⋊C₈

yes

characteristic

C₂²×C₈₉

C₈×D₄

yes

—

C₂²×C₈₉

C₂×M₃₂

yes

—

C₂²×C₈₉

#504

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

100

C₂×D₈₉

—

101

C₂×D₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

#390

yes

characteristic

105

C₄×C₈₉

#408

yes

characteristic

106

C₄×C₈₉

#436

yes

—

107

Dic₈₉

—

108

#13190

—

maximal, Sylow

109

C₂×C₈₉

#1954

yes

characteristic

110

C₂×C₈₉

#2112

yes

characteristic

111

C₂×C₈₉

#2113

yes

characteristic

112

C₂×C₈₉

#2168

yes

—

113

D₈₉

—

114

C₂×C₈×D₄

—

115

C₂×C₄⋊C₁₆

D₈₉

yes

characteristic, complemented

116

C₂×C₂²⋊C₁₆

—

117

C₂×#346

—

118

C₈₉

#13190

yes

characteristic, complemented, Sylow

119

C₂³×C₈

—

120

C₂×C₄×D₄

—

121

C₂²×C₁₆

—

122

C₂²×C₁₆

C₂×D₈₉

yes

—

123

C₈×D₄

—

178

—

124

C₈×D₄

—

178

—

125

C₂×C₄⋊C₈

—

126

C₂×C₂²⋊C₈

—

127

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

128

C₄⋊C₁₆

—

129

C₂²⋊C₁₆

—

178

—

130

#346

—

178

—

131

C₂²×D₄

—

132

C₂³×C₄

—

133

C₂²×C₈

—

134

C₂²×C₈

—

178

—

135

C₂²×C₈

—

178

—

136

C₂²×C₈

—

178

—

137

C₂²×C₈

—

178

—

138

C₂²×C₈

C₄×D₈₉

yes

characteristic

139

C₂²×C₈

C₂²×D₈₉

yes

characteristic

140

C₄×D₄

—

178

—

141

C₄×D₄

—

178

—

142

C₂×C₄⋊C₄

—

143

C₂×C₂²⋊C₄

—

144

C₂×C₄²

C₄×D₈₉

yes

characteristic

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

—

148

C₂×C₁₆

—

178

—

149

C₂×C₁₆

—

178

—

150

C₄⋊C₈

—

178

—

151

C₂²⋊C₈

—

178

—

152

C₄×C₈

D₃₅₆

yes

—

153

C₄×C₈

C₂²⋊D₈₉

yes

—

154

C₂⁴

—

155

C₂×D₄

—

178

—

156

C₂×D₄

—

178

—

157

C₂²×C₄

—

158

C₂²×C₄

—

178

—

159

C₂²×C₄

—

178

—

160

C₂²×C₄

—

178

—

161

C₂²×C₄

—

178

—

162

C₂²×C₄

C₈×D₈₉

yes

characteristic

163

C₂²×C₄

C₈×D₈₉

yes

characteristic

164

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

165

C₂×C₈

—

166

C₂×C₈

—

356

—

167

C₂×C₈

—

356

—

168

C₂×C₈

—

356

—

169

C₂×C₈

—

178

—

170

C₂×C₈

—

178

—

171

C₂×C₈

#13083551

yes

—

172

C₂×C₈

D₄×D₈₉

yes

—

173

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

174

C₂×C₈

C₂×D₃₅₆

yes

characteristic

175

C₂×C₈

#13083575

yes

—

176

C₄⋊C₄

—

178

—

177

C₂²⋊C₄

—

178

—

178

C₄²

#13083551

yes

—

179

C₄²

#13083557

yes

—

180

C₁₆

—

181

C₁₆

—

178

—

182

C₂³

—

183

C₂³

—

178

—

184

C₂³

—

178

—

185

C₂³

—

178

—

186

C₂³

—

178

—

187

C₂³

C₂×C₈×D₈₉

yes

characteristic

188

D₄

—

178

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

356

—

192

C₂×C₄

—

356

—

193

C₂×C₄

—

356

—

194

C₂×C₄

—

178

—

195

C₂×C₄

—

178

—

196

C₂×C₄

#15667924

yes

—

197

C₂×C₄

#15667924

yes

—

198

C₂×C₄

C₂×#13083551

yes

characteristic

199

C₂×C₄

#15667974

yes

—

200

C₂×C₄

C₂×#13083557

yes

characteristic

201

C₂×C₄

#15668020

yes

—

202

C₈

—

203

C₈

—

356

—

204

C₈

#15667987

yes

—

205

C₈

#15668001

yes

characteristic

206

C₈

#15668008

yes

characteristic

207

C₂²

—

356

—

208

C₂²

—

356

—

209

C₂²

—

356

—

210

C₂²

—

178

—

211

C₂²

—

178

—

212

C₂²

C₂×#15667924

yes

characteristic

213

C₂²

#19151663

yes

—

214

C₂²

M₃₂×D₈₉

yes

—

215

C₂²

#19152014

yes

—

216

C₄

—

217

C₄

—

218

C₄

—

356

—

219

C₄

#19151499

yes

characteristic

220

C₄

#19151566

yes

characteristic

221

C₄

#19151675

yes

—

222

C₂

—

356

—

223

C₂

#26021045

yes

characteristic

224

C₂

#26021862

yes

characteristic

225

C₂

#26021865

yes

characteristic

226

C₂

#26022076

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂²×C₈
Fitting	C₂×C₄⋊C₁₆×C₈₉	C₂
prime radical	C₂²×D₃₅₆	C₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₈₉
hypocenter	C₈₉	#13190
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₈₉

commutator, socle

C₂³×C₈₉

C₂²×C₈

Fitting

C₂×C₄⋊C₁₆×C₈₉

C₂

prime radical

C₂²×D₃₅₆

C₈

cosocle

C₂²×C₈×C₈₉

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
2. C₂×#19151377	C₂	semidirect
3. C₂×#19151374	C₂	semidirect
4. C₂×C₄⋊C₁₆×C₈₉	C₂	semidirect
30. C₂×#13083549	D₄	semidirect
115. C₂×C₄⋊C₁₆	D₈₉	semidirect
118. C₈₉	#13190	semidirect

H ≅ G/N

type

2. C₂×#19151377

C₂

semidirect

3. C₂×#19151374

C₂

semidirect

4. C₂×C₄⋊C₁₆×C₈₉

C₂

semidirect

30. C₂×#13083549

D₄

semidirect

115. C₂×C₄⋊C₁₆

D₈₉

semidirect

118. C₈₉

#13190

semidirect

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

subgroup	index
C₂×C₈×D₃₅₆	2
C₂×#19151377	2
C₂×#19151374	2
C₂×C₄⋊C₁₆×C₈₉	2
#13190	89

subgroup

index

C₂×C₈×D₃₅₆

C₂×#19151377

C₂×#19151374

C₂×C₄⋊C₁₆×C₈₉

#13190

Subgroups — #36472586

Conjugacy classes of subgroups

Complements

Maximal subgroups