Group #36471878 — subgroups

Subgroups — #36471878

Order 22784.

490 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 131 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	#26033355	C₂	1	1	yes	maximal, characteristic, complemented
2	#26021968	C₂	1	2	yes	maximal, complemented
3	#26020298	C₂	1	1	yes	maximal, characteristic, complemented
4	#26018353	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3058	C₂	1	1	yes	maximal, characteristic
6	#19152015	—	2	4	no	—
7	C₂×#15667952	—	2	2	no	—
8	C₂×#15667952	C₂²	1	2	yes	—
9	#19151636	C₂²	1	2	yes	—
10	#19151572	—	2	1	no	—
11	#19151399	—	2	4	no	—
12	#19151355	—	2	1	no	—
13	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
15	#535×C₈₉	—	2	1	no	—
16	#469×C₈₉	C₄	1	4	yes	complemented
17	#466×C₈₉	—	2	2	no	—
18	#427×C₈₉	C₂²	1	1	yes	characteristic
19	#418×C₈₉	—	2	1	no	—
20	#15667971	—	2	2	no	—
21	#15667952	—	2	4	no	—
22	#15667952	—	2	2	no	—
23	#15667952	—	2	2	no	—
24	C₂×#13083549	—	2	4	no	—
25	C₂×#13083549	D₄	1	4	yes	complemented
26	#15667946	—	2	2	no	—
27	#15667944	—	2	2	no	—
28	#15667927	—	4	2	no	—
29	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
30	C₂²×D₄×C₈₉	—	2	1	no	—
31	C₂×D₈×C₈₉	—	2	2	no	—
32	C₂×D₈×C₈₉	—	2	1	no	—
33	C₂×D₈×C₈₉	—	2	2	no	—
34	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
35	#131×C₈₉	—	2	2	no	—
36	#131×C₈₉	—	2	2	no	—
37	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₈₉	D₄	1	2	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
41	#127×C₈₉	—	4	1	no	—
42	#124×C₈₉	—	4	1	no	—
43	#121×C₈₉	—	2	4	no	—
44	#120×C₈₉	—	4	2	no	—
45	#117×C₈₉	—	2	1	no	—
46	#107×C₈₉	—	2	1	no	—
47	#106×C₈₉	C₂×C₄	1	2	yes	—
48	#102×C₈₉	—	2	4	no	—
49	C₄⋊Dic₈₉	—	4	2	no	—
50	C₂²⋊Dic₈₉	—	4	2	no	—
51	C₄×Dic₈₉	—	4	2	no	—
52	#13083549	—	2	4	no	—
53	C₂⁴×C₈₉	—	4	1	no	—
54	#41×C₈₉	—	2	2	no	—
55	#41×C₈₉	—	2	2	no	—
56	C₂×Q₈×C₈₉	SD₁₆	1	1	yes	characteristic
57	C₂×D₄×C₈₉	—	2	2	no	—
58	C₂×D₄×C₈₉	—	4	4	no	—
59	C₂×D₄×C₈₉	—	4	2	no	—
60	C₂×D₄×C₈₉	—	4	1	no	—
61	C₂×D₄×C₈₉	—	4	2	no	—
62	C₂×D₄×C₈₉	D₈	1	2	yes	—
63	C₂×D₄×C₈₉	SD₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
66	D₈×C₈₉	—	2	4	no	—
67	D₈×C₈₉	—	4	1	no	—
68	D₈×C₈₉	—	4	1	no	—
69	M₁₆×C₈₉	—	2	2	no	—
70	M₁₆×C₈₉	—	2	4	no	—
71	C₂×C₈×C₈₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	#41	1	2	yes	—
78	C₄⋊C₄×C₈₉	—	2	2	no	—
79	C₂²⋊C₄×C₈₉	—	4	1	no	—
80	C₂²⋊C₄×C₈₉	—	4	4	no	—
81	C₄²×C₈₉	—	4	1	no	—
82	C₂³×C₈₉	—	4	2	no	—
83	C₂³×C₈₉	—	8	2	no	—
84	C₂³×C₈₉	—	16	2	no	—
85	C₂³×C₈₉	#102	1	2	yes	—
86	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
87	Q₈×C₈₉	—	2	2	no	—
88	D₄×C₈₉	—	2	4	no	—
89	D₄×C₈₉	—	2	2	no	—
90	D₄×C₈₉	—	4	2	no	—
91	D₄×C₈₉	—	4	2	no	—
92	D₄×C₈₉	—	8	2	no	—
93	D₄×C₈₉	—	16	4	no	—
94	C₂×C₄×C₈₉	—	2	2	no	—
95	C₂×C₄×C₈₉	—	2	2	no	—
96	C₂×C₄×C₈₉	—	4	2	no	—
97	C₂×C₄×C₈₉	#102	1	2	yes	—
98	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₈₉	#121	1	2	yes	—
100	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₈₉	#135	1	2	yes	—
102	C₂×Dic₈₉	—	8	2	no	—
103	C₈×C₈₉	—	2	2	no	—
104	C₈×C₈₉	C₄×D₄	1	2	yes	—
105	C₈×C₈₉	#120	1	1	yes	characteristic
106	C₈×C₈₉	#123	1	1	yes	characteristic
107	C₂²×C₈₉	—	2	2	no	—
108	C₂²×C₈₉	—	4	1	no	—
109	C₂²×C₈₉	—	4	2	no	—
110	C₂²×C₈₉	—	8	4	no	—
111	C₂²×C₈₉	—	8	2	no	—
112	C₂²×C₈₉	—	16	4	no	—
113	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
114	C₂²×C₈₉	#466	1	2	yes	—
115	C₄×C₈₉	—	2	2	no	—
116	C₄×C₈₉	—	8	2	no	—
117	C₄×C₈₉	#386	1	1	yes	characteristic
118	C₄×C₈₉	#416	1	1	yes	characteristic
119	C₄×C₈₉	#465	1	2	yes	—
120	Dic₈₉	—	16	2	no	—
121	#13074	—	89	1	no	maximal, Sylow
122	C₂×C₈₉	—	2	2	no	—
123	C₂×C₈₉	—	2	1	no	—
124	C₂×C₈₉	—	4	2	no	—
125	C₂×C₈₉	—	16	2	no	—
126	C₂×C₈₉	#1893	1	1	yes	characteristic
127	#3407	—	89	1	no	—
128	#3058	D₈₉	1	1	yes	characteristic
129	#2140	—	89	2	no	—
130	#1812	—	89	1	no	—
131	#1384	—	89	2	no	—
132	C₈₉	#13074	1	1	yes	characteristic, complemented, Sylow
133	C₂²×D₈	C₂×D₈₉	1	1	yes	characteristic
134	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
135	#535	—	2	1	no	—
136	#504	—	178	4	no	—
137	C₂×M₃₂	—	89	2	no	—
138	C₂×M₃₂	—	178	2	no	—
139	#469	Dic₈₉	1	4	yes	complemented
140	#466	—	2	2	no	—
141	#427	—	89	2	no	—
142	#427	C₂×D₈₉	1	1	yes	characteristic
143	#418	—	2	1	no	—
144	#410	—	178	1	no	—
145	#357	—	178	4	no	—
146	H(3,ℤ/4)	—	178	1	no	—
147	C₂×#41	C₂²⋊D₈₉	1	1	yes	characteristic
148	C₂²×D₄	—	2	1	no	—
149	C₂×D₈	—	2	2	no	—
150	C₂×D₈	—	2	1	no	—
151	C₂×D₈	—	2	2	no	—
152	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
156	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
158	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
159	#127	—	4	1	no	—
160	#124	—	4	1	no	—
161	#121	—	2	4	no	—
162	#120	—	4	2	no	—
163	#117	—	2	1	no	—
164	#117	—	178	2	no	—
165	M₃₂	—	178	4	no	—
166	M₃₂	—	178	2	no	—
167	M₃₂	—	178	2	no	—
168	C₂×C₁₆	—	89	4	no	—
169	C₂×C₁₆	—	178	4	no	—
170	#107	—	2	1	no	—
171	#107	—	178	2	no	—
172	#106	—	178	2	no	—
173	#106	C₂×Dic₈₉	1	2	yes	—
174	#102	—	2	4	no	—
175	#99	—	356	2	no	—
176	C₂⁴	—	4	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#13083562	1	1	yes	characteristic
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	—	4	4	no	—
182	C₂×D₄	—	4	2	no	—
183	C₂×D₄	—	4	1	no	—
184	C₂×D₄	—	4	2	no	—
185	C₂×D₄	#13083559	1	2	yes	—
186	C₂×D₄	#13083562	1	1	yes	characteristic
187	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
188	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	C₂²⋊Dic₈₉	1	2	yes	—
197	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
198	C₂×C₈	D₄×D₈₉	1	2	yes	—
199	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
200	C₂×C₈	#13083573	1	2	yes	—
201	C₄⋊C₄	—	2	2	no	—
202	C₄⋊C₄	—	356	2	no	—
203	C₂²⋊C₄	—	4	1	no	—
204	C₂²⋊C₄	—	4	4	no	—
205	C₂²⋊C₄	—	356	2	no	—
206	C₄²	—	4	1	no	—
207	C₄²	—	356	2	no	—
208	C₁₆	—	178	4	no	—
209	C₂³	—	4	2	no	—
210	C₂³	—	8	2	no	—
211	C₂³	—	16	2	no	—
212	C₂³	#15667933	1	2	yes	—
213	C₂³	C₂×#13083559	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	4	2	no	—
218	D₄	—	4	2	no	—
219	D₄	—	8	2	no	—
220	D₄	—	16	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	2	no	—
224	C₂×C₄	—	712	2	no	—
225	C₂×C₄	#15667933	1	2	yes	—
226	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
227	C₂×C₄	#15667984	1	2	yes	—
228	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
229	C₂×C₄	#15668032	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	D₄×Dic₈₉	1	2	yes	—
232	C₈	#15667980	1	1	yes	characteristic
233	C₈	#15667993	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	8	4	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	16	4	no	—
240	C₂²	C₂×#15667933	1	1	yes	characteristic
241	C₂²	#19151832	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	8	2	no	—
244	C₄	—	1424	2	no	—
245	C₄	#19151478	1	1	yes	characteristic
246	C₄	#19151594	1	1	yes	characteristic
247	C₄	#19151825	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	16	2	no	—
252	C₂	#26020681	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26033355

C₂

yes

maximal, characteristic, complemented

#26021968

C₂

yes

maximal, complemented

#26020298

C₂

yes

maximal, characteristic, complemented

#26018353

C₂

yes

maximal, complemented

C₈₉×#3058

C₂

yes

maximal, characteristic

#19152015

—

C₂×#15667952

—

C₂×#15667952

C₂²

yes

—

#19151636

C₂²

yes

—

#19151572

—

#19151399

—

#19151355

—

C₂²×D₈×C₈₉

C₂²

yes

characteristic

C₂×#131×C₈₉

C₂²

yes

characteristic

#535×C₈₉

—

#469×C₈₉

C₄

yes

complemented

#466×C₈₉

—

#427×C₈₉

C₂²

yes

characteristic

#418×C₈₉

—

—

—

—

—

—

D₄

yes

—

—

—

C₂×#41×C₈₉

D₄

yes

characteristic

C₂²×D₄×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

C₂×C₄

yes

—

#131×C₈₉

—

#131×C₈₉

—

C₂×M₁₆×C₈₉

C₂×C₄

yes

—

C₂×M₁₆×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

D₄

yes

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

#127×C₈₉

—

#124×C₈₉

—

#121×C₈₉

—

#120×C₈₉

—

#117×C₈₉

—

#107×C₈₉

—

#106×C₈₉

C₂×C₄

yes

—

#102×C₈₉

—

C₄⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

#13083549

—

C₂⁴×C₈₉

—

#41×C₈₉

—

#41×C₈₉

—

C₂×Q₈×C₈₉

SD₁₆

yes

characteristic

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

D₈

yes

—

C₂×D₄×C₈₉

SD₁₆

yes

characteristic

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

D₈×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#102

yes

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

#121

yes

—

100

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₈₉

#135

yes

—

102

C₂×Dic₈₉

—

103

C₈×C₈₉

—

104

C₈×C₈₉

C₄×D₄

yes

—

105

C₈×C₈₉

#120

yes

characteristic

106

C₈×C₈₉

#123

yes

characteristic

107

C₂²×C₈₉

—

108

C₂²×C₈₉

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

—

111

C₂²×C₈₉

—

112

C₂²×C₈₉

—

113

C₂²×C₈₉

C₂×#102

yes

characteristic

114

C₂²×C₈₉

#466

yes

—

115

C₄×C₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

#386

yes

characteristic

118

C₄×C₈₉

#416

yes

characteristic

119

C₄×C₈₉

#465

yes

—

120

Dic₈₉

—

121

#13074

—

maximal, Sylow

122

C₂×C₈₉

—

123

C₂×C₈₉

—

124

C₂×C₈₉

—

125

C₂×C₈₉

—

126

C₂×C₈₉

#1893

yes

characteristic

127

#3407

—

128

#3058

D₈₉

yes

characteristic

129

#2140

—

130

#1812

—

131

#1384

—

132

C₈₉

#13074

yes

characteristic, complemented, Sylow

133

C₂²×D₈

C₂×D₈₉

yes

characteristic

134

C₂×#131

C₂×D₈₉

yes

characteristic

135

#535

—

136

#504

—

178

—

137

C₂×M₃₂

—

138

C₂×M₃₂

—

178

—

139

#469

Dic₈₉

yes

complemented

140

#466

—

141

#427

—

142

#427

C₂×D₈₉

yes

characteristic

143

#418

—

144

#410

—

178

—

145

#357

—

178

—

146

H(3,ℤ/4)

—

178

—

147

C₂×#41

C₂²⋊D₈₉

yes

characteristic

148

C₂²×D₄

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂×D₈

C₂×Dic₈₉

yes

—

153

#131

—

154

#131

—

155

C₂×M₁₆

C₂×Dic₈₉

yes

—

156

C₂×M₁₆

C₂²⋊D₈₉

yes

characteristic

157

C₂²×C₈

C₂²⋊D₈₉

yes

—

158

C₂²×C₈

C₂²×D₈₉

yes

characteristic

159

#127

—

160

#124

—

161

#121

—

162

#120

—

163

#117

—

164

#117

—

178

—

165

M₃₂

—

178

—

166

M₃₂

—

178

—

167

M₃₂

—

178

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

178

—

170

#107

—

171

#107

—

178

—

172

#106

—

178

—

173

#106

C₂×Dic₈₉

yes

—

174

#102

—

175

#99

—

356

—

176

C₂⁴

—

177

#41

—

178

#41

—

179

C₂×Q₈

#13083562

yes

characteristic

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂×D₄

—

183

C₂×D₄

—

184

C₂×D₄

—

185

C₂×D₄

#13083559

yes

—

186

C₂×D₄

#13083562

yes

characteristic

187

C₂²×C₄

C₂²⋊Dic₈₉

yes

—

188

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

C₂²⋊Dic₈₉

yes

—

197

C₂×C₈

C₂²×Dic₈₉

yes

characteristic

198

C₂×C₈

D₄×D₈₉

yes

—

199

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

200

C₂×C₈

#13083573

yes

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

356

—

203

C₂²⋊C₄

—

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

356

—

206

C₄²

—

207

C₄²

—

356

—

208

C₁₆

—

178

—

209

C₂³

—

210

C₂³

—

211

C₂³

—

212

C₂³

#15667933

yes

—

213

C₂³

C₂×#13083559

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

218

D₄

—

219

D₄

—

220

D₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

712

—

225

C₂×C₄

#15667933

yes

—

226

C₂×C₄

C₂×C₂²⋊Dic₈₉

yes

characteristic

227

C₂×C₄

#15667984

yes

—

228

C₂×C₄

C₂×#13083562

yes

characteristic

229

C₂×C₄

#15668032

yes

—

230

C₈

—

231

C₈

D₄×Dic₈₉

yes

—

232

C₈

#15667980

yes

characteristic

233

C₈

#15667993

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

240

C₂²

C₂×#15667933

yes

characteristic

241

C₂²

#19151832

yes

—

242

C₄

—

243

C₄

—

244

C₄

—

1424

—

245

C₄

#19151478

yes

characteristic

246

C₄

#19151594

yes

characteristic

247

C₄

#19151825

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

252

C₂

#26020681

yes

characteristic

	subgroup	G/H
center	C₂	#26020681
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting, prime radical	C₈₉×#3058	C₂
socle	C₂×C₈₉	#1893
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#3058	D₈₉
hypocenter	C₈₉	#13074
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

subgroup

G/H

center

C₂

#26020681

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting, prime radical

C₈₉×#3058

C₂

socle

C₂×C₈₉

#1893

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3058

N	H ≅ G/N	type
1. #26033355	C₂	semidirect
2. #26021968	C₂	semidirect
3. #26020298	C₂	semidirect
4. #26018353	C₂	semidirect
16. #469×C₈₉	C₄	semidirect
25. C₂×#13083549	D₄	semidirect
132. C₈₉	#13074	semidirect
139. #469	Dic₈₉	semidirect

H ≅ G/N

type

1. #26033355

C₂

semidirect

2. #26021968

C₂

semidirect

3. #26020298

C₂

semidirect

4. #26018353

C₂

semidirect

16. #469×C₈₉

C₄

semidirect

25. C₂×#13083549

D₄

semidirect

132. C₈₉

#13074

semidirect

139. #469

Dic₈₉

semidirect

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

subgroup	index
#26033355	2
#26021968	2
#26020298	2
#26018353	2
C₈₉×#3058	2
#13074	89

subgroup

index

C₈₉×#3058

Subgroups — #36471878

Conjugacy classes of subgroups

Complements

Maximal subgroups