Group #36459162 — subgroups

Subgroups — #36459162

Order 22784.

402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 123 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	#26020380	C₂	1	1	yes	maximal, characteristic, complemented
2	#26020252	C₂	1	2	yes	maximal
3	#26018136	C₂	1	2	yes	maximal, complemented
4	#26018087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1954	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
7	C₂×#15667933	—	2	2	no	—
8	#19151468	C₂²	1	2	yes	—
9	#19151361	—	2	2	no	—
10	#19151360	—	2	2	no	—
11	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
14	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×#10623494	—	2	2	no	—
16	C₂×C₄⋊Dic₈₉	—	2	2	no	—
17	C₂×C₄⋊Dic₈₉	—	2	2	no	—
18	C₂×C₄⋊Dic₈₉	—	2	2	no	—
19	C₄⋊#10623494	—	2	2	no	—
20	C₄⋊#10623494	—	2	2	no	—
21	#15667933	—	4	4	no	—
22	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₈₉	—	2	1	no	—
24	C₂²×C₈×C₈₉	—	2	1	no	—
25	C₂²×C₈×C₈₉	D₄	1	2	yes	—
26	C₄×D₄×C₈₉	—	2	2	no	—
27	C₄×D₄×C₈₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
30	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₈×C₈₉	—	2	2	no	—
32	C₂²⋊C₈×C₈₉	—	4	4	no	—
33	C₄×C₈×C₈₉	—	2	2	no	—
34	C₂²×Dic₈₉	—	4	2	no	—
35	C₂×#10623494	—	4	2	no	—
36	C₂×#10623494	—	4	2	no	—
37	C₂×#10623494	—	4	2	no	—
38	C₄⋊Dic₈₉	—	4	2	no	—
39	C₄⋊Dic₈₉	—	4	2	no	—
40	C₄⋊Dic₈₉	—	4	2	no	—
41	C₄⋊Dic₈₉	—	4	2	no	—
42	C₄⋊Dic₈₉	—	8	2	no	—
43	C₂⁴×C₈₉	—	2	1	no	—
44	C₂×D₄×C₈₉	—	2	2	no	—
45	C₂×D₄×C₈₉	—	2	1	no	—
46	C₂×D₄×C₈₉	—	2	2	no	—
47	C₂×D₄×C₈₉	D₈	1	2	yes	—
48	C₂²×C₄×C₈₉	—	2	1	no	—
49	C₂²×C₄×C₈₉	—	4	1	no	—
50	C₂²×C₄×C₈₉	—	4	1	no	—
51	C₂²×C₄×C₈₉	—	4	2	no	—
52	C₂²×C₄×C₈₉	—	4	2	no	—
53	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
56	C₂×C₈×C₈₉	—	2	2	no	—
57	C₂×C₈×C₈₉	—	2	2	no	—
58	C₂×C₈×C₈₉	—	2	2	no	—
59	C₂×C₈×C₈₉	—	4	1	no	—
60	C₂×C₈×C₈₉	—	4	2	no	—
61	C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₂²⋊C₄×C₈₉	—	4	2	no	—
63	C₄²×C₈₉	#41	1	2	yes	—
64	C₄²×C₈₉	#41	1	2	yes	—
65	C₂³×C₈₉	—	2	2	no	—
66	C₂³×C₈₉	—	4	1	no	—
67	C₂³×C₈₉	—	4	2	no	—
68	C₂³×C₈₉	—	4	1	no	—
69	C₂³×C₈₉	—	4	2	no	—
70	C₂³×C₈₉	#121	1	1	yes	characteristic
71	D₄×C₈₉	—	2	4	no	—
72	D₄×C₈₉	—	4	2	no	—
73	C₂×C₄×C₈₉	—	2	2	no	—
74	C₂×C₄×C₈₉	—	4	1	no	—
75	C₂×C₄×C₈₉	—	4	2	no	—
76	C₂×C₄×C₈₉	—	8	2	no	—
77	C₂×C₄×C₈₉	—	8	1	no	—
78	C₂×C₄×C₈₉	—	8	1	no	—
79	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
80	C₂×C₄×C₈₉	#123	1	2	yes	—
81	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
82	C₂×C₄×C₈₉	#126	1	2	yes	—
83	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₈₉	#135	1	2	yes	—
85	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
86	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₈₉	#137	1	2	yes	—
88	C₂×Dic₈₉	—	8	2	no	—
89	C₂×Dic₈₉	—	8	2	no	—
90	C₂×Dic₈₉	—	8	2	no	—
91	C₈×C₈₉	—	4	2	no	—
92	C₈×C₈₉	—	8	1	no	—
93	#10623494	—	8	2	no	—
94	C₂²×C₈₉	—	4	2	no	—
95	C₂²×C₈₉	—	4	4	no	—
96	C₂²×C₈₉	—	8	1	no	—
97	C₂²×C₈₉	—	8	1	no	—
98	C₂²×C₈₉	—	8	2	no	—
99	C₂²×C₈₉	#397	1	1	yes	characteristic
100	C₂²×C₈₉	#463	1	2	yes	—
101	C₂²×C₈₉	#466	1	1	yes	characteristic
102	C₂²×C₈₉	#470	1	1	yes	characteristic
103	C₂²×C₈₉	#471	1	2	yes	—
104	C₄×C₈₉	—	2	2	no	—
105	C₄×C₈₉	—	8	1	no	—
106	C₄×C₈₉	#480	1	2	yes	—
107	C₄×C₈₉	#482	1	2	yes	—
108	C₄×C₈₉	#485	1	2	yes	—
109	C₄×C₈₉	#488	1	1	yes	characteristic
110	C₄×C₈₉	#490	1	1	yes	characteristic
111	Dic₈₉	—	16	2	no	—
112	#10621	—	89	1	no	maximal, Sylow
113	C₂×C₈₉	—	8	2	no	—
114	C₂×C₈₉	#1681	1	2	yes	—
115	C₂×C₈₉	#1703	1	2	yes	—
116	C₂×C₈₉	#2073	1	1	yes	characteristic
117	C₂×C₈₉	#2075	1	1	yes	characteristic
118	C₂×C₈₉	#2079	1	1	yes	characteristic
119	#1954	D₈₉	1	1	yes	characteristic
120	#1834	—	89	1	no	—
121	#1802	—	89	2	no	—
122	#1296	—	89	2	no	—
123	#1277	—	89	1	no	—
124	C₈₉	#10621	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
126	C₂×C₄⋊C₈	—	89	2	no	—
127	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
128	C₂×#102	—	178	2	no	—
129	C₂×C₂²⋊C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
131	#384	—	89	2	no	—
132	#340	—	178	2	no	—
133	#340	—	178	2	no	—
134	C₂²×D₄	D₃₅₆	1	1	yes	characteristic
135	C₂³×C₄	—	2	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	178	2	no	—
138	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
139	C₄×D₄	—	2	2	no	—
140	C₄×D₄	—	2	2	no	—
141	C₂×C₄⋊C₄	—	178	2	no	—
142	C₂×C₄⋊C₄	—	178	2	no	—
143	C₂×C₄⋊C₄	—	178	2	no	—
144	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
145	C₂×C₂²⋊C₄	—	2	1	no	—
146	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	178	2	no	—
149	C₄⋊C₈	—	178	2	no	—
150	#102	—	356	4	no	—
151	C₂²⋊C₈	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	C₂⁴	—	2	1	no	—
154	C₂×D₄	—	2	2	no	—
155	C₂×D₄	—	2	1	no	—
156	C₂×D₄	—	2	2	no	—
157	C₂×D₄	D₇₁₂	1	2	yes	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	4	1	no	—
160	C₂²×C₄	—	4	1	no	—
161	C₂²×C₄	—	4	2	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	—	356	2	no	—
164	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
166	C₂²×C₄	#13083574	1	1	yes	characteristic
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	356	2	no	—
173	C₂×C₈	—	356	2	no	—
174	C₂×C₈	—	356	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	356	2	no	—
177	C₄⋊C₄	—	356	2	no	—
178	C₄⋊C₄	—	356	2	no	—
179	C₄⋊C₄	—	356	2	no	—
180	C₄⋊C₄	—	712	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	#13083573	1	2	yes	—
183	C₄²	#13083573	1	2	yes	—
184	C₂³	—	2	2	no	—
185	C₂³	—	4	1	no	—
186	C₂³	—	4	2	no	—
187	C₂³	—	4	1	no	—
188	C₂³	—	4	2	no	—
189	C₂³	#15667986	1	1	yes	characteristic
190	D₄	—	2	4	no	—
191	D₄	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	8	2	no	—
196	C₂×C₄	—	8	1	no	—
197	C₂×C₄	—	8	1	no	—
198	C₂×C₄	—	712	2	no	—
199	C₂×C₄	—	712	2	no	—
200	C₂×C₄	—	712	2	no	—
201	C₂×C₄	#15667993	1	1	yes	characteristic
202	C₂×C₄	#15667996	1	2	yes	—
203	C₂×C₄	#15667999	1	1	yes	characteristic
204	C₂×C₄	#15668005	1	2	yes	—
205	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
206	C₂×C₄	#15668032	1	2	yes	—
207	C₂×C₄	#15668034	1	1	yes	characteristic
208	C₂×C₄	#15668038	1	2	yes	—
209	C₂×C₄	#15668045	1	2	yes	—
210	C₈	—	4	2	no	—
211	C₈	—	8	1	no	—
212	C₈	—	712	2	no	—
213	C₂²	—	4	2	no	—
214	C₂²	—	4	4	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	1	no	—
217	C₂²	—	8	2	no	—
218	C₂²	#19151523	1	1	yes	characteristic
219	C₂²	#19151813	1	2	yes	—
220	C₂²	#19151834	1	1	yes	characteristic
221	C₂²	#19151856	1	1	yes	characteristic
222	C₂²	#19151861	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	8	1	no	—
225	C₄	—	1424	2	no	—
226	C₄	#19151912	1	2	yes	—
227	C₄	#19151919	1	2	yes	—
228	C₄	#19151940	1	2	yes	—
229	C₄	#19151952	1	1	yes	characteristic
230	C₄	#19151962	1	1	yes	characteristic
231	C₂	—	8	2	no	—
232	C₂	#26019689	1	2	yes	—
233	C₂	#26019827	1	2	yes	—
234	C₂	#26021665	1	1	yes	characteristic
235	C₂	#26021675	1	1	yes	characteristic
236	C₂	#26021697	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26020380

C₂

yes

maximal, characteristic, complemented

#26020252

C₂

yes

maximal

#26018136

C₂

yes

maximal, complemented

#26018087

C₂

yes

maximal, characteristic, complemented

C₈₉×#1954

C₂

yes

maximal, characteristic

C₂×C₄⋊#10623494

C₂²

yes

—

C₂×#15667933

—

#19151468

C₂²

yes

—

#19151361

—

#19151360

—

C₂×C₄×D₄×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊C₈×C₈₉

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₈₉

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₄⋊#10623494

—

C₄⋊#10623494

—

#15667933

—

C₂²×D₄×C₈₉

D₄

yes

characteristic

C₂³×C₄×C₈₉

—

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

D₄

yes

—

C₄×D₄×C₈₉

—

C₄×D₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₂²⋊C₈×C₈₉

—

C₄×C₈×C₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₂⁴×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

D₈

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

#41

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#121

yes

characteristic

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#123

yes

characteristic

C₂×C₄×C₈₉

#123

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

C₂×C₄×C₈₉

#126

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

#135

yes

characteristic

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#397

yes

characteristic

100

C₂²×C₈₉

#463

yes

—

101

C₂²×C₈₉

#466

yes

characteristic

102

C₂²×C₈₉

#470

yes

characteristic

103

C₂²×C₈₉

#471

yes

—

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

#480

yes

—

107

C₄×C₈₉

#482

yes

—

108

C₄×C₈₉

#485

yes

—

109

C₄×C₈₉

#488

yes

characteristic

110

C₄×C₈₉

#490

yes

characteristic

111

Dic₈₉

—

112

#10621

—

maximal, Sylow

113

C₂×C₈₉

—

114

C₂×C₈₉

#1681

yes

—

115

C₂×C₈₉

#1703

yes

—

116

C₂×C₈₉

#2073

yes

characteristic

117

C₂×C₈₉

#2075

yes

characteristic

118

C₂×C₈₉

#2079

yes

characteristic

119

#1954

D₈₉

yes

characteristic

120

#1834

—

121

#1802

—

122

#1296

—

123

#1277

—

124

C₈₉

#10621

yes

characteristic, complemented, Sylow

125

C₂×C₄×D₄

C₂×D₈₉

yes

characteristic

126

C₂×C₄⋊C₈

—

127

C₂×C₄⋊C₈

C₂×D₈₉

yes

characteristic

128

C₂×#102

—

178

—

129

C₂×C₂²⋊C₈

—

130

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

131

#384

—

132

#340

—

178

—

133

#340

—

178

—

134

C₂²×D₄

D₃₅₆

yes

characteristic

135

C₂³×C₄

—

136

C₂²×C₈

—

137

C₂²×C₈

—

178

—

138

C₂²×C₈

C₂²⋊D₈₉

yes

—

139

C₄×D₄

—

140

C₄×D₄

—

141

C₂×C₄⋊C₄

—

178

—

142

C₂×C₄⋊C₄

—

178

—

143

C₂×C₄⋊C₄

—

178

—

144

C₂×C₄⋊C₄

D₃₅₆

yes

characteristic

145

C₂×C₂²⋊C₄

—

146

C₂×C₄²

C₂²×D₈₉

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

178

—

149

C₄⋊C₈

—

178

—

150

#102

—

356

—

151

C₂²⋊C₈

—

152

C₄×C₈

—

153

C₂⁴

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

D₇₁₂

yes

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

163

C₂²×C₄

—

356

—

164

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

165

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

166

C₂²×C₄

#13083574

yes

characteristic

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

356

—

173

C₂×C₈

—

356

—

174

C₂×C₈

—

356

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

356

—

177

C₄⋊C₄

—

356

—

178

C₄⋊C₄

—

356

—

179

C₄⋊C₄

—

356

—

180

C₄⋊C₄

—

712

—

181

C₂²⋊C₄

—

182

C₄²

#13083573

yes

—

183

C₄²

#13083573

yes

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

—

188

C₂³

—

189

C₂³

#15667986

yes

characteristic

190

D₄

—

191

D₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

712

—

199

C₂×C₄

—

712

—

200

C₂×C₄

—

712

—

201

C₂×C₄

#15667993

yes

characteristic

202

C₂×C₄

#15667996

yes

—

203

C₂×C₄

#15667999

yes

characteristic

204

C₂×C₄

#15668005

yes

—

205

C₂×C₄

C₂×D₇₁₂

yes

characteristic

206

C₂×C₄

#15668032

yes

—

207

C₂×C₄

#15668034

yes

characteristic

208

C₂×C₄

#15668038

yes

—

209

C₂×C₄

#15668045

yes

—

210

C₈

—

211

C₈

—

212

C₈

—

712

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

#19151523

yes

characteristic

219

C₂²

#19151813

yes

—

220

C₂²

#19151834

yes

characteristic

221

C₂²

#19151856

yes

characteristic

222

C₂²

#19151861

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

1424

—

226

C₄

#19151912

yes

—

227

C₄

#19151919

yes

—

228

C₄

#19151940

yes

—

229

C₄

#19151952

yes

characteristic

230

C₄

#19151962

yes

characteristic

231

C₂

—

232

C₂

#26019689

yes

—

233

C₂

#26019827

yes

—

234

C₂

#26021665

yes

characteristic

235

C₂

#26021675

yes

characteristic

236

C₂

#26021697

yes

characteristic

	subgroup	G/H
center	C₂³	#15667986
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1954	C₂
socle	C₂³×C₈₉	#121
prime radical	C₂²×D₄×C₈₉	D₄
hypercenter	#1954	D₈₉
hypocenter	C₈₉	#10621
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

subgroup

G/H

center

C₂³

#15667986

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1954

C₂

socle

C₂³×C₈₉

#121

prime radical

C₂²×D₄×C₈₉

D₄

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1954

N	H ≅ G/N	type
1. #26020380	C₂	semidirect
3. #26018136	C₂	semidirect
4. #26018087	C₂	semidirect
124. C₈₉	#10621	semidirect

H ≅ G/N

type

1. #26020380

C₂

semidirect

3. #26018136

C₂

semidirect

4. #26018087

C₂

semidirect

124. C₈₉

#10621

semidirect

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

subgroup	index
#26020380	2
#26020252	2
#26018136	2
#26018087	2
C₈₉×#1954	2
#10621	89

subgroup

index

C₈₉×#1954

Subgroups — #36459162

Conjugacy classes of subgroups

Complements

Maximal subgroups