Group #36457441 — subgroups

Subgroups — #36457441

Order 22784.

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

normal subgroups only

This group has 504 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	#26025281	C₂	1	1	yes	maximal, characteristic
2	#26021201	C₂	1	2	yes	maximal
3	#26018135	C₂	1	1	yes	maximal, characteristic
4	#26018092	C₂	1	2	yes	maximal
5	C₈₉×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668011	—	2	2	no	—
7	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
8	#19151518	—	2	2	no	—
9	#19151494	—	2	2	no	—
10	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
11	#19151360	—	2	2	no	—
12	#19151360	—	2	2	no	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#103×C₈₉	—	2	2	no	—
15	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	#384×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₇₈	—	2	2	no	—
18	C₂²×#10623494	—	2	2	no	—
19	#15668011	—	4	4	no	—
20	#15668011	—	4	4	no	—
21	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
23	C₂×#13083553	—	2	4	no	—
24	C₂×C₄×Dic₈₉	—	2	2	no	—
25	C₄⋊#10623494	—	2	2	no	—
26	C₄⋊#10623494	—	2	2	no	—
27	#15667919	—	2	2	no	—
28	#15667919	—	2	2	no	—
29	C₂²×Q₈×C₈₉	—	2	1	no	—
30	C₂²×C₈×C₈₉	—	2	1	no	—
31	C₄⋊Q₈×C₈₉	—	2	2	no	—
32	C₄⋊Q₈×C₈₉	—	2	1	no	—
33	C₄⋊Q₈×C₈₉	Q₈	1	2	yes	complemented
34	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
37	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
38	#103×C₈₉	—	4	4	no	—
39	C₄×C₈×C₈₉	—	2	2	no	—
40	C₂×Dic₁₇₈	—	4	8	no	—
41	C₂×Dic₁₇₈	—	8	2	no	—
42	C₂²×Dic₈₉	—	2	2	no	—
43	C₂²×Dic₈₉	—	2	2	no	—
44	C₂×#10623494	—	4	2	no	—
45	C₂×#10623494	—	4	2	no	—
46	C₂×#10623494	—	4	2	no	—
47	C₄⋊Dic₈₉	—	2	2	no	—
48	C₄⋊Dic₈₉	—	2	2	no	—
49	C₄⋊Dic₈₉	SD₁₆	1	4	yes	—
50	C₄⋊Dic₈₉	Q₁₆	1	4	yes	—
51	#13083553	—	4	8	no	—
52	C₄×Dic₈₉	—	4	2	no	—
53	C₄×Dic₈₉	—	4	2	no	—
54	C₂×Q₈×C₈₉	—	2	2	no	—
55	C₂×Q₈×C₈₉	—	4	2	no	—
56	C₂×Q₈×C₈₉	—	4	2	no	—
57	C₂×Q₈×C₈₉	—	4	1	no	—
58	C₂²×C₄×C₈₉	—	2	2	no	—
59	C₂²×C₄×C₈₉	—	4	1	no	—
60	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₈₉	—	2	2	no	—
63	C₂×C₈×C₈₉	—	4	1	no	—
64	C₂×C₈×C₈₉	—	4	1	no	—
65	C₄⋊C₄×C₈₉	—	2	4	no	—
66	C₄⋊C₄×C₈₉	—	4	2	no	—
67	C₄⋊C₄×C₈₉	—	4	2	no	—
68	C₄⋊C₄×C₈₉	—	4	2	no	—
69	C₄⋊C₄×C₈₉	—	4	2	no	—
70	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
71	C₄²×C₈₉	#41	1	2	yes	—
72	C₄²×C₈₉	#41	1	1	yes	characteristic
73	C₂³×C₈₉	#120	1	1	yes	characteristic
74	Q₈×C₈₉	—	4	4	no	—
75	Q₈×C₈₉	—	8	2	no	—
76	C₂×C₄×C₈₉	—	2	1	no	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	4	2	no	—
79	C₂×C₄×C₈₉	—	4	4	no	—
80	C₂×C₄×C₈₉	—	4	2	no	—
81	C₂×C₄×C₈₉	—	8	1	no	—
82	C₂×C₄×C₈₉	—	8	1	no	—
83	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
84	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×C₈₉	#124	1	2	yes	—
86	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
88	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
90	C₂×C₄×C₈₉	#137	1	2	yes	—
91	C₂×Dic₈₉	—	2	4	no	—
92	C₂×Dic₈₉	—	2	4	no	—
93	C₂×Dic₈₉	—	4	2	no	—
94	C₂×Dic₈₉	—	4	2	no	—
95	C₂×Dic₈₉	—	4	2	no	—
96	C₂×Dic₈₉	—	4	2	no	—
97	Dic₁₇₈	—	8	8	no	—
98	C₈×C₈₉	—	4	2	no	—
99	#10623494	—	8	2	no	—
100	C₂²×C₈₉	#393	1	1	yes	characteristic
101	C₂²×C₈₉	#450	1	2	yes	—
102	C₂²×C₈₉	#451	1	2	yes	—
103	C₂²×C₈₉	#453	1	1	yes	characteristic
104	C₂²×C₈₉	#454	1	1	yes	characteristic
105	C₄×C₈₉	—	2	1	no	—
106	C₄×C₈₉	—	2	1	no	—
107	C₄×C₈₉	—	8	2	no	—
108	C₄×C₈₉	—	8	2	no	—
109	C₄×C₈₉	#475	1	2	yes	—
110	C₄×C₈₉	#477	1	2	yes	—
111	C₄×C₈₉	#487	1	2	yes	—
112	C₄×C₈₉	#489	1	2	yes	—
113	Dic₈₉	—	4	4	no	—
114	Dic₈₉	—	4	4	no	—
115	#10349	—	89	1	no	maximal, Sylow
116	C₂×C₈₉	#1629	1	1	yes	characteristic
117	C₂×C₈₉	#1633	1	1	yes	characteristic
118	C₂×C₈₉	#1637	1	2	yes	—
119	C₂×C₈₉	#2024	1	2	yes	—
120	C₂×C₈₉	#2027	1	1	yes	characteristic
121	#2551	—	89	1	no	—
122	#1987	—	89	2	no	—
123	#1956	D₈₉	1	1	yes	characteristic
124	#1296	—	89	1	no	—
125	#1279	—	89	2	no	—
126	C₈₉	#10349	1	1	yes	characteristic, complemented, Sylow
127	C₂×C₄⋊Q₈	—	178	2	no	—
128	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
129	C₂×C₄⋊C₈	—	89	2	no	—
130	C₂×#103	—	2	2	no	—
131	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
132	#395	—	178	2	no	—
133	#389	—	178	2	no	—
134	#384	C₂×D₈₉	1	1	yes	characteristic
135	C₄×C₄⋊C₄	—	89	2	no	—
136	#340	—	178	2	no	—
137	#340	—	178	2	no	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	—	178	2	no	—
140	C₂²×C₈	—	2	1	no	—
141	C₂²×C₈	—	178	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	—	356	4	no	—
145	C₄⋊Q₈	—	356	4	no	—
146	C₄⋊Q₈	Dic₁₇₈	1	2	yes	complemented
147	C₂×C₄⋊C₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	89	2	no	—
150	C₂×C₄⋊C₄	—	89	2	no	—
151	C₂×C₄⋊C₄	—	178	4	no	—
152	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
153	C₂×C₄²	—	178	2	no	—
154	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
155	C₄⋊C₈	—	178	2	no	—
156	C₄⋊C₈	—	178	2	no	—
157	#103	—	4	4	no	—
158	C₄×C₈	—	2	2	no	—
159	#95	—	178	2	no	—
160	#95	—	178	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	1	no	—
165	C₂×Q₈	—	356	8	no	—
166	C₂×Q₈	—	712	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	—	178	2	no	—
170	C₂²×C₄	—	178	2	no	—
171	C₂²×C₄	D₄×D₈₉	1	2	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	356	2	no	—
177	C₂×C₈	—	356	2	no	—
178	C₂×C₈	—	356	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	89	4	no	—
185	C₄⋊C₄	—	89	4	no	—
186	C₄⋊C₄	—	356	8	no	—
187	C₄⋊C₄	—	178	2	no	—
188	C₄⋊C₄	—	178	2	no	—
189	C₄²	—	356	2	no	—
190	C₄²	—	356	2	no	—
191	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
192	C₄²	#13083573	1	2	yes	—
193	C₄²	#13083574	1	1	yes	characteristic
194	C₂³	#15667980	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	712	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	356	2	no	—
206	C₂×C₄	—	356	2	no	—
207	C₂×C₄	—	356	2	no	—
208	C₂×C₄	—	356	2	no	—
209	C₂×C₄	—	178	4	no	—
210	C₂×C₄	—	178	4	no	—
211	C₂×C₄	#15667989	1	2	yes	—
212	C₂×C₄	#15667991	1	1	yes	characteristic
213	C₂×C₄	#15667998	1	2	yes	—
214	C₂×C₄	#15667999	1	1	yes	characteristic
215	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
216	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
217	C₂×C₄	#15668039	1	2	yes	—
218	C₂×C₄	#15668044	1	2	yes	—
219	C₈	—	4	2	no	—
220	C₈	—	712	2	no	—
221	C₂²	#19151510	1	1	yes	characteristic
222	C₂²	#19151747	1	2	yes	—
223	C₂²	#19151752	1	2	yes	—
224	C₂²	#19151765	1	1	yes	characteristic
225	C₂²	#19151770	1	1	yes	characteristic
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	356	4	no	—
231	C₄	—	356	4	no	—
232	C₄	#19151881	1	2	yes	—
233	C₄	#19151891	1	2	yes	—
234	C₄	#19151947	1	2	yes	—
235	C₄	#19151959	1	2	yes	—
236	C₂	#26019366	1	1	yes	characteristic
237	C₂	#26019390	1	1	yes	characteristic
238	C₂	#26019414	1	2	yes	—
239	C₂	#26021391	1	2	yes	—
240	C₂	#26021408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26025281

C₂

yes

maximal, characteristic

#26021201

C₂

yes

maximal

#26018135

C₂

yes

maximal, characteristic

#26018092

C₂

yes

maximal

C₈₉×#1956

C₂

yes

maximal, characteristic

C₂×#15668011

—

C₂×C₄⋊#10623494

C₂²

yes

—

#19151518

—

#19151494

—

C₄×C₄⋊Dic₈₉

C₂²

yes

—

#19151360

—

#19151360

—

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₂×#103×C₈₉

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#384×C₈₉

C₂²

yes

characteristic

C₂²×Dic₁₇₈

—

C₂²×#10623494

—

#15668011

—

#15668011

—

C₂×C₄⋊Dic₈₉

D₄

yes

—

C₂×C₄⋊Dic₈₉

D₄

yes

—

C₂×#13083553

—

C₂×C₄×Dic₈₉

—

—

—

—

—

C₂²×Q₈×C₈₉

—

C₂²×C₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

Q₈

yes

complemented

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#103×C₈₉

—

C₄×C₈×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

SD₁₆

yes

—

C₄⋊Dic₈₉

Q₁₆

yes

—

#13083553

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂×Q₈

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

yes

C₂³×C₈₉

yes

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₈₉

#124

yes

—

C₂×C₄×C₈₉

#124

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

—

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₈₉

#137

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

C₈×C₈₉

—

#10623494

—

100

C₂²×C₈₉

#393

yes

characteristic

101

C₂²×C₈₉

#450

yes

—

102

C₂²×C₈₉

#451

yes

—

103

C₂²×C₈₉

#453

yes

characteristic

104

C₂²×C₈₉

#454

yes

characteristic

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

—

108

C₄×C₈₉

—

109

C₄×C₈₉

#475

yes

—

110

C₄×C₈₉

#477

yes

—

111

C₄×C₈₉

#487

yes

—

112

C₄×C₈₉

#489

yes

—

113

Dic₈₉

—

114

Dic₈₉

—

115

#10349

—

maximal, Sylow

116

C₂×C₈₉

#1629

yes

characteristic

117

C₂×C₈₉

#1633

yes

characteristic

118

C₂×C₈₉

#1637

yes

—

119

C₂×C₈₉

#2024

yes

—

120

C₂×C₈₉

#2027

yes

characteristic

121

#2551

—

122

#1987

—

123

#1956

D₈₉

yes

characteristic

124

#1296

—

125

#1279

—

126

C₈₉

#10349

yes

characteristic, complemented, Sylow

127

C₂×C₄⋊Q₈

—

178

—

128

C₂×C₄⋊Q₈

C₂×D₈₉

yes

characteristic

129

C₂×C₄⋊C₈

—

130

C₂×#103

—

131

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

132

#395

—

178

—

133

#389

—

178

—

134

#384

C₂×D₈₉

yes

characteristic

135

C₄×C₄⋊C₄

—

136

#340

—

178

—

137

#340

—

178

—

138

C₂²×Q₈

—

139

C₂²×Q₈

—

178

—

140

C₂²×C₈

—

141

C₂²×C₈

—

178

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

356

—

145

C₄⋊Q₈

—

356

—

146

C₄⋊Q₈

Dic₁₇₈

yes

complemented

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

178

—

152

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

153

C₂×C₄²

—

178

—

154

C₂×C₄²

C₂²×D₈₉

yes

characteristic

155

C₄⋊C₈

—

178

—

156

C₄⋊C₈

—

178

—

157

#103

—

158

C₄×C₈

—

159

#95

—

178

—

160

#95

—

178

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

356

—

166

C₂×Q₈

—

712

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

178

—

170

C₂²×C₄

—

178

—

171

C₂²×C₄

D₄×D₈₉

yes

—

172

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

356

—

177

C₂×C₈

—

356

—

178

C₂×C₈

—

356

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

356

—

187

C₄⋊C₄

—

178

—

188

C₄⋊C₄

—

178

—

189

C₄²

—

356

—

190

C₄²

—

356

—

191

C₄²

C₂×Dic₁₇₈

yes

characteristic

192

C₄²

#13083573

yes

—

193

C₄²

#13083574

yes

characteristic

194

C₂³

#15667980

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

712

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

356

—

206

C₂×C₄

—

356

—

207

C₂×C₄

—

356

—

208

C₂×C₄

—

356

—

209

C₂×C₄

—

178

—

210

C₂×C₄

—

178

—

211

C₂×C₄

#15667989

yes

—

212

C₂×C₄

#15667991

yes

characteristic

213

C₂×C₄

#15667998

yes

—

214

C₂×C₄

#15667999

yes

characteristic

215

C₂×C₄

SD₁₆×D₈₉

yes

—

216

C₂×C₄

Q₁₆×D₈₉

yes

—

217

C₂×C₄

#15668039

yes

—

218

C₂×C₄

#15668044

yes

—

219

C₈

—

220

C₈

—

712

—

221

C₂²

#19151510

yes

characteristic

222

C₂²

#19151747

yes

—

223

C₂²

#19151752

yes

—

224

C₂²

#19151765

yes

characteristic

225

C₂²

#19151770

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

356

—

231

C₄

—

356

—

232

C₄

#19151881

yes

—

233

C₄

#19151891

yes

—

234

C₄

#19151947

yes

—

235

C₄

#19151959

yes

—

236

C₂

#26019366

yes

characteristic

237

C₂

#26019390

yes

characteristic

238

C₂

#26019414

yes

—

239

C₂

#26021391

yes

—

240

C₂

#26021408

yes

characteristic

	subgroup	G/H
center	C₂³	#15667980
commutator, cosocle	C₂×C₄²×C₈₉	C₂³
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1956	C₂
socle, prime radical	C₂³×C₈₉	#120
hypercenter	#1956	D₈₉
hypocenter	C₈₉	#10349
LCS	G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#15667980

commutator, cosocle

C₂×C₄²×C₈₉

C₂³

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1956

C₂

C₂³×C₈₉

D₈₉

C₈₉

G ▷ C₂×C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
33. C₄⋊Q₈×C₈₉	Q₈	semidirect
126. C₈₉	#10349	semidirect
146. C₄⋊Q₈	Dic₁₇₈	semidirect

H ≅ G/N

type

33. C₄⋊Q₈×C₈₉

Q₈

semidirect

126. C₈₉

#10349

semidirect

146. C₄⋊Q₈

Dic₁₇₈

semidirect

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

subgroup	index
#26025281	2
#26021201	2
#26018135	2
#26018092	2
C₈₉×#1956	2
#10349	89

subgroup

index

C₈₉×#1956

Subgroups — #36457441

Conjugacy classes of subgroups

Complements

Maximal subgroups