Group #36448004 — subgroups

Subgroups — #36448004

Order 22784.

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

normal subgroups only

This group has 422 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	#26020248	C₂	1	1	yes	maximal, characteristic
2	#26018576	C₂	1	1	yes	maximal, characteristic
3	#26018155	C₂	1	2	yes	maximal
4	#26018110	C₂	1	2	yes	maximal
5	C₈₉×#2351	C₂	1	1	yes	maximal, characteristic
6	#19151651	C₂²	1	2	yes	—
7	#19151622	C₂²	1	2	yes	—
8	C₂×#15667931	—	2	1	no	—
9	#19151367	—	2	1	no	—
10	#19151324	—	2	2	no	—
11	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
12	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	#389×C₈₉	—	2	1	no	—
14	#389×C₈₉	—	2	2	no	—
15	#382×C₈₉	C₄	1	2	yes	—
16	#382×C₈₉	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₈₉	C₄	1	2	yes	—
18	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#13083558	—	2	2	no	—
20	C₄⋊#10623494	—	2	2	no	—
21	C₄⋊#10623494	—	2	2	no	—
22	C₄⋊#10623494	—	2	2	no	—
23	#15667931	—	4	2	no	—
24	C₂²⋊#10623494	—	2	2	no	—
25	C₄×#10623494	—	2	2	no	—
26	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
27	C₄×Q₈×C₈₉	—	2	2	no	—
28	C₄×Q₈×C₈₉	—	2	2	no	—
29	C₄×Q₈×C₈₉	—	4	2	no	—
30	C₄×Q₈×C₈₉	—	4	2	no	—
31	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
33	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
37	C₂×C₄²×C₈₉	—	2	2	no	—
38	C₂×C₄²×C₈₉	—	2	1	no	—
39	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
41	#95×C₈₉	—	2	2	no	—
42	#95×C₈₉	—	2	1	no	—
43	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
44	#95×C₈₉	C₂×C₄	1	2	yes	—
45	#95×C₈₉	C₂×C₄	1	1	yes	characteristic
46	#13083558	—	4	2	no	—
47	#13083558	—	4	2	no	—
48	C₂×#10623494	—	4	2	no	—
49	C₂×#10623494	—	4	2	no	—
50	C₂×Q₈×C₈₉	—	2	2	no	—
51	C₂×Q₈×C₈₉	—	2	2	no	—
52	C₂×Q₈×C₈₉	D₈	1	2	yes	—
53	C₂×Q₈×C₈₉	SD₁₆	1	2	yes	—
54	C₂²×C₄×C₈₉	—	2	1	no	—
55	C₂²×C₄×C₈₉	—	2	1	no	—
56	C₂²×C₄×C₈₉	—	2	2	no	—
57	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
62	C₄⋊C₄×C₈₉	—	2	4	no	—
63	C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₄⋊C₄×C₈₉	—	4	2	no	—
65	C₄⋊C₄×C₈₉	—	4	4	no	—
66	C₄⋊C₄×C₈₉	—	4	4	no	—
67	C₄⋊C₄×C₈₉	—	4	1	no	—
68	C₄⋊C₄×C₈₉	—	4	1	no	—
69	C₄²×C₈₉	—	2	2	no	—
70	C₄²×C₈₉	—	2	2	no	—
71	C₄²×C₈₉	—	4	4	no	—
72	C₄²×C₈₉	—	4	1	no	—
73	C₄²×C₈₉	—	4	1	no	—
74	C₄²×C₈₉	#41	1	2	yes	—
75	C₄²×C₈₉	#41	1	2	yes	—
76	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₈₉	—	2	4	no	—
78	Q₈×C₈₉	—	2	4	no	—
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	—	2	2	no	—
81	C₂×C₄×C₈₉	—	2	2	no	—
82	C₂×C₄×C₈₉	—	2	2	no	—
83	C₂×C₄×C₈₉	—	4	1	no	—
84	C₂×C₄×C₈₉	—	4	1	no	—
85	C₂×C₄×C₈₉	—	4	1	no	—
86	C₂×C₄×C₈₉	—	4	1	no	—
87	C₂×C₄×C₈₉	—	4	2	no	—
88	C₂×C₄×C₈₉	—	4	1	no	—
89	C₂×C₄×C₈₉	—	4	2	no	—
90	C₂×C₄×C₈₉	—	4	1	no	—
91	C₂×C₄×C₈₉	—	4	2	no	—
92	C₂×C₄×C₈₉	—	4	2	no	—
93	C₂×C₄×C₈₉	—	4	1	no	—
94	C₂×C₄×C₈₉	#102	1	4	yes	—
95	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
96	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
97	C₂×C₄×C₈₉	#123	1	2	yes	—
98	C₂×C₄×C₈₉	#123	1	2	yes	—
99	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
100	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₈₉	#137	1	2	yes	—
102	#10623494	—	8	2	no	—
103	#10623494	—	8	2	no	—
104	C₂²×C₈₉	—	2	1	no	—
105	C₂²×C₈₉	—	2	1	no	—
106	C₂²×C₈₉	#381	1	1	yes	characteristic
107	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
108	C₂²×C₈₉	#419	1	1	yes	characteristic
109	C₄×C₈₉	—	2	4	no	—
110	C₄×C₈₉	—	2	2	no	—
111	C₄×C₈₉	—	2	1	no	—
112	C₄×C₈₉	—	2	1	no	—
113	C₄×C₈₉	—	4	2	no	—
114	C₄×C₈₉	—	4	2	no	—
115	C₄×C₈₉	—	8	2	no	—
116	C₄×C₈₉	—	8	1	no	—
117	C₄×C₈₉	#480	1	2	yes	—
118	C₄×C₈₉	#483	1	2	yes	—
119	#8766	—	89	1	no	maximal, Sylow
120	C₂×C₈₉	—	2	1	no	—
121	C₂×C₈₉	—	2	1	no	—
122	C₂×C₈₉	#1823	1	1	yes	characteristic
123	C₂×C₈₉	#1827	1	1	yes	characteristic
124	C₂×C₈₉	#1830	1	1	yes	characteristic
125	#2351	D₈₉	1	1	yes	characteristic
126	#1801	—	89	1	no	—
127	#1461	—	89	1	no	—
128	#1303	—	89	2	no	—
129	#1286	—	89	2	no	—
130	C₈₉	#8766	1	1	yes	characteristic, complemented, Sylow
131	C₂×C₄×Q₈	—	2	1	no	—
132	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
133	#431	—	89	2	no	—
134	#423	—	89	2	no	—
135	C₂×#101	—	178	1	no	—
136	#389	—	2	1	no	—
137	#389	—	2	2	no	—
138	#382	Dic₈₉	1	2	yes	—
139	#382	C₂×D₈₉	1	1	yes	characteristic
140	C₄×C₄⋊C₄	Dic₈₉	1	2	yes	—
141	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
142	#343	—	178	1	no	—
143	#324	—	178	2	no	—
144	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
145	C₂×M₁₆	—	178	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₄×Q₈	—	4	2	no	—
149	C₄×Q₈	—	4	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	2	yes	—
155	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	—	2	1	no	—
158	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
159	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
160	C₄⋊C₈	—	178	2	no	—
161	C₄⋊C₈	—	178	2	no	—
162	C₄⋊C₈	—	178	2	no	—
163	#101	—	356	2	no	—
164	C₂²⋊C₈	—	178	2	no	—
165	C₄×C₈	—	178	2	no	—
166	#95	—	2	2	no	—
167	#95	—	2	1	no	—
168	#95	C₂×Dic₈₉	1	1	yes	characteristic
169	#95	C₂×Dic₈₉	1	2	yes	—
170	#95	C₂×Dic₈₉	1	1	yes	characteristic
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	#13083559	1	2	yes	—
174	C₂×Q₈	#13083562	1	2	yes	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
179	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
180	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
183	M₁₆	—	356	2	no	—
184	M₁₆	—	356	2	no	—
185	C₂×C₈	—	356	2	no	—
186	C₂×C₈	—	356	2	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	4	2	no	—
190	C₄⋊C₄	—	4	4	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	4	no	—
194	C₄²	—	2	2	no	—
195	C₄²	—	2	2	no	—
196	C₄²	—	4	1	no	—
197	C₄²	—	4	1	no	—
198	C₄²	—	4	4	no	—
199	C₄²	#13083574	1	2	yes	—
200	C₄²	#13083574	1	2	yes	—
201	C₂³	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
202	Q₈	—	2	4	no	—
203	Q₈	—	2	4	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	1	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	1	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	#15667933	1	4	yes	—
220	C₂×C₄	#15667971	1	1	yes	characteristic
221	C₂×C₄	#15667971	1	1	yes	characteristic
222	C₂×C₄	#15667995	1	2	yes	—
223	C₂×C₄	#15667995	1	2	yes	—
224	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
225	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
226	C₂×C₄	#15668043	1	2	yes	—
227	C₈	—	712	2	no	—
228	C₈	—	712	2	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#19151461	1	1	yes	characteristic
232	C₂²	C₂×#15667933	1	1	yes	characteristic
233	C₂²	#19151607	1	1	yes	characteristic
234	C₄	—	2	2	no	—
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	4	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	8	1	no	—
241	C₄	—	8	2	no	—
242	C₄	#19151911	1	2	yes	—
243	C₄	#19151928	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	#26020338	1	1	yes	characteristic
247	C₂	#26020356	1	1	yes	characteristic
248	C₂	#26020366	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26020248

C₂

yes

maximal, characteristic

#26018576

C₂

yes

maximal, characteristic

#26018155

C₂

yes

maximal

#26018110

C₂

yes

maximal

C₈₉×#2351

C₂

yes

maximal, characteristic

#19151651

C₂²

yes

—

#19151622

C₂²

yes

—

C₂×#15667931

—

#19151367

—

#19151324

—

C₂×C₄×Q₈×C₈₉

—

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

#389×C₈₉

—

#389×C₈₉

—

#382×C₈₉

C₄

yes

—

#382×C₈₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₈₉

C₄

yes

—

C₄×C₄⋊C₄×C₈₉

C₂²

yes

—

—

—

—

—

—

—

C₂²×Q₈×C₈₉

D₄

yes

characteristic

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

D₄

yes

characteristic

C₂×C₄⋊C₄×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#95×C₈₉

—

#95×C₈₉

—

#95×C₈₉

C₂×C₄

yes

characteristic

#95×C₈₉

C₂×C₄

yes

—

#95×C₈₉

C₂×C₄

yes

—

—

—

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

D₈

yes

—

C₂×Q₈×C₈₉

SD₁₆

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#102

yes

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

—

C₂×C₄×C₈₉

#123

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

100

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

101

C₂×C₄×C₈₉

#137

yes

—

102

#10623494

—

103

#10623494

—

104

C₂²×C₈₉

—

105

C₂²×C₈₉

—

106

C₂²×C₈₉

#381

yes

characteristic

107

C₂²×C₈₉

C₂×#102

yes

characteristic

108

C₂²×C₈₉

#419

yes

characteristic

109

C₄×C₈₉

—

110

C₄×C₈₉

—

111

C₄×C₈₉

—

112

C₄×C₈₉

—

113

C₄×C₈₉

—

114

C₄×C₈₉

—

115

C₄×C₈₉

—

116

C₄×C₈₉

—

117

C₄×C₈₉

#480

yes

—

118

C₄×C₈₉

#483

yes

—

119

#8766

—

maximal, Sylow

120

C₂×C₈₉

—

121

C₂×C₈₉

—

122

C₂×C₈₉

#1823

yes

characteristic

123

C₂×C₈₉

#1827

yes

characteristic

124

C₂×C₈₉

#1830

yes

characteristic

125

#2351

D₈₉

yes

characteristic

126

#1801

—

127

#1461

—

128

#1303

—

129

#1286

—

130

C₈₉

#8766

yes

characteristic, complemented, Sylow

131

C₂×C₄×Q₈

—

132

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

133

#431

—

134

#423

—

135

C₂×#101

—

178

—

136

#389

—

137

#389

—

138

#382

Dic₈₉

yes

—

139

#382

C₂×D₈₉

yes

characteristic

140

C₄×C₄⋊C₄

Dic₈₉

yes

—

141

C₄×C₄⋊C₄

C₂×D₈₉

yes

characteristic

142

#343

—

178

—

143

#324

—

178

—

144

C₂²×Q₈

C₂²⋊D₈₉

yes

characteristic

145

C₂×M₁₆

—

178

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

—

155

C₂×C₄⋊C₄

C₂²⋊D₈₉

yes

characteristic

156

C₂×C₄²

—

157

C₂×C₄²

—

158

C₂×C₄²

C₂×Dic₈₉

yes

—

159

C₂×C₄²

C₂²×D₈₉

yes

characteristic

160

C₄⋊C₈

—

178

—

161

C₄⋊C₈

—

178

—

162

C₄⋊C₈

—

178

—

163

#101

—

356

—

164

C₂²⋊C₈

—

178

—

165

C₄×C₈

—

178

—

166

#95

—

167

#95

—

168

#95

C₂×Dic₈₉

yes

characteristic

169

#95

C₂×Dic₈₉

yes

—

170

#95

C₂×Dic₈₉

yes

characteristic

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

#13083559

yes

—

174

C₂×Q₈

#13083562

yes

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

C₂²⋊Dic₈₉

yes

—

179

C₂²×C₄

C₂²⋊Dic₈₉

yes

—

180

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

181

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

182

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

183

M₁₆

—

356

—

184

M₁₆

—

356

—

185

C₂×C₈

—

356

—

186

C₂×C₈

—

356

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄²

—

195

C₄²

—

196

C₄²

—

197

C₄²

—

198

C₄²

—

199

C₄²

#13083574

yes

—

200

C₄²

#13083574

yes

—

201

C₂³

C₂×C₂²⋊Dic₈₉

yes

characteristic

202

Q₈

—

203

Q₈

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

#15667933

yes

—

220

C₂×C₄

#15667971

yes

characteristic

221

C₂×C₄

#15667971

yes

characteristic

222

C₂×C₄

#15667995

yes

—

223

C₂×C₄

#15667995

yes

—

224

C₂×C₄

C₂×#13083559

yes

characteristic

225

C₂×C₄

C₂×#13083562

yes

characteristic

226

C₂×C₄

#15668043

yes

—

227

C₈

—

712

—

228

C₈

—

712

—

229

C₂²

—

230

C₂²

—

231

C₂²

#19151461

yes

characteristic

232

C₂²

C₂×#15667933

yes

characteristic

233

C₂²

#19151607

yes

characteristic

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

#19151911

yes

—

243

C₄

#19151928

yes

—

244

C₂

—

245

C₂

—

246

C₂

#26020338

yes

characteristic

247

C₂

#26020356

yes

characteristic

248

C₂

#26020366

yes

characteristic

	subgroup	G/H
center	C₂²	#19151461
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#2351	C₂
socle	C₂²×C₈₉	#381
prime radical	C₂³×C₈₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#2351	D₈₉
hypocenter	C₈₉	#8766
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2351

subgroup

G/H

center

C₂²

#19151461

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#2351

C₂

socle

C₂²×C₈₉

#381

prime radical

C₂³×C₈₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2351

N	H ≅ G/N	type
130. C₈₉	#8766	semidirect

H ≅ G/N

type

130. C₈₉

#8766

semidirect

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

subgroup	index
#26020248	2
#26018576	2
#26018155	2
#26018110	2
C₈₉×#2351	2
#8766	89

subgroup

index

C₈₉×#2351

Subgroups — #36448004

Conjugacy classes of subgroups

Complements

Maximal subgroups