Group #36472936 — subgroups

Subgroups — #36472936

Order 22784.

566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19151975	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151412	C₂	1	2	yes	maximal, complemented
3	#26021969	C₂	1	2	yes	maximal, complemented
4	#26020131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#364×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₁₂	—	2	1	no	—
7	C₂²×D₇₁₂	C₂²	1	2	yes	—
8	C₂×#15668009	—	2	1	no	—
9	#19151975	—	2	2	no	—
10	#19151975	C₄	1	4	yes	complemented
11	C₂×#15667948	C₂²	1	1	yes	characteristic
12	#19151636	C₂²	1	1	yes	characteristic
13	#19151553	—	2	1	no	—
14	#19151412	—	2	4	no	—
15	#19151400	—	2	4	no	—
16	#19151358	—	2	1	no	—
17	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
19	#364×C₈₉	—	2	2	no	—
20	C₂²×D₃₅₆	—	2	2	no	—
21	C₂²×D₃₅₆	—	4	2	no	—
22	C₂×D₇₁₂	—	2	4	no	—
23	C₂×D₇₁₂	—	2	2	no	—
24	C₂×D₇₁₂	—	2	2	no	—
25	C₂×D₇₁₂	—	2	2	no	—
26	C₂×D₇₁₂	—	2	2	no	—
27	C₂×D₇₁₂	—	2	2	no	—
28	C₂×D₇₁₂	—	4	1	no	—
29	C₂×D₇₁₂	—	4	1	no	—
30	C₂×D₇₁₂	—	4	2	no	—
31	C₂×D₇₁₂	C₂×C₄	1	4	yes	—
32	C₂×#13083558	—	2	1	no	—
33	#15668009	—	2	4	no	—
34	#15668009	—	4	2	no	—
35	#15667971	—	2	1	no	—
36	#15667948	—	2	1	no	—
37	#15667948	D₄	1	2	yes	complemented
38	#15667946	D₄	1	2	yes	complemented
39	#15667944	—	2	1	no	—
40	#15667922	—	4	1	no	—
41	C₈×Dic₈₉	—	4	1	no	—
42	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
45	M₃₂×C₈₉	—	2	2	no	—
46	M₃₂×C₈₉	—	2	2	no	—
47	C₂×C₁₆×C₈₉	—	2	2	no	—
48	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₈₉	D₄	1	2	yes	—
50	C₂³×D₈₉	—	4	2	no	—
51	C₂×D₃₅₆	—	2	4	no	—
52	C₂×D₃₅₆	—	4	2	no	—
53	C₂×D₃₅₆	—	4	2	no	—
54	C₂×D₃₅₆	—	4	2	no	—
55	C₂×D₃₅₆	—	4	2	no	—
56	C₂×D₃₅₆	—	4	8	no	—
57	C₂×D₃₅₆	—	4	2	no	—
58	C₂×D₃₅₆	—	8	8	no	—
59	D₇₁₂	—	2	4	no	—
60	D₇₁₂	—	2	4	no	—
61	D₇₁₂	—	4	4	no	—
62	D₇₁₂	—	4	4	no	—
63	D₇₁₂	—	4	2	no	—
64	D₇₁₂	—	4	2	no	—
65	#13083558	—	2	2	no	—
66	#13083558	—	4	1	no	—
67	C₂×#10623494	—	4	1	no	—
68	C₄⋊Dic₈₉	—	2	2	no	—
69	C₂²⋊Dic₈₉	—	4	1	no	—
70	C₄×Dic₈₉	—	4	1	no	—
71	C₂²×C₄×C₈₉	—	2	1	no	—
72	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
74	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
75	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
76	C₂×C₈×C₈₉	SD₁₆	1	2	yes	—
77	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
82	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
83	C₄²×C₈₉	—	2	1	no	—
84	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
85	C₁₆×C₈₉	—	4	2	no	—
86	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
87	C₂²×D₈₉	—	4	4	no	—
88	C₂²×D₈₉	—	8	8	no	—
89	C₂²×D₈₉	—	8	2	no	—
90	C₂²×D₈₉	—	8	2	no	—
91	C₂×C₄×C₈₉	—	2	4	no	—
92	C₂×C₄×C₈₉	—	2	2	no	—
93	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×Dic₈₉	—	4	2	no	—
100	D₃₅₆	—	4	4	no	—
101	D₃₅₆	—	4	4	no	—
102	D₃₅₆	—	8	16	no	—
103	D₃₅₆	—	8	2	no	—
104	D₃₅₆	—	8	2	no	—
105	C₈×C₈₉	#102	1	2	yes	—
106	C₈×C₈₉	#102	1	2	yes	—
107	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
108	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
109	C₈×C₈₉	#124	1	1	yes	characteristic
110	C₈×C₈₉	#127	1	1	yes	characteristic
111	#10623494	—	4	2	no	—
112	C₂²×C₈₉	—	2	2	no	—
113	C₂²×C₈₉	#418	1	1	yes	characteristic
114	C₂²×C₈₉	#459	1	1	yes	characteristic
115	C₂²×C₈₉	#460	1	1	yes	characteristic
116	C₂×D₈₉	—	8	8	no	—
117	C₂×D₈₉	—	8	4	no	—
118	C₂×D₈₉	—	16	4	no	—
119	C₂×D₈₉	—	16	4	no	—
120	C₄×C₈₉	—	2	4	no	—
121	C₄×C₈₉	#390	1	1	yes	characteristic
122	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
123	C₄×C₈₉	#459	1	1	yes	characteristic
124	C₄×C₈₉	#460	1	1	yes	characteristic
125	Dic₈₉	—	8	2	no	—
126	#13261	—	89	1	no	maximal, Sylow
127	C₂×C₈₉	—	2	1	no	—
128	C₂×C₈₉	—	2	1	no	—
129	C₂×C₈₉	#1982	1	1	yes	characteristic
130	C₂×C₈₉	#2213	1	2	yes	—
131	D₈₉	—	16	4	no	—
132	C₂×#493	—	89	1	no	—
133	C₂×#364	D₈₉	1	1	yes	characteristic, complemented
134	C₂×#361	—	89	2	no	—
135	#2140	—	89	2	no	—
136	#1772	—	89	1	no	—
137	C₈₉	#13261	1	1	yes	characteristic, complemented, Sylow
138	C₂²×D₈	—	89	2	no	—
139	C₂²×D₈	—	178	1	no	—
140	C₂×#127	—	178	1	no	—
141	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
142	#493	—	89	4	no	—
143	#493	—	178	2	no	—
144	C₂×#108	—	89	1	no	—
145	#427	—	89	1	no	—
146	#405	—	178	1	no	—
147	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
148	#364	—	2	2	no	—
149	#361	—	178	4	no	—
150	#357	—	178	4	no	—
151	#339	—	178	1	no	—
152	C₂²×D₄	—	356	2	no	—
153	C₂²×D₄	—	178	2	no	—
154	C₂×D₈	—	89	4	no	—
155	C₂×D₈	—	356	1	no	—
156	C₂×D₈	—	356	1	no	—
157	C₂×D₈	—	356	2	no	—
158	C₂×D₈	—	178	4	no	—
159	C₂×D₈	—	178	2	no	—
160	C₂×D₈	—	178	2	no	—
161	C₂×D₈	—	178	2	no	—
162	C₂×D₈	—	178	2	no	—
163	C₂×D₈	—	178	2	no	—
164	C₂×M₁₆	—	178	1	no	—
165	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
166	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
167	#127	—	356	2	no	—
168	#127	—	178	4	no	—
169	#117	—	178	1	no	—
170	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
171	M₃₂	—	2	2	no	—
172	M₃₂	—	2	2	no	—
173	C₂×C₁₆	—	2	2	no	—
174	#108	—	89	2	no	—
175	#108	—	178	1	no	—
176	#107	—	89	2	no	—
177	#106	—	178	1	no	—
178	#97	—	356	1	no	—
179	C₄×C₈	—	356	1	no	—
180	C₄×C₈	C₄×D₈₉	1	2	yes	—
181	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
182	C₂⁴	—	356	2	no	—
183	C₂×D₄	—	356	8	no	—
184	C₂×D₄	—	356	2	no	—
185	C₂×D₄	—	356	2	no	—
186	C₂×D₄	—	356	2	no	—
187	C₂×D₄	—	356	2	no	—
188	C₂×D₄	—	356	2	no	—
189	C₂×D₄	—	178	4	no	—
190	C₂×D₄	—	712	8	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
193	D₈	—	356	2	no	—
194	D₈	—	356	2	no	—
195	D₈	—	356	4	no	—
196	D₈	—	356	4	no	—
197	D₈	—	178	4	no	—
198	D₈	—	178	4	no	—
199	M₁₆	—	356	1	no	—
200	M₁₆	—	178	2	no	—
201	C₂×C₈	—	356	1	no	—
202	C₂×C₈	#13083551	1	2	yes	—
203	C₂×C₈	D₇₁₂	1	1	yes	characteristic
204	C₂×C₈	D₇₁₂	1	1	yes	characteristic
205	C₂×C₈	#13083563	1	2	yes	—
206	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
207	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
208	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
209	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
210	C₂×C₈	#13083575	1	1	yes	characteristic
211	C₂×C₈	#13083575	1	1	yes	characteristic
212	C₄⋊C₄	—	178	2	no	—
213	C₂²⋊C₄	—	356	1	no	—
214	C₄²	—	2	1	no	—
215	C₄²	—	356	1	no	—
216	C₄²	#13083551	1	2	yes	—
217	C₁₆	—	4	2	no	—
218	C₂³	—	356	4	no	—
219	C₂³	—	712	8	no	—
220	C₂³	—	712	2	no	—
221	C₂³	—	712	2	no	—
222	C₂³	#15668040	1	1	yes	characteristic
223	D₄	—	356	4	no	—
224	D₄	—	356	4	no	—
225	D₄	—	712	16	no	—
226	D₄	—	712	2	no	—
227	D₄	—	712	2	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	356	2	no	—
231	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
232	C₂×C₄	#15667987	1	1	yes	characteristic
233	C₂×C₄	#15667987	1	1	yes	characteristic
234	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
235	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
236	C₂×C₄	#15668040	1	1	yes	characteristic
237	C₈	—	356	2	no	—
238	C₈	#15667934	1	2	yes	—
239	C₈	#15667934	1	2	yes	—
240	C₈	#15667974	1	1	yes	characteristic
241	C₈	#15667974	1	1	yes	characteristic
242	C₈	#15668001	1	1	yes	characteristic
243	C₈	#15668008	1	1	yes	characteristic
244	C₂²	—	2	2	no	—
245	C₂²	—	1424	4	no	—
246	C₂²	—	1424	4	no	—
247	C₂²	—	712	8	no	—
248	C₂²	—	712	4	no	—
249	C₂²	#19151604	1	1	yes	characteristic
250	C₂²	#19151794	1	1	yes	characteristic
251	C₂²	#19151799	1	1	yes	characteristic
252	C₄	—	2	4	no	—
253	C₄	—	712	2	no	—
254	C₄	#19151499	1	1	yes	characteristic
255	C₄	C₂×#15667934	1	1	yes	characteristic
256	C₄	#19151794	1	1	yes	characteristic
257	C₄	#19151799	1	1	yes	characteristic
258	C₂	—	2	1	no	—
259	C₂	—	2	1	no	—
260	C₂	—	1424	4	no	—
261	C₂	#26021178	1	1	yes	characteristic
262	C₂	#26022329	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151975

C₂

yes

maximal, characteristic

C₂×#19151412

C₂

yes

maximal, complemented

#26021969

C₂

yes

maximal, complemented

#26020131

C₂

yes

maximal, characteristic, complemented

C₂×#364×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₁₂

—

C₂²×D₇₁₂

C₂²

yes

—

C₂×#15668009

—

#19151975

—

#19151975

C₄

yes

complemented

C₂×#15667948

C₂²

yes

characteristic

#19151636

C₂²

yes

—

—

—

—

C₂×M₃₂×C₈₉

C₂²

yes

—

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

#364×C₈₉

—

C₂²×D₃₅₆

—

C₂²×D₃₅₆

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

—

C₂×D₇₁₂

C₂×C₄

yes

—

—

—

—

—

—

D₄

yes

complemented

#15667946

D₄

yes

complemented

#15667944

—

#15667922

—

C₈×Dic₈₉

—

C₂²×C₈×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

characteristic

M₃₂×C₈₉

—

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

D₄

yes

—

C₂³×D₈₉

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

C₂×D₃₅₆

—

D₇₁₂

—

D₇₁₂

—

D₇₁₂

—

D₇₁₂

—

D₇₁₂

—

D₇₁₂

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₂²⋊Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

D₈

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₄²×C₈₉

—

C₄²×C₈₉

C₂²⋊C₄

yes

—

C₁₆×C₈₉

—

C₂³×C₈₉

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₈₉

—

100

D₃₅₆

—

101

D₃₅₆

—

102

D₃₅₆

—

103

D₃₅₆

—

104

D₃₅₆

—

105

C₈×C₈₉

#102

yes

—

106

C₈×C₈₉

#102

yes

—

107

C₈×C₈₉

C₄×D₄

yes

characteristic

108

C₈×C₈₉

C₄×D₄

yes

characteristic

109

C₈×C₈₉

#124

yes

characteristic

110

C₈×C₈₉

#127

yes

characteristic

111

#10623494

—

112

C₂²×C₈₉

—

113

C₂²×C₈₉

#418

yes

characteristic

114

C₂²×C₈₉

#459

yes

characteristic

115

C₂²×C₈₉

#460

yes

characteristic

116

C₂×D₈₉

—

117

C₂×D₈₉

—

118

C₂×D₈₉

—

119

C₂×D₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

#390

yes

characteristic

122

C₄×C₈₉

C₂×#102

yes

characteristic

123

C₄×C₈₉

#459

yes

characteristic

124

C₄×C₈₉

#460

yes

characteristic

125

Dic₈₉

—

126

#13261

—

maximal, Sylow

127

C₂×C₈₉

—

128

C₂×C₈₉

—

129

C₂×C₈₉

#1982

yes

characteristic

130

C₂×C₈₉

#2213

yes

—

131

D₈₉

—

132

C₂×#493

—

133

C₂×#364

D₈₉

yes

characteristic, complemented

134

C₂×#361

—

135

#2140

—

136

#1772

—

137

C₈₉

#13261

yes

characteristic, complemented, Sylow

138

C₂²×D₈

—

139

C₂²×D₈

—

178

—

140

C₂×#127

—

178

—

141

C₂×M₃₂

C₂×D₈₉

yes

—

142

#493

—

143

#493

—

178

—

144

C₂×#108

—

145

#427

—

146

#405

—

178

—

147

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

148

#364

—

149

#361

—

178

—

150

#357

—

178

—

151

#339

—

178

—

152

C₂²×D₄

—

356

—

153

C₂²×D₄

—

178

—

154

C₂×D₈

—

155

C₂×D₈

—

356

—

156

C₂×D₈

—

356

—

157

C₂×D₈

—

356

—

158

C₂×D₈

—

178

—

159

C₂×D₈

—

178

—

160

C₂×D₈

—

178

—

161

C₂×D₈

—

178

—

162

C₂×D₈

—

178

—

163

C₂×D₈

—

178

—

164

C₂×M₁₆

—

178

—

165

C₂²×C₈

D₃₅₆

yes

characteristic

166

C₂²×C₈

C₂²×D₈₉

yes

characteristic

167

#127

—

356

—

168

#127

—

178

—

169

#117

—

178

—

170

C₂×C₄²

D₃₅₆

yes

characteristic

171

M₃₂

—

172

M₃₂

—

173

C₂×C₁₆

—

174

#108

—

175

#108

—

178

—

176

#107

—

177

#106

—

178

—

178

#97

—

356

—

179

C₄×C₈

—

356

—

180

C₄×C₈

C₄×D₈₉

yes

—

181

C₄×C₈

C₂²⋊D₈₉

yes

—

182

C₂⁴

—

356

—

183

C₂×D₄

—

356

—

184

C₂×D₄

—

356

—

185

C₂×D₄

—

356

—

186

C₂×D₄

—

356

—

187

C₂×D₄

—

356

—

188

C₂×D₄

—

356

—

189

C₂×D₄

—

178

—

190

C₂×D₄

—

712

—

191

C₂²×C₄

—

192

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

193

D₈

—

356

—

194

D₈

—

356

—

195

D₈

—

356

—

196

D₈

—

356

—

197

D₈

—

178

—

198

D₈

—

178

—

199

M₁₆

—

356

—

200

M₁₆

—

178

—

201

C₂×C₈

—

356

—

202

C₂×C₈

#13083551

yes

—

203

C₂×C₈

D₇₁₂

yes

characteristic

204

C₂×C₈

D₇₁₂

yes

characteristic

205

C₂×C₈

#13083563

yes

—

206

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

207

C₂×C₈

D₄×D₈₉

yes

characteristic

208

C₂×C₈

D₄×D₈₉

yes

characteristic

209

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

210

C₂×C₈

#13083575

yes

characteristic

211

C₂×C₈

#13083575

yes

characteristic

212

C₄⋊C₄

—

178

—

213

C₂²⋊C₄

—

356

—

214

C₄²

—

215

C₄²

—

356

—

216

C₄²

#13083551

yes

—

217

C₁₆

—

218

C₂³

—

356

—

219

C₂³

—

712

—

220

C₂³

—

712

—

221

C₂³

—

712

—

222

C₂³

#15668040

yes

characteristic

223

D₄

—

356

—

224

D₄

—

356

—

225

D₄

—

712

—

226

D₄

—

712

—

227

D₄

—

712

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

356

—

231

C₂×C₄

C₂×#13083551

yes

characteristic

232

C₂×C₄

#15667987

yes

characteristic

233

C₂×C₄

#15667987

yes

characteristic

234

C₂×C₄

C₂×D₇₁₂

yes

characteristic

235

C₂×C₄

C₂×#13083563

yes

characteristic

236

C₂×C₄

#15668040

yes

characteristic

237

C₈

—

356

—

238

C₈

#15667934

yes

—

239

C₈

#15667934

yes

—

240

C₈

#15667974

yes

characteristic

241

C₈

#15667974

yes

characteristic

242

C₈

#15668001

yes

characteristic

243

C₈

#15668008

yes

characteristic

244

C₂²

—

245

C₂²

—

1424

—

246

C₂²

—

1424

—

247

C₂²

—

712

—

248

C₂²

—

712

—

249

C₂²

#19151604

yes

characteristic

250

C₂²

#19151794

yes

characteristic

251

C₂²

#19151799

yes

characteristic

252

C₄

—

253

C₄

—

712

—

254

C₄

#19151499

yes

characteristic

255

C₄

C₂×#15667934

yes

characteristic

256

C₄

#19151794

yes

characteristic

257

C₄

#19151799

yes

characteristic

258

C₂

—

259

C₂

—

260

C₂

—

1424

—

261

C₂

#26021178

yes

characteristic

262

C₂

#26022329

yes

—

	subgroup	G/H
center	C₂²	#19151794
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×#364×C₈₉	C₂
socle	C₂²×C₈₉	#459
prime radical	C₂×#19151975	C₂
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#364	D₈₉
hypocenter	C₈₉	#13261
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#19151794

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×#364×C₈₉

C₂

C₂²×C₈₉

C₂

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

N	H ≅ G/N	type
2. C₂×#19151412	C₂	semidirect
3. #26021969	C₂	semidirect
4. #26020131	C₂	semidirect
5. C₂×#364×C₈₉	C₂	semidirect
10. #19151975	C₄	semidirect
37. #15667948	D₄	semidirect
38. #15667946	D₄	semidirect
133. C₂×#364	D₈₉	semidirect
137. C₈₉	#13261	semidirect

H ≅ G/N

type

2. C₂×#19151412

C₂

semidirect

3. #26021969

C₂

semidirect

4. #26020131

C₂

semidirect

5. C₂×#364×C₈₉

C₂

semidirect

10. #19151975

C₄

semidirect

37. #15667948

D₄

semidirect

38. #15667946

D₄

semidirect

133. C₂×#364

D₈₉

semidirect

137. C₈₉

#13261

semidirect

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

subgroup	index
C₂×#19151975	2
C₂×#19151412	2
#26021969	2
#26020131	2
C₂×#364×C₈₉	2
#13261	89

subgroup

index

C₂×#364×C₈₉

Subgroups — #36472936

Conjugacy classes of subgroups

Complements

Maximal subgroups