Group #36472941 — subgroups

Subgroups — #36472941

Order 22784.

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

normal subgroups only

This group has 462 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×#19151978	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151415	C₂	1	2	yes	maximal
3	#26021973	C₂	1	2	yes	maximal
4	#26020131	C₂	1	1	yes	maximal, characteristic
5	C₂×#364×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₅₆	—	2	1	no	—
7	C₂²×Dic₃₅₆	C₂²	1	2	yes	—
8	C₂×#15668012	—	2	1	no	—
9	#19151978	—	2	2	no	—
10	#19151978	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	#19151415	—	2	4	no	—
15	#19151403	—	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×Dic₁₇₈	—	2	2	no	—
21	C₂×Dic₃₅₆	—	2	4	no	—
22	C₂×Dic₃₅₆	—	2	2	no	—
23	C₂×Dic₃₅₆	—	2	2	no	—
24	C₂×Dic₃₅₆	—	2	2	no	—
25	C₂×Dic₃₅₆	—	2	2	no	—
26	C₂×Dic₃₅₆	—	2	2	no	—
27	C₂×Dic₃₅₆	—	4	1	no	—
28	C₂×Dic₃₅₆	—	4	1	no	—
29	C₂×Dic₃₅₆	—	4	2	no	—
30	C₂×Dic₃₅₆	C₂×C₄	1	4	yes	—
31	C₂×#13083558	—	2	1	no	—
32	#15668012	—	2	4	no	—
33	#15668012	—	4	2	no	—
34	#15667971	—	2	1	no	—
35	C₂×C₄⋊Dic₈₉	—	4	2	no	—
36	#15667948	—	2	1	no	—
37	#15667948	D₄	1	2	yes	—
38	#15667946	D₄	1	2	yes	—
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	C₂×Dic₁₇₈	—	2	4	no	—
51	C₂×Dic₁₇₈	—	4	2	no	—
52	C₂×Dic₁₇₈	—	4	2	no	—
53	C₂×Dic₁₇₈	—	4	2	no	—
54	C₂×Dic₁₇₈	—	4	2	no	—
55	C₂×Dic₁₇₈	—	4	2	no	—
56	C₂²×Dic₈₉	—	4	2	no	—
57	Dic₃₅₆	—	2	4	no	—
58	Dic₃₅₆	—	2	4	no	—
59	Dic₃₅₆	—	4	4	no	—
60	Dic₃₅₆	—	4	4	no	—
61	Dic₃₅₆	—	4	2	no	—
62	Dic₃₅₆	—	4	2	no	—
63	#13083558	—	2	2	no	—
64	#13083558	—	4	1	no	—
65	C₂×#10623494	—	4	1	no	—
66	C₄⋊Dic₈₉	—	2	2	no	—
67	C₄⋊Dic₈₉	—	4	8	no	—
68	C₂²⋊Dic₈₉	—	4	1	no	—
69	C₄×Dic₈₉	—	4	1	no	—
70	C₂²×C₄×C₈₉	—	2	1	no	—
71	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
73	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
74	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
75	C₂×C₈×C₈₉	SD₁₆	1	2	yes	—
76	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₈₉	C₂×D₄	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	#41	1	1	yes	characteristic
81	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
82	C₄²×C₈₉	—	2	1	no	—
83	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
84	C₁₆×C₈₉	—	4	2	no	—
85	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₈₉	—	2	4	no	—
87	C₂×C₄×C₈₉	—	2	2	no	—
88	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
91	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×Dic₈₉	—	4	4	no	—
95	C₂×Dic₈₉	—	4	2	no	—
96	C₂×Dic₈₉	—	8	2	no	—
97	C₂×Dic₈₉	—	8	2	no	—
98	Dic₁₇₈	—	4	4	no	—
99	Dic₁₇₈	—	4	4	no	—
100	Dic₁₇₈	—	8	2	no	—
101	Dic₁₇₈	—	8	2	no	—
102	C₈×C₈₉	#102	1	2	yes	—
103	C₈×C₈₉	#102	1	2	yes	—
104	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
105	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
106	C₈×C₈₉	#124	1	1	yes	characteristic
107	C₈×C₈₉	#127	1	1	yes	characteristic
108	#10623494	—	4	2	no	—
109	C₂²×C₈₉	—	2	2	no	—
110	C₂²×C₈₉	#418	1	1	yes	characteristic
111	C₂²×C₈₉	#459	1	1	yes	characteristic
112	C₂²×C₈₉	#460	1	1	yes	characteristic
113	C₄×C₈₉	—	2	4	no	—
114	C₄×C₈₉	#390	1	1	yes	characteristic
115	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
116	C₄×C₈₉	#459	1	1	yes	characteristic
117	C₄×C₈₉	#460	1	1	yes	characteristic
118	Dic₈₉	—	8	2	no	—
119	Dic₈₉	—	8	4	no	—
120	#13262	—	89	1	no	maximal, Sylow
121	C₂×C₈₉	—	2	1	no	—
122	C₂×C₈₉	—	2	1	no	—
123	C₂×C₈₉	#1982	1	1	yes	characteristic
124	C₂×C₈₉	#2214	1	2	yes	—
125	C₂×#494	—	89	1	no	—
126	C₂×#364	D₈₉	1	1	yes	characteristic
127	C₂×#362	—	89	2	no	—
128	#2141	—	89	2	no	—
129	#1772	—	89	1	no	—
130	C₈₉	#13262	1	1	yes	characteristic, complemented, Sylow
131	C₂²×Q₁₆	—	89	2	no	—
132	C₂²×Q₁₆	—	178	1	no	—
133	C₂×C₄⋊Q₈	—	178	1	no	—
134	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
135	#494	—	89	4	no	—
136	#494	—	178	2	no	—
137	C₂×#108	—	89	1	no	—
138	#427	—	89	1	no	—
139	#405	—	178	1	no	—
140	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
141	#364	—	2	2	no	—
142	#362	—	178	4	no	—
143	#358	—	178	4	no	—
144	#339	—	178	1	no	—
145	C₂²×Q₈	—	178	2	no	—
146	C₂×Q₁₆	—	89	4	no	—
147	C₂×Q₁₆	—	356	1	no	—
148	C₂×Q₁₆	—	356	1	no	—
149	C₂×Q₁₆	—	356	2	no	—
150	C₂×Q₁₆	—	178	4	no	—
151	C₂×Q₁₆	—	178	2	no	—
152	C₂×Q₁₆	—	178	2	no	—
153	C₂×Q₁₆	—	178	2	no	—
154	C₂×Q₁₆	—	178	2	no	—
155	C₂×Q₁₆	—	178	2	no	—
156	C₂×M₁₆	—	178	1	no	—
157	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
159	C₄⋊Q₈	—	356	2	no	—
160	C₄⋊Q₈	—	178	4	no	—
161	#117	—	178	1	no	—
162	C₂×C₄⋊C₄	—	356	2	no	—
163	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
164	M₃₂	—	2	2	no	—
165	M₃₂	—	2	2	no	—
166	C₂×C₁₆	—	2	2	no	—
167	#108	—	89	2	no	—
168	#108	—	178	1	no	—
169	#107	—	89	2	no	—
170	#106	—	178	1	no	—
171	#97	—	356	1	no	—
172	C₄×C₈	—	356	1	no	—
173	C₄×C₈	C₄×D₈₉	1	2	yes	—
174	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
175	C₂×Q₈	—	356	2	no	—
176	C₂×Q₈	—	356	2	no	—
177	C₂×Q₈	—	356	2	no	—
178	C₂×Q₈	—	356	2	no	—
179	C₂×Q₈	—	356	2	no	—
180	C₂×Q₈	—	178	4	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	356	2	no	—
183	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
184	Q₁₆	—	356	2	no	—
185	Q₁₆	—	356	2	no	—
186	Q₁₆	—	356	4	no	—
187	Q₁₆	—	356	4	no	—
188	Q₁₆	—	178	4	no	—
189	Q₁₆	—	178	4	no	—
190	M₁₆	—	356	1	no	—
191	M₁₆	—	178	2	no	—
192	C₂×C₈	—	356	1	no	—
193	C₂×C₈	#13083551	1	2	yes	—
194	C₂×C₈	D₇₁₂	1	1	yes	characteristic
195	C₂×C₈	D₇₁₂	1	1	yes	characteristic
196	C₂×C₈	#13083563	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
198	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
199	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
201	C₂×C₈	#13083575	1	1	yes	characteristic
202	C₂×C₈	#13083575	1	1	yes	characteristic
203	C₄⋊C₄	—	356	8	no	—
204	C₄⋊C₄	—	178	2	no	—
205	C₂²⋊C₄	—	356	1	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	356	1	no	—
208	C₄²	#13083551	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₂³	#15668040	1	1	yes	characteristic
211	Q₈	—	356	4	no	—
212	Q₈	—	356	4	no	—
213	Q₈	—	712	2	no	—
214	Q₈	—	712	2	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	356	2	no	—
218	C₂×C₄	—	356	4	no	—
219	C₂×C₄	—	712	2	no	—
220	C₂×C₄	—	712	2	no	—
221	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
222	C₂×C₄	#15667987	1	1	yes	characteristic
223	C₂×C₄	#15667987	1	1	yes	characteristic
224	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
225	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
226	C₂×C₄	#15668040	1	1	yes	characteristic
227	C₈	—	356	2	no	—
228	C₈	#15667934	1	2	yes	—
229	C₈	#15667934	1	2	yes	—
230	C₈	#15667974	1	1	yes	characteristic
231	C₈	#15667974	1	1	yes	characteristic
232	C₈	#15668001	1	1	yes	characteristic
233	C₈	#15668008	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	#19151604	1	1	yes	characteristic
236	C₂²	#19151794	1	1	yes	characteristic
237	C₂²	#19151799	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	712	4	no	—
240	C₄	—	712	2	no	—
241	C₄	#19151499	1	1	yes	characteristic
242	C₄	C₂×#15667934	1	1	yes	characteristic
243	C₄	#19151794	1	1	yes	characteristic
244	C₄	#19151799	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	#26021178	1	1	yes	characteristic
248	C₂	#26022334	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151978

C₂

yes

maximal, characteristic

C₂×#19151415

C₂

yes

maximal

#26021973

C₂

yes

maximal

#26020131

C₂

yes

maximal, characteristic

C₂×#364×C₈₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₅₆

—

C₂²×Dic₃₅₆

C₂²

yes

—

C₂×#15668012

—

#19151978

—

#19151978

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×Dic₁₇₈

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₈₉

—

#15667948

—

#15667948

D₄

yes

—

#15667946

D₄

yes

—

#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

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

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

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

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

100

Dic₁₇₈

—

101

Dic₁₇₈

—

102

C₈×C₈₉

#102

yes

—

103

C₈×C₈₉

#102

yes

—

104

C₈×C₈₉

C₄×D₄

yes

characteristic

105

C₈×C₈₉

C₄×D₄

yes

characteristic

106

C₈×C₈₉

#124

yes

characteristic

107

C₈×C₈₉

#127

yes

characteristic

108

#10623494

—

109

C₂²×C₈₉

—

110

C₂²×C₈₉

#418

yes

characteristic

111

C₂²×C₈₉

#459

yes

characteristic

112

C₂²×C₈₉

#460

yes

characteristic

113

C₄×C₈₉

—

114

C₄×C₈₉

#390

yes

characteristic

115

C₄×C₈₉

C₂×#102

yes

characteristic

116

C₄×C₈₉

#459

yes

characteristic

117

C₄×C₈₉

#460

yes

characteristic

118

Dic₈₉

—

119

Dic₈₉

—

120

#13262

—

maximal, Sylow

121

C₂×C₈₉

—

122

C₂×C₈₉

—

123

C₂×C₈₉

#1982

yes

characteristic

124

C₂×C₈₉

#2214

yes

—

125

C₂×#494

—

126

C₂×#364

D₈₉

yes

characteristic

127

C₂×#362

—

128

#2141

—

129

#1772

—

130

C₈₉

#13262

yes

characteristic, complemented, Sylow

131

C₂²×Q₁₆

—

132

C₂²×Q₁₆

—

178

—

133

C₂×C₄⋊Q₈

—

178

—

134

C₂×M₃₂

C₂×D₈₉

yes

—

135

#494

—

136

#494

—

178

—

137

C₂×#108

—

138

#427

—

139

#405

—

178

—

140

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

141

#364

—

142

#362

—

178

—

143

#358

—

178

—

144

#339

—

178

—

145

C₂²×Q₈

—

178

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

356

—

148

C₂×Q₁₆

—

356

—

149

C₂×Q₁₆

—

356

—

150

C₂×Q₁₆

—

178

—

151

C₂×Q₁₆

—

178

—

152

C₂×Q₁₆

—

178

—

153

C₂×Q₁₆

—

178

—

154

C₂×Q₁₆

—

178

—

155

C₂×Q₁₆

—

178

—

156

C₂×M₁₆

—

178

—

157

C₂²×C₈

D₃₅₆

yes

characteristic

158

C₂²×C₈

C₂²×D₈₉

yes

characteristic

159

C₄⋊Q₈

—

356

—

160

C₄⋊Q₈

—

178

—

161

#117

—

178

—

162

C₂×C₄⋊C₄

—

356

—

163

C₂×C₄²

D₃₅₆

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

178

—

169

#107

—

170

#106

—

178

—

171

#97

—

356

—

172

C₄×C₈

—

356

—

173

C₄×C₈

C₄×D₈₉

yes

—

174

C₄×C₈

C₂²⋊D₈₉

yes

—

175

C₂×Q₈

—

356

—

176

C₂×Q₈

—

356

—

177

C₂×Q₈

—

356

—

178

C₂×Q₈

—

356

—

179

C₂×Q₈

—

356

—

180

C₂×Q₈

—

178

—

181

C₂²×C₄

—

182

C₂²×C₄

—

356

—

183

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

184

Q₁₆

—

356

—

185

Q₁₆

—

356

—

186

Q₁₆

—

356

—

187

Q₁₆

—

356

—

188

Q₁₆

—

178

—

189

Q₁₆

—

178

—

190

M₁₆

—

356

—

191

M₁₆

—

178

—

192

C₂×C₈

—

356

—

193

C₂×C₈

#13083551

yes

—

194

C₂×C₈

D₇₁₂

yes

characteristic

195

C₂×C₈

D₇₁₂

yes

characteristic

196

C₂×C₈

#13083563

yes

—

197

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

198

C₂×C₈

D₄×D₈₉

yes

characteristic

199

C₂×C₈

D₄×D₈₉

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

201

C₂×C₈

#13083575

yes

characteristic

202

C₂×C₈

#13083575

yes

characteristic

203

C₄⋊C₄

—

356

—

204

C₄⋊C₄

—

178

—

205

C₂²⋊C₄

—

356

—

206

C₄²

—

207

C₄²

—

356

—

208

C₄²

#13083551

yes

—

209

C₁₆

—

210

C₂³

#15668040

yes

characteristic

211

Q₈

—

356

—

212

Q₈

—

356

—

213

Q₈

—

712

—

214

Q₈

—

712

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

356

—

218

C₂×C₄

—

356

—

219

C₂×C₄

—

712

—

220

C₂×C₄

—

712

—

221

C₂×C₄

C₂×#13083551

yes

characteristic

222

C₂×C₄

#15667987

yes

characteristic

223

C₂×C₄

#15667987

yes

characteristic

224

C₂×C₄

C₂×D₇₁₂

yes

characteristic

225

C₂×C₄

C₂×#13083563

yes

characteristic

226

C₂×C₄

#15668040

yes

characteristic

227

C₈

—

356

—

228

C₈

#15667934

yes

—

229

C₈

#15667934

yes

—

230

C₈

#15667974

yes

characteristic

231

C₈

#15667974

yes

characteristic

232

C₈

#15668001

yes

characteristic

233

C₈

#15668008

yes

characteristic

234

C₂²

—

235

C₂²

#19151604

yes

characteristic

236

C₂²

#19151794

yes

characteristic

237

C₂²

#19151799

yes

characteristic

238

C₄

—

239

C₄

—

712

—

240

C₄

—

712

—

241

C₄

#19151499

yes

characteristic

242

C₄

C₂×#15667934

yes

characteristic

243

C₄

#19151794

yes

characteristic

244

C₄

#19151799

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

#26021178

yes

characteristic

248

C₂

#26022334

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	C₂³×C₈₉	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#364	D₈₉
hypocenter	C₈₉	#13262
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

C₂³×C₈₉

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
10. #19151978	C₄	semidirect
130. C₈₉	#13262	semidirect

H ≅ G/N

type

10. #19151978

C₄

semidirect

130. C₈₉

#13262

semidirect

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

subgroup	index
C₂×#19151978	2
C₂×#19151415	2
#26021973	2
#26020131	2
C₂×#364×C₈₉	2
#13262	89

subgroup

index

C₂×#364×C₈₉

Subgroups — #36472941

Conjugacy classes of subgroups

Complements

Maximal subgroups