Group #29598526 — subgroups

Subgroups — #29598526

Order 15616.

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×#16840142	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839579	C₂	1	2	yes	maximal
3	#21447540	C₂	1	2	yes	maximal
4	#21445698	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#364	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₄₄	—	2	1	no	—
7	C₂²×Dic₂₄₄	C₂²	1	2	yes	—
8	C₂×#14519777	—	2	1	no	—
9	#16840142	—	2	2	no	—
10	#16840142	C₄	1	4	yes	complemented
11	C₂×#14519713	C₂²	1	1	yes	characteristic
12	#16839800	C₂²	1	1	yes	characteristic
13	#16839717	—	2	1	no	—
14	#16839579	—	2	4	no	—
15	#16839567	—	2	4	no	—
16	#16839522	—	2	1	no	—
17	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#364	—	2	2	no	—
20	C₂²×Dic₁₂₂	—	2	2	no	—
21	C₂×Dic₂₄₄	—	2	2	no	—
22	C₂×Dic₂₄₄	—	2	2	no	—
23	C₂×Dic₂₄₄	—	2	2	no	—
24	C₂×Dic₂₄₄	—	2	2	no	—
25	C₂×Dic₂₄₄	—	2	4	no	—
26	C₂×Dic₂₄₄	—	2	2	no	—
27	C₂×Dic₂₄₄	—	4	1	no	—
28	C₂×Dic₂₄₄	—	4	1	no	—
29	C₂×Dic₂₄₄	—	4	2	no	—
30	C₂×Dic₂₄₄	C₂×C₄	1	4	yes	—
31	C₂×#11758194	—	2	1	no	—
32	#14519777	—	2	4	no	—
33	#14519777	—	4	2	no	—
34	#14519736	—	2	1	no	—
35	C₂×C₄⋊Dic₆₁	—	4	2	no	—
36	#14519713	—	2	1	no	—
37	#14519713	D₄	1	2	yes	—
38	#14519711	D₄	1	2	yes	—
39	#14519709	—	2	1	no	—
40	#14519687	—	4	1	no	—
41	C₈×Dic₆₁	—	4	1	no	—
42	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
45	M₃₂×C₆₁	—	2	2	no	—
46	M₃₂×C₆₁	—	2	2	no	—
47	C₂×C₁₆×C₆₁	—	2	2	no	—
48	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₆₁	D₄	1	2	yes	—
50	C₂²×C₄×C₆₁	—	2	1	no	—
51	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₆₁	—	4	2	no	—
53	C₂×Dic₁₂₂	—	2	4	no	—
54	C₂×Dic₁₂₂	—	4	2	no	—
55	C₂×Dic₁₂₂	—	4	2	no	—
56	C₂×Dic₁₂₂	—	4	2	no	—
57	C₂×Dic₁₂₂	—	4	2	no	—
58	C₂×Dic₁₂₂	—	4	2	no	—
59	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
61	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
62	C₂×C₈×C₆₁	SD₁₆	1	2	yes	—
63	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
68	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
69	C₄²×C₆₁	—	2	1	no	—
70	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
71	C₂²⋊Dic₆₁	—	4	1	no	—
72	C₄⋊Dic₆₁	—	2	2	no	—
73	C₄⋊Dic₆₁	—	4	8	no	—
74	C₄×Dic₆₁	—	4	1	no	—
75	#11758194	—	2	2	no	—
76	#11758194	—	4	1	no	—
77	C₂×#92418	—	4	1	no	—
78	Dic₂₄₄	—	2	4	no	—
79	Dic₂₄₄	—	2	4	no	—
80	Dic₂₄₄	—	4	4	no	—
81	Dic₂₄₄	—	4	4	no	—
82	Dic₂₄₄	—	4	2	no	—
83	Dic₂₄₄	—	4	2	no	—
84	C₁₆×C₆₁	—	4	2	no	—
85	C₂³×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₆₁	—	2	4	no	—
87	C₂×C₄×C₆₁	—	2	2	no	—
88	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
90	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
91	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×Dic₆₁	—	4	4	no	—
95	C₂×Dic₆₁	—	4	2	no	—
96	C₂×Dic₆₁	—	8	2	no	—
97	C₂×Dic₆₁	—	8	2	no	—
98	Dic₁₂₂	—	4	4	no	—
99	Dic₁₂₂	—	4	4	no	—
100	Dic₁₂₂	—	8	2	no	—
101	Dic₁₂₂	—	8	2	no	—
102	C₈×C₆₁	#102	1	2	yes	—
103	C₈×C₆₁	#102	1	2	yes	—
104	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
105	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
106	C₈×C₆₁	#124	1	1	yes	characteristic
107	C₈×C₆₁	#127	1	1	yes	characteristic
108	#92418	—	4	2	no	—
109	#13262	—	61	1	no	maximal, Sylow
110	C₂²×C₆₁	—	2	2	no	—
111	C₂²×C₆₁	#418	1	1	yes	characteristic
112	C₂²×C₆₁	#459	1	1	yes	characteristic
113	C₂²×C₆₁	#460	1	1	yes	characteristic
114	C₄×C₆₁	—	2	4	no	—
115	C₄×C₆₁	#390	1	1	yes	characteristic
116	C₄×C₆₁	C₂×#102	1	1	yes	characteristic
117	C₄×C₆₁	#459	1	1	yes	characteristic
118	C₄×C₆₁	#460	1	1	yes	characteristic
119	Dic₆₁	—	8	2	no	—
120	Dic₆₁	—	8	4	no	—
121	C₂×#494	—	61	1	no	—
122	C₂×#364	D₆₁	1	1	yes	characteristic
123	C₂×#362	—	61	2	no	—
124	#2141	—	61	2	no	—
125	#1772	—	61	1	no	—
126	C₂×C₆₁	—	2	1	no	—
127	C₂×C₆₁	—	2	1	no	—
128	C₂×C₆₁	#1982	1	1	yes	characteristic
129	C₂×C₆₁	#2214	1	2	yes	—
130	C₂²×Q₁₆	—	61	2	no	—
131	C₂²×Q₁₆	—	122	1	no	—
132	C₂×C₄⋊Q₈	—	122	1	no	—
133	C₂×M₃₂	C₂×D₆₁	1	2	yes	—
134	#494	—	61	4	no	—
135	#494	—	122	2	no	—
136	C₂×#108	—	61	1	no	—
137	#427	—	61	1	no	—
138	#405	—	122	1	no	—
139	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
140	#364	—	2	2	no	—
141	#362	—	122	4	no	—
142	#358	—	122	4	no	—
143	#339	—	122	1	no	—
144	C₆₁	#13262	1	1	yes	characteristic, complemented, Sylow
145	C₂²×Q₈	—	122	2	no	—
146	C₂×Q₁₆	—	61	4	no	—
147	C₂×Q₁₆	—	122	4	no	—
148	C₂×Q₁₆	—	122	2	no	—
149	C₂×Q₁₆	—	122	2	no	—
150	C₂×Q₁₆	—	122	2	no	—
151	C₂×Q₁₆	—	122	2	no	—
152	C₂×Q₁₆	—	122	2	no	—
153	C₂×Q₁₆	—	244	2	no	—
154	C₂×Q₁₆	—	244	1	no	—
155	C₂×Q₁₆	—	244	1	no	—
156	C₂×M₁₆	—	122	1	no	—
157	C₂²×C₈	D₂₄₄	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
159	C₄⋊Q₈	—	122	4	no	—
160	C₄⋊Q₈	—	244	2	no	—
161	#117	—	122	1	no	—
162	C₂×C₄⋊C₄	—	244	2	no	—
163	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
164	M₃₂	—	2	2	no	—
165	M₃₂	—	2	2	no	—
166	C₂×C₁₆	—	2	2	no	—
167	#108	—	61	2	no	—
168	#108	—	122	1	no	—
169	#107	—	61	2	no	—
170	#106	—	122	1	no	—
171	#97	—	244	1	no	—
172	C₄×C₈	—	244	1	no	—
173	C₄×C₈	C₄×D₆₁	1	2	yes	—
174	C₄×C₈	C₂²⋊D₆₁	1	2	yes	—
175	C₂×Q₈	—	122	4	no	—
176	C₂×Q₈	—	244	2	no	—
177	C₂×Q₈	—	244	2	no	—
178	C₂×Q₈	—	244	2	no	—
179	C₂×Q₈	—	244	2	no	—
180	C₂×Q₈	—	244	2	no	—
181	C₂²×C₄	—	2	1	no	—
182	C₂²×C₄	—	244	2	no	—
183	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
184	Q₁₆	—	122	4	no	—
185	Q₁₆	—	122	4	no	—
186	Q₁₆	—	244	4	no	—
187	Q₁₆	—	244	4	no	—
188	Q₁₆	—	244	2	no	—
189	Q₁₆	—	244	2	no	—
190	M₁₆	—	122	2	no	—
191	M₁₆	—	244	1	no	—
192	C₂×C₈	—	244	1	no	—
193	C₂×C₈	#11758190	1	2	yes	—
194	C₂×C₈	D₄₈₈	1	1	yes	characteristic
195	C₂×C₈	D₄₈₈	1	1	yes	characteristic
196	C₂×C₈	#11758198	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
198	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
199	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
200	C₂×C₈	#11758226	1	1	yes	characteristic
201	C₂×C₈	#11758226	1	1	yes	characteristic
202	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
203	C₄⋊C₄	—	122	2	no	—
204	C₄⋊C₄	—	244	8	no	—
205	C₂²⋊C₄	—	244	1	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	244	1	no	—
208	C₄²	#11758198	1	2	yes	—
209	C₁₆	—	4	2	no	—
210	C₂³	#14519805	1	1	yes	characteristic
211	Q₈	—	488	2	no	—
212	Q₈	—	488	2	no	—
213	Q₈	—	244	4	no	—
214	Q₈	—	244	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	488	2	no	—
218	C₂×C₄	—	488	2	no	—
219	C₂×C₄	—	244	2	no	—
220	C₂×C₄	—	244	4	no	—
221	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
222	C₂×C₄	#14519752	1	1	yes	characteristic
223	C₂×C₄	#14519752	1	1	yes	characteristic
224	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
225	C₂×C₄	C₂×#11758190	1	1	yes	characteristic
226	C₂×C₄	#14519805	1	1	yes	characteristic
227	C₈	—	244	2	no	—
228	C₈	#14519699	1	2	yes	—
229	C₈	#14519699	1	2	yes	—
230	C₈	#14519739	1	1	yes	characteristic
231	C₈	#14519739	1	1	yes	characteristic
232	C₈	#14519766	1	1	yes	characteristic
233	C₈	#14519773	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	#16839768	1	1	yes	characteristic
236	C₂²	#16839958	1	1	yes	characteristic
237	C₂²	#16839963	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	488	4	no	—
240	C₄	—	488	2	no	—
241	C₄	#16839663	1	1	yes	characteristic
242	C₄	C₂×#14519699	1	1	yes	characteristic
243	C₄	#16839958	1	1	yes	characteristic
244	C₄	#16839963	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	#21446745	1	1	yes	characteristic
248	C₂	#21447901	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16840142

C₂

yes

maximal, characteristic

C₂×#16839579

C₂

yes

maximal

#21447540

C₂

yes

maximal

#21445698

C₂

yes

maximal, characteristic

C₂×C₆₁×#364

C₂

yes

maximal, characteristic

C₂²×Dic₂₄₄

—

C₂²×Dic₂₄₄

C₂²

yes

—

C₂×#14519777

—

#16840142

—

#16840142

C₄

yes

complemented

C₂×#14519713

C₂²

yes

characteristic

#16839800

C₂²

yes

—

—

—

—

C₂×M₃₂×C₆₁

C₂²

yes

—

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₆₁×#364

—

C₂²×Dic₁₂₂

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

C₂×C₄

yes

—

—

—

—

—

C₂×C₄⋊Dic₆₁

—

#14519713

—

#14519713

D₄

yes

—

#14519711

D₄

yes

—

#14519709

—

#14519687

—

C₈×Dic₆₁

—

C₂²×C₈×C₆₁

D₄

yes

characteristic

C₂²×C₈×C₆₁

C₂³

yes

characteristic

C₂×C₄²×C₆₁

D₄

yes

characteristic

M₃₂×C₆₁

—

M₃₂×C₆₁

—

C₂×C₁₆×C₆₁

—

C₄×C₈×C₆₁

C₂×C₄

yes

—

C₄×C₈×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×Dic₆₁

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

—

C₂×C₈×C₆₁

D₈

yes

characteristic

C₂×C₈×C₆₁

D₈

yes

characteristic

C₂×C₈×C₆₁

SD₁₆

yes

—

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

C₂×C₈×C₆₁

yes

C₂×C₈×C₆₁

yes

C₄²×C₆₁

—

C₄²×C₆₁

C₂²⋊C₄

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758194

—

#11758194

—

C₂×#92418

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

Dic₂₄₄

—

C₁₆×C₆₁

—

C₂³×C₆₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₂²⋊C₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

C₂×D₈

yes

characteristic

C₂×C₄×C₆₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₁

AGL(1,ℤ/8)

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

100

Dic₁₂₂

—

101

Dic₁₂₂

—

102

C₈×C₆₁

#102

yes

—

103

C₈×C₆₁

#102

yes

—

104

C₈×C₆₁

C₄×D₄

yes

characteristic

105

C₈×C₆₁

C₄×D₄

yes

characteristic

106

C₈×C₆₁

#124

yes

characteristic

107

C₈×C₆₁

#127

yes

characteristic

108

#92418

—

109

#13262

—

maximal, Sylow

110

C₂²×C₆₁

—

111

C₂²×C₆₁

#418

yes

characteristic

112

C₂²×C₆₁

#459

yes

characteristic

113

C₂²×C₆₁

#460

yes

characteristic

114

C₄×C₆₁

—

115

C₄×C₆₁

#390

yes

characteristic

116

C₄×C₆₁

C₂×#102

yes

characteristic

117

C₄×C₆₁

#459

yes

characteristic

118

C₄×C₆₁

#460

yes

characteristic

119

Dic₆₁

—

120

Dic₆₁

—

121

C₂×#494

—

122

C₂×#364

D₆₁

yes

characteristic

123

C₂×#362

—

124

#2141

—

125

#1772

—

126

C₂×C₆₁

—

127

C₂×C₆₁

—

128

C₂×C₆₁

#1982

yes

characteristic

129

C₂×C₆₁

#2214

yes

—

130

C₂²×Q₁₆

—

131

C₂²×Q₁₆

—

122

—

132

C₂×C₄⋊Q₈

—

122

—

133

C₂×M₃₂

C₂×D₆₁

yes

—

134

#494

—

135

#494

—

122

—

136

C₂×#108

—

137

#427

—

138

#405

—

122

—

139

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

140

#364

—

141

#362

—

122

—

142

#358

—

122

—

143

#339

—

122

—

144

C₆₁

#13262

yes

characteristic, complemented, Sylow

145

C₂²×Q₈

—

122

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

122

—

148

C₂×Q₁₆

—

122

—

149

C₂×Q₁₆

—

122

—

150

C₂×Q₁₆

—

122

—

151

C₂×Q₁₆

—

122

—

152

C₂×Q₁₆

—

122

—

153

C₂×Q₁₆

—

244

—

154

C₂×Q₁₆

—

244

—

155

C₂×Q₁₆

—

244

—

156

C₂×M₁₆

—

122

—

157

C₂²×C₈

D₂₄₄

yes

characteristic

158

C₂²×C₈

C₂²×D₆₁

yes

characteristic

159

C₄⋊Q₈

—

122

—

160

C₄⋊Q₈

—

244

—

161

#117

—

122

—

162

C₂×C₄⋊C₄

—

244

—

163

C₂×C₄²

D₂₄₄

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

122

—

169

#107

—

170

#106

—

122

—

171

#97

—

244

—

172

C₄×C₈

—

244

—

173

C₄×C₈

C₄×D₆₁

yes

—

174

C₄×C₈

C₂²⋊D₆₁

yes

—

175

C₂×Q₈

—

122

—

176

C₂×Q₈

—

244

—

177

C₂×Q₈

—

244

—

178

C₂×Q₈

—

244

—

179

C₂×Q₈

—

244

—

180

C₂×Q₈

—

244

—

181

C₂²×C₄

—

182

C₂²×C₄

—

244

—

183

C₂²×C₄

C₂×D₂₄₄

yes

characteristic

184

Q₁₆

—

122

—

185

Q₁₆

—

122

—

186

Q₁₆

—

244

—

187

Q₁₆

—

244

—

188

Q₁₆

—

244

—

189

Q₁₆

—

244

—

190

M₁₆

—

122

—

191

M₁₆

—

244

—

192

C₂×C₈

—

244

—

193

C₂×C₈

#11758190

yes

—

194

C₂×C₈

D₄₈₈

yes

characteristic

195

C₂×C₈

D₄₈₈

yes

characteristic

196

C₂×C₈

#11758198

yes

—

197

C₂×C₈

C₂×C₄×D₆₁

yes

characteristic

198

C₂×C₈

D₄×D₆₁

yes

characteristic

199

C₂×C₈

D₄×D₆₁

yes

characteristic

200

C₂×C₈

#11758226

yes

characteristic

201

C₂×C₈

#11758226

yes

characteristic

202

C₂×C₈

C₂×C₂²⋊D₆₁

yes

characteristic

203

C₄⋊C₄

—

122

—

204

C₄⋊C₄

—

244

—

205

C₂²⋊C₄

—

244

—

206

C₄²

—

207

C₄²

—

244

—

208

C₄²

#11758198

yes

—

209

C₁₆

—

210

C₂³

#14519805

yes

characteristic

211

Q₈

—

488

—

212

Q₈

—

488

—

213

Q₈

—

244

—

214

Q₈

—

244

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

488

—

218

C₂×C₄

—

488

—

219

C₂×C₄

—

244

—

220

C₂×C₄

—

244

—

221

C₂×C₄

C₂×#11758198

yes

characteristic

222

C₂×C₄

#14519752

yes

characteristic

223

C₂×C₄

#14519752

yes

characteristic

224

C₂×C₄

C₂×D₄₈₈

yes

characteristic

225

C₂×C₄

C₂×#11758190

yes

characteristic

226

C₂×C₄

#14519805

yes

characteristic

227

C₈

—

244

—

228

C₈

#14519699

yes

—

229

C₈

#14519699

yes

—

230

C₈

#14519739

yes

characteristic

231

C₈

#14519739

yes

characteristic

232

C₈

#14519766

yes

characteristic

233

C₈

#14519773

yes

characteristic

234

C₂²

—

235

C₂²

#16839768

yes

characteristic

236

C₂²

#16839958

yes

characteristic

237

C₂²

#16839963

yes

characteristic

238

C₄

—

239

C₄

—

488

—

240

C₄

—

488

—

241

C₄

#16839663

yes

characteristic

242

C₄

C₂×#14519699

yes

characteristic

243

C₄

#16839958

yes

characteristic

244

C₄

#16839963

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

#21446745

yes

characteristic

248

C₂

#21447901

yes

—

	subgroup	G/H
center	C₂²	#16839958
commutator	C₂×C₈×C₆₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₁
Fitting	C₂×C₆₁×#364	C₂
socle	C₂²×C₆₁	#459
prime radical	C₂³×C₆₁	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₆₁	C₂³
hypercenter	C₂×#364	D₆₁
hypocenter	C₆₁	#13262
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

subgroup

G/H

center

C₂²

#16839958

commutator

C₂×C₈×C₆₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₁

Fitting

C₂×C₆₁×#364

C₂

C₂²×C₆₁

C₂³×C₆₁

C₂²×C₈×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

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

N	H ≅ G/N	type
10. #16840142	C₄	semidirect
144. C₆₁	#13262	semidirect

H ≅ G/N

type

10. #16840142

C₄

semidirect

144. C₆₁

#13262

semidirect

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

subgroup	index
C₂×#16840142	2
C₂×#16839579	2
#21447540	2
#21445698	2
C₂×C₆₁×#364	2
#13262	61

subgroup

index

C₂×C₆₁×#364

Subgroups — #29598526

Conjugacy classes of subgroups

Complements

Maximal subgroups