Group #31915418 — subgroups

Subgroups — #31915418

Order 18176.

314 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17985816	C₂	1	1	yes	maximal, characteristic
2	#22590059	C₂	1	1	yes	maximal, characteristic
3	C₂×#17985776	C₂	1	1	yes	maximal, characteristic
4	#22589209	C₂	1	1	yes	maximal, characteristic
5	#22589094	C₂	1	1	yes	maximal, characteristic
6	#22586438	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1386	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₂₈₄	C₂²	1	1	yes	characteristic
9	C₂×#14556068	C₂²	1	1	yes	characteristic
10	C₂×#14556064	C₂²	1	1	yes	characteristic
11	#17986026	—	2	1	no	—
12	C₂×#14556051	—	2	1	no	—
13	C₂×#14556038	C₂²	1	1	yes	characteristic
14	#17985904	—	2	1	no	—
15	#17985816	—	2	2	no	—
16	#17985802	C₄	1	4	yes	complemented
17	#17985776	—	2	2	no	—
18	#17985758	—	2	1	no	—
19	C₂×M₃₂×C₇₁	C₂²	1	1	yes	characteristic
20	#427×C₇₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₇₁	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₄₂	—	2	1	no	—
23	C₂×Dic₂₈₄	—	2	1	no	—
24	C₂×Dic₂₈₄	—	2	1	no	—
25	C₂×Dic₂₈₄	—	2	1	no	—
26	C₂×Dic₂₈₄	—	2	1	no	—
27	C₂×Dic₂₈₄	—	2	1	no	—
28	C₂×Dic₂₈₄	C₂×C₄	1	2	yes	—
29	C₂×#11765849	—	2	1	no	—
30	C₂²×C₇₁⋊C₈	D₄	1	1	yes	characteristic
31	C₂×C₄×Dic₇₁	D₄	1	1	yes	characteristic
32	#14556068	—	2	1	no	—
33	#14556068	—	2	1	no	—
34	C₂×C₇₁⋊C₁₆	C₂×C₄	1	2	yes	—
35	#14556064	—	2	1	no	—
36	#14556064	—	2	1	no	—
37	C₄⋊(C₇₁⋊C₈)	—	4	2	no	—
38	#14556051	—	4	2	no	—
39	#14556038	—	2	1	no	—
40	#14556038	—	2	1	no	—
41	C₇₁⋊#95	—	4	2	no	—
42	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
43	#117×C₇₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
45	M₃₂×C₇₁	—	2	1	no	—
46	M₃₂×C₇₁	D₄	1	2	yes	—
47	C₂×C₁₆×C₇₁	—	2	1	no	—
48	#107×C₇₁	C₂×C₄	1	2	yes	—
49	#106×C₇₁	—	2	1	no	—
50	#106×C₇₁	—	2	1	no	—
51	#106×C₇₁	—	2	1	no	—
52	C₂×Dic₁₄₂	—	2	2	no	—
53	C₂×Dic₁₄₂	—	4	1	no	—
54	C₂×Dic₁₄₂	—	4	1	no	—
55	C₂×Dic₁₄₂	—	4	1	no	—
56	C₂×Dic₁₄₂	—	4	1	no	—
57	C₂×Dic₁₄₂	—	4	1	no	—
58	C₂²×Dic₇₁	—	2	1	no	—
59	C₂²×Dic₇₁	—	4	1	no	—
60	Dic₂₈₄	—	2	2	no	—
61	Dic₂₈₄	—	2	2	no	—
62	Dic₂₈₄	—	4	1	no	—
63	Dic₂₈₄	—	4	1	no	—
64	#11765849	—	4	1	no	—
65	#11765849	—	4	1	no	—
66	C₂×C₇₁⋊C₈	—	2	1	no	—
67	C₂×C₇₁⋊C₈	—	2	1	no	—
68	C₂×C₇₁⋊C₈	—	2	1	no	—
69	C₂×C₇₁⋊C₈	—	4	1	no	—
70	C₄×Dic₇₁	—	2	1	no	—
71	C₄×Dic₇₁	—	2	1	no	—
72	C₇₁⋊C₁₆	—	2	2	no	—
73	C₂²×C₄×C₇₁	—	4	1	no	—
74	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
78	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
79	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
80	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
81	C₄⋊C₄×C₇₁	—	2	2	no	—
82	C₄⋊C₄×C₇₁	—	4	1	no	—
83	C₄⋊C₄×C₇₁	—	4	1	no	—
84	C₂²⋊C₄×C₇₁	—	4	1	no	—
85	C₄²×C₇₁	—	4	1	no	—
86	C₁₆×C₇₁	—	2	2	no	—
87	C₂³×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₇₁	—	4	2	no	—
89	C₂×C₄×C₇₁	—	8	2	no	—
90	C₂×C₄×C₇₁	—	8	1	no	—
91	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
93	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
94	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
97	C₂×Dic₇₁	—	4	2	no	—
98	C₂×Dic₇₁	—	4	2	no	—
99	C₂×Dic₇₁	—	4	1	no	—
100	C₂×Dic₇₁	—	8	1	no	—
101	C₂×Dic₇₁	—	8	1	no	—
102	Dic₁₄₂	—	4	2	no	—
103	Dic₁₄₂	—	4	2	no	—
104	Dic₁₄₂	—	8	1	no	—
105	Dic₁₄₂	—	8	1	no	—
106	C₈×C₇₁	#117	1	1	yes	characteristic
107	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
108	C₈×C₇₁	#123	1	1	yes	characteristic
109	C₈×C₇₁	#126	1	1	yes	characteristic
110	C₇₁⋊C₈	—	4	1	no	—
111	C₇₁⋊C₈	—	8	1	no	—
112	C₂²×C₇₁	—	2	2	no	—
113	C₂²×C₇₁	#442	1	1	yes	characteristic
114	C₂²×C₇₁	#468	1	1	yes	characteristic
115	C₂²×C₇₁	#490	1	1	yes	characteristic
116	C₄×C₇₁	—	8	2	no	—
117	C₄×C₇₁	—	16	1	no	—
118	C₄×C₇₁	#388	1	1	yes	characteristic
119	C₄×C₇₁	#440	1	1	yes	characteristic
120	C₄×C₇₁	#469	1	1	yes	characteristic
121	C₄×C₇₁	#489	1	1	yes	characteristic
122	Dic₇₁	—	8	1	no	—
123	Dic₇₁	—	8	2	no	—
124	#13154	—	71	1	no	maximal, Sylow
125	C₂×C₇₁	—	2	1	no	—
126	C₂×C₇₁	—	2	1	no	—
127	C₂×C₇₁	#1936	1	1	yes	characteristic
128	C₂×C₇₁	#2180	1	2	yes	—
129	C₂×#362	—	71	1	no	—
130	#2141	—	71	1	no	—
131	C₂×#347	—	71	1	no	—
132	#1971	—	71	1	no	—
133	#1946	—	71	1	no	—
134	#1386	D₇₁	1	1	yes	characteristic
135	#1383	—	71	1	no	—
136	C₇₁	#13154	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₁₆	—	71	1	no	—
138	C₂×M₃₂	—	71	1	no	—
139	C₂×M₃₂	C₂×D₇₁	1	1	yes	characteristic
140	C₂×#108	—	71	1	no	—
141	#427	C₂×D₇₁	1	1	yes	characteristic
142	C₂×#106	C₂×D₇₁	1	1	yes	characteristic
143	#424	—	142	1	no	—
144	C₂×#103	—	142	1	no	—
145	C₂×#97	—	71	1	no	—
146	#391	—	142	1	no	—
147	#362	—	142	2	no	—
148	#358	—	71	4	no	—
149	#347	—	142	2	no	—
150	#339	—	142	1	no	—
151	C₂²×Q₈	—	142	1	no	—
152	C₂×Q₁₆	—	71	2	no	—
153	C₂×Q₁₆	—	142	1	no	—
154	C₂×Q₁₆	—	142	1	no	—
155	C₂×Q₁₆	—	142	1	no	—
156	C₂×Q₁₆	—	142	1	no	—
157	C₂×Q₁₆	—	142	1	no	—
158	C₂×M₁₆	—	142	1	no	—
159	C₂²×C₈	—	71	1	no	—
160	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
161	#117	—	2	1	no	—
162	C₂×C₄⋊C₄	—	2	1	no	—
163	C₂×C₄²	—	71	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	—	142	1	no	—
166	M₃₂	—	142	1	no	—
167	M₃₂	D₂₈₄	1	2	yes	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	71	2	no	—
170	#108	—	142	1	no	—
171	#108	—	142	1	no	—
172	#107	C₄×D₇₁	1	2	yes	—
173	#106	—	2	1	no	—
174	#106	—	2	1	no	—
175	#106	—	2	1	no	—
176	C₄⋊C₈	—	284	2	no	—
177	#103	—	284	2	no	—
178	#97	—	142	1	no	—
179	#97	—	142	1	no	—
180	#95	—	284	2	no	—
181	C₂×Q₈	—	284	1	no	—
182	C₂×Q₈	—	284	1	no	—
183	C₂×Q₈	—	284	1	no	—
184	C₂×Q₈	—	284	1	no	—
185	C₂×Q₈	—	284	1	no	—
186	C₂×Q₈	—	142	2	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	284	1	no	—
189	C₂²×C₄	—	142	1	no	—
190	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
191	Q₁₆	—	284	1	no	—
192	Q₁₆	—	284	1	no	—
193	Q₁₆	—	142	2	no	—
194	Q₁₆	—	142	2	no	—
195	M₁₆	—	284	1	no	—
196	M₁₆	—	284	1	no	—
197	C₂×C₈	—	284	1	no	—
198	C₂×C₈	—	142	1	no	—
199	C₂×C₈	—	142	1	no	—
200	C₂×C₈	—	142	1	no	—
201	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
202	C₂×C₈	C₂×D₂₈₄	1	1	yes	characteristic
203	C₂×C₈	#11765864	1	1	yes	characteristic
204	C₂×C₈	#11765864	1	1	yes	characteristic
205	C₂×C₈	#11765865	1	1	yes	characteristic
206	C₂×C₈	#11765866	1	1	yes	characteristic
207	C₄⋊C₄	—	2	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	4	1	no	—
210	C₂²⋊C₄	—	4	1	no	—
211	C₄²	—	4	1	no	—
212	C₄²	—	142	1	no	—
213	C₄²	—	142	1	no	—
214	C₁₆	—	2	2	no	—
215	C₁₆	—	142	2	no	—
216	C₂³	#14556152	1	1	yes	characteristic
217	Q₈	—	284	2	no	—
218	Q₈	—	284	2	no	—
219	Q₈	—	568	1	no	—
220	Q₈	—	568	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	284	2	no	—
225	C₂×C₄	—	284	2	no	—
226	C₂×C₄	—	284	1	no	—
227	C₂×C₄	—	568	1	no	—
228	C₂×C₄	—	568	1	no	—
229	C₂×C₄	(C₂²⋊D₇₁)⋊C₄	1	1	yes	characteristic
230	C₂×C₄	#14556103	1	1	yes	characteristic
231	C₂×C₄	#14556114	1	1	yes	characteristic
232	C₂×C₄	#14556155	1	1	yes	characteristic
233	C₂×C₄	#14556155	1	1	yes	characteristic
234	C₂×C₄	#14556160	1	1	yes	characteristic
235	C₈	—	284	1	no	—
236	C₈	—	568	1	no	—
237	C₈	#14556086	1	1	yes	characteristic
238	C₈	C₄×D₂₈₄	1	1	yes	characteristic
239	C₈	#14556112	1	1	yes	characteristic
240	C₈	#14556123	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	#17986108	1	1	yes	characteristic
243	C₂²	#17986246	1	1	yes	characteristic
244	C₂²	#17986362	1	1	yes	characteristic
245	C₄	—	8	2	no	—
246	C₄	—	16	1	no	—
247	C₄	—	568	1	no	—
248	C₄	—	568	2	no	—
249	C₄	#17985891	1	1	yes	characteristic
250	C₄	#17986102	1	1	yes	characteristic
251	C₄	#17986253	1	1	yes	characteristic
252	C₄	#17986360	1	1	yes	characteristic
253	C₂	—	2	1	no	—
254	C₂	—	2	1	no	—
255	C₂	#22589038	1	1	yes	characteristic
256	C₂	#22590228	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17985816

C₂

yes

maximal, characteristic

#22590059

C₂

yes

maximal, characteristic

C₂×#17985776

C₂

yes

maximal, characteristic

#22589209

C₂

yes

maximal, characteristic

#22589094

C₂

yes

maximal, characteristic

#22586438

C₂

yes

maximal, characteristic

C₇₁×#1386

C₂

yes

maximal, characteristic

C₂²×Dic₂₈₄

C₂²

yes

characteristic

C₂×#14556068

C₂²

yes

characteristic

C₂×#14556064

C₂²

yes

—

—

C₂²

yes

—

—

C₄

yes

complemented

#17985776

—

#17985758

—

C₂×M₃₂×C₇₁

C₂²

yes

characteristic

#427×C₇₁

C₂²

yes

characteristic

C₂×#106×C₇₁

C₂²

yes

characteristic

C₂²×Dic₁₄₂

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂×C₄

yes

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

D₄

yes

characteristic

C₂×C₄×Dic₇₁

D₄

yes

characteristic

#14556068

—

#14556068

—

C₂×C₇₁⋊C₁₆

C₂×C₄

yes

—

#14556064

—

#14556064

—

C₄⋊(C₇₁⋊C₈)

—

#14556051

—

#14556038

—

#14556038

—

C₇₁⋊#95

—

C₂²×C₈×C₇₁

C₂³

yes

characteristic

#117×C₇₁

—

C₂×C₄⋊C₄×C₇₁

—

M₃₂×C₇₁

—

M₃₂×C₇₁

D₄

yes

—

C₂×C₁₆×C₇₁

—

#107×C₇₁

C₂×C₄

yes

—

#106×C₇₁

—

#106×C₇₁

—

#106×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₇₁⋊C₁₆

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₂×C₈×C₇₁

yes

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₁₆×C₇₁

—

C₂³×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₄×D₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

100

C₂×Dic₇₁

—

101

C₂×Dic₇₁

—

102

Dic₁₄₂

—

103

Dic₁₄₂

—

104

Dic₁₄₂

—

105

Dic₁₄₂

—

106

C₈×C₇₁

#117

yes

characteristic

107

C₈×C₇₁

C₄×D₄

yes

characteristic

108

C₈×C₇₁

#123

yes

characteristic

109

C₈×C₇₁

#126

yes

characteristic

110

C₇₁⋊C₈

—

111

C₇₁⋊C₈

—

112

C₂²×C₇₁

—

113

C₂²×C₇₁

#442

yes

characteristic

114

C₂²×C₇₁

#468

yes

characteristic

115

C₂²×C₇₁

#490

yes

characteristic

116

C₄×C₇₁

—

117

C₄×C₇₁

—

118

C₄×C₇₁

#388

yes

characteristic

119

C₄×C₇₁

#440

yes

characteristic

120

C₄×C₇₁

#469

yes

characteristic

121

C₄×C₇₁

#489

yes

characteristic

122

Dic₇₁

—

123

Dic₇₁

—

124

#13154

—

maximal, Sylow

125

C₂×C₇₁

—

126

C₂×C₇₁

—

127

C₂×C₇₁

#1936

yes

characteristic

128

C₂×C₇₁

#2180

yes

—

129

C₂×#362

—

130

#2141

—

131

C₂×#347

—

132

#1971

—

133

#1946

—

134

#1386

D₇₁

yes

characteristic

135

#1383

—

136

C₇₁

#13154

yes

characteristic, complemented, Sylow

137

C₂²×Q₁₆

—

138

C₂×M₃₂

—

139

C₂×M₃₂

C₂×D₇₁

yes

characteristic

140

C₂×#108

—

141

#427

C₂×D₇₁

yes

characteristic

142

C₂×#106

C₂×D₇₁

yes

characteristic

143

#424

—

142

—

144

C₂×#103

—

142

—

145

C₂×#97

—

146

#391

—

142

—

147

#362

—

142

—

148

#358

—

149

#347

—

142

—

150

#339

—

142

—

151

C₂²×Q₈

—

142

—

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

142

—

154

C₂×Q₁₆

—

142

—

155

C₂×Q₁₆

—

142

—

156

C₂×Q₁₆

—

142

—

157

C₂×Q₁₆

—

142

—

158

C₂×M₁₆

—

142

—

159

C₂²×C₈

—

160

C₂²×C₈

C₂²×D₇₁

yes

characteristic

161

#117

—

162

C₂×C₄⋊C₄

—

163

C₂×C₄²

—

164

M₃₂

—

165

M₃₂

—

142

—

166

M₃₂

—

142

—

167

M₃₂

D₂₈₄

yes

—

168

C₂×C₁₆

—

169

C₂×C₁₆

—

170

#108

—

142

—

171

#108

—

142

—

172

#107

C₄×D₇₁

yes

—

173

#106

—

174

#106

—

175

#106

—

176

C₄⋊C₈

—

284

—

177

#103

—

284

—

178

#97

—

142

—

179

#97

—

142

—

180

#95

—

284

—

181

C₂×Q₈

—

284

—

182

C₂×Q₈

—

284

—

183

C₂×Q₈

—

284

—

184

C₂×Q₈

—

284

—

185

C₂×Q₈

—

284

—

186

C₂×Q₈

—

142

—

187

C₂²×C₄

—

188

C₂²×C₄

—

284

—

189

C₂²×C₄

—

142

—

190

C₂²×C₄

D₄×D₇₁

yes

characteristic

191

Q₁₆

—

284

—

192

Q₁₆

—

284

—

193

Q₁₆

—

142

—

194

Q₁₆

—

142

—

195

M₁₆

—

284

—

196

M₁₆

—

284

—

197

C₂×C₈

—

284

—

198

C₂×C₈

—

142

—

199

C₂×C₈

—

142

—

200

C₂×C₈

—

142

—

201

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

202

C₂×C₈

C₂×D₂₈₄

yes

characteristic

203

C₂×C₈

#11765864

yes

characteristic

204

C₂×C₈

#11765864

yes

characteristic

205

C₂×C₈

#11765865

yes

characteristic

206

C₂×C₈

#11765866

yes

characteristic

207

C₄⋊C₄

—

208

C₄⋊C₄

—

209

C₄⋊C₄

—

210

C₂²⋊C₄

—

211

C₄²

—

212

C₄²

—

142

—

213

C₄²

—

142

—

214

C₁₆

—

215

C₁₆

—

142

—

216

C₂³

#14556152

yes

characteristic

217

Q₈

—

284

—

218

Q₈

—

284

—

219

Q₈

—

568

—

220

Q₈

—

568

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

284

—

225

C₂×C₄

—

284

—

226

C₂×C₄

—

284

—

227

C₂×C₄

—

568

—

228

C₂×C₄

—

568

—

229

C₂×C₄

(C₂²⋊D₇₁)⋊C₄

yes

characteristic

230

C₂×C₄

#14556103

yes

characteristic

231

C₂×C₄

#14556114

yes

characteristic

232

C₂×C₄

#14556155

yes

characteristic

233

C₂×C₄

#14556155

yes

characteristic

234

C₂×C₄

#14556160

yes

characteristic

235

C₈

—

284

—

236

C₈

—

568

—

237

C₈

#14556086

yes

characteristic

238

C₈

C₄×D₂₈₄

yes

characteristic

239

C₈

#14556112

yes

characteristic

240

C₈

#14556123

yes

characteristic

241

C₂²

—

242

C₂²

#17986108

yes

characteristic

243

C₂²

#17986246

yes

characteristic

244

C₂²

#17986362

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

568

—

248

C₄

—

568

—

249

C₄

#17985891

yes

characteristic

250

C₄

#17986102

yes

characteristic

251

C₄

#17986253

yes

characteristic

252

C₄

#17986360

yes

characteristic

253

C₂

—

254

C₂

—

255

C₂

#22589038

yes

characteristic

256

C₂

#22590228

yes

—

	subgroup	G/H
center	C₂²	#17986108
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₁
Fitting	C₇₁×#1386	C₂
socle	C₂²×C₇₁	#442
prime radical	C₂³×C₇₁	AGL(1,ℤ/8)
cosocle	C₂²×C₈×C₇₁	C₂³
hypercenter	#1386	D₇₁
hypocenter	C₇₁	#13154
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

subgroup

G/H

center

C₂²

#17986108

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₁

Fitting

C₇₁×#1386

C₂

C₂²×C₇₁

C₂³×C₇₁

C₂²×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1386

N	H ≅ G/N	type
16. #17985802	C₄	semidirect
136. C₇₁	#13154	semidirect

H ≅ G/N

type

16. #17985802

C₄

semidirect

136. C₇₁

#13154

semidirect

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

subgroup	index
C₂×#17985816	2
#22590059	2
C₂×#17985776	2
#22589209	2
#22589094	2
#22586438	2
C₇₁×#1386	2
#13154	71

subgroup

index

C₇₁×#1386

Subgroups — #31915418

Conjugacy classes of subgroups

Complements

Maximal subgroups