Group #31902252 — subgroups

Subgroups — #31902252

Order 18176.

294 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 93 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	#22589313	C₂	1	1	yes	maximal, characteristic
2	#22588515	C₂	1	1	yes	maximal, characteristic
3	#22587024	C₂	1	1	yes	maximal, characteristic
4	#22587020	C₂	1	1	yes	maximal, characteristic
5	#22586199	C₂	1	1	yes	maximal, characteristic
6	#22586199	C₂	1	1	yes	maximal, characteristic
7	C₇₁×#1281	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556128	C₂²	1	1	yes	characteristic
9	C₂×#14556064	—	2	1	no	—
10	C₂×#14556064	—	2	1	no	—
11	#17986023	C₂²	1	1	yes	characteristic
12	#17986023	C₂²	1	1	yes	characteristic
13	#17985865	C₂²	1	1	yes	characteristic
14	#17985762	—	2	1	no	—
15	#17985762	—	2	1	no	—
16	#17985747	—	2	2	no	—
17	#17985746	—	2	2	no	—
18	#431×C₇₁	C₂²	1	1	yes	characteristic
19	#431×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#97×C₇₁	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₄₂	—	2	1	no	—
22	C₂×#11765849	—	2	1	no	—
23	C₂×#11765849	—	2	1	no	—
24	#14556128	—	2	1	no	—
25	#14556128	—	2	1	no	—
26	#14556128	—	2	1	no	—
27	#14556128	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₇₁	—	2	1	no	—
29	C₂×C₄⋊Dic₇₁	—	2	1	no	—
30	C₂×C₄⋊Dic₇₁	—	2	1	no	—
31	#14556064	—	4	2	no	—
32	#14556064	—	4	2	no	—
33	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
34	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
35	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
36	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
37	C₇₁⋊#95	—	2	1	no	—
38	C₇₁⋊#95	—	2	1	no	—
39	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₁	—	2	1	no	—
43	C₄⋊C₈×C₇₁	—	2	1	no	—
44	C₂²⋊C₈×C₇₁	—	2	1	no	—
45	C₂²⋊C₈×C₇₁	—	2	1	no	—
46	#97×C₇₁	—	2	1	no	—
47	#97×C₇₁	—	2	1	no	—
48	C₄×C₈×C₇₁	—	2	1	no	—
49	C₄×C₈×C₇₁	—	2	1	no	—
50	C₂×Dic₁₄₂	—	2	2	no	—
51	C₂×Dic₁₄₂	—	4	1	no	—
52	C₂×Dic₁₄₂	—	8	2	no	—
53	C₂²×Dic₇₁	—	4	1	no	—
54	C₂²×Dic₇₁	—	4	1	no	—
55	#11765849	—	4	1	no	—
56	#11765849	—	4	1	no	—
57	#11765849	—	4	1	no	—
58	#11765849	—	4	1	no	—
59	C₂×C₇₁⋊C₈	—	4	1	no	—
60	C₂×C₇₁⋊C₈	—	4	1	no	—
61	C₄⋊Dic₇₁	—	2	2	no	—
62	C₄⋊Dic₇₁	—	2	2	no	—
63	C₄⋊Dic₇₁	—	4	1	no	—
64	C₄⋊Dic₇₁	—	4	1	no	—
65	C₄⋊Dic₇₁	—	4	1	no	—
66	C₄⋊Dic₇₁	—	4	1	no	—
67	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
69	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
70	C₂×C₈×C₇₁	—	2	1	no	—
71	C₂×C₈×C₇₁	—	2	1	no	—
72	C₂×C₈×C₇₁	—	2	1	no	—
73	C₂×C₈×C₇₁	—	2	1	no	—
74	C₂×C₈×C₇₁	—	4	1	no	—
75	C₂×C₈×C₇₁	—	4	1	no	—
76	C₂×C₈×C₇₁	SD₁₆	1	2	yes	—
77	C₂×C₈×C₇₁	Q₁₆	1	2	yes	—
78	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₇₁	#41	1	1	yes	characteristic
80	C₄²×C₇₁	#41	1	1	yes	characteristic
81	C₄²×C₇₁	#41	1	1	yes	characteristic
82	C₂³×C₇₁	#124	1	1	yes	characteristic
83	C₂×C₄×C₇₁	—	4	1	no	—
84	C₂×C₄×C₇₁	—	4	1	no	—
85	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
87	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
88	C₂×C₄×C₇₁	#123	1	1	yes	characteristic
89	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
90	C₂×C₄×C₇₁	#126	1	1	yes	characteristic
91	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
93	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
95	C₂×Dic₇₁	—	4	2	no	—
96	C₂×Dic₇₁	—	8	2	no	—
97	C₂×Dic₇₁	—	8	1	no	—
98	C₂×Dic₇₁	—	8	1	no	—
99	C₂×Dic₇₁	—	8	1	no	—
100	Dic₁₄₂	—	8	2	no	—
101	Dic₁₄₂	—	8	2	no	—
102	C₈×C₇₁	—	2	2	no	—
103	C₈×C₇₁	—	2	2	no	—
104	C₈×C₇₁	—	8	1	no	—
105	C₈×C₇₁	—	8	1	no	—
106	C₇₁⋊C₈	—	8	1	no	—
107	C₇₁⋊C₈	—	8	1	no	—
108	C₂²×C₇₁	—	2	1	no	—
109	C₂²×C₇₁	—	2	1	no	—
110	C₂²×C₇₁	#397	1	1	yes	characteristic
111	C₂²×C₇₁	#487	1	1	yes	characteristic
112	C₂²×C₇₁	#489	1	1	yes	characteristic
113	C₄×C₇₁	—	2	1	no	—
114	C₄×C₇₁	—	2	1	no	—
115	C₄×C₇₁	—	2	1	no	—
116	C₄×C₇₁	—	2	1	no	—
117	C₄×C₇₁	#460	1	1	yes	characteristic
118	C₄×C₇₁	#462	1	1	yes	characteristic
119	C₄×C₇₁	#483	1	1	yes	characteristic
120	C₄×C₇₁	#484	1	1	yes	characteristic
121	Dic₇₁	—	8	2	no	—
122	Dic₇₁	—	16	1	no	—
123	#10633	—	71	1	no	maximal, Sylow
124	C₂×C₇₁	—	2	1	no	—
125	C₂×C₇₁	—	2	1	no	—
126	C₂×C₇₁	#2072	1	1	yes	characteristic
127	C₂×C₇₁	#2081	1	1	yes	characteristic
128	C₂×C₇₁	#2082	1	1	yes	characteristic
129	#1993	—	71	1	no	—
130	#1849	—	71	1	no	—
131	#1549	—	71	1	no	—
132	#1548	—	71	1	no	—
133	#1286	—	71	1	no	—
134	#1286	—	71	1	no	—
135	#1281	D₇₁	1	1	yes	characteristic
136	C₇₁	#10633	1	1	yes	characteristic, complemented, Sylow
137	C₂×C₄⋊Q₈	—	71	1	no	—
138	#431	C₂×D₇₁	1	1	yes	characteristic
139	#431	C₂×D₇₁	1	1	yes	characteristic
140	C₂×#108	—	142	1	no	—
141	C₂×#108	—	142	1	no	—
142	#423	—	71	1	no	—
143	#423	—	71	1	no	—
144	C₂×#97	C₂×D₇₁	1	1	yes	characteristic
145	#382	—	71	1	no	—
146	#340	—	142	1	no	—
147	#340	—	142	1	no	—
148	#333	—	142	2	no	—
149	#332	—	142	2	no	—
150	C₂²×Q₈	—	142	1	no	—
151	C₂×M₁₆	—	142	1	no	—
152	C₂×M₁₆	—	142	1	no	—
153	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
154	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
155	C₄⋊Q₈	—	71	2	no	—
156	C₄⋊Q₈	—	142	1	no	—
157	C₄⋊Q₈	—	142	1	no	—
158	C₄⋊Q₈	—	142	1	no	—
159	C₂×C₄⋊C₄	—	142	1	no	—
160	C₂×C₄⋊C₄	—	142	1	no	—
161	C₂×C₄⋊C₄	—	142	1	no	—
162	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
163	#108	—	284	2	no	—
164	#108	—	284	2	no	—
165	C₄⋊C₈	—	2	1	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	142	1	no	—
168	C₄⋊C₈	—	142	1	no	—
169	C₄⋊C₈	—	142	1	no	—
170	C₄⋊C₈	—	142	1	no	—
171	C₂²⋊C₈	—	2	1	no	—
172	C₂²⋊C₈	—	2	1	no	—
173	#97	—	2	1	no	—
174	#97	—	2	1	no	—
175	C₄×C₈	—	2	1	no	—
176	C₄×C₈	—	2	1	no	—
177	#95	—	142	1	no	—
178	#95	—	142	1	no	—
179	C₂×Q₈	—	284	1	no	—
180	C₂×Q₈	—	568	2	no	—
181	C₂×Q₈	—	142	2	no	—
182	C₂²×C₄	—	284	1	no	—
183	C₂²×C₄	—	284	1	no	—
184	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
185	C₂²×C₄	#11765865	1	1	yes	characteristic
186	C₂²×C₄	#11765865	1	1	yes	characteristic
187	M₁₆	—	284	1	no	—
188	M₁₆	—	284	1	no	—
189	M₁₆	—	284	1	no	—
190	M₁₆	—	284	1	no	—
191	C₂×C₈	—	2	1	no	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	4	1	no	—
196	C₂×C₈	—	4	1	no	—
197	C₂×C₈	—	284	1	no	—
198	C₂×C₈	—	284	1	no	—
199	C₂×C₈	#11765854	1	2	yes	—
200	C₂×C₈	Dic₂₈₄	1	2	yes	—
201	C₄⋊C₄	—	284	1	no	—
202	C₄⋊C₄	—	284	1	no	—
203	C₄⋊C₄	—	284	1	no	—
204	C₄⋊C₄	—	284	1	no	—
205	C₄⋊C₄	—	142	2	no	—
206	C₄⋊C₄	—	142	2	no	—
207	C₄²	D₄×D₇₁	1	1	yes	characteristic
208	C₄²	#11765864	1	1	yes	characteristic
209	C₄²	#11765864	1	1	yes	characteristic
210	C₄²	#11765866	1	1	yes	characteristic
211	C₂³	#14556116	1	1	yes	characteristic
212	Q₈	—	568	2	no	—
213	Q₈	—	568	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	284	2	no	—
217	C₂×C₄	—	568	2	no	—
218	C₂×C₄	—	568	1	no	—
219	C₂×C₄	—	568	1	no	—
220	C₂×C₄	—	568	1	no	—
221	C₂×C₄	#14556103	1	1	yes	characteristic
222	C₂×C₄	#14556110	1	1	yes	characteristic
223	C₂×C₄	#14556110	1	1	yes	characteristic
224	C₂×C₄	#14556112	1	1	yes	characteristic
225	C₂×C₄	#14556123	1	1	yes	characteristic
226	C₂×C₄	#14556123	1	1	yes	characteristic
227	C₂×C₄	C₂×#11765854	1	1	yes	characteristic
228	C₂×C₄	C₂×Dic₂₈₄	1	1	yes	characteristic
229	C₂×C₄	#14556156	1	1	yes	characteristic
230	C₂×C₄	#14556161	1	1	yes	characteristic
231	C₈	—	2	2	no	—
232	C₈	—	2	2	no	—
233	C₈	—	8	1	no	—
234	C₈	—	8	1	no	—
235	C₈	—	568	1	no	—
236	C₈	—	568	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#17985926	1	1	yes	characteristic
240	C₂²	#17986350	1	1	yes	characteristic
241	C₂²	#17986359	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	568	2	no	—
247	C₄	—	1136	1	no	—
248	C₄	#17986200	1	1	yes	characteristic
249	C₄	#17986210	1	1	yes	characteristic
250	C₄	#17986330	1	1	yes	characteristic
251	C₄	#17986335	1	1	yes	characteristic
252	C₂	—	2	1	no	—
253	C₂	—	2	1	no	—
254	C₂	#22589750	1	1	yes	characteristic
255	C₂	#22589799	1	1	yes	characteristic
256	C₂	#22589806	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22589313

C₂

yes

maximal, characteristic

#22588515

C₂

yes

maximal, characteristic

#22587024

C₂

yes

maximal, characteristic

#22587020

C₂

yes

maximal, characteristic

#22586199

C₂

yes

maximal, characteristic

#22586199

C₂

yes

maximal, characteristic

C₇₁×#1281

C₂

yes

maximal, characteristic

C₂×#14556128

C₂²

yes

—

—

C₂²

yes

characteristic

#17986023

C₂²

yes

characteristic

#17985865

C₂²

yes

—

—

—

—

#431×C₇₁

C₂²

yes

characteristic

#431×C₇₁

C₂²

yes

characteristic

C₂×#97×C₇₁

C₂²

yes

characteristic

C₂²×Dic₁₄₂

—

—

—

—

—

—

D₄

yes

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

#14556064

—

#14556064

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₇₁⋊#95

—

C₇₁⋊#95

—

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂²×C₈×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

C₂²⋊C₈×C₇₁

—

#97×C₇₁

—

#97×C₇₁

—

C₄×C₈×C₇₁

—

C₄×C₈×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

—

—

—

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

C₂²×C₄×C₇₁

yes

C₂²×C₄×C₇₁

yes

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

SD₁₆

yes

—

C₂×C₈×C₇₁

Q₁₆

yes

—

C₄²×C₇₁

C₂×D₄

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₄²×C₇₁

yes

C₂³×C₇₁

yes

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₁₆

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

100

Dic₁₄₂

—

101

Dic₁₄₂

—

102

C₈×C₇₁

—

103

C₈×C₇₁

—

104

C₈×C₇₁

—

105

C₈×C₇₁

—

106

C₇₁⋊C₈

—

107

C₇₁⋊C₈

—

108

C₂²×C₇₁

—

109

C₂²×C₇₁

—

110

C₂²×C₇₁

#397

yes

characteristic

111

C₂²×C₇₁

#487

yes

characteristic

112

C₂²×C₇₁

#489

yes

characteristic

113

C₄×C₇₁

—

114

C₄×C₇₁

—

115

C₄×C₇₁

—

116

C₄×C₇₁

—

117

C₄×C₇₁

#460

yes

characteristic

118

C₄×C₇₁

#462

yes

characteristic

119

C₄×C₇₁

#483

yes

characteristic

120

C₄×C₇₁

#484

yes

characteristic

121

Dic₇₁

—

122

Dic₇₁

—

123

#10633

—

maximal, Sylow

124

C₂×C₇₁

—

125

C₂×C₇₁

—

126

C₂×C₇₁

#2072

yes

characteristic

127

C₂×C₇₁

#2081

yes

characteristic

128

C₂×C₇₁

#2082

yes

characteristic

129

#1993

—

130

#1849

—

131

#1549

—

132

#1548

—

133

#1286

—

134

#1286

—

135

#1281

D₇₁

yes

characteristic

136

C₇₁

#10633

yes

characteristic, complemented, Sylow

137

C₂×C₄⋊Q₈

—

138

#431

C₂×D₇₁

yes

characteristic

139

#431

C₂×D₇₁

yes

characteristic

140

C₂×#108

—

142

—

141

C₂×#108

—

142

—

142

#423

—

143

#423

—

144

C₂×#97

C₂×D₇₁

yes

characteristic

145

#382

—

146

#340

—

142

—

147

#340

—

142

—

148

#333

—

142

—

149

#332

—

142

—

150

C₂²×Q₈

—

142

—

151

C₂×M₁₆

—

142

—

152

C₂×M₁₆

—

142

—

153

C₂²×C₈

D₂₈₄

yes

characteristic

154

C₂²×C₈

D₂₈₄

yes

characteristic

155

C₄⋊Q₈

—

156

C₄⋊Q₈

—

142

—

157

C₄⋊Q₈

—

142

—

158

C₄⋊Q₈

—

142

—

159

C₂×C₄⋊C₄

—

142

—

160

C₂×C₄⋊C₄

—

142

—

161

C₂×C₄⋊C₄

—

142

—

162

C₂×C₄²

C₂²×D₇₁

yes

characteristic

163

#108

—

284

—

164

#108

—

284

—

165

C₄⋊C₈

—

166

C₄⋊C₈

—

167

C₄⋊C₈

—

142

—

168

C₄⋊C₈

—

142

—

169

C₄⋊C₈

—

142

—

170

C₄⋊C₈

—

142

—

171

C₂²⋊C₈

—

172

C₂²⋊C₈

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

C₄×C₈

—

177

#95

—

142

—

178

#95

—

142

—

179

C₂×Q₈

—

284

—

180

C₂×Q₈

—

568

—

181

C₂×Q₈

—

142

—

182

C₂²×C₄

—

284

—

183

C₂²×C₄

—

284

—

184

C₂²×C₄

C₂×D₂₈₄

yes

characteristic

185

C₂²×C₄

#11765865

yes

characteristic

186

C₂²×C₄

#11765865

yes

characteristic

187

M₁₆

—

284

—

188

M₁₆

—

284

—

189

M₁₆

—

284

—

190

M₁₆

—

284

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

284

—

198

C₂×C₈

—

284

—

199

C₂×C₈

#11765854

yes

—

200

C₂×C₈

Dic₂₈₄

yes

—

201

C₄⋊C₄

—

284

—

202

C₄⋊C₄

—

284

—

203

C₄⋊C₄

—

284

—

204

C₄⋊C₄

—

284

—

205

C₄⋊C₄

—

142

—

206

C₄⋊C₄

—

142

—

207

C₄²

D₄×D₇₁

yes

characteristic

208

C₄²

#11765864

yes

characteristic

209

C₄²

#11765864

yes

characteristic

210

C₄²

#11765866

yes

characteristic

211

C₂³

#14556116

yes

characteristic

212

Q₈

—

568

—

213

Q₈

—

568

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

284

—

217

C₂×C₄

—

568

—

218

C₂×C₄

—

568

—

219

C₂×C₄

—

568

—

220

C₂×C₄

—

568

—

221

C₂×C₄

#14556103

yes

characteristic

222

C₂×C₄

#14556110

yes

characteristic

223

C₂×C₄

#14556110

yes

characteristic

224

C₂×C₄

#14556112

yes

characteristic

225

C₂×C₄

#14556123

yes

characteristic

226

C₂×C₄

#14556123

yes

characteristic

227

C₂×C₄

C₂×#11765854

yes

characteristic

228

C₂×C₄

C₂×Dic₂₈₄

yes

characteristic

229

C₂×C₄

#14556156

yes

characteristic

230

C₂×C₄

#14556161

yes

characteristic

231

C₈

—

232

C₈

—

233

C₈

—

234

C₈

—

235

C₈

—

568

—

236

C₈

—

568

—

237

C₂²

—

238

C₂²

—

239

C₂²

#17985926

yes

characteristic

240

C₂²

#17986350

yes

characteristic

241

C₂²

#17986359

yes

characteristic

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

568

—

247

C₄

—

1136

—

248

C₄

#17986200

yes

characteristic

249

C₄

#17986210

yes

characteristic

250

C₄

#17986330

yes

characteristic

251

C₄

#17986335

yes

characteristic

252

C₂

—

253

C₂

—

254

C₂

#22589750

yes

characteristic

255

C₂

#22589799

yes

characteristic

256

C₂

#22589806

yes

characteristic

	subgroup	G/H
center	C₂²	#17985926
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1281	C₂
socle	C₂²×C₇₁	#397
prime radical	C₂³×C₇₁	#124
hypercenter	#1281	D₇₁
hypocenter	C₇₁	#10633
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

subgroup

G/H

center

C₂²

#17985926

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1281

C₂

C₂²×C₇₁

C₂³×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1281

N	H ≅ G/N	type
136. C₇₁	#10633	semidirect

H ≅ G/N

type

136. C₇₁

#10633

semidirect

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

subgroup	index
#22589313	2
#22588515	2
#22587024	2
#22587020	2
#22586199	2
C₇₁×#1281	2
#10633	71

subgroup

index

C₇₁×#1281

Subgroups — #31902252

Conjugacy classes of subgroups

Complements

Maximal subgroups