Group #31908936 — subgroups

Subgroups — #31908936

Order 18176.

314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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	#22598924	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#22587097	C₂	1	1	yes	maximal, characteristic
4	#22586399	C₂	1	1	yes	maximal, characteristic, complemented
5	#22586397	C₂	1	1	yes	maximal, characteristic, complemented
6	#22586389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₁×#1362	C₂	1	1	yes	maximal, characteristic, complemented
8	#17986554	—	2	1	no	—
9	C₂×C₁₆×D₇₁	—	2	1	no	—
10	#17986404	C₂²	1	1	yes	characteristic
11	#17986349	—	2	1	no	—
12	#17986237	—	2	1	no	—
13	#17986237	C₄	1	2	yes	—
14	Q₁₆×Dic₇₁	—	2	1	no	—
15	Q₁₆×Dic₇₁	C₄	1	2	yes	—
16	#17986021	—	2	1	no	—
17	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
18	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
19	Dic₇₁⋊C₁₆	—	2	1	no	—
20	#17985752	C₂²	1	1	yes	characteristic
21	#17985751	—	2	1	no	—
22	#494×C₇₁	C₂²	1	1	yes	characteristic
23	C₄⋊C₁₆×C₇₁	C₂²	1	1	yes	characteristic
24	#335×C₇₁	C₂²	1	1	yes	characteristic
25	C₂×#11765848	—	4	1	no	—
26	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
28	#14556128	—	2	1	no	—
29	#14556119	—	4	1	no	—
30	#14556108	—	4	1	no	—
31	#14556104	—	2	2	no	—
32	Q₈×Dic₇₁	—	2	2	no	—
33	#14556093	—	4	1	no	—
34	#14556086	—	4	1	no	—
35	C₄²×D₇₁	D₄	1	1	yes	characteristic
36	C₂×C₇₁⋊C₁₆	—	2	1	no	—
37	C₁₆×D₇₁	—	4	2	no	—
38	#14556062	—	2	1	no	—
39	#14556062	C₂×C₄	1	2	yes	—
40	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
41	Dic₇₁⋊C₈	—	4	1	no	—
42	#14556052	—	2	2	no	—
43	#14556052	—	2	2	no	—
44	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
45	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
46	C₈×Dic₇₁	D₄	1	1	yes	characteristic
47	C₂×Q₁₆×C₇₁	—	2	1	no	—
48	C₂×Q₁₆×C₇₁	C₂×C₄	1	2	yes	—
49	C₄⋊Q₈×C₇₁	—	2	1	no	—
50	C₂×C₁₆×C₇₁	—	2	1	no	—
51	C₄⋊C₈×C₇₁	—	2	1	no	—
52	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
53	C₂×Dic₁₄₂	—	4	1	no	—
54	C₂×C₄×D₇₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄×D₇₁	D₈	1	1	yes	characteristic
56	C₂×C₄×D₇₁	SD₁₆	1	1	yes	characteristic
57	#11765848	—	8	2	no	—
58	C₂×C₇₁⋊C₈	—	4	1	no	—
59	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
61	C₈×D₇₁	—	2	1	no	—
62	C₈×D₇₁	—	2	1	no	—
63	C₈×D₇₁	—	4	1	no	—
64	C₄⋊Dic₇₁	—	2	2	no	—
65	C₄⋊Dic₇₁	—	4	1	no	—
66	C₄⋊Dic₇₁	—	4	2	no	—
67	Dic₇₁⋊C₄	—	4	2	no	—
68	(C₂×D₇₁)⋊C₄	—	4	2	no	—
69	C₄×Dic₇₁	—	4	2	no	—
70	C₄×Dic₇₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₄×Dic₇₁	D₈	1	1	yes	characteristic
72	C₄×Dic₇₁	SD₁₆	1	1	yes	characteristic
73	C₇₁⋊C₁₆	—	4	1	no	—
74	C₂×Q₈×C₇₁	—	2	2	no	—
75	Q₁₆×C₇₁	—	4	2	no	—
76	Q₁₆×C₇₁	—	4	1	no	—
77	Q₁₆×C₇₁	—	4	1	no	—
78	C₂×C₈×C₇₁	—	4	1	no	—
79	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
81	C₄⋊C₄×C₇₁	—	4	1	no	—
82	C₄⋊C₄×C₇₁	—	4	1	no	—
83	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
84	C₁₆×C₇₁	—	4	1	no	—
85	C₂²×D₇₁	#102	1	1	yes	characteristic
86	Q₈×C₇₁	—	4	2	no	—
87	Q₈×C₇₁	—	4	2	no	—
88	C₂×C₄×C₇₁	—	4	2	no	—
89	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
92	C₂×Dic₇₁	—	4	2	no	—
93	C₂×Dic₇₁	#102	1	1	yes	characteristic
94	C₂×Dic₇₁	#102	1	1	yes	characteristic
95	C₂×Dic₇₁	#102	1	1	yes	characteristic
96	C₄×D₇₁	—	2	1	no	—
97	C₄×D₇₁	—	2	1	no	—
98	C₄×D₇₁	—	4	1	no	—
99	C₄×D₇₁	SD₃₂	1	2	yes	—
100	C₄×D₇₁	Q₃₂	1	2	yes	—
101	Dic₁₄₂	—	8	2	no	—
102	C₈×C₇₁	—	2	1	no	—
103	C₈×C₇₁	—	8	1	no	—
104	C₈×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₈×C₇₁	#137	1	1	yes	characteristic
106	C₇₁⋊C₈	—	2	1	no	—
107	C₇₁⋊C₈	—	2	1	no	—
108	C₇₁⋊C₈	—	8	1	no	—
109	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
110	C₂×D₇₁	—	2	1	no	—
111	C₂×D₇₁	—	2	1	no	—
112	C₂×D₇₁	#358	1	2	yes	—
113	C₄×C₇₁	—	2	1	no	—
114	C₄×C₇₁	—	8	2	no	—
115	C₄×C₇₁	#413	1	1	yes	characteristic
116	C₄×C₇₁	#417	1	1	yes	characteristic
117	C₄×C₇₁	C₂×SD₃₂	1	1	yes	characteristic
118	C₄×C₇₁	C₂×Q₃₂	1	1	yes	characteristic
119	Dic₇₁	—	2	1	no	—
120	Dic₇₁	—	2	1	no	—
121	Dic₇₁	—	8	2	no	—
122	Dic₇₁	#358	1	2	yes	—
123	#11983	—	71	1	no	maximal, Sylow
124	C₂×C₇₁	#1547	1	1	yes	characteristic
125	C₂×C₇₁	C₂×#358	1	1	yes	characteristic
126	C₂×C₇₁	#2148	1	1	yes	characteristic
127	D₇₁	—	2	2	no	—
128	#3170	—	71	1	no	—
129	C₂×C₄⋊C₁₆	—	71	1	no	—
130	#1567	—	71	1	no	—
131	#1365	—	71	1	no	—
132	#1365	—	71	1	no	—
133	#1362	—	71	1	no	—
134	#1362	D₇₁	1	1	yes	characteristic, complemented
135	C₇₁	#11983	1	1	yes	characteristic, complemented, Sylow
136	#533	—	142	1	no	—
137	C₂²×C₁₆	—	142	1	no	—
138	#500	—	71	1	no	—
139	#494	C₂×D₇₁	1	1	yes	characteristic
140	#487	—	142	1	no	—
141	#467	—	71	2	no	—
142	#467	—	142	1	no	—
143	C₄×Q₁₆	—	71	2	no	—
144	C₄×Q₁₆	—	142	1	no	—
145	#423	—	142	1	no	—
146	C₂×C₄×C₈	—	71	1	no	—
147	C₄⋊C₁₆	—	71	1	no	—
148	C₄⋊C₁₆	—	142	1	no	—
149	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
150	#335	—	71	1	no	—
151	#335	—	142	1	no	—
152	#335	C₂×D₇₁	1	1	yes	characteristic
153	C₂×Q₁₆	—	2	1	no	—
154	C₂×Q₁₆	C₄×D₇₁	1	2	yes	—
155	C₂×M₁₆	—	284	1	no	—
156	C₂²×C₈	—	71	1	no	—
157	C₂²×C₈	—	71	1	no	—
158	C₄⋊Q₈	—	2	1	no	—
159	C₄⋊Q₈	—	142	1	no	—
160	#125	—	284	1	no	—
161	C₂²⋊Q₈	—	284	1	no	—
162	C₂²⋊Q₈	—	142	2	no	—
163	C₄×Q₈	—	284	1	no	—
164	C₄×Q₈	—	142	2	no	—
165	#117	—	284	1	no	—
166	C₂×C₄²	—	71	1	no	—
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	284	2	no	—
169	C₂×C₁₆	—	142	1	no	—
170	#107	—	71	2	no	—
171	#107	—	142	1	no	—
172	C₄⋊C₈	—	2	1	no	—
173	C₄⋊C₈	—	284	1	no	—
174	C₄⋊C₈	—	142	1	no	—
175	#103	—	142	2	no	—
176	#103	—	142	2	no	—
177	C₄×C₈	—	71	1	no	—
178	C₄×C₈	—	71	1	no	—
179	C₄×C₈	—	71	1	no	—
180	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	284	1	no	—
183	C₂²×C₄	—	71	1	no	—
184	C₂²×C₄	—	71	1	no	—
185	C₂²×C₄	—	71	1	no	—
186	Q₁₆	—	4	2	no	—
187	Q₁₆	—	4	1	no	—
188	Q₁₆	—	4	1	no	—
189	M₁₆	—	568	2	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	284	1	no	—
192	C₂×C₈	—	284	1	no	—
193	C₂×C₈	—	71	1	no	—
194	C₂×C₈	—	71	1	no	—
195	C₂×C₈	—	142	1	no	—
196	C₂×C₈	—	142	1	no	—
197	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
198	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	1	no	—
201	C₄⋊C₄	—	284	2	no	—
202	C₄⋊C₄	—	284	2	no	—
203	C₄⋊C₄	—	284	1	no	—
204	C₄⋊C₄	—	142	2	no	—
205	C₂²⋊C₄	—	284	2	no	—
206	C₄²	—	284	2	no	—
207	C₄²	—	71	1	no	—
208	C₄²	—	71	1	no	—
209	C₄²	—	71	1	no	—
210	C₄²	D₄×D₇₁	1	1	yes	characteristic
211	C₁₆	—	4	1	no	—
212	C₁₆	—	284	1	no	—
213	C₂³	—	71	1	no	—
214	Q₈	—	4	2	no	—
215	Q₈	—	4	2	no	—
216	Q₈	—	568	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	284	1	no	—
219	C₂×C₄	—	284	2	no	—
220	C₂×C₄	—	71	1	no	—
221	C₂×C₄	—	71	2	no	—
222	C₂×C₄	—	71	2	no	—
223	C₂×C₄	—	71	1	no	—
224	C₂×C₄	—	71	1	no	—
225	C₂×C₄	—	142	1	no	—
226	C₂×C₄	—	142	1	no	—
227	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
228	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
229	C₂×C₄	SD₁₆×D₇₁	1	1	yes	characteristic
230	C₈	—	2	1	no	—
231	C₈	—	8	1	no	—
232	C₈	—	568	1	no	—
233	C₈	—	142	1	no	—
234	C₈	—	142	1	no	—
235	C₈	#14556152	1	1	yes	characteristic
236	C₈	#14556157	1	1	yes	characteristic
237	C₂²	—	71	2	no	—
238	C₂²	—	142	1	no	—
239	C₂²	—	142	1	no	—
240	C₂²	#102×D₇₁	1	1	yes	characteristic
241	C₄	—	2	1	no	—
242	C₄	—	8	2	no	—
243	C₄	—	568	2	no	—
244	C₄	—	71	2	no	—
245	C₄	—	142	1	no	—
246	C₄	—	142	1	no	—
247	C₄	#17985980	1	1	yes	characteristic
248	C₄	#17985997	1	1	yes	characteristic
249	C₄	SD₃₂×D₇₁	1	1	yes	characteristic
250	C₄	Q₃₂×D₇₁	1	1	yes	characteristic
251	C₂	—	142	2	no	—
252	C₂	#22587014	1	1	yes	characteristic
253	C₂	#358×D₇₁	1	1	yes	characteristic
254	C₂	#22590088	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22598924

C₂

yes

maximal, characteristic

C₄⋊C₁₆×D₇₁

C₂

yes

maximal, characteristic

#22587097

C₂

yes

maximal, characteristic

#22586399

C₂

yes

maximal, characteristic, complemented

#22586397

C₂

yes

maximal, characteristic, complemented

#22586389

C₂

yes

maximal, characteristic, complemented

C₇₁×#1362

C₂

yes

maximal, characteristic, complemented

#17986554

—

C₂×C₁₆×D₇₁

—

#17986404

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₇₁

—

Q₁₆×Dic₇₁

C₄

yes

—

#17986021

—

C₄×C₈×D₇₁

C₂²

yes

characteristic

C₄⋊(C₇₁⋊C₁₆)

C₂²

yes

characteristic

Dic₇₁⋊C₁₆

—

#17985752

C₂²

yes

characteristic

#17985751

—

#494×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

#335×C₇₁

C₂²

yes

characteristic

C₂×#11765848

—

C₂×C₈×D₇₁

C₂×C₄

yes

characteristic

C₂×C₈×D₇₁

D₄

yes

—

—

—

—

Q₈×Dic₇₁

—

#14556093

—

#14556086

—

C₄²×D₇₁

D₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

C₁₆×D₇₁

—

#14556062

—

#14556062

C₂×C₄

yes

—

C₄⋊(C₇₁⋊C₈)

—

Dic₇₁⋊C₈

—

#14556052

—

#14556052

—

C₄×C₇₁⋊C₈

D₄

yes

characteristic

C₈×Dic₇₁

C₂×C₄

yes

characteristic

C₈×Dic₇₁

D₄

yes

characteristic

C₂×Q₁₆×C₇₁

—

C₂×Q₁₆×C₇₁

C₂×C₄

yes

—

C₄⋊Q₈×C₇₁

—

C₂×C₁₆×C₇₁

—

C₄⋊C₈×C₇₁

—

C₄×C₈×C₇₁

C₂³

yes

characteristic

C₂×Dic₁₄₂

—

C₂×C₄×D₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₇₁

D₈

yes

characteristic

C₂×C₄×D₇₁

SD₁₆

yes

characteristic

#11765848

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₇₁

—

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

(C₂×D₇₁)⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

C₂²⋊C₄

yes

characteristic

C₄×Dic₇₁

D₈

yes

characteristic

C₄×Dic₇₁

SD₁₆

yes

characteristic

C₇₁⋊C₁₆

—

C₂×Q₈×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

Q₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

characteristic

C₁₆×C₇₁

—

C₂²×D₇₁

#102

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

yes

C₂×Dic₇₁

yes

C₂×Dic₇₁

yes

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

—

C₄×D₇₁

SD₃₂

yes

—

100

C₄×D₇₁

Q₃₂

yes

—

101

Dic₁₄₂

—

102

C₈×C₇₁

—

103

C₈×C₇₁

—

104

C₈×C₇₁

AGL(1,ℤ/8)

yes

characteristic

105

C₈×C₇₁

#137

yes

characteristic

106

C₇₁⋊C₈

—

107

C₇₁⋊C₈

—

108

C₇₁⋊C₈

—

109

C₂²×C₇₁

C₂×#102

yes

characteristic

110

C₂×D₇₁

—

111

C₂×D₇₁

—

112

C₂×D₇₁

#358

yes

—

113

C₄×C₇₁

—

114

C₄×C₇₁

—

115

C₄×C₇₁

#413

yes

characteristic

116

C₄×C₇₁

#417

yes

characteristic

117

C₄×C₇₁

C₂×SD₃₂

yes

characteristic

118

C₄×C₇₁

C₂×Q₃₂

yes

characteristic

119

Dic₇₁

—

120

Dic₇₁

—

121

Dic₇₁

—

122

Dic₇₁

#358

yes

—

123

#11983

—

maximal, Sylow

124

C₂×C₇₁

#1547

yes

characteristic

125

C₂×C₇₁

C₂×#358

yes

characteristic

126

C₂×C₇₁

#2148

yes

characteristic

127

D₇₁

—

128

#3170

—

129

C₂×C₄⋊C₁₆

—

130

#1567

—

131

#1365

—

132

#1365

—

133

#1362

—

134

#1362

D₇₁

yes

characteristic, complemented

135

C₇₁

#11983

yes

characteristic, complemented, Sylow

136

#533

—

142

—

137

C₂²×C₁₆

—

142

—

138

#500

—

139

#494

C₂×D₇₁

yes

characteristic

140

#487

—

142

—

141

#467

—

142

#467

—

142

—

143

C₄×Q₁₆

—

144

C₄×Q₁₆

—

142

—

145

#423

—

142

—

146

C₂×C₄×C₈

—

147

C₄⋊C₁₆

—

148

C₄⋊C₁₆

—

142

—

149

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

150

#335

—

151

#335

—

142

—

152

#335

C₂×D₇₁

yes

characteristic

153

C₂×Q₁₆

—

154

C₂×Q₁₆

C₄×D₇₁

yes

—

155

C₂×M₁₆

—

284

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₄⋊Q₈

—

159

C₄⋊Q₈

—

142

—

160

#125

—

284

—

161

C₂²⋊Q₈

—

284

—

162

C₂²⋊Q₈

—

142

—

163

C₄×Q₈

—

284

—

164

C₄×Q₈

—

142

—

165

#117

—

284

—

166

C₂×C₄²

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

284

—

169

C₂×C₁₆

—

142

—

170

#107

—

171

#107

—

142

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

284

—

174

C₄⋊C₈

—

142

—

175

#103

—

142

—

176

#103

—

142

—

177

C₄×C₈

—

178

C₄×C₈

—

179

C₄×C₈

—

180

C₄×C₈

C₂²×D₇₁

yes

characteristic

181

C₂×Q₈

—

182

C₂×Q₈

—

284

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

—

186

Q₁₆

—

187

Q₁₆

—

188

Q₁₆

—

189

M₁₆

—

568

—

190

C₂×C₈

—

191

C₂×C₈

—

284

—

192

C₂×C₈

—

284

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

142

—

196

C₂×C₈

—

142

—

197

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

198

C₂×C₈

D₄×D₇₁

yes

characteristic

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

284

—

202

C₄⋊C₄

—

284

—

203

C₄⋊C₄

—

284

—

204

C₄⋊C₄

—

142

—

205

C₂²⋊C₄

—

284

—

206

C₄²

—

284

—

207

C₄²

—

208

C₄²

—

209

C₄²

—

210

C₄²

D₄×D₇₁

yes

characteristic

211

C₁₆

—

212

C₁₆

—

284

—

213

C₂³

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

568

—

217

C₂×C₄

—

218

C₂×C₄

—

284

—

219

C₂×C₄

—

284

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

142

—

226

C₂×C₄

—

142

—

227

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

228

C₂×C₄

D₈×D₇₁

yes

characteristic

229

C₂×C₄

SD₁₆×D₇₁

yes

characteristic

230

C₈

—

231

C₈

—

232

C₈

—

568

—

233

C₈

—

142

—

234

C₈

—

142

—

235

C₈

#14556152

yes

characteristic

236

C₈

#14556157

yes

characteristic

237

C₂²

—

238

C₂²

—

142

—

239

C₂²

—

142

—

240

C₂²

#102×D₇₁

yes

characteristic

241

C₄

—

242

C₄

—

243

C₄

—

568

—

244

C₄

—

245

C₄

—

142

—

246

C₄

—

142

—

247

C₄

#17985980

yes

characteristic

248

C₄

#17985997

yes

characteristic

249

C₄

SD₃₂×D₇₁

yes

characteristic

250

C₄

Q₃₂×D₇₁

yes

characteristic

251

C₂

—

142

—

252

C₂

#22587014

yes

characteristic

253

C₂

#358×D₇₁

yes

characteristic

254

C₂

#22590088

yes

characteristic

	subgroup	G/H
center	C₂²	#102×D₇₁
commutator	C₂×C₈×C₇₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₇₁
Fitting	C₇₁×#1362	C₂
socle	C₂²×C₇₁	C₂×#102
prime radical	C₂²×D₇₁	#102
cosocle	C₄×C₈×C₇₁	C₂³
hypercenter	#1362	D₇₁
hypocenter	C₇₁	#11983
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

subgroup

G/H

center

C₂²

#102×D₇₁

commutator

C₂×C₈×C₇₁

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₇₁

Fitting

C₇₁×#1362

C₂

C₂²×C₇₁

C₂²×D₇₁

C₄×C₈×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #1362

N	H ≅ G/N	type
4. #22586399	C₂	semidirect
5. #22586397	C₂	semidirect
6. #22586389	C₂	semidirect
7. C₇₁×#1362	C₂	semidirect
134. #1362	D₇₁	semidirect
135. C₇₁	#11983	semidirect

H ≅ G/N

type

4. #22586399

C₂

semidirect

5. #22586397

C₂

semidirect

6. #22586389

C₂

semidirect

7. C₇₁×#1362

C₂

semidirect

134. #1362

D₇₁

semidirect

135. C₇₁

#11983

semidirect

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

subgroup	index
#22598924	2
C₄⋊C₁₆×D₇₁	2
#22587097	2
#22586399	2
#22586397	2
#22586389	2
C₇₁×#1362	2
#11983	71

subgroup

index

C₄⋊C₁₆×D₇₁

C₇₁×#1362

Subgroups — #31908936

Conjugacy classes of subgroups

Complements

Maximal subgroups