Group #31908784 — subgroups

Subgroups — #31908784

Order 18176.

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

normal subgroups only

This group has 310 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	#22590138	C₂	1	1	yes	maximal, characteristic
3	#335×D₇₁	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	#17986404	C₂²	1	1	yes	characteristic
10	#17986349	—	2	1	no	—
11	#17986237	—	2	1	no	—
12	#17986237	C₄	1	2	yes	—
13	Q₁₆×Dic₇₁	—	2	1	no	—
14	Q₁₆×Dic₇₁	C₄	1	2	yes	—
15	C₄⋊C₈×D₇₁	—	2	1	no	—
16	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
17	C₄⋊(C₇₁⋊C₁₆)	C₂²	1	1	yes	characteristic
18	(C₂×D₇₁)⋊C₁₆	—	2	1	no	—
19	C₁₆×Dic₇₁	—	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×C₈×D₇₁	—	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	#14556062	—	2	1	no	—
38	#14556062	C₂×C₄	1	2	yes	—
39	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
40	Dic₇₁⋊C₈	—	4	1	no	—
41	#14556052	—	2	2	no	—
42	#14556052	—	2	2	no	—
43	C₄×C₇₁⋊C₈	D₄	1	1	yes	characteristic
44	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
45	C₈×Dic₇₁	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₇₁	—	2	1	no	—
47	C₂×Q₁₆×C₇₁	C₂×C₄	1	2	yes	—
48	C₄⋊Q₈×C₇₁	—	2	1	no	—
49	C₂×C₁₆×C₇₁	—	2	1	no	—
50	C₄⋊C₈×C₇₁	—	2	1	no	—
51	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
52	C₂×Dic₁₄₂	—	4	1	no	—
53	C₂×C₄×D₇₁	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄×D₇₁	D₈	1	1	yes	characteristic
55	C₂×C₄×D₇₁	SD₁₆	1	1	yes	characteristic
56	C₂×C₇₁⋊C₈	—	4	1	no	—
57	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
59	C₈×D₇₁	—	2	1	no	—
60	C₈×D₇₁	—	2	1	no	—
61	C₈×D₇₁	—	4	1	no	—
62	C₈×D₇₁	—	8	2	no	—
63	C₄⋊Dic₇₁	—	2	2	no	—
64	C₄⋊Dic₇₁	—	4	1	no	—
65	C₄⋊Dic₇₁	—	4	2	no	—
66	Dic₇₁⋊C₄	—	4	2	no	—
67	(C₂×D₇₁)⋊C₄	—	4	2	no	—
68	C₄×Dic₇₁	—	4	2	no	—
69	C₄×Dic₇₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₄×Dic₇₁	D₈	1	1	yes	characteristic
71	C₄×Dic₇₁	SD₁₆	1	1	yes	characteristic
72	C₇₁⋊C₁₆	—	4	1	no	—
73	C₂×Q₈×C₇₁	—	2	2	no	—
74	Q₁₆×C₇₁	—	4	2	no	—
75	Q₁₆×C₇₁	—	4	1	no	—
76	Q₁₆×C₇₁	—	4	1	no	—
77	C₂×C₈×C₇₁	—	4	1	no	—
78	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
80	C₄⋊C₄×C₇₁	—	4	1	no	—
81	C₄⋊C₄×C₇₁	—	4	1	no	—
82	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
83	C₁₆×C₇₁	—	4	1	no	—
84	C₂²×D₇₁	#102	1	1	yes	characteristic
85	Q₈×C₇₁	—	4	2	no	—
86	Q₈×C₇₁	—	4	2	no	—
87	C₂×C₄×C₇₁	—	4	2	no	—
88	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×Dic₇₁	—	4	2	no	—
92	C₂×Dic₇₁	#102	1	1	yes	characteristic
93	C₂×Dic₇₁	#102	1	1	yes	characteristic
94	C₂×Dic₇₁	#102	1	1	yes	characteristic
95	C₄×D₇₁	—	2	1	no	—
96	C₄×D₇₁	—	2	1	no	—
97	C₄×D₇₁	—	4	1	no	—
98	C₄×D₇₁	SD₃₂	1	2	yes	—
99	C₄×D₇₁	Q₃₂	1	2	yes	—
100	Dic₁₄₂	—	8	2	no	—
101	C₈×C₇₁	—	2	1	no	—
102	C₈×C₇₁	—	8	1	no	—
103	C₈×C₇₁	#135	1	1	yes	characteristic
104	C₈×C₇₁	#135	1	1	yes	characteristic
105	C₇₁⋊C₈	—	2	1	no	—
106	C₇₁⋊C₈	—	2	1	no	—
107	C₇₁⋊C₈	—	8	1	no	—
108	C₂²×C₇₁	C₂×#102	1	1	yes	characteristic
109	C₂×D₇₁	—	2	1	no	—
110	C₂×D₇₁	—	2	1	no	—
111	C₂×D₇₁	#358	1	2	yes	—
112	C₄×C₇₁	—	2	1	no	—
113	C₄×C₇₁	—	8	2	no	—
114	C₄×C₇₁	#413	1	1	yes	characteristic
115	C₄×C₇₁	#416	1	1	yes	characteristic
116	C₄×C₇₁	C₂×SD₃₂	1	1	yes	characteristic
117	C₄×C₇₁	C₂×Q₃₂	1	1	yes	characteristic
118	Dic₇₁	—	2	1	no	—
119	Dic₇₁	—	2	1	no	—
120	Dic₇₁	—	8	2	no	—
121	Dic₇₁	#358	1	2	yes	—
122	#11949	—	71	1	no	maximal, Sylow
123	C₂×C₇₁	#1540	1	1	yes	characteristic
124	C₂×C₇₁	C₂×#358	1	1	yes	characteristic
125	C₂×C₇₁	#2148	1	1	yes	characteristic
126	D₇₁	—	2	2	no	—
127	#3170	—	71	1	no	—
128	#2162	—	71	1	no	—
129	C₂×#335	—	71	1	no	—
130	#1365	—	71	1	no	—
131	#1365	—	71	1	no	—
132	#1362	—	71	1	no	—
133	#1362	D₇₁	1	1	yes	characteristic, complemented
134	C₇₁	#11949	1	1	yes	characteristic, complemented, Sylow
135	#533	—	142	1	no	—
136	#500	—	71	1	no	—
137	#494	C₂×D₇₁	1	1	yes	characteristic
138	#487	—	142	1	no	—
139	#467	—	71	2	no	—
140	#467	—	142	1	no	—
141	C₄×Q₁₆	—	71	2	no	—
142	C₄×Q₁₆	—	142	1	no	—
143	C₂×C₄⋊C₈	—	142	1	no	—
144	C₂×C₄×C₈	—	71	1	no	—
145	C₄⋊C₁₆	—	71	1	no	—
146	C₄⋊C₁₆	C₂×D₇₁	1	1	yes	characteristic
147	C₂²⋊C₁₆	—	142	1	no	—
148	C₄×C₁₆	—	142	1	no	—
149	#335	—	71	1	no	—
150	#335	—	142	1	no	—
151	#335	C₂×D₇₁	1	1	yes	characteristic
152	C₂×Q₁₆	—	2	1	no	—
153	C₂×Q₁₆	C₄×D₇₁	1	2	yes	—
154	C₂²×C₈	—	284	1	no	—
155	C₂²×C₈	—	71	1	no	—
156	C₂²×C₈	—	71	1	no	—
157	C₄⋊Q₈	—	2	1	no	—
158	C₄⋊Q₈	—	142	1	no	—
159	#125	—	284	1	no	—
160	C₂²⋊Q₈	—	284	1	no	—
161	C₂²⋊Q₈	—	142	2	no	—
162	C₄×Q₈	—	284	1	no	—
163	C₄×Q₈	—	142	2	no	—
164	#117	—	284	1	no	—
165	C₂×C₄²	—	71	1	no	—
166	C₂×C₁₆	—	2	1	no	—
167	C₂×C₁₆	—	142	1	no	—
168	#107	—	71	2	no	—
169	#107	—	142	1	no	—
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	284	1	no	—
172	C₄⋊C₈	—	142	1	no	—
173	#103	—	142	2	no	—
174	#103	—	142	2	no	—
175	C₄×C₈	—	71	1	no	—
176	C₄×C₈	—	71	1	no	—
177	C₄×C₈	—	71	1	no	—
178	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
179	C₂×Q₈	—	2	2	no	—
180	C₂×Q₈	—	284	1	no	—
181	C₂²×C₄	—	71	1	no	—
182	C₂²×C₄	—	71	1	no	—
183	C₂²×C₄	—	71	1	no	—
184	Q₁₆	—	4	2	no	—
185	Q₁₆	—	4	1	no	—
186	Q₁₆	—	4	1	no	—
187	C₂×C₈	—	4	1	no	—
188	C₂×C₈	—	284	1	no	—
189	C₂×C₈	—	284	1	no	—
190	C₂×C₈	—	568	2	no	—
191	C₂×C₈	—	71	1	no	—
192	C₂×C₈	—	71	1	no	—
193	C₂×C₈	—	142	1	no	—
194	C₂×C₈	—	142	1	no	—
195	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
196	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
197	C₄⋊C₄	—	4	1	no	—
198	C₄⋊C₄	—	4	1	no	—
199	C₄⋊C₄	—	284	2	no	—
200	C₄⋊C₄	—	284	2	no	—
201	C₄⋊C₄	—	284	1	no	—
202	C₄⋊C₄	—	142	2	no	—
203	C₂²⋊C₄	—	284	2	no	—
204	C₄²	—	284	2	no	—
205	C₄²	—	71	1	no	—
206	C₄²	—	71	1	no	—
207	C₄²	—	71	1	no	—
208	C₄²	D₄×D₇₁	1	1	yes	characteristic
209	C₁₆	—	4	1	no	—
210	C₁₆	—	284	1	no	—
211	C₂³	—	71	1	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	4	2	no	—
214	Q₈	—	568	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	284	1	no	—
217	C₂×C₄	—	284	2	no	—
218	C₂×C₄	—	71	1	no	—
219	C₂×C₄	—	71	2	no	—
220	C₂×C₄	—	71	2	no	—
221	C₂×C₄	—	71	1	no	—
222	C₂×C₄	—	71	1	no	—
223	C₂×C₄	—	142	1	no	—
224	C₂×C₄	—	142	1	no	—
225	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
226	C₂×C₄	D₈×D₇₁	1	1	yes	characteristic
227	C₂×C₄	SD₁₆×D₇₁	1	1	yes	characteristic
228	C₈	—	2	1	no	—
229	C₈	—	8	1	no	—
230	C₈	—	568	1	no	—
231	C₈	—	142	1	no	—
232	C₈	—	142	1	no	—
233	C₈	#14556147	1	1	yes	characteristic
234	C₈	#14556149	1	1	yes	characteristic
235	C₂²	—	71	2	no	—
236	C₂²	—	142	1	no	—
237	C₂²	—	142	1	no	—
238	C₂²	#102×D₇₁	1	1	yes	characteristic
239	C₄	—	2	1	no	—
240	C₄	—	8	2	no	—
241	C₄	—	568	2	no	—
242	C₄	—	71	2	no	—
243	C₄	—	142	1	no	—
244	C₄	—	142	1	no	—
245	C₄	#17985980	1	1	yes	characteristic
246	C₄	#17985992	1	1	yes	characteristic
247	C₄	SD₃₂×D₇₁	1	1	yes	characteristic
248	C₄	Q₃₂×D₇₁	1	1	yes	characteristic
249	C₂	—	142	2	no	—
250	C₂	#22586986	1	1	yes	characteristic
251	C₂	#358×D₇₁	1	1	yes	characteristic
252	C₂	#22590088	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22598924

C₂

yes

maximal, characteristic

#22590138

C₂

yes

maximal, characteristic

#335×D₇₁

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

—

#17986404

C₂²

yes

—

—

C₄

yes

—

Q₁₆×Dic₇₁

—

Q₁₆×Dic₇₁

C₄

yes

—

C₄⋊C₈×D₇₁

—

C₄×C₈×D₇₁

C₂²

yes

characteristic

C₄⋊(C₇₁⋊C₁₆)

C₂²

yes

characteristic

(C₂×D₇₁)⋊C₁₆

—

C₁₆×Dic₇₁

—

#17985752

C₂²

yes

characteristic

#17985751

—

#494×C₇₁

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₁

C₂²

yes

characteristic

#335×C₇₁

C₂²

yes

characteristic

C₂×C₈×D₇₁

—

C₂×C₈×D₇₁

C₂×C₄

yes

characteristic

C₂×C₈×D₇₁

D₄

yes

—

—

—

—

Q₈×Dic₇₁

—

#14556093

—

#14556086

—

C₄²×D₇₁

D₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

#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

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₈×D₇₁

—

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

—

C₄×D₇₁

Q₃₂

yes

—

100

Dic₁₄₂

—

101

C₈×C₇₁

—

102

C₈×C₇₁

—

103

C₈×C₇₁

#135

yes

characteristic

104

C₈×C₇₁

#135

yes

characteristic

105

C₇₁⋊C₈

—

106

C₇₁⋊C₈

—

107

C₇₁⋊C₈

—

108

C₂²×C₇₁

C₂×#102

yes

characteristic

109

C₂×D₇₁

—

110

C₂×D₇₁

—

111

C₂×D₇₁

#358

yes

—

112

C₄×C₇₁

—

113

C₄×C₇₁

—

114

C₄×C₇₁

#413

yes

characteristic

115

C₄×C₇₁

#416

yes

characteristic

116

C₄×C₇₁

C₂×SD₃₂

yes

characteristic

117

C₄×C₇₁

C₂×Q₃₂

yes

characteristic

118

Dic₇₁

—

119

Dic₇₁

—

120

Dic₇₁

—

121

Dic₇₁

#358

yes

—

122

#11949

—

maximal, Sylow

123

C₂×C₇₁

#1540

yes

characteristic

124

C₂×C₇₁

C₂×#358

yes

characteristic

125

C₂×C₇₁

#2148

yes

characteristic

126

D₇₁

—

127

#3170

—

128

#2162

—

129

C₂×#335

—

130

#1365

—

131

#1365

—

132

#1362

—

133

#1362

D₇₁

yes

characteristic, complemented

134

C₇₁

#11949

yes

characteristic, complemented, Sylow

135

#533

—

142

—

136

#500

—

137

#494

C₂×D₇₁

yes

characteristic

138

#487

—

142

—

139

#467

—

140

#467

—

142

—

141

C₄×Q₁₆

—

142

C₄×Q₁₆

—

142

—

143

C₂×C₄⋊C₈

—

142

—

144

C₂×C₄×C₈

—

145

C₄⋊C₁₆

—

146

C₄⋊C₁₆

C₂×D₇₁

yes

characteristic

147

C₂²⋊C₁₆

—

142

—

148

C₄×C₁₆

—

142

—

149

#335

—

150

#335

—

142

—

151

#335

C₂×D₇₁

yes

characteristic

152

C₂×Q₁₆

—

153

C₂×Q₁₆

C₄×D₇₁

yes

—

154

C₂²×C₈

—

284

—

155

C₂²×C₈

—

156

C₂²×C₈

—

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

142

—

159

#125

—

284

—

160

C₂²⋊Q₈

—

284

—

161

C₂²⋊Q₈

—

142

—

162

C₄×Q₈

—

284

—

163

C₄×Q₈

—

142

—

164

#117

—

284

—

165

C₂×C₄²

—

166

C₂×C₁₆

—

167

C₂×C₁₆

—

142

—

168

#107

—

169

#107

—

142

—

170

C₄⋊C₈

—

171

C₄⋊C₈

—

284

—

172

C₄⋊C₈

—

142

—

173

#103

—

142

—

174

#103

—

142

—

175

C₄×C₈

—

176

C₄×C₈

—

177

C₄×C₈

—

178

C₄×C₈

C₂²×D₇₁

yes

characteristic

179

C₂×Q₈

—

180

C₂×Q₈

—

284

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

Q₁₆

—

185

Q₁₆

—

186

Q₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

284

—

189

C₂×C₈

—

284

—

190

C₂×C₈

—

568

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

—

142

—

194

C₂×C₈

—

142

—

195

C₂×C₈

C₂×C₄×D₇₁

yes

characteristic

196

C₂×C₈

D₄×D₇₁

yes

characteristic

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄⋊C₄

—

284

—

200

C₄⋊C₄

—

284

—

201

C₄⋊C₄

—

284

—

202

C₄⋊C₄

—

142

—

203

C₂²⋊C₄

—

284

—

204

C₄²

—

284

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

D₄×D₇₁

yes

characteristic

209

C₁₆

—

210

C₁₆

—

284

—

211

C₂³

—

212

Q₈

—

213

Q₈

—

214

Q₈

—

568

—

215

C₂×C₄

—

216

C₂×C₄

—

284

—

217

C₂×C₄

—

284

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

142

—

224

C₂×C₄

—

142

—

225

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

226

C₂×C₄

D₈×D₇₁

yes

characteristic

227

C₂×C₄

SD₁₆×D₇₁

yes

characteristic

228

C₈

—

229

C₈

—

230

C₈

—

568

—

231

C₈

—

142

—

232

C₈

—

142

—

233

C₈

#14556147

yes

characteristic

234

C₈

#14556149

yes

characteristic

235

C₂²

—

236

C₂²

—

142

—

237

C₂²

—

142

—

238

C₂²

#102×D₇₁

yes

characteristic

239

C₄

—

240

C₄

—

241

C₄

—

568

—

242

C₄

—

243

C₄

—

142

—

244

C₄

—

142

—

245

C₄

#17985980

yes

characteristic

246

C₄

#17985992

yes

characteristic

247

C₄

SD₃₂×D₇₁

yes

characteristic

248

C₄

Q₃₂×D₇₁

yes

characteristic

249

C₂

—

142

—

250

C₂

#22586986

yes

characteristic

251

C₂

#358×D₇₁

yes

characteristic

252

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	#11949
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
133. #1362	D₇₁	semidirect
134. C₇₁	#11949	semidirect

H ≅ G/N

type

4. #22586399

C₂

semidirect

5. #22586397

C₂

semidirect

6. #22586389

C₂

semidirect

7. C₇₁×#1362

C₂

semidirect

133. #1362

D₇₁

semidirect

134. C₇₁

#11949

semidirect

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

subgroup	index
#22598924	2
#22590138	2
#335×D₇₁	2
#22586399	2
#22586397	2
#22586389	2
C₇₁×#1362	2
#11949	71

subgroup

index

#335×D₇₁

C₇₁×#1362

Subgroups — #31908784

Conjugacy classes of subgroups

Complements

Maximal subgroups