Group #31890382 — subgroups

Subgroups — #31890382

Order 18176.

398 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 137 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×Q₈×C₇₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#22588336	C₂	1	1	yes	maximal, characteristic
3	#22587098	C₂	1	2	yes	maximal
4	#22586214	C₂	1	2	yes	maximal
5	C₇₁×#1801	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₇₁⋊C₈	—	2	2	no	—
7	Q₈×C₇₁⋊C₈	—	2	2	no	—
8	#17986023	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₇₁⋊C₈)	C₄	1	2	yes	—
10	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#14556047	—	2	1	no	—
12	C₂×C₄×C₇₁⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
14	#17985768	—	2	1	no	—
15	#17985751	—	2	2	no	—
16	#17985751	—	2	2	no	—
17	C₂×C₄×Q₈×C₇₁	C₂²	1	1	yes	characteristic
18	#423×C₇₁	C₂²	1	2	yes	—
19	C₂×#101×C₇₁	—	2	1	no	—
20	#343×C₇₁	—	2	1	no	—
21	C₂×#11765849	—	2	2	no	—
22	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
26	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
27	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
28	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
29	#14556047	—	4	2	no	—
30	C₄×C₇₁⋊C₈	—	2	2	no	—
31	C₄×C₇₁⋊C₈	—	2	2	no	—
32	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
33	C₄×C₇₁⋊C₈	D₄	1	2	yes	—
34	C₂²×Q₈×C₇₁	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₇₁	—	2	2	no	—
36	C₄×Q₈×C₇₁	—	2	2	no	—
37	C₄×Q₈×C₇₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₇₁	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₇₁	Q₈	1	2	yes	—
40	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
42	C₄⋊C₈×C₇₁	—	2	2	no	—
43	C₄⋊C₈×C₇₁	—	2	2	no	—
44	#101×C₇₁	—	4	2	no	—
45	#11765849	—	4	2	no	—
46	#11765849	—	4	2	no	—
47	C₂×C₇₁⋊C₈	—	2	2	no	—
48	C₂×C₇₁⋊C₈	—	2	2	no	—
49	C₂×C₇₁⋊C₈	—	4	1	no	—
50	C₂×C₇₁⋊C₈	—	4	2	no	—
51	C₂×C₇₁⋊C₈	—	4	2	no	—
52	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	2	yes	—
54	C₂×C₇₁⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×Q₈×C₇₁	—	2	2	no	—
56	C₂×Q₈×C₇₁	—	2	2	no	—
57	C₂×Q₈×C₇₁	D₈	1	2	yes	—
58	C₂×Q₈×C₇₁	Q₁₆	1	2	yes	—
59	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₇₁	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
64	M₁₆×C₇₁	—	4	2	no	—
65	M₁₆×C₇₁	—	4	2	no	—
66	C₂×C₈×C₇₁	—	4	2	no	—
67	C₄⋊C₄×C₇₁	—	2	2	no	—
68	C₄⋊C₄×C₇₁	—	2	4	no	—
69	C₄²×C₇₁	—	2	2	no	—
70	C₄²×C₇₁	—	2	2	no	—
71	C₄²×C₇₁	C₂×D₄	1	2	yes	—
72	C₄²×C₇₁	#41	1	2	yes	—
73	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
74	Q₈×C₇₁	—	2	4	no	—
75	Q₈×C₇₁	—	2	4	no	—
76	C₂×C₄×C₇₁	—	2	2	no	—
77	C₂×C₄×C₇₁	—	2	2	no	—
78	C₂×C₄×C₇₁	—	2	1	no	—
79	C₂×C₄×C₇₁	—	2	1	no	—
80	C₂×C₄×C₇₁	—	2	2	no	—
81	C₂×C₄×C₇₁	—	4	1	no	—
82	C₂×C₄×C₇₁	—	4	2	no	—
83	C₂×C₄×C₇₁	#107	1	4	yes	—
84	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#121	1	2	yes	—
87	C₂×C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
88	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₇₁	#135	1	2	yes	—
91	C₈×C₇₁	—	8	2	no	—
92	C₇₁⋊C₈	—	2	1	no	—
93	C₇₁⋊C₈	—	2	2	no	—
94	C₇₁⋊C₈	—	4	2	no	—
95	C₇₁⋊C₈	—	8	2	no	—
96	C₇₁⋊C₈	#101	1	2	yes	complemented
97	C₂²×C₇₁	—	2	1	no	—
98	C₂²×C₇₁	—	2	1	no	—
99	C₂²×C₇₁	#380	1	1	yes	characteristic
100	C₂²×C₇₁	C₂×#107	1	1	yes	characteristic
101	C₂²×C₇₁	#427	1	1	yes	characteristic
102	C₄×C₇₁	—	2	1	no	—
103	C₄×C₇₁	—	2	4	no	—
104	C₄×C₇₁	—	2	2	no	—
105	C₄×C₇₁	—	4	2	no	—
106	C₄×C₇₁	C₂×#101	1	1	yes	characteristic
107	C₄×C₇₁	#413	1	1	yes	characteristic
108	C₄×C₇₁	#466	1	2	yes	—
109	C₄×C₇₁	#467	1	2	yes	—
110	#8617	—	71	1	no	maximal, Sylow
111	C₂×C₇₁	—	2	1	no	—
112	C₂×C₇₁	—	2	1	no	—
113	C₂×C₇₁	#1801	1	1	yes	characteristic
114	C₂×C₇₁	#1808	1	1	yes	characteristic
115	C₂×C₇₁	#1813	1	1	yes	characteristic
116	C₂×C₈×Q₈	—	71	1	no	—
117	#1801	—	71	1	no	—
118	#1801	D₇₁	1	1	yes	characteristic
119	#1567	—	71	2	no	—
120	#1292	—	71	2	no	—
121	C₇₁	#8617	1	1	yes	characteristic, complemented, Sylow
122	C₂×C₄×Q₈	C₂×D₇₁	1	1	yes	characteristic
123	C₈×Q₈	—	142	2	no	—
124	C₈×Q₈	—	142	2	no	—
125	#423	—	71	2	no	—
126	#423	C₂×D₇₁	1	2	yes	—
127	C₂×C₄⋊C₈	—	71	2	no	—
128	C₂×C₄⋊C₈	—	71	1	no	—
129	C₂×#101	—	2	1	no	—
130	C₂×#101	—	142	1	no	—
131	C₂×C₄×C₈	—	71	1	no	—
132	C₂×C₄×C₈	—	71	2	no	—
133	#343	—	2	1	no	—
134	#343	—	142	1	no	—
135	#335	—	142	2	no	—
136	#335	—	142	2	no	—
137	C₂²×Q₈	C₂²⋊D₇₁	1	1	yes	characteristic
138	C₂×M₁₆	—	2	2	no	—
139	C₂×M₁₆	—	142	2	no	—
140	C₂²×C₈	—	71	1	no	—
141	C₂²×C₈	—	71	2	no	—
142	C₂²×C₈	—	71	1	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	C₂×C₄⋊C₄	Dic₁₄₂	1	2	yes	—
146	C₂×C₄⋊C₄	C₂²⋊D₇₁	1	1	yes	characteristic
147	C₂×C₄²	C₄×D₇₁	1	2	yes	—
148	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	C₄⋊C₈	—	142	4	no	—
152	C₄⋊C₈	—	142	2	no	—
153	C₄⋊C₈	—	142	2	no	—
154	C₄⋊C₈	—	142	2	no	—
155	#101	—	4	2	no	—
156	#101	—	284	2	no	—
157	C₄×C₈	—	71	2	no	—
158	C₄×C₈	—	71	2	no	—
159	C₄×C₈	—	142	2	no	—
160	C₄×C₈	—	142	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	#11765850	1	2	yes	—
164	C₂×Q₈	#11765855	1	2	yes	—
165	C₂²×C₄	Dic₇₁⋊C₄	1	2	yes	—
166	C₂²×C₄	Dic₇₁⋊C₄	1	2	yes	—
167	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
169	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
170	M₁₆	—	4	2	no	—
171	M₁₆	—	4	2	no	—
172	M₁₆	—	284	2	no	—
173	M₁₆	—	284	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	284	2	no	—
176	C₂×C₈	—	284	2	no	—
177	C₂×C₈	—	284	1	no	—
178	C₂×C₈	—	71	1	no	—
179	C₂×C₈	—	71	1	no	—
180	C₂×C₈	—	71	2	no	—
181	C₂×C₈	—	142	2	no	—
182	C₂×C₈	—	142	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	2	2	no	—
187	C₄²	D₄×D₇₁	1	2	yes	—
188	C₄²	#11765864	1	2	yes	—
189	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
190	Q₈	—	2	4	no	—
191	Q₈	—	2	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	#14556061	1	4	yes	—
200	C₂×C₄	C₂²⋊C₄×D₇₁	1	1	yes	characteristic
201	C₂×C₄	#14556084	1	1	yes	characteristic
202	C₂×C₄	#14556100	1	2	yes	—
203	C₂×C₄	#14556105	1	2	yes	—
204	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
205	C₂×C₄	C₂×#11765855	1	1	yes	characteristic
206	C₂×C₄	#14556148	1	2	yes	—
207	C₈	—	8	2	no	—
208	C₈	—	284	2	no	—
209	C₈	—	568	2	no	—
210	C₈	—	71	2	no	—
211	C₈	—	142	1	no	—
212	C₈	—	142	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#17985857	1	1	yes	characteristic
216	C₂²	C₂×#14556061	1	1	yes	characteristic
217	C₂²	#17986035	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	4	no	—
220	C₄	—	2	2	no	—
221	C₄	—	4	2	no	—
222	C₄	#101×D₇₁	1	1	yes	characteristic
223	C₄	#17985982	1	1	yes	characteristic
224	C₄	#17986233	1	2	yes	—
225	C₄	#17986238	1	2	yes	—
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	#22588334	1	1	yes	characteristic
229	C₂	#22588367	1	1	yes	characteristic
230	C₂	#22588388	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×C₇₁⋊C₈

C₂

yes

maximal, characteristic

#22588336

C₂

yes

maximal, characteristic

#22587098

C₂

yes

maximal

#22586214

C₂

yes

maximal

C₇₁×#1801

C₂

yes

maximal, characteristic

Q₈×C₇₁⋊C₈

—

Q₈×C₇₁⋊C₈

—

#17986023

C₂²

yes

—

C₂×C₄⋊(C₇₁⋊C₈)

C₄

yes

—

C₂×C₄⋊(C₇₁⋊C₈)

C₂²

yes

characteristic

C₂×#14556047

—

C₂×C₄×C₇₁⋊C₈

C₄

yes

—

C₂×C₄×C₇₁⋊C₈

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

—

C₂×#101×C₇₁

—

#343×C₇₁

—

C₂×#11765849

—

C₂²×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₇₁⋊C₈

C₂×C₄

yes

—

C₂²×C₇₁⋊C₈

C₂×C₄

yes

characteristic

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

C₄⋊(C₇₁⋊C₈)

—

#14556047

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₄×C₇₁⋊C₈

D₄

yes

—

C₂²×Q₈×C₇₁

D₄

yes

characteristic

C₂×M₁₆×C₇₁

—

C₄×Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

C₂×C₄⋊C₄×C₇₁

D₄

yes

characteristic

C₂×C₄⋊C₄×C₇₁

Q₈

yes

—

C₂×C₄²×C₇₁

C₂×C₄

yes

—

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

C₄⋊C₈×C₇₁

—

#101×C₇₁

—

#11765849

—

#11765849

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

—

C₂×C₇₁⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

—

C₂×Q₈×C₇₁

D₈

yes

—

C₂×Q₈×C₇₁

Q₁₆

yes

—

C₂²×C₄×C₇₁

C₄⋊C₄

yes

—

C₂²×C₄×C₇₁

C₄⋊C₄

yes

—

C₂²×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₁

C₂×Q₈

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

C₂×D₄

yes

—

C₄²×C₇₁

#41

yes

—

C₂³×C₇₁

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₇₁

—

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

#107

yes

—

C₂×C₄×C₇₁

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₁

yes

C₂×C₄×C₇₁

yes

—

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₁

C₂×D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₇₁

#135

yes

—

C₈×C₇₁

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

—

C₇₁⋊C₈

#101

yes

complemented

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

#380

yes

characteristic

100

C₂²×C₇₁

C₂×#107

yes

characteristic

101

C₂²×C₇₁

#427

yes

characteristic

102

C₄×C₇₁

—

103

C₄×C₇₁

—

104

C₄×C₇₁

—

105

C₄×C₇₁

—

106

C₄×C₇₁

C₂×#101

yes

characteristic

107

C₄×C₇₁

#413

yes

characteristic

108

C₄×C₇₁

#466

yes

—

109

C₄×C₇₁

#467

yes

—

110

#8617

—

maximal, Sylow

111

C₂×C₇₁

—

112

C₂×C₇₁

—

113

C₂×C₇₁

#1801

yes

characteristic

114

C₂×C₇₁

#1808

yes

characteristic

115

C₂×C₇₁

#1813

yes

characteristic

116

C₂×C₈×Q₈

—

117

#1801

—

118

#1801

D₇₁

yes

characteristic

119

#1567

—

120

#1292

—

121

C₇₁

#8617

yes

characteristic, complemented, Sylow

122

C₂×C₄×Q₈

C₂×D₇₁

yes

characteristic

123

C₈×Q₈

—

142

—

124

C₈×Q₈

—

142

—

125

#423

—

126

#423

C₂×D₇₁

yes

—

127

C₂×C₄⋊C₈

—

128

C₂×C₄⋊C₈

—

129

C₂×#101

—

130

C₂×#101

—

142

—

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

#343

—

134

#343

—

142

—

135

#335

—

142

—

136

#335

—

142

—

137

C₂²×Q₈

C₂²⋊D₇₁

yes

characteristic

138

C₂×M₁₆

—

139

C₂×M₁₆

—

142

—

140

C₂²×C₈

—

141

C₂²×C₈

—

142

C₂²×C₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

C₂×C₄⋊C₄

Dic₁₄₂

yes

—

146

C₂×C₄⋊C₄

C₂²⋊D₇₁

yes

characteristic

147

C₂×C₄²

C₄×D₇₁

yes

—

148

C₂×C₄²

C₂²×D₇₁

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

142

—

152

C₄⋊C₈

—

142

—

153

C₄⋊C₈

—

142

—

154

C₄⋊C₈

—

142

—

155

#101

—

156

#101

—

284

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

142

—

160

C₄×C₈

—

142

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

#11765850

yes

—

164

C₂×Q₈

#11765855

yes

—

165

C₂²×C₄

Dic₇₁⋊C₄

yes

—

166

C₂²×C₄

Dic₇₁⋊C₄

yes

—

167

C₂²×C₄

C₂×C₄×D₇₁

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

169

C₂²×C₄

C₂×Dic₁₄₂

yes

characteristic

170

M₁₆

—

171

M₁₆

—

172

M₁₆

—

284

—

173

M₁₆

—

284

—

174

C₂×C₈

—

175

C₂×C₈

—

284

—

176

C₂×C₈

—

284

—

177

C₂×C₈

—

284

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

142

—

182

C₂×C₈

—

142

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₇₁

yes

—

188

C₄²

#11765864

yes

—

189

C₂³

C₂×Dic₇₁⋊C₄

yes

characteristic

190

Q₈

—

191

Q₈

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#14556061

yes

—

200

C₂×C₄

C₂²⋊C₄×D₇₁

yes

characteristic

201

C₂×C₄

#14556084

yes

characteristic

202

C₂×C₄

#14556100

yes

—

203

C₂×C₄

#14556105

yes

—

204

C₂×C₄

C₂×#11765850

yes

characteristic

205

C₂×C₄

C₂×#11765855

yes

characteristic

206

C₂×C₄

#14556148

yes

—

207

C₈

—

208

C₈

—

284

—

209

C₈

—

568

—

210

C₈

—

211

C₈

—

142

—

212

C₈

—

142

—

213

C₂²

—

214

C₂²

—

215

C₂²

#17985857

yes

characteristic

216

C₂²

C₂×#14556061

yes

characteristic

217

C₂²

#17986035

yes

characteristic

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

#101×D₇₁

yes

characteristic

223

C₄

#17985982

yes

characteristic

224

C₄

#17986233

yes

—

225

C₄

#17986238

yes

—

226

C₂

—

227

C₂

—

228

C₂

#22588334

yes

characteristic

229

C₂

#22588367

yes

characteristic

230

C₂

#22588388

yes

characteristic

	subgroup	G/H
center	C₂²	#17985857
commutator	C₂²×C₄×C₇₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1801	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂³×C₇₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₇₁	C₂³
hypercenter	#1801	D₇₁
hypocenter	C₇₁	#8617
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

subgroup

G/H

center

C₂²

#17985857

commutator

C₂²×C₄×C₇₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1801

C₂

socle

C₂²×C₇₁

#380

prime radical

C₂³×C₇₁

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₇₁

C₂³

D₇₁

C₇₁

G ▷ C₂²×C₄×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1801

N	H ≅ G/N	type
96. C₇₁⋊C₈	#101	semidirect
121. C₇₁	#8617	semidirect

H ≅ G/N

type

96. C₇₁⋊C₈

#101

semidirect

121. C₇₁

#8617

semidirect

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

subgroup	index
C₂×Q₈×C₇₁⋊C₈	2
#22588336	2
#22587098	2
#22586214	2
C₇₁×#1801	2
#8617	71

subgroup

index

C₂×Q₈×C₇₁⋊C₈

C₇₁×#1801

Subgroups — #31890382

Conjugacy classes of subgroups

Complements

Maximal subgroups