Group #31900585 — subgroups

Subgroups — #31900585

Order 18176.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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	#22591633	C₂	1	1	yes	maximal, characteristic
2	#22586839	C₂	1	2	yes	maximal
3	#22586241	C₂	1	2	yes	maximal
4	#22586169	C₂	1	1	yes	maximal, characteristic
5	C₇₁×#1995	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₄₂	—	2	1	no	—
7	#17986052	C₂²	1	2	yes	—
8	#17985931	—	2	2	no	—
9	#17985920	—	2	2	no	—
10	C₄×C₄⋊Dic₇₁	—	2	1	no	—
11	C₄×C₄⋊Dic₇₁	C₂²	1	2	yes	—
12	#17985736	—	2	2	no	—
13	#17985736	—	2	2	no	—
14	#533×C₇₁	C₂²	1	1	yes	characteristic
15	#423×C₇₁	C₂²	1	1	yes	characteristic
16	#376×C₇₁	C₂²	1	1	yes	characteristic
17	#339×C₇₁	—	2	1	no	—
18	#339×C₇₁	—	2	1	no	—
19	C₂²×Dic₁₄₂	—	2	1	no	—
20	C₄×Dic₁₄₂	—	4	2	no	—
21	C₄×Dic₁₄₂	—	4	2	no	—
22	C₂×C₄⋊Dic₇₁	—	2	2	no	—
23	C₂×C₄⋊Dic₇₁	—	2	1	no	—
24	C₂×C₄⋊Dic₇₁	—	2	2	no	—
25	C₂×Dic₇₁⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₇₁	—	2	2	no	—
27	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
28	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
29	C₄×C₇₁⋊C₈	—	2	2	no	—
30	C₇₁⋊#95	—	2	1	no	—
31	C₇₁⋊#95	—	2	1	no	—
32	C₇₁⋊#95	D₄	1	2	yes	—
33	C₇₁⋊#95	D₄	1	2	yes	—
34	C₂×M₁₆×C₇₁	—	2	1	no	—
35	C₄⋊Q₈×C₇₁	Q₈	1	2	yes	complemented
36	#125×C₇₁	—	2	1	no	—
37	C₂²⋊Q₈×C₇₁	—	2	2	no	—
38	C₄×Q₈×C₇₁	—	2	2	no	—
39	#117×C₇₁	—	2	1	no	—
40	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₇₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₁	—	2	2	no	—
44	#95×C₇₁	—	2	2	no	—
45	C₂×Dic₁₄₂	—	4	4	no	—
46	C₂×Dic₁₄₂	—	4	2	no	—
47	C₂²×Dic₇₁	—	2	2	no	—
48	C₂²×Dic₇₁	—	2	2	no	—
49	C₂×C₇₁⋊C₈	—	4	2	no	—
50	C₄⋊Dic₇₁	—	4	4	no	—
51	C₄⋊Dic₇₁	—	4	4	no	—
52	C₄⋊Dic₇₁	—	4	2	no	—
53	Dic₇₁⋊C₄	—	4	4	no	—
54	C₄×Dic₇₁	—	4	2	no	—
55	C₄×Dic₇₁	—	4	2	no	—
56	C₂×Q₈×C₇₁	—	2	2	no	—
57	C₂²×C₄×C₇₁	—	2	1	no	—
58	C₂²×C₄×C₇₁	—	2	1	no	—
59	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
61	M₁₆×C₇₁	—	4	1	no	—
62	M₁₆×C₇₁	—	4	1	no	—
63	C₂×C₈×C₇₁	—	4	1	no	—
64	C₄⋊C₄×C₇₁	—	2	2	no	—
65	C₄⋊C₄×C₇₁	—	2	2	no	—
66	C₄⋊C₄×C₇₁	—	4	2	no	—
67	C₂²⋊C₄×C₇₁	—	4	1	no	—
68	C₄²×C₇₁	—	2	1	no	—
69	C₄²×C₇₁	—	2	1	no	—
70	C₄²×C₇₁	—	4	1	no	—
71	C₄²×C₇₁	SD₁₆	1	2	yes	—
72	C₄²×C₇₁	Q₁₆	1	2	yes	—
73	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
74	C₄²×C₇₁	#41	1	2	yes	—
75	C₄²×C₇₁	#41	1	1	yes	characteristic
76	C₂³×C₇₁	#120	1	1	yes	characteristic
77	Q₈×C₇₁	—	8	2	no	—
78	C₂×C₄×C₇₁	—	2	2	no	—
79	C₂×C₄×C₇₁	—	2	2	no	—
80	C₂×C₄×C₇₁	—	4	2	no	—
81	C₂×C₄×C₇₁	—	4	2	no	—
82	C₂×C₄×C₇₁	—	4	2	no	—
83	C₂×C₄×C₇₁	—	4	2	no	—
84	C₂×C₄×C₇₁	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₇₁	#124	1	2	yes	—
87	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
88	C₂×C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₇₁	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₇₁	#137	1	1	yes	characteristic
92	C₂×Dic₇₁	—	2	4	no	—
93	C₂×Dic₇₁	—	4	2	no	—
94	C₂×Dic₇₁	—	4	2	no	—
95	C₂×Dic₇₁	—	4	2	no	—
96	C₂×Dic₇₁	—	4	2	no	—
97	C₂×Dic₇₁	—	4	2	no	—
98	Dic₁₄₂	—	4	8	no	—
99	C₈×C₇₁	—	8	1	no	—
100	C₇₁⋊C₈	—	8	2	no	—
101	C₂²×C₇₁	—	2	2	no	—
102	C₂²×C₇₁	#393	1	1	yes	characteristic
103	C₂²×C₇₁	#450	1	1	yes	characteristic
104	C₂²×C₇₁	#451	1	1	yes	characteristic
105	C₄×C₇₁	—	2	2	no	—
106	C₄×C₇₁	—	2	2	no	—
107	C₄×C₇₁	—	4	2	no	—
108	C₄×C₇₁	—	4	2	no	—
109	C₄×C₇₁	—	8	2	no	—
110	C₄×C₇₁	#475	1	1	yes	characteristic
111	C₄×C₇₁	#477	1	1	yes	characteristic
112	C₄×C₇₁	#487	1	1	yes	characteristic
113	C₄×C₇₁	#489	1	1	yes	characteristic
114	Dic₇₁	—	4	4	no	—
115	Dic₇₁	—	8	2	no	—
116	#10371	—	71	1	no	maximal, Sylow
117	C₂×C₇₁	—	2	1	no	—
118	C₂×C₇₁	—	2	1	no	—
119	C₂×C₇₁	#2024	1	1	yes	characteristic
120	C₂×C₇₁	#2031	1	2	yes	—
121	#2399	—	71	1	no	—
122	#1995	D₇₁	1	1	yes	characteristic
123	#1503	—	71	2	no	—
124	#1303	—	71	2	no	—
125	#1274	—	71	1	no	—
126	C₇₁	#10371	1	1	yes	characteristic, complemented, Sylow
127	#533	C₂×D₇₁	1	1	yes	characteristic
128	C₂×C₄×Q₈	—	142	1	no	—
129	#431	—	71	2	no	—
130	#423	C₂×D₇₁	1	1	yes	characteristic
131	#398	—	142	2	no	—
132	#395	—	142	2	no	—
133	C₄×C₄⋊C₄	—	71	2	no	—
134	C₄×C₄⋊C₄	—	142	1	no	—
135	#376	C₂×D₇₁	1	1	yes	characteristic
136	#339	—	2	1	no	—
137	#339	—	2	1	no	—
138	#328	—	142	2	no	—
139	#328	—	142	2	no	—
140	C₂²×Q₈	—	142	1	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₄⋊Q₈	Dic₁₄₂	1	2	yes	complemented
143	#125	—	2	1	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	284	2	no	—
147	C₄×Q₈	—	284	2	no	—
148	#117	—	2	1	no	—
149	C₂×C₄⋊C₄	—	142	2	no	—
150	C₂×C₄⋊C₄	—	142	1	no	—
151	C₂×C₄⋊C₄	—	142	2	no	—
152	C₂×C₄⋊C₄	—	142	2	no	—
153	C₂×C₄²	—	142	2	no	—
154	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
155	C₂×C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
156	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	142	2	no	—
159	C₂²⋊C₈	—	142	2	no	—
160	C₄×C₈	—	142	2	no	—
161	#95	—	2	2	no	—
162	#95	—	71	2	no	—
163	#95	—	71	2	no	—
164	#95	—	142	1	no	—
165	#95	—	142	1	no	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	284	2	no	—
168	C₂×Q₈	—	284	4	no	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	142	2	no	—
172	C₂²×C₄	—	142	2	no	—
173	C₂²×C₄	D₄×D₇₁	1	2	yes	—
174	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
175	M₁₆	—	4	1	no	—
176	M₁₆	—	4	1	no	—
177	C₂×C₈	—	4	1	no	—
178	C₂×C₈	—	284	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	284	4	no	—
183	C₄⋊C₄	—	284	2	no	—
184	C₄⋊C₄	—	284	4	no	—
185	C₄⋊C₄	—	284	4	no	—
186	C₂²⋊C₄	—	4	1	no	—
187	C₄²	—	2	1	no	—
188	C₄²	—	2	1	no	—
189	C₄²	—	4	1	no	—
190	C₄²	—	284	2	no	—
191	C₄²	—	284	2	no	—
192	C₄²	#11765852	1	2	yes	—
193	C₄²	#11765855	1	2	yes	—
194	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
195	C₄²	#11765864	1	2	yes	—
196	C₄²	#11765865	1	1	yes	characteristic
197	C₂³	#14556096	1	1	yes	characteristic
198	Q₈	—	8	2	no	—
199	Q₈	—	284	8	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	284	2	no	—
207	C₂×C₄	—	284	2	no	—
208	C₂×C₄	—	284	2	no	—
209	C₂×C₄	—	284	2	no	—
210	C₂×C₄	—	284	2	no	—
211	C₂×C₄	—	142	4	no	—
212	C₂×C₄	#14556105	1	2	yes	—
213	C₂×C₄	#14556107	1	1	yes	characteristic
214	C₂×C₄	#14556114	1	2	yes	—
215	C₂×C₄	#14556115	1	1	yes	characteristic
216	C₂×C₄	C₂×#11765852	1	1	yes	characteristic
217	C₂×C₄	C₂×#11765855	1	1	yes	characteristic
218	C₂×C₄	#14556153	1	1	yes	characteristic
219	C₂×C₄	#14556158	1	1	yes	characteristic
220	C₈	—	8	1	no	—
221	C₈	—	568	2	no	—
222	C₂²	—	2	2	no	—
223	C₂²	#17985911	1	1	yes	characteristic
224	C₂²	#17986149	1	1	yes	characteristic
225	C₂²	#17986154	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	2	no	—
231	C₄	—	284	4	no	—
232	C₄	—	568	2	no	—
233	C₄	#17986284	1	1	yes	characteristic
234	C₄	#17986294	1	1	yes	characteristic
235	C₄	#17986349	1	1	yes	characteristic
236	C₄	#17986358	1	1	yes	characteristic
237	C₂	—	2	1	no	—
238	C₂	—	2	1	no	—
239	C₂	#22589481	1	1	yes	characteristic
240	C₂	#22589510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22591633

C₂

yes

maximal, characteristic

#22586839

C₂

yes

maximal

#22586241

C₂

yes

maximal

#22586169

C₂

yes

maximal, characteristic

C₇₁×#1995

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₂

—

#17986052

C₂²

yes

—

#17985931

—

#17985920

—

C₄×C₄⋊Dic₇₁

—

C₄×C₄⋊Dic₇₁

C₂²

yes

—

#17985736

—

#17985736

—

#533×C₇₁

C₂²

yes

characteristic

#423×C₇₁

C₂²

yes

characteristic

#376×C₇₁

C₂²

yes

characteristic

#339×C₇₁

—

#339×C₇₁

—

C₂²×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₄×Dic₁₄₂

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

C₂×C₄⋊Dic₇₁

—

C₂×Dic₇₁⋊C₄

—

C₂×C₄×Dic₇₁

—

C₄⋊(C₇₁⋊C₈)

—

C₂²⋊(C₇₁⋊C₈)

—

C₄×C₇₁⋊C₈

—

C₇₁⋊#95

—

C₇₁⋊#95

—

C₇₁⋊#95

D₄

yes

—

C₇₁⋊#95

D₄

yes

—

C₂×M₁₆×C₇₁

—

C₄⋊Q₈×C₇₁

Q₈

yes

complemented

#125×C₇₁

—

C₂²⋊Q₈×C₇₁

—

C₄×Q₈×C₇₁

—

#117×C₇₁

—

C₂×C₄²×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

D₄

yes

characteristic

C₂×C₄²×C₇₁

C₂³

yes

characteristic

C₄⋊C₈×C₇₁

—

#95×C₇₁

—

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

C₂²×Dic₇₁

—

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₄×Dic₇₁

—

C₂×Q₈×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

—

C₂²×C₄×C₇₁

C₂×D₄

yes

—

C₂²×C₄×C₇₁

C₂×D₄

yes

characteristic

M₁₆×C₇₁

—

M₁₆×C₇₁

—

C₂×C₈×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

—

C₄²×C₇₁

SD₁₆

yes

—

C₄²×C₇₁

Q₁₆

yes

—

C₄²×C₇₁

C₂×Q₈

yes

characteristic

C₄²×C₇₁

#41

yes

—

C₄²×C₇₁

yes

C₂³×C₇₁

yes

Q₈×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₁

#124

yes

—

C₂×C₄×C₇₁

#124

yes

characteristic

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

—

C₂×Dic₇₁

—

Dic₁₄₂

—

C₈×C₇₁

—

100

C₇₁⋊C₈

—

101

C₂²×C₇₁

—

102

C₂²×C₇₁

#393

yes

characteristic

103

C₂²×C₇₁

#450

yes

characteristic

104

C₂²×C₇₁

#451

yes

characteristic

105

C₄×C₇₁

—

106

C₄×C₇₁

—

107

C₄×C₇₁

—

108

C₄×C₇₁

—

109

C₄×C₇₁

—

110

C₄×C₇₁

#475

yes

characteristic

111

C₄×C₇₁

#477

yes

characteristic

112

C₄×C₇₁

#487

yes

characteristic

113

C₄×C₇₁

#489

yes

characteristic

114

Dic₇₁

—

115

Dic₇₁

—

116

#10371

—

maximal, Sylow

117

C₂×C₇₁

—

118

C₂×C₇₁

—

119

C₂×C₇₁

#2024

yes

characteristic

120

C₂×C₇₁

#2031

yes

—

121

#2399

—

122

#1995

D₇₁

yes

characteristic

123

#1503

—

124

#1303

—

125

#1274

—

126

C₇₁

#10371

yes

characteristic, complemented, Sylow

127

#533

C₂×D₇₁

yes

characteristic

128

C₂×C₄×Q₈

—

142

—

129

#431

—

130

#423

C₂×D₇₁

yes

characteristic

131

#398

—

142

—

132

#395

—

142

—

133

C₄×C₄⋊C₄

—

134

C₄×C₄⋊C₄

—

142

—

135

#376

C₂×D₇₁

yes

characteristic

136

#339

—

137

#339

—

138

#328

—

142

—

139

#328

—

142

—

140

C₂²×Q₈

—

142

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

Dic₁₄₂

yes

complemented

143

#125

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

284

—

147

C₄×Q₈

—

284

—

148

#117

—

149

C₂×C₄⋊C₄

—

142

—

150

C₂×C₄⋊C₄

—

142

—

151

C₂×C₄⋊C₄

—

142

—

152

C₂×C₄⋊C₄

—

142

—

153

C₂×C₄²

—

142

—

154

C₂×C₄²

C₂²⋊D₇₁

yes

characteristic

155

C₂×C₄²

C₂²⋊D₇₁

yes

characteristic

156

C₂×C₄²

C₂²×D₇₁

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

142

—

159

C₂²⋊C₈

—

142

—

160

C₄×C₈

—

142

—

161

#95

—

162

#95

—

163

#95

—

164

#95

—

142

—

165

#95

—

142

—

166

C₂×Q₈

—

167

C₂×Q₈

—

284

—

168

C₂×Q₈

—

284

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

142

—

172

C₂²×C₄

—

142

—

173

C₂²×C₄

D₄×D₇₁

yes

—

174

C₂²×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

175

M₁₆

—

176

M₁₆

—

177

C₂×C₈

—

178

C₂×C₈

—

284

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

284

—

183

C₄⋊C₄

—

284

—

184

C₄⋊C₄

—

284

—

185

C₄⋊C₄

—

284

—

186

C₂²⋊C₄

—

187

C₄²

—

188

C₄²

—

189

C₄²

—

190

C₄²

—

284

—

191

C₄²

—

284

—

192

C₄²

#11765852

yes

—

193

C₄²

#11765855

yes

—

194

C₄²

C₂×Dic₁₄₂

yes

characteristic

195

C₄²

#11765864

yes

—

196

C₄²

#11765865

yes

characteristic

197

C₂³

#14556096

yes

characteristic

198

Q₈

—

199

Q₈

—

284

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

284

—

207

C₂×C₄

—

284

—

208

C₂×C₄

—

284

—

209

C₂×C₄

—

284

—

210

C₂×C₄

—

284

—

211

C₂×C₄

—

142

—

212

C₂×C₄

#14556105

yes

—

213

C₂×C₄

#14556107

yes

characteristic

214

C₂×C₄

#14556114

yes

—

215

C₂×C₄

#14556115

yes

characteristic

216

C₂×C₄

C₂×#11765852

yes

characteristic

217

C₂×C₄

C₂×#11765855

yes

characteristic

218

C₂×C₄

#14556153

yes

characteristic

219

C₂×C₄

#14556158

yes

characteristic

220

C₈

—

221

C₈

—

568

—

222

C₂²

—

223

C₂²

#17985911

yes

characteristic

224

C₂²

#17986149

yes

characteristic

225

C₂²

#17986154

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

284

—

232

C₄

—

568

—

233

C₄

#17986284

yes

characteristic

234

C₄

#17986294

yes

characteristic

235

C₄

#17986349

yes

characteristic

236

C₄

#17986358

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#22589481

yes

characteristic

240

C₂

#22589510

yes

—

	subgroup	G/H
center	C₂×C₄	#14556115
commutator, cosocle	C₂×C₄²×C₇₁	C₂³
Frattini	C₂×C₄²	C₂²×D₇₁
Fitting	C₇₁×#1995	C₂
socle	C₂²×C₇₁	#393
prime radical	C₂³×C₇₁	#120
hypercenter	#1995	D₇₁
hypocenter	C₇₁	#10371
LCS	G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

subgroup

G/H

center

C₂×C₄

#14556115

commutator, cosocle

C₂×C₄²×C₇₁

C₂³

Frattini

C₂×C₄²

C₂²×D₇₁

Fitting

C₇₁×#1995

C₂

C₂²×C₇₁

C₂³×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₄²×C₇₁ ▷ C₂²×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1995

N	H ≅ G/N	type
35. C₄⋊Q₈×C₇₁	Q₈	semidirect
126. C₇₁	#10371	semidirect
142. C₄⋊Q₈	Dic₁₄₂	semidirect

H ≅ G/N

type

35. C₄⋊Q₈×C₇₁

Q₈

semidirect

126. C₇₁

#10371

semidirect

142. C₄⋊Q₈

Dic₁₄₂

semidirect

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

subgroup	index
#22591633	2
#22586839	2
#22586241	2
#22586169	2
C₇₁×#1995	2
#10371	71

subgroup

index

C₇₁×#1995

Subgroups — #31900585

Conjugacy classes of subgroups

Complements

Maximal subgroups