Group #15765932 — subgroups

Subgroups — #15765932

Order 3328.

504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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	#13119865	C₂	1	1	yes	maximal, characteristic
2	#13115785	C₂	1	2	yes	maximal
3	#13112719	C₂	1	1	yes	maximal, characteristic
4	#13112676	C₂	1	2	yes	maximal
5	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×#88142	—	2	2	no	—
8	C₂×C₁₃×#103	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#384	C₂²	1	1	yes	characteristic
11	#11718640	—	2	2	no	—
12	#11718634	—	2	2	no	—
13	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	#11718121	—	2	2	no	—
16	#11718121	—	2	2	no	—
17	C₂²×Q₈×C₁₃	—	2	1	no	—
18	C₂²×Dic₂₆	—	2	2	no	—
19	C₂²×C₈×C₁₃	—	2	1	no	—
20	C₁₃×C₄⋊Q₈	—	2	2	no	—
21	C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₁₃×C₄⋊Q₈	Q₈	1	2	yes	complemented
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
28	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
29	C₂×#6101	—	2	4	no	—
30	C₂×C₄×Dic₁₃	—	2	2	no	—
31	C₂²×#1055	—	2	2	no	—
32	#88142	—	4	4	no	—
33	#88142	—	4	4	no	—
34	C₁₃×#103	—	4	4	no	—
35	C₄×C₈×C₁₃	—	2	2	no	—
36	#88071	—	2	2	no	—
37	#88071	—	2	2	no	—
38	C₄⋊#1055	—	2	2	no	—
39	C₄⋊#1055	—	2	2	no	—
40	#10349	—	13	1	no	maximal, Sylow
41	C₂×Q₈×C₁₃	—	2	2	no	—
42	C₂×Q₈×C₁₃	—	4	2	no	—
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂×Q₈×C₁₃	—	4	1	no	—
45	C₂²×C₄×C₁₃	—	2	2	no	—
46	C₂²×C₄×C₁₃	—	4	1	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×Dic₁₃	—	2	2	no	—
50	C₂²×Dic₁₃	—	2	2	no	—
51	C₂×Dic₂₆	—	4	8	no	—
52	C₂×Dic₂₆	—	8	2	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	4	1	no	—
55	C₂×C₈×C₁₃	—	4	1	no	—
56	C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₁₃×C₄⋊C₄	—	4	2	no	—
58	C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₄⋊C₄	—	4	2	no	—
61	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
62	C₄²×C₁₃	#41	1	1	yes	characteristic
63	C₄²×C₁₃	#41	1	2	yes	—
64	C₄⋊Dic₁₃	—	2	2	no	—
65	C₄⋊Dic₁₃	—	2	2	no	—
66	C₄⋊Dic₁₃	SD₁₆	1	4	yes	—
67	C₄⋊Dic₁₃	Q₁₆	1	4	yes	—
68	#6101	—	4	8	no	—
69	C₄×Dic₁₃	—	4	2	no	—
70	C₄×Dic₁₃	—	4	2	no	—
71	C₂×#1055	—	4	2	no	—
72	C₂×#1055	—	4	2	no	—
73	C₂×#1055	—	4	2	no	—
74	#2551	—	13	1	no	—
75	#1987	—	13	2	no	—
76	#1956	D₁₃	1	1	yes	characteristic
77	#1296	—	13	1	no	—
78	#1279	—	13	2	no	—
79	C₂³×C₁₃	#120	1	1	yes	characteristic
80	Q₈×C₁₃	—	4	4	no	—
81	Q₈×C₁₃	—	8	2	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	4	2	no	—
85	C₂×C₄×C₁₃	—	4	4	no	—
86	C₂×C₄×C₁₃	—	4	2	no	—
87	C₂×C₄×C₁₃	—	8	1	no	—
88	C₂×C₄×C₁₃	—	8	1	no	—
89	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
91	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
92	C₂×C₄×C₁₃	#124	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
94	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
96	C₂×C₄×C₁₃	#137	1	2	yes	—
97	C₂×Dic₁₃	—	2	4	no	—
98	C₂×Dic₁₃	—	2	4	no	—
99	C₂×Dic₁₃	—	4	2	no	—
100	C₂×Dic₁₃	—	4	2	no	—
101	C₂×Dic₁₃	—	4	2	no	—
102	C₂×Dic₁₃	—	4	2	no	—
103	Dic₂₆	—	8	8	no	—
104	C₈×C₁₃	—	4	2	no	—
105	#1055	—	8	2	no	—
106	C₂×C₄⋊Q₈	—	26	2	no	—
107	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
108	C₂×C₄⋊C₈	—	13	2	no	—
109	C₂×#103	—	2	2	no	—
110	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
111	#395	—	26	2	no	—
112	#389	—	26	2	no	—
113	#384	C₂×D₁₃	1	1	yes	characteristic
114	C₄×C₄⋊C₄	—	13	2	no	—
115	#340	—	26	2	no	—
116	#340	—	26	2	no	—
117	C₂²×C₁₃	#393	1	1	yes	characteristic
118	C₂²×C₁₃	#450	1	2	yes	—
119	C₂²×C₁₃	#451	1	2	yes	—
120	C₂²×C₁₃	#453	1	1	yes	characteristic
121	C₂²×C₁₃	#454	1	1	yes	characteristic
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	8	2	no	—
125	C₄×C₁₃	—	8	2	no	—
126	C₄×C₁₃	#475	1	2	yes	—
127	C₄×C₁₃	#477	1	2	yes	—
128	C₄×C₁₃	#487	1	2	yes	—
129	C₄×C₁₃	#489	1	2	yes	—
130	Dic₁₃	—	4	4	no	—
131	Dic₁₃	—	4	4	no	—
132	C₂²×Q₈	—	2	1	no	—
133	C₂²×Q₈	—	26	2	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	26	2	no	—
136	C₄⋊Q₈	—	2	1	no	—
137	C₄⋊Q₈	—	2	2	no	—
138	C₄⋊Q₈	—	52	4	no	—
139	C₄⋊Q₈	—	52	4	no	—
140	C₄⋊Q₈	Dic₂₆	1	2	yes	complemented
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	13	2	no	—
144	C₂×C₄⋊C₄	—	13	2	no	—
145	C₂×C₄⋊C₄	—	26	4	no	—
146	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	2	yes	—
147	C₂×C₄²	—	26	2	no	—
148	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
149	C₄⋊C₈	—	26	2	no	—
150	C₄⋊C₈	—	26	2	no	—
151	#103	—	4	4	no	—
152	C₄×C₈	—	2	2	no	—
153	#95	—	26	2	no	—
154	#95	—	26	2	no	—
155	C₂×C₁₃	#1629	1	1	yes	characteristic
156	C₂×C₁₃	#1633	1	1	yes	characteristic
157	C₂×C₁₃	#1637	1	2	yes	—
158	C₂×C₁₃	#2024	1	2	yes	—
159	C₂×C₁₃	#2027	1	1	yes	characteristic
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	1	no	—
164	C₂×Q₈	—	52	8	no	—
165	C₂×Q₈	—	104	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	4	1	no	—
168	C₂²×C₄	—	26	2	no	—
169	C₂²×C₄	—	26	2	no	—
170	C₂²×C₄	D₄×D₁₃	1	2	yes	—
171	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	52	2	no	—
176	C₂×C₈	—	52	2	no	—
177	C₂×C₈	—	52	2	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	13	4	no	—
184	C₄⋊C₄	—	13	4	no	—
185	C₄⋊C₄	—	26	2	no	—
186	C₄⋊C₄	—	26	2	no	—
187	C₄⋊C₄	—	52	8	no	—
188	C₄²	—	52	2	no	—
189	C₄²	—	52	2	no	—
190	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
191	C₄²	#6127	1	1	yes	characteristic
192	C₄²	#6129	1	2	yes	—
193	C₁₃	#10349	1	1	yes	characteristic, complemented, Sylow
194	C₂³	#88191	1	1	yes	characteristic
195	Q₈	—	4	4	no	—
196	Q₈	—	8	2	no	—
197	Q₈	—	104	8	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	4	4	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	8	1	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	26	4	no	—
206	C₂×C₄	—	26	4	no	—
207	C₂×C₄	—	52	2	no	—
208	C₂×C₄	—	52	2	no	—
209	C₂×C₄	—	52	2	no	—
210	C₂×C₄	—	52	2	no	—
211	C₂×C₄	#88132	1	2	yes	—
212	C₂×C₄	#88139	1	2	yes	—
213	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
214	C₂×C₄	#88168	1	2	yes	—
215	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
216	C₂×C₄	#88172	1	2	yes	—
217	C₂×C₄	#88178	1	1	yes	characteristic
218	C₂×C₄	#88190	1	1	yes	characteristic
219	C₈	—	4	2	no	—
220	C₈	—	104	2	no	—
221	C₂²	#11718608	1	1	yes	characteristic
222	C₂²	#11718723	1	1	yes	characteristic
223	C₂²	#11718738	1	1	yes	characteristic
224	C₂²	#11718830	1	2	yes	—
225	C₂²	#11718847	1	2	yes	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	8	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	52	4	no	—
231	C₄	—	52	4	no	—
232	C₄	#11718452	1	2	yes	—
233	C₄	#11718453	1	2	yes	—
234	C₄	#11718455	1	2	yes	—
235	C₄	#11718456	1	2	yes	—
236	C₂	#13113950	1	1	yes	characteristic
237	C₂	#13113974	1	1	yes	characteristic
238	C₂	#13113998	1	2	yes	—
239	C₂	#13115975	1	2	yes	—
240	C₂	#13115992	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13119865

C₂

yes

maximal, characteristic

#13115785

C₂

yes

maximal

#13112719

C₂

yes

maximal, characteristic

#13112676

C₂

yes

maximal

C₁₃×#1956

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#88142

—

C₂×C₁₃×#103

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

characteristic

#11718640

—

#11718634

—

C₄×C₄⋊Dic₁₃

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

#11718121

—

#11718121

—

C₂²×Q₈×C₁₃

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

Q₈

yes

complemented

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×C₄⋊Dic₁₃

D₄

yes

—

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂²×#1055

—

#88142

—

#88142

—

C₁₃×#103

—

C₄×C₈×C₁₃

—

—

—

—

—

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

C₄²×C₁₃

yes

C₄²×C₁₃

yes

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

SD₁₆

yes

—

C₄⋊Dic₁₃

Q₁₆

yes

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic

#1296

—

#1279

—

C₂³×C₁₃

#120

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₂×C₄×C₁₃

C₂×Q₁₆

yes

—

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

100

C₂×Dic₁₃

—

101

C₂×Dic₁₃

—

102

C₂×Dic₁₃

—

103

Dic₂₆

—

104

C₈×C₁₃

—

105

#1055

—

106

C₂×C₄⋊Q₈

—

107

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

108

C₂×C₄⋊C₈

—

109

C₂×#103

—

110

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

111

#395

—

112

#389

—

113

#384

C₂×D₁₃

yes

characteristic

114

C₄×C₄⋊C₄

—

115

#340

—

116

#340

—

117

C₂²×C₁₃

#393

yes

characteristic

118

C₂²×C₁₃

#450

yes

—

119

C₂²×C₁₃

#451

yes

—

120

C₂²×C₁₃

#453

yes

characteristic

121

C₂²×C₁₃

#454

yes

characteristic

122

C₄×C₁₃

—

123

C₄×C₁₃

—

124

C₄×C₁₃

—

125

C₄×C₁₃

—

126

C₄×C₁₃

#475

yes

—

127

C₄×C₁₃

#477

yes

—

128

C₄×C₁₃

#487

yes

—

129

C₄×C₁₃

#489

yes

—

130

Dic₁₃

—

131

Dic₁₃

—

132

C₂²×Q₈

—

133

C₂²×Q₈

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

Dic₂₆

yes

complemented

141

C₂×C₄⋊C₄

—

142

C₂×C₄⋊C₄

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂²×D₁₃

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

C₄×C₈

—

153

#95

—

154

#95

—

155

C₂×C₁₃

#1629

yes

characteristic

156

C₂×C₁₃

#1633

yes

characteristic

157

C₂×C₁₃

#1637

yes

—

158

C₂×C₁₃

#2024

yes

—

159

C₂×C₁₃

#2027

yes

characteristic

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

104

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

D₄×D₁₃

yes

—

171

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄²

—

189

C₄²

—

190

C₄²

C₂×Dic₂₆

yes

characteristic

191

C₄²

#6127

yes

characteristic

192

C₄²

#6129

yes

—

193

C₁₃

#10349

yes

characteristic, complemented, Sylow

194

C₂³

#88191

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

104

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

#88132

yes

—

212

C₂×C₄

#88139

yes

—

213

C₂×C₄

SD₁₆×D₁₃

yes

—

214

C₂×C₄

#88168

yes

—

215

C₂×C₄

Q₁₆×D₁₃

yes

—

216

C₂×C₄

#88172

yes

—

217

C₂×C₄

#88178

yes

characteristic

218

C₂×C₄

#88190

yes

characteristic

219

C₈

—

220

C₈

—

104

—

221

C₂²

#11718608

yes

characteristic

222

C₂²

#11718723

yes

characteristic

223

C₂²

#11718738

yes

characteristic

224

C₂²

#11718830

yes

—

225

C₂²

#11718847

yes

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#11718452

yes

—

233

C₄

#11718453

yes

—

234

C₄

#11718455

yes

—

235

C₄

#11718456

yes

—

236

C₂

#13113950

yes

characteristic

237

C₂

#13113974

yes

characteristic

238

C₂

#13113998

yes

—

239

C₂

#13115975

yes

—

240

C₂

#13115992

yes

characteristic

	subgroup	G/H
center	C₂³	#88191
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1956	C₂
socle, prime radical	C₂³×C₁₃	#120
hypercenter	#1956	D₁₃
hypocenter	C₁₃	#10349
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#88191

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1956

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
22. C₁₃×C₄⋊Q₈	Q₈	semidirect
140. C₄⋊Q₈	Dic₂₆	semidirect
193. C₁₃	#10349	semidirect

H ≅ G/N

type

22. C₁₃×C₄⋊Q₈

Q₈

semidirect

140. C₄⋊Q₈

Dic₂₆

semidirect

193. C₁₃

#10349

semidirect

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

subgroup	index
#13119865	2
#13115785	2
#13112719	2
#13112676	2
C₁₃×#1956	2
#10349	13

subgroup

index

C₁₃×#1956

Subgroups — #15765932

Conjugacy classes of subgroups

Complements

Maximal subgroups