Group #15756059 — subgroups

Subgroups — #15756059

Order 3328.

378 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 123 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×C₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	#13114974	C₂	1	1	yes	maximal, characteristic
3	#13113266	C₂	1	2	yes	maximal
4	#13112732	C₂	1	2	yes	maximal
5	C₁₃×#1564	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
7	C₁₃×#431	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88054	—	2	1	no	—
10	C₂×C₈×Dic₁₃	—	2	1	no	—
11	#11718585	C₂²	1	2	yes	—
12	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
13	C₈×Dic₂₆	—	2	1	no	—
14	C₈×Dic₂₆	—	2	1	no	—
15	C₈×Dic₂₆	C₄	1	2	yes	—
16	C₈×Dic₂₆	C₄	1	2	yes	—
17	C₁₃×#335	—	2	1	no	—
18	C₁₃×#334	—	2	1	no	—
19	#11718144	—	2	1	no	—
20	#11718144	—	2	1	no	—
21	#11718048	—	2	4	no	—
22	C₂²×Dic₂₆	Q₈	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₃	Q₈	1	1	yes	characteristic
27	C₂×#6101	—	2	1	no	—
28	C₂×C₄×Dic₁₃	—	2	1	no	—
29	C₂×#6099	—	2	2	no	—
30	C₂²×#1055	—	2	1	no	—
31	C₄×Dic₂₆	—	2	1	no	—
32	C₄×Dic₂₆	—	2	1	no	—
33	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
34	C₄×Dic₂₆	D₄	1	2	yes	—
35	C₁₃×C₄⋊C₈	—	2	2	no	—
36	C₁₃×C₂²⋊C₈	—	2	2	no	—
37	C₄×C₈×C₁₃	—	2	2	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
42	#88054	—	2	2	no	—
43	#88054	—	2	2	no	—
44	C₈×Dic₁₃	—	2	2	no	—
45	C₈×Dic₁₃	—	2	2	no	—
46	C₄⋊#1055	—	2	1	no	—
47	C₄⋊#1055	—	2	2	no	—
48	C₄⋊#1055	—	2	2	no	—
49	C₄⋊#1055	C₂×C₄	1	2	yes	—
50	#8661	—	13	1	no	maximal, Sylow
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
54	C₂²×Dic₁₃	—	2	1	no	—
55	C₂²×Dic₁₃	—	2	1	no	—
56	C₂×Dic₂₆	—	2	1	no	—
57	C₂×Dic₂₆	—	2	4	no	—
58	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
59	C₂×C₈×C₁₃	—	2	2	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	4	2	no	—
62	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₃	#41	1	1	yes	characteristic
70	C₄⋊Dic₁₃	—	2	1	no	—
71	C₄⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
72	#6101	—	2	2	no	—
73	#6101	—	2	2	no	—
74	C₄×Dic₁₃	—	2	2	no	—
75	C₄×Dic₁₃	—	2	2	no	—
76	#6099	—	4	2	no	—
77	#6099	—	4	2	no	—
78	C₂×#1055	—	2	2	no	—
79	C₂×#1055	—	4	2	no	—
80	C₂×#1055	—	4	2	no	—
81	C₂×C₈×Q₈	—	13	1	no	—
82	#1837	—	13	1	no	—
83	#1564	D₁₃	1	1	yes	characteristic
84	#1487	—	13	2	no	—
85	#1301	—	13	2	no	—
86	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	4	1	no	—
89	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
92	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
93	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#135	1	2	yes	—
96	C₂×C₄×C₁₃	#137	1	2	yes	—
97	C₂×Dic₁₃	—	2	4	no	—
98	C₂×Dic₁₃	—	2	2	no	—
99	C₂×Dic₁₃	—	2	2	no	—
100	C₂×Dic₁₃	—	4	2	no	—
101	Dic₂₆	—	2	4	no	—
102	Dic₂₆	—	2	2	no	—
103	Dic₂₆	#108	1	4	yes	—
104	C₈×C₁₃	—	2	1	no	—
105	C₈×C₁₃	—	2	1	no	—
106	C₈×C₁₃	—	2	1	no	—
107	C₈×C₁₃	—	2	1	no	—
108	C₈×C₁₃	—	8	2	no	—
109	#1055	—	4	2	no	—
110	#1055	—	8	2	no	—
111	C₂×C₄×Q₈	—	13	1	no	—
112	C₈×Q₈	—	13	2	no	—
113	C₈×Q₈	—	13	2	no	—
114	C₈×Q₈	—	26	1	no	—
115	C₈×Q₈	—	26	1	no	—
116	#431	C₂×D₁₃	1	2	yes	—
117	#423	—	13	2	no	—
118	C₂×C₄⋊C₈	—	13	1	no	—
119	C₂×C₄⋊C₈	—	26	1	no	—
120	C₂×C₄×C₈	—	26	1	no	—
121	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
122	#341	—	26	1	no	—
123	#341	—	26	1	no	—
124	#335	—	2	1	no	—
125	#334	—	2	1	no	—
126	Q₈⋊C₈	—	26	4	no	—
127	C₂²×C₁₃	—	2	1	no	—
128	C₂²×C₁₃	—	2	1	no	—
129	C₂²×C₁₃	#380	1	1	yes	characteristic
130	C₂²×C₁₃	#479	1	2	yes	—
131	C₄×C₁₃	—	2	1	no	—
132	C₄×C₁₃	—	2	1	no	—
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	#416	1	1	yes	characteristic
135	C₄×C₁₃	#419	1	1	yes	characteristic
136	C₄×C₁₃	C₂×#108	1	2	yes	—
137	C₄×C₁₃	#464	1	2	yes	—
138	Dic₁₃	—	2	4	no	—
139	Dic₁₃	—	4	2	no	—
140	C₂²×Q₈	—	13	1	no	—
141	C₂×M₁₆	—	26	2	no	—
142	C₂²×C₈	—	26	1	no	—
143	C₂²×C₈	D₅₂	1	1	yes	characteristic
144	C₂²×C₈	D₅₂	1	1	yes	characteristic
145	C₄×Q₈	—	13	2	no	—
146	C₄×Q₈	—	13	2	no	—
147	C₄×Q₈	—	26	1	no	—
148	C₄×Q₈	—	26	1	no	—
149	C₂×C₄⋊C₄	—	13	1	no	—
150	C₂×C₄⋊C₄	—	26	1	no	—
151	C₂×C₄²	—	26	1	no	—
152	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	13	2	no	—
155	C₄⋊C₈	—	26	2	no	—
156	C₄⋊C₈	—	26	2	no	—
157	C₄⋊C₈	—	26	2	no	—
158	C₄⋊C₈	—	26	2	no	—
159	C₄⋊C₈	—	26	1	no	—
160	C₂²⋊C₈	—	2	2	no	—
161	C₄×C₈	—	2	2	no	—
162	C₄×C₈	—	26	2	no	—
163	C₄×C₈	—	26	2	no	—
164	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
165	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
167	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
168	C₂×C₁₃	—	2	2	no	—
169	C₂×C₁₃	#1805	1	1	yes	characteristic
170	C₂×C₁₃	#1810	1	1	yes	characteristic
171	C₂×C₁₃	#1814	1	1	yes	characteristic
172	C₂×Q₈	—	13	2	no	—
173	C₂×Q₈	—	26	4	no	—
174	C₂×Q₈	—	26	1	no	—
175	C₂²×C₄	—	26	1	no	—
176	C₂²×C₄	—	26	1	no	—
177	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
178	C₂²×C₄	#6129	1	1	yes	characteristic
179	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
180	M₁₆	—	52	2	no	—
181	M₁₆	—	52	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	26	2	no	—
186	C₂×C₈	—	52	2	no	—
187	C₂×C₈	—	52	2	no	—
188	C₂×C₈	#6103	1	1	yes	characteristic
189	C₂×C₈	#6103	1	1	yes	characteristic
190	C₂×C₈	#6103	1	1	yes	characteristic
191	C₂×C₈	#6103	1	1	yes	characteristic
192	C₄⋊C₄	—	13	2	no	—
193	C₄⋊C₄	—	26	2	no	—
194	C₄⋊C₄	—	26	2	no	—
195	C₄⋊C₄	—	26	1	no	—
196	C₄²	—	26	2	no	—
197	C₄²	—	26	2	no	—
198	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
199	C₄²	D₄×D₁₃	1	1	yes	characteristic
200	C₄²	#6131	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
202	C₁₃	#8661	1	1	yes	characteristic, complemented, Sylow
203	C₂³	#88151	1	1	yes	characteristic
204	Q₈	—	13	4	no	—
205	Q₈	—	26	4	no	—
206	Q₈	—	26	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	1	no	—
209	C₂×C₄	—	26	4	no	—
210	C₂×C₄	—	26	2	no	—
211	C₂×C₄	—	26	2	no	—
212	C₂×C₄	—	52	2	no	—
213	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
214	C₂×C₄	#88146	1	1	yes	characteristic
215	C₂×C₄	#88149	1	1	yes	characteristic
216	C₂×C₄	#88158	1	2	yes	—
217	C₂×C₄	#88163	1	2	yes	—
218	C₂×C₄	C₂×#6103	1	1	yes	characteristic
219	C₂×C₄	#88192	1	1	yes	characteristic
220	C₂×C₄	#88200	1	1	yes	characteristic
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	2	1	no	—
225	C₈	—	8	2	no	—
226	C₈	—	52	2	no	—
227	C₈	—	104	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#11718490	1	2	yes	—
231	C₂²	#11718648	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	26	4	no	—
236	C₄	—	52	2	no	—
237	C₄	#11718506	1	2	yes	—
238	C₄	D₁₃×#108	1	2	yes	—
239	C₄	#11718774	1	1	yes	characteristic
240	C₄	#11718781	1	1	yes	characteristic
241	C₂	—	2	2	no	—
242	C₂	#13114852	1	1	yes	characteristic
243	C₂	#13114871	1	1	yes	characteristic
244	C₂	#13114887	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₂₆

C₂

yes

maximal, characteristic

#13114974

C₂

yes

maximal, characteristic

#13113266

C₂

yes

maximal

#13112732

C₂

yes

maximal

C₁₃×#1564

C₂

yes

maximal, characteristic

C₂×C₄×Dic₂₆

C₂²

yes

characteristic

C₁₃×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88054

—

C₂×C₈×Dic₁₃

—

#11718585

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

characteristic

C₈×Dic₂₆

—

C₈×Dic₂₆

—

C₈×Dic₂₆

C₄

yes

—

C₈×Dic₂₆

C₄

yes

—

C₁₃×#335

—

C₁₃×#334

—

#11718144

—

#11718144

—

#11718048

—

C₂²×Dic₂₆

Q₈

yes

characteristic

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

Q₈

yes

characteristic

C₂×#6101

—

C₂×C₄×Dic₁₃

—

C₂×#6099

—

C₂²×#1055

—

C₄×Dic₂₆

—

C₄×Dic₂₆

—

C₄×Dic₂₆

C₂×C₄

yes

—

C₄×Dic₂₆

D₄

yes

—

C₁₃×C₄⋊C₈

—

C₁₃×C₂²⋊C₈

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

C₄×C₈×C₁₃

D₄

yes

characteristic

#88054

—

#88054

—

C₈×Dic₁₃

—

C₈×Dic₁₃

—

—

—

—

C₂×C₄

yes

—

#8661

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²⋊C₄

yes

characteristic

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

C₄⋊C₄

yes

—

#6101

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

C₂×C₈×Q₈

—

#1837

—

#1564

D₁₃

yes

characteristic

#1487

—

#1301

—

C₂³×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

100

C₂×Dic₁₃

—

101

Dic₂₆

—

102

Dic₂₆

—

103

Dic₂₆

#108

yes

—

104

C₈×C₁₃

—

105

C₈×C₁₃

—

106

C₈×C₁₃

—

107

C₈×C₁₃

—

108

C₈×C₁₃

—

109

#1055

—

110

#1055

—

111

C₂×C₄×Q₈

—

112

C₈×Q₈

—

113

C₈×Q₈

—

114

C₈×Q₈

—

115

C₈×Q₈

—

116

#431

C₂×D₁₃

yes

—

117

#423

—

118

C₂×C₄⋊C₈

—

119

C₂×C₄⋊C₈

—

120

C₂×C₄×C₈

—

121

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

122

#341

—

123

#341

—

124

#335

—

125

#334

—

126

Q₈⋊C₈

—

127

C₂²×C₁₃

—

128

C₂²×C₁₃

—

129

C₂²×C₁₃

#380

yes

characteristic

130

C₂²×C₁₃

#479

yes

—

131

C₄×C₁₃

—

132

C₄×C₁₃

—

133

C₄×C₁₃

—

134

C₄×C₁₃

#416

yes

characteristic

135

C₄×C₁₃

#419

yes

characteristic

136

C₄×C₁₃

C₂×#108

yes

—

137

C₄×C₁₃

#464

yes

—

138

Dic₁₃

—

139

Dic₁₃

—

140

C₂²×Q₈

—

141

C₂×M₁₆

—

142

C₂²×C₈

—

143

C₂²×C₈

D₅₂

yes

characteristic

144

C₂²×C₈

D₅₂

yes

characteristic

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

—

152

C₂×C₄²

C₂²×D₁₃

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

C₄⋊C₈

—

156

C₄⋊C₈

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₂²⋊C₈

—

161

C₄×C₈

—

162

C₄×C₈

—

163

C₄×C₈

—

164

C₄×C₈

C₄×D₁₃

yes

characteristic

165

C₄×C₈

C₄×D₁₃

yes

characteristic

166

C₄×C₈

C₂²⋊D₁₃

yes

characteristic

167

C₄×C₈

C₂²⋊D₁₃

yes

characteristic

168

C₂×C₁₃

—

169

C₂×C₁₃

#1805

yes

characteristic

170

C₂×C₁₃

#1810

yes

characteristic

171

C₂×C₁₃

#1814

yes

characteristic

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×D₅₂

yes

characteristic

178

C₂²×C₄

#6129

yes

characteristic

179

C₂²×C₄

Q₈×D₁₃

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

187

C₂×C₈

—

188

C₂×C₈

#6103

yes

characteristic

189

C₂×C₈

#6103

yes

characteristic

190

C₂×C₈

#6103

yes

characteristic

191

C₂×C₈

#6103

yes

characteristic

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄²

—

197

C₄²

—

198

C₄²

C₂×C₄×D₁₃

yes

characteristic

199

C₄²

D₄×D₁₃

yes

characteristic

200

C₄²

#6131

yes

characteristic

201

C₄²

C₂×C₂²⋊D₁₃

yes

characteristic

202

C₁₃

#8661

yes

characteristic, complemented, Sylow

203

C₂³

#88151

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

C₄⋊C₄×D₁₃

yes

characteristic

214

C₂×C₄

#88146

yes

characteristic

215

C₂×C₄

#88149

yes

characteristic

216

C₂×C₄

#88158

yes

—

217

C₂×C₄

#88163

yes

—

218

C₂×C₄

C₂×#6103

yes

characteristic

219

C₂×C₄

#88192

yes

characteristic

220

C₂×C₄

#88200

yes

characteristic

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

225

C₈

—

226

C₈

—

227

C₈

—

104

—

228

C₂²

—

229

C₂²

—

230

C₂²

#11718490

yes

—

231

C₂²

#11718648

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

#11718506

yes

—

238

C₄

D₁₃×#108

yes

—

239

C₄

#11718774

yes

characteristic

240

C₄

#11718781

yes

characteristic

241

C₂

—

242

C₂

#13114852

yes

characteristic

243

C₂

#13114871

yes

characteristic

244

C₂

#13114887

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#88149
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1564	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂³×C₁₃	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1564	D₁₃
hypocenter	C₁₃	#8661
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂×C₄

#88149

commutator

C₄²×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1564

C₂

socle

C₂²×C₁₃

#380

prime radical

C₂³×C₁₃

C₂²⋊Q₈

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
202. C₁₃	#8661	semidirect

H ≅ G/N

type

202. C₁₃

#8661

semidirect

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

subgroup	index
C₂×C₈×Dic₂₆	2
#13114974	2
#13113266	2
#13112732	2
C₁₃×#1564	2
#8661	13

subgroup

index

C₂×C₈×Dic₂₆

C₁₃×#1564

Subgroups — #15756059

Conjugacy classes of subgroups

Complements

Maximal subgroups