Finite Group Databasebeta

← #13119113

Subgroups — #13119113

Order 1664.

700 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D13C212yesmaximal
2C13×#397C211yesmaximal, characteristic, complemented
3#11718650C212yesmaximal, complemented
4#11718616C211yesmaximal, characteristic
5#11718614C211yesmaximal, characteristic, complemented
6#11718613C212yesmaximal, complemented
7#11718329C212yesmaximal, complemented
8#11718325C212yesmaximal, complemented
9#11718325C212yesmaximal, complemented
10C24×D13C2211yescharacteristic
11C22×C4×D13C2212yes—
12C22×C4×D13C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic, complemented
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2211yescharacteristic
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic, complemented
23C2×#6101C2212yescomplemented
24C22⋊C4×D13—28no—
25C13×#95C2211yescharacteristic, complemented
26C13×#95C2212yescomplemented
27#88071C2212yescomplemented
28#88071C2211yescharacteristic, complemented
29#88071C2212yescomplemented
30#88071C2212yescomplemented
31#88071C2212yescomplemented
32C24×C13C2311yescharacteristic
33C23×D13—24no—
34C23×D13—24no—
35C23×D13—41no—
36C23×D13—41no—
37C23×D13D414yes—
38C23×D13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C2×C4×D13—24no—
47C2×C4×D13—24no—
48C2×C4×D13—24no—
49C2×C4×D13—24no—
50C2×C4×D13—42no—
51C2×C4×D13—42no—
52C13×C4⋊C4—41no—
53C13×C22⋊C4—24no—
54C13×C22⋊C4—41no—
55C22⋊Dic13—24no—
56C22⋊Dic13—41no—
57#6103—24no—
58#6103—24no—
59#6103—24no—
60#6103—24no—
61C4⋊Dic13—41no—
62#6101—42no—
63#2483—131nomaximal, Sylow
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—21no—
67C23×C13—21no—
68C23×C13C2×D412yes—
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—22no—
74C22×D13—216no—
75C22×D13—44no—
76C22×D13—44no—
77C22×D13—44no—
78C22×D13—48no—
79C22×D13C2×D414yes—
80C22×D13#4114yes—
81C22×D13#4114yes—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C4×D13—48no—
102C4×D13—48no—
103C22×C22⋊C4—132no—
104#397—132no—
105#397—131no—
106#397D1311yescharacteristic, complemented
107#385—132no—
108#385—132no—
109#381—132no—
110#381—132no—
111#379—131no—
112C22×C13—24no—
113C22×C13—22no—
114C22×C13—41no—
115C22×C13—41no—
116C22×C13—42no—
117C22×C13C22×D411yescharacteristic
118C22×C13C2×#4112yes—
119C22×C13C2×#4112yes—
120C22×C13H(5,𝔽2)11yescharacteristic
121C22×C13H(5,𝔽2)11yescharacteristic
122C2×D13—24no—
123C2×D13—24no—
124C2×D13—24no—
125C2×D13—24no—
126C2×D13—24no—
127C2×D13—24no—
128C2×D13—416no—
129C2×D13#12318yes—
130C4×C13—42no—
131C4×C13—42no—
132C4×C13—41no—
133C4×C13—41no—
134Dic13—42no—
135Dic13—42no—
136Dic13—42no—
137C25—131no—
138C23×C4—132no—
139C23×C4—132no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—131no—
142C2×C4⋊C4C2×D1311yescharacteristic, complemented
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—132no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—131no—
149C2×C22⋊C4—268no—
150C2×C22⋊C4C2×D1312yes—
151C2×C22⋊C4C2×D1311yescharacteristic
152#95—131no—
153#95—132no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95C2×D1311yescharacteristic, complemented
158#95C2×D1312yescomplemented
159C2×C13—42no—
160C2×C13C2×#12312yes—
161C2×C13#53411yescharacteristic
162C2×C13#55111yescharacteristic
163C2×C13#55111yescharacteristic
164C2×C13#55112yes—
165D13—28no—
166C24—132no—
167C24—134no—
168C24—264no—
169C24—264no—
170C24—521no—
171C24—521no—
172C24C22×D1311yescharacteristic
173C22×C4—132no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—264no—
177C22×C4—264no—
178C22×C4—264no—
179C22×C4—264no—
180C22×C4—522no—
181C22×C4—522no—
182C22×C4C22×D1312yes—
183C22×C4C22×D1311yescharacteristic
184C22×C4C22×D1311yescharacteristic
185C22×C4C22×D1312yes—
186C4⋊C4—41no—
187C4⋊C4—522no—
188C4⋊C4—521no—
189C22⋊C4—24no—
190C22⋊C4—41no—
191C22⋊C4—264no—
192C22⋊C4—264no—
193C22⋊C4—264no—
194C22⋊C4—264no—
195C22⋊C4—264no—
196C22⋊C4—521no—
197C13#248311yescharacteristic, complemented, Sylow
198C23—21no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—134no—
203C23—134no—
204C23—134no—
205C23—2616no—
206C23—262no—
207C23—262no—
208C23—262no—
209C23—262no—
210C23—524no—
211C23—524no—
212C23—524no—
213C23—528no—
214C23D4×D1312yes—
215C23C23×D1311yescharacteristic
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—528no—
236C2×C4—528no—
237C22—22no—
238C22—24no—
239C22—41no—
240C22—41no—
241C22—42no—
242C22—138no—
243C22—264no—
244C22—264no—
245C22—264no—
246C22—264no—
247C22—264no—
248C22—264no—
249C22—5216no—
250C22C2×D4×D1311yescharacteristic
251C22#8825111yescharacteristic
252C22#41×D1312yes—
253C22#41×D1312yes—
254C22#8825611yescharacteristic
255C4—42no—
256C4—42no—
257C4—41no—
258C4—41no—
259C4—522no—
260C4—522no—
261C4—522no—
262C2—42no—
263C2—268no—
264C2#1171931011yescharacteristic
265C2D13×#12312yes—
266C2#1171936411yescharacteristic
267C2#1171938411yescharacteristic
268C2#1171941012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×D13C22
hypercenter#397D13
hypocenterC13#2483
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#397C2semidirect
3. #11718650C2semidirect
5. #11718614C2semidirect
6. #11718613C2semidirect
7. #11718329C2semidirect
8. #11718325C2semidirect
9. #11718325C2semidirect
13. C2×C13×C4⋊C4C22semidirect
22. C2×C4⋊Dic13C22semidirect
23. C2×#6101C22semidirect
25. C13×#95C22semidirect
26. C13×#95C22semidirect
27. #88071C22semidirect
28. #88071C22semidirect
29. #88071C22semidirect
30. #88071C22semidirect
31. #88071C22semidirect
106. #397D13semidirect
142. C2×C4⋊C4C2×D13semidirect
157. #95C2×D13semidirect
158. #95C2×D13semidirect
197. C13#2483semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D132
C13×#3972
#117186502
#117186162
#117186142
#117186132
#117183292
#117183252
#248313