Finite Group Databasebeta

← #13121880

Subgroups — #13121880

Order 1664.

560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C13×#393C211yesmaximal, characteristic, complemented
2#11718892C212yesmaximal, complemented
3#11718616C212yesmaximal
4#11718616C211yesmaximal, characteristic
5#11718614C211yesmaximal, characteristic, complemented
6#11718606C212yesmaximal, complemented
7#11718336C212yesmaximal, complemented
8#11718331C212yesmaximal, complemented
9#11718330C212yesmaximal, complemented
10C24×D13C2211yescharacteristic
11C22×Q8×C13C2211yescharacteristic, complemented
12C2×C13×C22⋊C4C2212yes—
13C2×C13×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic13C2212yes—
15C2×C22⋊Dic13C2211yescharacteristic
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic, complemented
23C2×#6101C2212yescomplemented
24C2×C4×Dic13C2212yescomplemented
25C13×#95C2211yescharacteristic, complemented
26C13×#95C2212yescomplemented
27#88071C2212yescomplemented
28#88071C2212yescomplemented
29#88071C2211yescharacteristic, complemented
30#88071C2212yescomplemented
31C24×C13C2311yescharacteristic
32C23×D13—22no—
33C23×D13—24no—
34C23×D13—41no—
35C23×D13—42no—
36C23×D13—41no—
37C23×D13C2312yes—
38C2×Q8×C13—42no—
39C2×Q8×C13—41no—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C13×C22⋊C4—42no—
48C13×C22⋊C4—41no—
49C22⋊Dic13—24no—
50C22⋊Dic13—41no—
51#6103—24no—
52#6103—24no—
53#6103—42no—
54#6103—42no—
55#6103—42no—
56#6103—42no—
57C4⋊Dic13—41no—
58#6101—42no—
59C4×Dic13—42no—
60#2736—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—21no—
63C23×C13—21no—
64C23×C13—22no—
65C23×C13#4112yes—
66C23×C13C2411yescharacteristic
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—44no—
74C22×D13—48no—
75C22×D13—48no—
76C22×D13—44no—
77C22×D13—44no—
78C22×D13#4114yes—
79Q8×C13—44no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99#397—131no—
100#397—132no—
101#393—132no—
102#393D1311yescharacteristic, complemented
103#388—132no—
104#388—132no—
105#388—132no—
106#379—132no—
107#379—131no—
108C22×C13—22no—
109C22×C13—24no—
110C22×C13—42no—
111C22×C13—41no—
112C22×C13—41no—
113C22×C13C2×#4111yescharacteristic
114C22×C13C2×#4112yes—
115C22×C13H(5,𝔽2)12yes—
116C22×C13H(5,𝔽2)11yescharacteristic
117C22×C13H(5,𝔽2)11yescharacteristic
118C2×D13—24no—
119C2×D13—24no—
120C2×D13—24no—
121C2×D13—416no—
122C2×D13—42no—
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13—42no—
129C4×C13—41no—
130Dic13—42no—
131Dic13—42no—
132Dic13—42no—
133C25—131no—
134C22×Q8C2×D1311yescharacteristic, complemented
135C2×C4⋊C4—132no—
136C2×C4⋊C4—131no—
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—131no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4C2×D1312yes—
146C2×C22⋊C4C2×D1311yescharacteristic
147C2×C42—132no—
148#95—132no—
149#95—132no—
150#95—132no—
151#95—131no—
152#95C2×D1311yescharacteristic, complemented
153#95C2×D1312yescomplemented
154C2×C13—42no—
155C2×C13#53811yescharacteristic
156C2×C13#53812yes—
157C2×C13#55112yes—
158C2×C13#55111yescharacteristic
159C2×C13H(3,𝔽4)11yescharacteristic
160D13—44no—
161C24—132no—
162C24—264no—
163C24—262no—
164C24—522no—
165C24—521no—
166C24—521no—
167C24C22×D1311yescharacteristic
168C2×Q8—42no—
169C2×Q8—41no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4C22×D1312yes—
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1312yes—
177C4⋊C4—522no—
178C4⋊C4—521no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—264no—
182C22⋊C4—264no—
183C22⋊C4—264no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C22⋊C4—521no—
189C42—522no—
190C13#273611yescharacteristic, complemented, Sylow
191C23—22no—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—134no—
196C23—262no—
197C23—262no—
198C23—262no—
199C23—262no—
200C23—262no—
201C23—262no—
202C23—528no—
203C23—524no—
204C23—524no—
205C23—528no—
206C23—524no—
207C23#613112yes—
208C23C23×D1311yescharacteristic
209Q8—44no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C22—24no—
230C22—22no—
231C22—41no—
232C22—42no—
233C22—41no—
234C22—264no—
235C22—264no—
236C22—264no—
237C22—5216no—
238C22—522no—
239C22—522no—
240C22—522no—
241C22—522no—
242C22#8825112yes—
243C22#8825111yescharacteristic
244C22C2×#613111yescharacteristic
245C22#41×D1312yes—
246C22#8825611yescharacteristic
247C4—42no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—522no—
252C4—522no—
253C4—522no—
254C2—42no—
255C2—524no—
256C2#1171929911yescharacteristic
257C2#1171934212yes—
258C2#1171934911yescharacteristic
259C2#1171938312yes—
260C2#1171938411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×D13C22
hypercenter#393D13
hypocenterC13#2736
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C13×#393C2semidirect
2. #11718892C2semidirect
5. #11718614C2semidirect
6. #11718606C2semidirect
7. #11718336C2semidirect
8. #11718331C2semidirect
9. #11718330C2semidirect
11. C22×Q8×C13C22semidirect
22. C2×C4⋊Dic13C22semidirect
23. C2×#6101C22semidirect
24. C2×C4×Dic13C22semidirect
25. C13×#95C22semidirect
26. C13×#95C22semidirect
27. #88071C22semidirect
28. #88071C22semidirect
29. #88071C22semidirect
30. #88071C22semidirect
102. #393D13semidirect
134. C22×Q8C2×D13semidirect
152. #95C2×D13semidirect
153. #95C2×D13semidirect
190. C13#2736semidirect

Maximal subgroups

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

subgroupindex
C13×#3932
#117188922
#117186162
#117186142
#117186062
#117183362
#117183312
#117183302
#273613