Finite Group Databasebeta

← #13121883

Subgroups — #13121883

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×#397C211yesmaximal, characteristic, complemented
2#11718651C212yesmaximal, complemented
3#11718616C212yesmaximal
4#11718616C211yesmaximal, characteristic
5#11718612C212yesmaximal, complemented
6#11718608C211yesmaximal, characteristic, complemented
7#11718335C212yesmaximal, complemented
8#11718334C212yesmaximal, complemented
9#11718331C212yesmaximal, complemented
10C24×D13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic, complemented
12C2×C13×C4⋊C4C2211yescharacteristic, complemented
13C2×C13×C22⋊C4C2212yes—
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2212yescomplemented
24C2×C4×Dic13C2212yescomplemented
25C13×#95C2212yescomplemented
26C13×#95C2211yescharacteristic, complemented
27#88071C2211yescharacteristic, complemented
28#88071C2212yescomplemented
29#88071C2212yescomplemented
30#88071C2212yescomplemented
31C24×C13C2311yescharacteristic
32C23×D13—22no—
33C23×D13—24no—
34C23×D13—41no—
35C23×D13—42no—
36C23×D13—41no—
37C23×D13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×Dic26—41no—
46C2×Dic26—42no—
47C13×C4⋊C4—41no—
48C13×C22⋊C4—24no—
49C13×C22⋊C4—41no—
50C22⋊Dic13—41no—
51C22⋊Dic13—42no—
52#6103—24no—
53#6103—24no—
54#6103—42no—
55#6103—42no—
56#6103—42no—
57#6103—42no—
58C4⋊Dic13—42no—
59C4×Dic13—42no—
60#2736—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—21no—
63C23×C13—22no—
64C23×C13—21no—
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—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98Dic26—44no—
99#397—132no—
100#397D1311yescharacteristic, complemented
101#393—131no—
102#393—132no—
103#388—132no—
104#388—132no—
105#388—132no—
106#379—131no—
107#379—132no—
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)11yescharacteristic
116C22×C13H(5,𝔽2)11yescharacteristic
117C22×C13H(5,𝔽2)12yes—
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—42no—
128C4×C13—41no—
129C4×C13—41no—
130Dic13—42no—
131Dic13—42no—
132Dic13—42no—
133C25—131no—
134C22×Q8—131no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4C2×D1311yescharacteristic, complemented
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—131no—
140C2×C22⋊C4—132no—
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—131no—
150#95—132no—
151#95—132no—
152#95C2×D1312yescomplemented
153#95C2×D1311yescharacteristic, complemented
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—521no—
165C24—522no—
166C24—521no—
167C24C22×D1311yescharacteristic
168C2×Q8—521no—
169C2×Q8—522no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1312yes—
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1312yes—
177C4⋊C4—41no—
178C4⋊C4—522no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—264no—
182C22⋊C4—264no—
183C22⋊C4—522no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C22⋊C4—522no—
187C22⋊C4—521no—
188C22⋊C4—522no—
189C42—522no—
190C13#273611yescharacteristic, complemented, Sylow
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
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#612912yes—
208C23C23×D1311yescharacteristic
209Q8—524no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
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—22no—
230C22—24no—
231C22—41no—
232C22—41no—
233C22—42no—
234C22—264no—
235C22—264no—
236C22—264no—
237C22—5216no—
238C22—522no—
239C22—522no—
240C22—522no—
241C22—522no—
242C22C2×#612911yescharacteristic
243C22#8825111yescharacteristic
244C22#41×D1312yes—
245C22#8825611yescharacteristic
246C22#8825612yes—
247C4—42no—
248C4—42no—
249C4—41no—
250C4—41no—
251C4—522no—
252C4—522no—
253C4—522no—
254C2—42no—
255C2—524no—
256C2#1171932211yescharacteristic
257C2#1171936312yes—
258C2#1171936411yescharacteristic
259C2#1171938811yescharacteristic
260C2#1171940912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×D13C22
hypercenter#397D13
hypocenterC13#2736
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C13×#397C2semidirect
2. #11718651C2semidirect
5. #11718612C2semidirect
6. #11718608C2semidirect
7. #11718335C2semidirect
8. #11718334C2semidirect
9. #11718331C2semidirect
11. C22×Dic26C22semidirect
12. C2×C13×C4⋊C4C22semidirect
23. C2×C4⋊Dic13C22semidirect
24. C2×C4×Dic13C22semidirect
25. C13×#95C22semidirect
26. C13×#95C22semidirect
27. #88071C22semidirect
28. #88071C22semidirect
29. #88071C22semidirect
30. #88071C22semidirect
100. #397D13semidirect
136. C2×C4⋊C4C2×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×#3972
#117186512
#117186162
#117186122
#117186082
#117183352
#117183342
#117183312
#273613