Finite Group Databasebeta

← #13121882

Subgroups — #13121882

Order 1664.

560 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 125 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×#379C211yesmaximal, characteristic
2#11718908C212yesmaximal
3#11718614C211yesmaximal, characteristic, complemented
4#11718613C212yesmaximal, complemented
5#11718612C212yesmaximal, complemented
6#11718608C212yesmaximal, complemented
7#11718608C211yesmaximal, characteristic, complemented
8#11718606C212yesmaximal, complemented
9#11718605C212yesmaximal, complemented
10C25×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic, complemented
12C2×C13×C22⋊C4C2212yes—
13C2×C13×C22⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22C2×C4⋊Dic13C2211yescharacteristic, complemented
23C2×#6101C2212yescomplemented
24C2×C4×Dic13C2212yescomplemented
25#88071C2212yescomplemented
26#88071C2212yescomplemented
27#88071C2211yescharacteristic, complemented
28#88071C2212yescomplemented
29#88071C2212yescomplemented
30#88071C2211yescharacteristic, complemented
31C24×C13—22no—
32C24×C13—24no—
33C24×C13—42no—
34C24×C13—41no—
35C24×C13—41no—
36C24×C13C2311yescharacteristic
37C24×C13C2312yes—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×Dic26—41no—
46C2×Dic26—42no—
47C13×C22⋊C4—24no—
48C13×C22⋊C4—41no—
49C13×C22⋊C4—42no—
50C13×C22⋊C4—41no—
51C22⋊Dic13—24no—
52C22⋊Dic13—24no—
53C22⋊Dic13—42no—
54C22⋊Dic13—42no—
55C22⋊Dic13—42no—
56C22⋊Dic13—42no—
57C4⋊Dic13—41no—
58#6101—42no—
59C4×Dic13—42no—
60#2736—131nomaximal, Sylow
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—21no—
69C23×C13—21no—
70C23×C13—22no—
71C23×C13—48no—
72C23×C13—44no—
73C23×C13—44no—
74C23×C13—48no—
75C23×C13—44no—
76C23×C13#4112yes—
77C23×C13#4114yes—
78C23×C13C2411yescharacteristic
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
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#397—131no—
101#393—131no—
102#393—132no—
103#388—132no—
104#388—132no—
105#388—132no—
106#379—132no—
107#379D1311yescharacteristic
108C22×C13—22no—
109C22×C13—24no—
110C22×C13—24no—
111C22×C13—24no—
112C22×C13—24no—
113C22×C13—416no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—41no—
119C22×C13—42no—
120C22×C13—41no—
121C22×C13C2×#4111yescharacteristic
122C22×C13C2×#4112yes—
123C22×C13H(5,𝔽2)11yescharacteristic
124C22×C13H(5,𝔽2)11yescharacteristic
125C22×C13H(5,𝔽2)12yes—
126C4×C13—42no—
127C4×C13—41no—
128C4×C13—41no—
129Dic13—42no—
130Dic13—42no—
131Dic13—42no—
132Dic13—42no—
133C25C2×D1311yescharacteristic
134C22×Q8—131no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—131no—
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4C2×D1312yes—
144C2×C22⋊C4C2×D1311yescharacteristic
145C2×C22⋊C4C2×D1312yes—
146C2×C22⋊C4C2×D1311yescharacteristic
147C2×C42—132no—
148#95—132no—
149#95—131no—
150#95—132no—
151#95—132no—
152#95—132no—
153#95—131no—
154C2×C13—42no—
155C2×C13—44no—
156C2×C13#53811yescharacteristic
157C2×C13#53812yes—
158C2×C13#55112yes—
159C2×C13#55111yescharacteristic
160C2×C13H(3,𝔽4)11yescharacteristic
161C24—22no—
162C24—24no—
163C24—41no—
164C24—42no—
165C24—41no—
166C24C22×D1311yescharacteristic
167C24C22×D1312yes—
168C2×Q8—521no—
169C2×Q8—522no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—132no—
173C22×C4—132no—
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1312yes—
177C4⋊C4—522no—
178C4⋊C4—521no—
179C22⋊C4—24no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C22⋊C4—41no—
183C22⋊C4—264no—
184C22⋊C4—264no—
185C22⋊C4—522no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C22⋊C4—522no—
189C42—522no—
190C13#273611yescharacteristic, complemented, Sylow
191C23—22no—
192C23—22no—
193C23—22no—
194C23—21no—
195C23—21no—
196C23—22no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—48no—
202C23—44no—
203C23—44no—
204C23—48no—
205C23—44no—
206C23#612712yes—
207C23#612914yes—
208C23C23×D1311yescharacteristic
209Q8—524no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
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—24no—
232C22—24no—
233C22—24no—
234C22—416no—
235C22—42no—
236C22—42no—
237C22—41no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22C2×#612711yescharacteristic
243C22C2×#612912yes—
244C22#8825111yescharacteristic
245C22#8825111yescharacteristic
246C22#8825112yes—
247C4—41no—
248C4—42no—
249C4—41no—
250C4—522no—
251C4—522no—
252C4—522no—
253C4—522no—
254C2—42no—
255C2—44no—
256C2#1171919911yescharacteristic
257C2#1171920012yes—
258C2#1171929211yescharacteristic
259C2#1171929812yes—
260C2#1171929911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#379C2
prime radicalC25×C13C22
hypercenter#379D13
hypocenterC13#2736
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
3. #11718614C2semidirect
4. #11718613C2semidirect
5. #11718612C2semidirect
6. #11718608C2semidirect
7. #11718608C2semidirect
8. #11718606C2semidirect
9. #11718605C2semidirect
11. C22×Dic26C22semidirect
22. C2×C4⋊Dic13C22semidirect
23. C2×#6101C22semidirect
24. C2×C4×Dic13C22semidirect
25. #88071C22semidirect
26. #88071C22semidirect
27. #88071C22semidirect
28. #88071C22semidirect
29. #88071C22semidirect
30. #88071C22semidirect
190. C13#2736semidirect

Maximal subgroups

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

subgroupindex
C13×#3792
#117189082
#117186142
#117186132
#117186122
#117186082
#117186062
#117186052
#273613