Finite Group Databasebeta

← #13124937

Subgroups — #13124937

Order 1664.

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

normal subgroups only

This group has 444 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
1#11719433C211yesmaximal, characteristic, complemented
2C4×D4×D13C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718748C211yesmaximal, characteristic, complemented
5#11718680C211yesmaximal, characteristic, complemented
6#11718550C212yesmaximal, complemented
7#11718545C212yesmaximal, complemented
8#11718502C211yesmaximal, characteristic, complemented
9#11718496C211yesmaximal, characteristic, complemented
10#11718437C212yesmaximal
11#11718418C212yesmaximal, complemented
12C2×D4×D13C2211yescharacteristic
13C22×C4×D13—21no—
14C13×C4⋊Q8C2211yescharacteristic, complemented
15C4×D4×C13C2211yescharacteristic
16#88200—21no—
17Q8×Dic13—21no—
18D4×Dic13C2211yescharacteristic
19C2×#6105C2212yes—
20C4×C22⋊D13—21no—
21C2×#6095C2212yes—
22#88151C2212yes—
23#88147C2211yescharacteristic
24#88146—21no—
25C4⋊C4×D13C2211yescharacteristic
26#88144—21no—
27#88141C2212yescomplemented
28#88135—21no—
29C22⋊C4×D13—21no—
30C4×D52C2211yescharacteristic
31C42×D13C2211yescharacteristic
32#88123C2211yescharacteristic, complemented
33C13×#107C2212yescomplemented
34C13×C4⋊C8C2211yescharacteristic, complemented
35C13×#102C2212yes—
36#88060C2212yes—
37#88056C2212yescomplemented
38#88055C2212yescomplemented
39#88050C2212yescomplemented
40#88049C2212yes—
41#88047C2212yescomplemented
42C4⋊#1055C2211yescharacteristic, complemented
43C23×D13—21no—
44C2×Q8×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C2×C22⋊D13—21no—
48C22×Dic13—21no—
49D4×D13—22no—
50D4×D13—22no—
51C2×D52C2311yescharacteristic
52C2×C4×D13—21no—
53C2×C4×D13—21no—
54C2×C4×D13—21no—
55C2×C4×D13—44no—
56C2×C4×D13D411yescharacteristic
57C2×C4×D13D411yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×Dic26C2312yes—
60C2×C8×C13C2312yes—
61C13×C4⋊C4—21no—
62C13×C4⋊C4C2312yes—
63C13×C4⋊C4C2311yescharacteristic
64C13×C22⋊C4—21no—
65C42×C13C2311yescharacteristic
66C22⋊Dic13—21no—
67#6105—24no—
68#6103—22no—
69#6103—21no—
70#6103—21no—
71C4⋊Dic13—21no—
72C4⋊Dic13—21no—
73C4⋊Dic13—22no—
74C4⋊Dic13C2311yescharacteristic
75#6101—21no—
76#6101—22no—
77C4×Dic13—22no—
78C4×Dic13D411yescharacteristic
79C4×Dic13D411yescharacteristic
80C4×Dic13C2311yescharacteristic
81C2×#1055C2312yes—
82#6095—24no—
83#3110—131nomaximal, Sylow
84C23×C13—21no—
85C22×D13—24no—
86C22×D13—21no—
87C22×D13—42no—
88C22×D13—42no—
89C22×D13C2×D411yescharacteristic
90Q8×C13—42no—
91D4×C13—21no—
92D4×C13#4112yes—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—42no—
96C2×C4×C13C2×D411yescharacteristic
97C2×C4×C13C2×D411yescharacteristic
98C2×C4×C13C2411yescharacteristic
99C22⋊D13—24no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105C2×Dic13C2×D411yescharacteristic
106D52—21no—
107D52#4112yes—
108C4×D13—22no—
109C4×D13—22no—
110C4×D13—21no—
111C4×D13—21no—
112C4×D13—42no—
113C4×D13—42no—
114C4×D13—42no—
115Dic26—22no—
116Dic26—22no—
117C8×C13—22no—
118#1055—22no—
119#533—131no—
120C2×C4×D4—131no—
121#484—132no—
122#474—131no—
123#474D1311yescharacteristic, complemented
124#461—131no—
125#461—131no—
126#450—132no—
127#440—132no—
128#440—132no—
129#432—131no—
130C22×C13—22no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13C22×D411yescharacteristic
134C2×D13—21no—
135C2×D13—21no—
136C2×D13—22no—
137C2×D13—48no—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13#13712yes—
141C4×C13—21no—
142C4×C13—41no—
143C4×C13—42no—
144C4×C13AGL(1,ℤ/8)12yes—
145C4×C13C2×#4111yescharacteristic
146C4×C13C2×#4111yescharacteristic
147Dic13—21no—
148Dic13—21no—
149Dic13—21no—
150Dic13—42no—
151Dic13—41no—
152C22×D4—131no—
153C23×C4—261no—
154C2×SD16—132no—
155C2×SD16—132no—
156C4⋊Q8—131no—
157C4⋊Q8C2×D1311yescharacteristic, complemented
158#125—261no—
159C22⋊Q8—132no—
160C22⋊Q8—261no—
161C4×Q8—132no—
162C4×Q8—261no—
163C4×D4—131no—
164C4×D4—131no—
165C4×D4—131no—
166C4×D4—261no—
167C4×D4—261no—
168C4×D4C2×D1311yescharacteristic
169#117—261no—
170C2×C4⋊C4—131no—
171C2×C22⋊C4—261no—
172C2×C42—131no—
173#107—132no—
174#107C2×D1312yescomplemented
175C4⋊C8—131no—
176C4⋊C8C2×D1311yescharacteristic, complemented
177#103—132no—
178#103—132no—
179#102—132no—
180#102C2×D1312yes—
181C22⋊C8—132no—
182#97—132no—
183C2×C13—42no—
184C2×C13#52511yescharacteristic
185C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C13C2×#13711yescharacteristic
187D13—22no—
188D13—42no—
189C24—261no—
190C2×Q8—21no—
191C2×Q8—132no—
192C2×D4—131no—
193C2×D4—261no—
194C2×D4—262no—
195C2×D4—262no—
196C2×D4C22×D1311yescharacteristic
197C22×C4—21no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4—524no—
206SD16—264no—
207SD16—264no—
208C2×C8—132no—
209C2×C8C22×D1312yes—
210C4⋊C4—21no—
211C4⋊C4—131no—
212C4⋊C4—261no—
213C4⋊C4—262no—
214C4⋊C4—262no—
215C4⋊C4—261no—
216C4⋊C4—261no—
217C4⋊C4C22×D1312yes—
218C4⋊C4C22×D1311yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—261no—
221C22⋊C4—262no—
222C22⋊C4—261no—
223C22⋊C4—261no—
224C42—131no—
225C42—131no—
226C42—131no—
227C42—262no—
228C42C22×D1311yescharacteristic
229C13#311011yescharacteristic, complemented, Sylow
230C23—21no—
231C23—131no—
232C23—264no—
233C23—261no—
234C23—522no—
235C23—522no—
236Q8—42no—
237Q8—262no—
238Q8—262no—
239D4—21no—
240D4—132no—
241D4—264no—
242D4—261no—
243D4#613112yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—131no—
248C2×C4—131no—
249C2×C4—131no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—261no—
253C2×C4—261no—
254C2×C4—262no—
255C2×C4—261no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4D4×D1311yescharacteristic
261C2×C4D4×D1311yescharacteristic
262C2×C4C23×D1311yescharacteristic
263C8—22no—
264C8—262no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—132no—
269C22—261no—
270C22—261no—
271C22—262no—
272C22—528no—
273C22—521no—
274C22—521no—
275C22C2×D4×D1311yescharacteristic
276C4—21no—
277C4—41no—
278C4—42no—
279C4—261no—
280C4—261no—
281C4—261no—
282C4—521no—
283C4—522no—
284C4#8816512yes—
285C4C2×#613111yescharacteristic
286C4#41×D1311yescharacteristic
287C2—42no—
288C2—262no—
289C2—522no—
290C2#1171933211yescharacteristic
291C2C2×#8816511yescharacteristic
292C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radicalC2×D4×D13C22
hypercenter#474D13
hypocenterC13#3110
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#474C2semidirect
4. #11718748C2semidirect
5. #11718680C2semidirect
6. #11718550C2semidirect
7. #11718545C2semidirect
8. #11718502C2semidirect
9. #11718496C2semidirect
11. #11718418C2semidirect
14. C13×C4⋊Q8C22semidirect
27. #88141C22semidirect
32. #88123C22semidirect
33. C13×#107C22semidirect
34. C13×C4⋊C8C22semidirect
37. #88056C22semidirect
38. #88055C22semidirect
39. #88050C22semidirect
41. #88047C22semidirect
42. C4⋊#1055C22semidirect
123. #474D13semidirect
157. C4⋊Q8C2×D13semidirect
174. #107C2×D13semidirect
176. C4⋊C8C2×D13semidirect
229. C13#3110semidirect

Maximal subgroups

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

subgroupindex
#117194332
C4×D4×D132
C13×#4742
#117187482
#117186802
#117185502
#117185452
#117185022
#117184962
#117184372
#117184182
#311013