Finite Group Databasebeta

← #16018270

Subgroups — #16018270

Order 3328.

682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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#13125349C211yesmaximal, characteristic, complemented
2D13×#493C211yesmaximal, characteristic
3#13117079C211yesmaximal, characteristic, complemented
4#13117078C211yesmaximal, characteristic, complemented
5#13117077C211yesmaximal, characteristic, complemented
6#13117058C214yesmaximal, complemented
7#13116550C214yesmaximal, complemented
8#13116429C211yesmaximal, characteristic, complemented
9C13×#2244C211yesmaximal, characteristic, complemented
10C2×D8×D13—21no—
11C2×D8×D13C2212yes—
12D13×#127—21no—
13#11719393—21no—
14C13×#499C2211yescharacteristic, complemented
15C13×#493C2211yescharacteristic
16#11718812—21no—
17#11718812C2212yes—
18#11718734—21no—
19#11718725—21no—
20C2×#88038C2212yes—
21#11718541C2212yes—
22#11718535C2212yescomplemented
23#11718521—21no—
24#11718516—21no—
25#11718356C2211yescharacteristic
26C4×C8×D13C2211yescharacteristic
27#11718344C2211yescharacteristic, complemented
28C13×#357C2214yescomplemented
29C13×#346C2211yescharacteristic, complemented
30#11718154C2214yescomplemented
31#11718101C2214yescomplemented
32C16×Dic13C2212yescomplemented
33#11718083C2214yescomplemented
34#11718053C2211yescharacteristic, complemented
35C2×D4×D13—22no—
36C2×D4×D13—42no—
37C2×C13×D8—21no—
38C2×C13×D8C2312yes—
39C13×#127—21no—
40C13×#125—21no—
41#88194—22no—
42#88194—42no—
43C2×#6104—22no—
44C2×#6104—22no—
45D8×D13—28no—
46D8×D13—44no—
47C2×D104—21no—
48C2×D104C2312yes—
49C2×C8×D13D411yescharacteristic
50C2×C8×D13C2311yescharacteristic
51#88150—42no—
52#88146—22no—
53#88142—22no—
54#88141—42no—
55#88128—21no—
56C42×D13D411yescharacteristic
57#88124—21no—
58C2×C13×C16C2312yes—
59C13×#107C2312yes—
60C13×#106—21no—
61C4×C8×C13C2311yescharacteristic
62#88058C2312yes—
63#88057—21no—
64C8×Dic13D411yescharacteristic
65C8×Dic13C2311yescharacteristic
66C2×#6090C2312yes—
67#88048—22no—
68#88047—22no—
69C4×#1055D411yescharacteristic
70#88038—24no—
71#33704—131nomaximal, Sylow
72C23×D13—42no—
73C2×D4×C13—22no—
74C2×D4×C13—42no—
75C2×C22⋊D13—44no—
76C2×C22⋊D13—42no—
77D4×D13—44no—
78D4×D13—44no—
79D4×D13—88no—
80C2×D52—22no—
81C2×D52—42no—
82C2×C4×D13D812yes—
83C2×C4×D13C2×D411yescharacteristic
84C2×Dic26—42no—
85C13×D8—24no—
86C13×D8—42no—
87C2×C8×C13C2×D411yescharacteristic
88C2×C8×C13C2411yescharacteristic
89C13×C4⋊C4—22no—
90C13×C4⋊C4—42no—
91C42×C13C2×D411yescharacteristic
92#6104—44no—
93#6104—44no—
94#6103—42no—
95C4⋊Dic13—22no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—42no—
99C4×Dic13D812yes—
100C4×Dic13C2×D411yescharacteristic
101C2×#1055C2×D411yescharacteristic
102C2×#1055C2×D411yescharacteristic
103D104—24no—
104D104—42no—
105C8×D13SD1614yes—
106C8×D13#4114yes—
107C13×C16—22no—
108#6090—22no—
109#3160—131no—
110C2×#493—131no—
111#2244—131no—
112#2244—131no—
113#2244—131no—
114#2244D1311yescharacteristic, complemented
115#2240—134no—
116#2140—134no—
117C4×M32—131no—
118C23×C13—42no—
119C22×D13—42no—
120C22×D13—88no—
121C22×D13—84no—
122C22×D13C2×D811yescharacteristic
123D4×C13—42no—
124D4×C13—42no—
125D4×C13—84no—
126C2×C4×C13—42no—
127C2×C4×C13C2×D812yes—
128C2×C4×C13C22×D411yescharacteristic
129C22⋊D13—84no—
130C22⋊D13—88no—
131C2×Dic13—42no—
132C2×Dic13C2×D811yescharacteristic
133C2×Dic13C2×D812yes—
134D52—42no—
135D52—42no—
136D52—84no—
137C4×D13—24no—
138C4×D13#12412yes—
139C4×D13C2×SD1612yes—
140Dic26—84no—
141C8×C13C2×SD1612yes—
142C8×C13C2×#4112yes—
143#1055#12412yes—
144#1055C2×SD1612yes—
145C22×D8—132no—
146C22×D8—261no—
147#533—261no—
148C2×#127—261no—
149C2×M32—132no—
150#500—132no—
151#499—131no—
152#499—261no—
153#499C2×D1311yescharacteristic, complemented
154#498—261no—
155#493—132no—
156#493—131no—
157#493—261no—
158#493—261no—
159#493C2×D1311yescharacteristic
160#427—132no—
161#427—261no—
162C2×C4×C8—131no—
163#357—134no—
164#357—134no—
165#357—134no—
166#357C2×D1314yescomplemented
167#346—131no—
168#346C2×D1311yescharacteristic, complemented
169C4×C16—132no—
170C22×C13—82no—
171C22×C13—84no—
172C22×C13C22×D811yescharacteristic
173C2×D13—22no—
174C2×D13—82no—
175C2×D13—84no—
176C2×D13—168no—
177C2×D13#48612yes—
178C4×C13—22no—
179C4×C13—82no—
180C4×C13C2×#12411yescharacteristic
181C4×C13C22×SD1611yescharacteristic
182Dic13—82no—
183Dic13#48612yes—
184Dic13#50914yes—
185C22×D4—262no—
186C22×D4—522no—
187C2×D8—21no—
188C2×D8—132no—
189C2×D8—268no—
190C2×D8—262no—
191C2×D8—262no—
192C2×D8—261no—
193C2×D8—524no—
194C2×D8C22×D1312yes—
195C22×C8—131no—
196C22×C8—131no—
197C4⋊Q8—262no—
198#127—21no—
199#127—262no—
200#127—261no—
201#127—522no—
202#125—21no—
203#125—261no—
204C22⋊Q8—522no—
205C4×Q8—522no—
206#117—262no—
207C2×C42—131no—
208M32—264no—
209C2×C16—132no—
210C2×C16C22×D1312yes—
211#107—132no—
212#107—262no—
213#107C22×D1312yes—
214#106—21no—
215#106—262no—
216#106—261no—
217C4×C8—131no—
218C4×C8—131no—
219C4×C8—131no—
220C4×C8C22×D1311yescharacteristic
221C2×C13—162no—
222C2×C13C2×#48611yescharacteristic
223C2×C13C2×#50912yes—
224D13—22no—
225D13—162no—
226C24—522no—
227C2×Q8—522no—
228C2×D4—22no—
229C2×D4—42no—
230C2×D4—262no—
231C2×D4—524no—
232C2×D4—524no—
233C2×D4—524no—
234C2×D4—522no—
235C2×D4—522no—
236C2×D4—1048no—
237C22×C4—131no—
238C22×C4—132no—
239D8—24no—
240D8—42no—
241D8—264no—
242D8—524no—
243D8—524no—
244D8—522no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—134no—
248C2×C8—134no—
249C2×C8D4×D1311yescharacteristic
250C2×C8C23×D1311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—262no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C22⋊C4—522no—
257C42—132no—
258C42—131no—
259C42—522no—
260C42D4×D1311yescharacteristic
261C16—22no—
262C16—262no—
263C13#3370411yescharacteristic, complemented, Sylow
264C23—42no—
265C23—131no—
266C23—522no—
267C23—1044no—
268C23—1048no—
269Q8—1044no—
270D4—42no—
271D4—42no—
272D4—84no—
273D4—522no—
274D4—522no—
275D4—1044no—
276D4—1044no—
277D4—1048no—
278C2×C4—42no—
279C2×C4—131no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—264no—
284C2×C4—522no—
285C2×C4D8×D1312yes—
286C2×C4C2×D4×D1311yescharacteristic
287C8—132no—
288C8—132no—
289C8SD16×D1312yes—
290C8#41×D1312yes—
291C22—82no—
292C22—84no—
293C22—132no—
294C22—262no—
295C22—1042no—
296C22—1044no—
297C22—2088no—
298C22C2×D8×D1311yescharacteristic
299C4—22no—
300C4—82no—
301C4—132no—
302C4—134no—
303C4—1042no—
304C4D13×#12411yescharacteristic
305C4C2×SD16×D1311yescharacteristic
306C2—162no—
307C2—262no—
308C2—2082no—
309C2D13×#48611yescharacteristic
310C2D13×#50912yes—
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2244C2
socleC22×C13C22×D8
prime radicalD13×#493C2
hypercenter#2244D13
hypocenterC13#33704
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2244

Complements

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

NH ≅ G/Ntype
1. #13125349C2semidirect
3. #13117079C2semidirect
4. #13117078C2semidirect
5. #13117077C2semidirect
6. #13117058C2semidirect
7. #13116550C2semidirect
8. #13116429C2semidirect
9. C13×#2244C2semidirect
14. C13×#499C22semidirect
22. #11718535C22semidirect
27. #11718344C22semidirect
28. C13×#357C22semidirect
29. C13×#346C22semidirect
30. #11718154C22semidirect
31. #11718101C22semidirect
32. C16×Dic13C22semidirect
33. #11718083C22semidirect
34. #11718053C22semidirect
114. #2244D13semidirect
153. #499C2×D13semidirect
166. #357C2×D13semidirect
168. #346C2×D13semidirect
263. C13#33704semidirect

Maximal subgroups

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

subgroupindex
#131253492
D13×#4932
#131170792
#131170782
#131170772
#131170582
#131165502
#131164292
C13×#22442
#3370413