Finite Group Databasebeta

← #15848143

Subgroups — #15848143

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125964C211yesmaximal, characteristic, complemented
2#13124300C211yesmaximal, characteristic
3#13123860C211yesmaximal, characteristic, complemented
4#13114247C214yesmaximal, complemented
5#13114213C214yesmaximal, complemented
6#13113606C211yesmaximal, characteristic, complemented
7#13113517C211yesmaximal, characteristic, complemented
8#13113486C211yesmaximal, characteristic, complemented
9C2×C13×#476C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C2×#88186—21no—
13#11719182C2211yescharacteristic
14C13×#476—22no—
15C13×#476C2214yes—
16C2×C13×#106—21no—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#102—21no—
19C2×C22⋊#1055—22no—
20#11718749C2212yescomplemented
21#11718745—22no—
22#11718740C2212yescomplemented
23#11718680C2212yes—
24#11718677—22no—
25#11718676C2212yes—
26D4×#1055—22no—
27D4×#1055C2214yes—
28#11718629—22no—
29#11718627—21no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718138C2214yescomplemented
34#11718077C2212yescomplemented
35#11718074C2212yescomplemented
36#11718072C2214yescomplemented
37C22×Q8×C13—21no—
38C22×D4×C13D411yescharacteristic
39C23×C4×C13—21no—
40C2×#6127—21no—
41C22×C8×C13—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8—21no—
45C13×C4⋊Q8C2312yes—
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C4×D4×C13D412yes—
49C4×D4×C13C2312yes—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C22⋊C4—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6105—22no—
56#88186—44no—
57C2×#6104—22no—
58#88184—21no—
59#88184—21no—
60C2×#6099—21no—
61C22×#1055—24no—
62#88129—21no—
63#88128C2311yescharacteristic
64C4×D52—21no—
65C4×D52—21no—
66#88123C2311yescharacteristic
67C13×#106—24no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8C2312yes—
70C13×#102—24no—
71C22⋊#1055—21no—
72C22⋊#1055—24no—
73C22⋊#1055D412yes—
74#88050—22no—
75#88049—22no—
76#88049—24no—
77#88048—24no—
78C4⋊#1055—21no—
79C4⋊#1055D412yes—
80C4⋊#1055C2312yes—
81C4⋊#1055C2312yes—
82C4×#1055—21no—
83C4×#1055C2312yes—
84#19391—131nomaximal, Sylow
85C24×C13—21no—
86C2×Q8×C13—22no—
87C2×Q8×C13—41no—
88C2×Q8×C13—82no—
89C2×D4×C13—21no—
90C2×D4×C13—22no—
91C2×D4×C13SD1614yes—
92C2×D4×C13C2×D412yes—
93C22×C4×C13—21no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—41no—
97C22×C4×C13—82no—
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13#4111yescharacteristic
101C2×C22⋊D13—41no—
102#6127—42no—
103#6127—42no—
104C2×D52—21no—
105C2×D52—21no—
106C2×D52—21no—
107C2×C4×D13—41no—
108C2×Dic26—21no—
109C2×C8×C13—22no—
110C2×C8×C13—42no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4C2×D412yes—
117C13×C22⋊C4—22no—
118C13×C22⋊C4—22no—
119C42×C13C2×D411yescharacteristic
120C42×C13C2×D411yescharacteristic
121C42×C13#4111yescharacteristic
122C42×C13C2411yescharacteristic
123#6105—44no—
124#6104—44no—
125#6103—41no—
126#6103—41no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129#6099—42no—
130C2×#1055—22no—
131C2×#1055—22no—
132C2×#1055—84no—
133C2×#1055C2×D414yes—
134#3227—131no—
135C2×#476D1311yescharacteristic, complemented
136#3036—131no—
137#2972—131no—
138#1677—134no—
139#1671—134no—
140#1570—131no—
141#1548—131no—
142#1540—131no—
143C23×C13—22no—
144C23×C13—24no—
145C23×C13—81no—
146C23×C13—81no—
147C23×C13#12111yescharacteristic
148C22×D13—41no—
149Q8×C13—82no—
150Q8×C13—82no—
151D4×C13—22no—
152D4×C13—24no—
153D4×C13C2×SD1614yes—
154C2×C4×C13—22no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—44no—
158C2×C4×C13—42no—
159C2×C4×C13—82no—
160C2×C4×C13—81no—
161C2×C4×C13—82no—
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12111yescharacteristic
165C2×C4×C13C2×SD1612yes—
166C2×C4×C13#13512yes—
167C2×C4×C13C22×D411yescharacteristic
168C2×C4×C13C22×D411yescharacteristic
169C2×C4×C13C2×#4111yescharacteristic
170C22⋊D13—82no—
171C2×Dic13—41no—
172D52—41no—
173D52—41no—
174D52—42no—
175D52—81no—
176C4×D13—82no—
177Dic26—41no—
178Dic26—41no—
179C8×C13—42no—
180#1055—24no—
181#1055—42no—
182#1055—42no—
183C2×AGL(1,ℤ/8)—261no—
184#532—131no—
185C2×C4⋊Q8C2×D1311yescharacteristic
186C2×C4×D4C2×D1311yescharacteristic
187#498—132no—
188#486—132no—
189#481—262no—
190#476—22no—
191#476—262no—
192#476C2×D1314yes—
193#463—262no—
194#461—132no—
195#459—132no—
196C8×D4—134no—
197C8×D4—262no—
198#431—131no—
199#431—131no—
200C2×#106—21no—
201#423—131no—
202C2×C4⋊C8C2×D1311yescharacteristic
203#417—261no—
204C2×#102—21no—
205C2×C22⋊C8—262no—
206#334—134no—
207#333—134no—
208#332—132no—
209#331—132no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—24no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—84no—
216C22×C13#46512yes—
217C22×C13C2×#12111yescharacteristic
218C2×D13—81no—
219C2×D13—81no—
220C2×D13—81no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—42no—
225C4×C13—82no—
226C4×C13#46512yes—
227C4×C13C22×SD1611yescharacteristic
228C4×C13C2×#13511yescharacteristic
229C4×C13#57712yes—
230Dic13—81no—
231C2×#41—261no—
232C22×Q8—21no—
233C22×D4C22⋊D1311yescharacteristic
234C23×C4—21no—
235AGL(1,ℤ/8)—524no—
236C2×SD16—262no—
237C2×D8—262no—
238C2×M16—261no—
239C22×C8—21no—
240C22×C8—264no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—131no—
245C4⋊Q8C22×D1312yes—
246#127—131no—
247#124—261no—
248#121—261no—
249#121—261no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—261no—
253C4×D4—261no—
254C4×D4C22⋊D1312yes—
255C4×D4C22×D1312yes—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C22⋊D1311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D1311yescharacteristic
261#106—24no—
262#106—264no—
263C4⋊C8—21no—
264C4⋊C8—132no—
265C4⋊C8—132no—
266C4⋊C8—132no—
267C4⋊C8—261no—
268C4⋊C8C22×D1312yes—
269#103—262no—
270#102—24no—
271#102—264no—
272#102—262no—
273C22⋊C8—132no—
274C22⋊C8—264no—
275C22⋊C8—261no—
276C4×C8—132no—
277C4×C8—261no—
278C2×C13—22no—
279C2×C13—44no—
280C2×C13#304211yescharacteristic
281C2×C13C2×#46511yescharacteristic
282C2×C13#306811yescharacteristic
283D13—161no—
284C24—21no—
285#41—522no—
286#41—522no—
287C2×Q8—22no—
288C2×Q8—41no—
289C2×Q8—82no—
290C2×Q8—261no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—521no—
297C2×D4#610614yes—
298C2×D4C2×C22⋊D1312yes—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—82no—
304C22×C4—521no—
305C22×C4D4×D1311yescharacteristic
306C22×C4#612911yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308SD16—524no—
309D8—524no—
310M16—522no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—134no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—1044no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4C2×C22⋊D1312yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—521no—
328C22⋊C4—521no—
329C42D4×D1311yescharacteristic
330C42#612911yescharacteristic
331C42C2×C22⋊D1311yescharacteristic
332C42C23×D1311yescharacteristic
333C13#1939111yescharacteristic, complemented, Sylow
334C23—22no—
335C23—24no—
336C23—81no—
337C23—81no—
338C23—521no—
339C23#8819311yescharacteristic
340Q8—82no—
341Q8—82no—
342Q8—521no—
343Q8—521no—
344D4—24no—
345D4—22no—
346D4—522no—
347D4—521no—
348D4—521no—
349D4—1041no—
350D4—1042no—
351D4C2×#610614yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—521no—
361C2×C4—1042no—
362C2×C4#8819311yescharacteristic
363C2×C4#8819311yescharacteristic
364C2×C4#8819311yescharacteristic
365C2×C4C2×#610612yes—
366C2×C4#8820412yes—
367C2×C4C2×D4×D1311yescharacteristic
368C2×C4C2×#612911yescharacteristic
369C2×C4C22×C22⋊D1311yescharacteristic
370C8—42no—
371C8—264no—
372C8—522no—
373C8—522no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—1041no—
381C22—1041no—
382C22—1041no—
383C22#1171870912yes—
384C22C2×#8819311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—82no—
390C4—1041no—
391C4#1171870912yes—
392C4#1171946712yes—
393C4C22×#610611yescharacteristic
394C4C2×#8820411yescharacteristic
395C2—22no—
396C2—44no—
397C2—2081no—
398C2#1312434511yescharacteristic
399C2C2×#1171870911yescharacteristic
400C2#1312456111yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#476C2
socleC22×C13C2×#121
prime radical#13124300C2
hypercenterC2×#476D13
hypocenterC13#19391
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13125964C2semidirect
3. #13123860C2semidirect
4. #13114247C2semidirect
5. #13114213C2semidirect
6. #13113606C2semidirect
7. #13113517C2semidirect
8. #13113486C2semidirect
9. C2×C13×#476C2semidirect
20. #11718749C22semidirect
22. #11718740C22semidirect
33. #11718138C22semidirect
34. #11718077C22semidirect
35. #11718074C22semidirect
36. #11718072C22semidirect
135. C2×#476D13semidirect
333. C13#19391semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131243002
#131238602
#131142472
#131142132
#131136062
#131135172
#131134862
C2×C13×#4762
#1939113