Finite Group Databasebeta

← #16795235

Subgroups — #16795235

Order 3328.

782 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#13131686C211yesmaximal, characteristic, complemented
2#13131683C211yesmaximal, characteristic, complemented
3#13130433C214yesmaximal, complemented
4#13130416C214yesmaximal, complemented
5#13130385C211yesmaximal, characteristic, complemented
6#13130137C211yesmaximal, characteristic, complemented
7#13130135C211yesmaximal, characteristic, complemented
8#13130039C211yesmaximal, characteristic, complemented
9C2×#11718417C211yesmaximal, characteristic
10C2×D4×Dic13C2211yescharacteristic
11C22×#6104C411yescharacteristic
12C2×#88147C2211yescharacteristic
13C2×C22⋊#1057—22no—
14D4×#1057—22no—
15D4×#1057C2214yescomplemented
16D13⋊(C22⋊C8)—22no—
17#11719119C2211yescharacteristic
18#11719119C2211yescharacteristic
19#11719119C2211yescharacteristic
20#11719119C2211yescharacteristic
21#11719073—22no—
22#11719073C2214yescomplemented
23C2×C13×#102C411yescharacteristic
24C2×#88061C411yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C2×#88047C411yescharacteristic
27#11718417C412yes—
28#11718417C412yes—
29#11718417C2212yes—
30#11718417C2212yes—
31D4⋊#1057C2214yescomplemented
32#11718256C2212yescomplemented
33#11718255C2212yescomplemented
34#11718251C2212yescomplemented
35C8×#1057C2212yescomplemented
36#11718243C2214yescomplemented
37C22×D4×C13C2×C411yescharacteristic
38C23×Dic13—21no—
39C22×D52C2×C411yescharacteristic
40C22×C4×D13—21no—
41C22×#1057—24no—
42C2×D13⋊C8—24no—
43C22×C8×C13C2×C411yescharacteristic
44C2×C13×C4⋊C4C2×C411yescharacteristic
45C2×C22⋊Dic13—21no—
46D4×Dic13—21no—
47D4×Dic13—21no—
48D4×Dic13C2×C412yes—
49D4×Dic13C2312yes—
50C2×#6104C818yescomplemented
51C2×#6104C2×C412yes—
52C2×#6104C2×C412yes—
53C2×#6103—21no—
54C2×C4⋊Dic13C2×C411yescharacteristic
55C2×C4×Dic13C2311yescharacteristic
56C22×#1055C2×C411yescharacteristic
57#88147—21no—
58#88147—21no—
59#88147C2×C412yes—
60#88147C2312yes—
61C22⋊#1057—21no—
62C22⋊#1057—21no—
63C22⋊#1057—21no—
64C22⋊#1057—24no—
65C22⋊#1057D412yes—
66#88111—24no—
67C4⋊#1057—21no—
68C4⋊#1057D412yes—
69C4⋊#1057C2312yes—
70C4⋊#1057C2312yes—
71C4×#1057—21no—
72C4×#1057—21no—
73C4×#1057C2312yes—
74C4×#1057C2312yes—
75C13×#102C2×C412yes—
76C13×#102C2×C412yes—
77#88061C2×C412yes—
78#88061C2×C412yes—
79C8×Dic13C2×C411yescharacteristic
80C8×Dic13C2×C411yescharacteristic
81C8×Dic13C2311yescharacteristic
82C8×Dic13C2311yescharacteristic
83#88047C2×C412yes—
84#88047C2×C412yes—
85#17854—131nomaximal, Sylow
86C24×C13—21no—
87C23×D13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—22no—
90C2×D4×C13C2×C814yescomplemented
91C2×D4×C13C22×C412yes—
92C22×C4×C13—21no—
93C22×C4×C13C22×C411yescharacteristic
94C22×Dic13—21no—
95C22×Dic13—22no—
96C22×Dic13—22no—
97C22×Dic13—82no—
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13#4111yescharacteristic
100C2×D52—21no—
101C2×D52—22no—
102C2×D52C2×C814yescomplemented
103C2×D52C22×C412yes—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—82no—
107C2×#1057—22no—
108C2×#1057—22no—
109C2×#1057—22no—
110C2×#1057—84no—
111C2×#1057C2×D414yes—
112D13⋊C8—84no—
113C2×C8×C13—22no—
114C2×C8×C13C22×C411yescharacteristic
115C2×C8×C13C22×C411yescharacteristic
116C13×C4⋊C4—21no—
117C13×C4⋊C4C22×C412yes—
118C22⋊Dic13—22no—
119C22⋊Dic13—22no—
120#6104C2×C818yescomplemented
121#6104C2×C818yescomplemented
122#6103—22no—
123#6103—22no—
124C4⋊Dic13—21no—
125C4⋊Dic13C22×C412yes—
126C4×Dic13C22×C411yescharacteristic
127C4×Dic13C2×D411yescharacteristic
128C4×Dic13#4111yescharacteristic
129C4×Dic13C2411yescharacteristic
130C2×#1055C2×C814yescomplemented
131C2×#1055C22×C411yescharacteristic
132C2×#1055C22×C411yescharacteristic
133#2972—131no—
134#2972—131no—
135C2×C4×D8—131no—
136#1580—134no—
137C8×D8—134no—
138#1564—131no—
139#1478—131no—
140#1478—131no—
141#1450—131no—
142C23×C13—22no—
143C23×C13—24no—
144C23×C13—81no—
145C23×C13—81no—
146C23×C13C4×D411yescharacteristic
147C22×D13—22no—
148C22×D13—24no—
149C22×D13—81no—
150C22×D13—81no—
151D4×C13—22no—
152D4×C13—24no—
153D4×C13C22×C814yes—
154C2×C4×C13—22no—
155C2×C4×C13—81no—
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13C22×C812yes—
158C2×C4×C13#13112yes—
159C2×C4×C13C23×C411yescharacteristic
160C2×Dic13—22no—
161C2×Dic13—22no—
162C2×Dic13—41no—
163C2×Dic13—44no—
164C2×Dic13—82no—
165C2×Dic13—81no—
166C2×Dic13C4×D411yescharacteristic
167C2×Dic13C4×D411yescharacteristic
168C2×Dic13C22×D411yescharacteristic
169C2×Dic13C2×#4111yescharacteristic
170D52—22no—
171D52—24no—
172D52C22×C814yes—
173C4×D13—44no—
174C4×D13—82no—
175#1057—24no—
176#1057—42no—
177#1057—42no—
178#1057—42no—
179C8×C13—21no—
180C8×C13—21no—
181#1055C22×C812yes—
182#1055C22×C812yes—
183C22×D8—131no—
184C2×C4×D4—131no—
185C2×C4×D4—131no—
186C4×D8—132no—
187C4×D8—132no—
188C4×D8—132no—
189C4×D8—132no—
190C8×D4—134no—
191C8×D4—134no—
192C8×D4—262no—
193C8×D4—262no—
194#431—131no—
195#431—131no—
196#431—131no—
197#431—131no—
198C2×#107—131no—
199C2×#102—131no—
200C2×#102#26111yescharacteristic
201C2×C22⋊C8—262no—
202C2×C22⋊C8—262no—
203C2×C4×C8—131no—
204#335—132no—
205#334—132no—
206D4⋊C8—134no—
207D4⋊C8—134no—
208#322—132no—
209C82—132no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—24no—
213C22×C13—42no—
214C22×C13—42no—
215C22×C13—84no—
216C22×C13C8×D412yes—
217C22×C13C2×C4×D411yescharacteristic
218C2×D13—24no—
219C2×D13—42no—
220C2×D13—42no—
221C2×D13—84no—
222C4×C13—42no—
223C4×C13C8×D412yes—
224C4×C13C23×C811yescharacteristic
225C4×C13C2×#13111yescharacteristic
226Dic13—21no—
227Dic13—21no—
228Dic13—21no—
229Dic13—42no—
230Dic13#57612yes—
231C22×D4—131no—
232C22×D4C2×#26111yescharacteristic
233C23×C4—261no—
234C23×C4—261no—
235C2×D8—138no—
236C2×D8—132no—
237C2×D8—132no—
238C22×C8—131no—
239C22×C8—264no—
240C22×C8—264no—
241C22×C8C2×#26111yescharacteristic
242C4×D4—132no—
243C4×D4—132no—
244C4×D4—132no—
245C4×D4—132no—
246C4×D4—261no—
247C4×D4—261no—
248C4×D4—261no—
249C4×D4—261no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4C2×#26111yescharacteristic
252C2×C22⋊C4—261no—
253C2×C22⋊C4—261no—
254C2×C42—131no—
255#107—132no—
256#107—132no—
257C4⋊C8—132no—
258C4⋊C8—132no—
259C4⋊C8—132no—
260C4⋊C8—261no—
261#102—132no—
262#102—132no—
263#102C2×#26112yes—
264#102C2×#26112yes—
265C22⋊C8—132no—
266C22⋊C8—264no—
267C22⋊C8—264no—
268C22⋊C8—261no—
269C22⋊C8—261no—
270C22⋊C8—261no—
271C4×C8—132no—
272C4×C8—131no—
273C4×C8—131no—
274C4×C8—131no—
275C4×C8—131no—
276C4×C8—132no—
277C4×C8—261no—
278C4×C8—261no—
279C2×C13—22no—
280C2×C13—44no—
281C2×C13C2×C8×D411yescharacteristic
282C2×C13#294811yescharacteristic
283C2×C13#295711yescharacteristic
284D13—44no—
285C24—21no—
286C24—261no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—134no—
290C2×D4—132no—
291C2×D4—262no—
292C2×D4—261no—
293C2×D4D13⋊C814yescomplemented
294C2×D4C22×#26112yes—
295C22×C4—21no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—262no—
301C22×C4—262no—
302C22×C4—261no—
303C22×C4—1042no—
304C22×C4—1042no—
305C22×C4C22×#26111yescharacteristic
306D8—138no—
307D8—138no—
308C2×C8—22no—
309C2×C8—134no—
310C2×C8—131no—
311C2×C8—131no—
312C2×C8—134no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—262no—
316C2×C8—1044no—
317C2×C8—1044no—
318C2×C8C22×#26111yescharacteristic
319C2×C8C22×#26111yescharacteristic
320C4⋊C4—21no—
321C4⋊C4—132no—
322C4⋊C4—261no—
323C4⋊C4C22×#26112yes—
324C22⋊C4—262no—
325C22⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C42—131no—
329C42—131no—
330C42—131no—
331C42—131no—
332C13#1785411yescharacteristic, complemented, Sylow
333C23—22no—
334C23—24no—
335C23—81no—
336C23—81no—
337C23—262no—
338C23—264no—
339C23—1041no—
340C23—1041no—
341C23D4×#26111yescharacteristic
342D4—24no—
343D4—22no—
344D4—134no—
345D4—264no—
346D4—262no—
347D4C2×D13⋊C814yes—
348C2×C4—22no—
349C2×C4—81no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—524no—
357C2×C4—524no—
358C2×C4—521no—
359C2×C4—1042no—
360C2×C4—1042no—
361C2×C4—1041no—
362C2×C4C2×D13⋊C812yes—
363C2×C4#8823812yes—
364C2×C4D4×#26111yescharacteristic
365C2×C4C23×#26111yescharacteristic
366C8—21no—
367C8—21no—
368C8—132no—
369C8—132no—
370C8—264no—
371C8—522no—
372C8—522no—
373C8—522no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—264no—
381C22—522no—
382C22—522no—
383C22—1044no—
384C22#1171906312yes—
385C22C2×D4×#26111yescharacteristic
386C4—42no—
387C4—132no—
388C4—261no—
389C4—261no—
390C4—261no—
391C4—522no—
392C4#1171906312yes—
393C4C22×D13⋊C811yescharacteristic
394C4C2×#8823811yescharacteristic
395C2—22no—
396C2—44no—
397C2—524no—
398C2C2×#1171906311yescharacteristic
399C2#1313159511yescharacteristic
400C2#1313161411yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C13×#102C4
socleC22×C13C2×C4×D4
prime radicalC22×#6104C4
cosocleC4×Dic13C24
hypercenterC2×#102#261
hypocenterC13#17854
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #13131686C2semidirect
2. #13131683C2semidirect
3. #13130433C2semidirect
4. #13130416C2semidirect
5. #13130385C2semidirect
6. #13130137C2semidirect
7. #13130135C2semidirect
8. #13130039C2semidirect
15. D4×#1057C22semidirect
22. #11719073C22semidirect
31. D4⋊#1057C22semidirect
32. #11718256C22semidirect
33. #11718255C22semidirect
34. #11718251C22semidirect
35. C8×#1057C22semidirect
36. #11718243C22semidirect
50. C2×#6104C8semidirect
90. C2×D4×C13C2×C8semidirect
102. C2×D52C2×C8semidirect
120. #6104C2×C8semidirect
121. #6104C2×C8semidirect
130. C2×#1055C2×C8semidirect
293. C2×D4D13⋊C8semidirect
332. C13#17854semidirect

Maximal subgroups

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

subgroupindex
#131316862
#131316832
#131304332
#131304162
#131303852
#131301372
#131301352
#131300392
C2×#117184172
#1785413