Finite Group Databasebeta

← #16020682

Subgroups — #16020682

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127849C211yesmaximal, characteristic, complemented
2#13117079C211yesmaximal, characteristic, complemented
3#13117075C211yesmaximal, characteristic, complemented
4#13117070C211yesmaximal, characteristic, complemented
5#13116997C211yesmaximal, characteristic, complemented
6#13116990C211yesmaximal, characteristic, complemented
7#13116970C211yesmaximal, characteristic, complemented
8#13116891C211yesmaximal, characteristic, complemented
9#13116891C211yesmaximal, characteristic, complemented
10#13116871C211yesmaximal, characteristic
11#13116745C211yesmaximal, characteristic, complemented
12#13116710C211yesmaximal, characteristic, complemented
13#13116700C211yesmaximal, characteristic, complemented
14C4×#88066C211yesmaximal, characteristic, complemented
15C13×#3380C211yesmaximal, characteristic, complemented
16C13×#554—21no—
17#11719290—21no—
18C13×#500C2211yescharacteristic
19C13×#499C2211yescharacteristic
20C13×#499C2211yescharacteristic
21C13×#478—21no—
22C13×#478—21no—
23C13×#476—21no—
24C8×Q8×C13C2211yescharacteristic
25C4×C13×D8C2211yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C4×C13×D8C2211yescharacteristic
28C2×#88067C2211yescharacteristic
29C2×#88066C2211yescharacteristic
30C2×#88066C2211yescharacteristic
31#11718509—21no—
32#11718505—21no—
33#11718505—21no—
34C4×Dic52C2211yescharacteristic
35#11718357C2211yescharacteristic
36#11718357C2211yescharacteristic
37#11718356C2211yescharacteristic
38C4×D104C2211yescharacteristic
39C4×D104C2211yescharacteristic
40#11718154C2211yescharacteristic
41#11718084C2211yescharacteristic
42#11718084C2211yescharacteristic
43#11718084C2211yescharacteristic
44#11718083C2211yescharacteristic
45#11718083C2211yescharacteristic
46#11718083C2211yescharacteristic
47#11718083C2211yescharacteristic
48#11718083C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718081C2211yescharacteristic
52#11718081C2211yescharacteristic
53C4⋊#6090C2211yescharacteristic
54C4⋊#6090C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56#11718053C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×D8C2311yescharacteristic
60C13×C4⋊Q8—21no—
61C13×#125—21no—
62C13×#125—21no—
63C13×C22⋊Q8—41no—
64C13×C22⋊Q8—41no—
65C13×C22⋊Q8—41no—
66C4×Q8×C13D411yescharacteristic
67C4×D4×C13—21no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C2×C13×C4⋊C4—41no—
71#88201—41no—
72C2×Dic52C2311yescharacteristic
73C2×D104—21no—
74C2×D104C2311yescharacteristic
75C2×D104C2311yescharacteristic
76C2×#6095—21no—
77C2×#6095—21no—
78#88148—41no—
79#88148—41no—
80#88147—41no—
81#88129—21no—
82#88129—21no—
83#88128—21no—
84C4×D52—21no—
85C4×D52—21no—
86C4×Dic26—21no—
87C13×#107—21no—
88C13×#107C2311yescharacteristic
89C13×#107C2311yescharacteristic
90C13×#107C2311yescharacteristic
91C13×#106—21no—
92C13×#106—21no—
93C13×C4⋊C8D411yescharacteristic
94C13×C4⋊C8D411yescharacteristic
95C13×C4⋊C8D411yescharacteristic
96C13×#102—21no—
97C13×#102—21no—
98C13×#102—21no—
99C4×C8×C13C2311yescharacteristic
100C4×C8×C13C2311yescharacteristic
101C4×C8×C13C2311yescharacteristic
102#88067—22no—
103#88066—22no—
104#88066—22no—
105#88061—21no—
106#88061—21no—
107#88058C2311yescharacteristic
108#88056—21no—
109C2×#6090C2311yescharacteristic
110C2×#6090C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#33937—131nomaximal, Sylow
114C2×Q8×C13—41no—
115C2×Q8×C13D811yescharacteristic
116C2×D4×C13—21no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C2×D52—21no—
121C2×D52—21no—
122C2×D52—41no—
123C2×D52—41no—
124C2×C4×D13—41no—
125C2×C4×D13—41no—
126C2×Dic26—21no—
127C13×D8—21no—
128C13×D8#4112yes—
129C2×C8×C13C2×D411yescharacteristic
130C2×C8×C13C2×D411yescharacteristic
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2411yescharacteristic
133C13×C4⋊C4—21no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4D811yescharacteristic
142C13×C4⋊C4D811yescharacteristic
143C13×C4⋊C4D811yescharacteristic
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C42×C13C2×D411yescharacteristic
150#6103—41no—
151#6103—41no—
152#6103—41no—
153#6103—41no—
154#6103—41no—
155#6103—41no—
156C4⋊Dic13—21no—
157#6101—41no—
158C4×Dic13—41no—
159Dic52—21no—
160Dic52—21no—
161D104—21no—
162D104—21no—
163D104—21no—
164D104—21no—
165D104—81no—
166#6095—81no—
167#6095—81no—
168#6090—21no—
169#6090—21no—
170#6090—21no—
171#6090—21no—
172#3396—131no—
173#3380D1311yescharacteristic, complemented
174#2244—131no—
175#2243—131no—
176#2242—131no—
177#2229—131no—
178#2228—131no—
179#2224—131no—
180#2210—131no—
181#2210—131no—
182#2206—131no—
183#2183—131no—
184#2177—131no—
185#2175—131no—
186C4×D16—131no—
187C23×C13—41no—
188C22×D13—41no—
189C22×D13—41no—
190Q8×C13—41no—
191Q8×C13—161no—
192D4×C13—22no—
193D4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—41no—
197C2×C4×C13—82no—
198C2×C4×C13—161no—
199C2×C4×C13—161no—
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C2×D811yescharacteristic
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C22×D411yescharacteristic
207C2×Dic13—41no—
208C2×Dic13—41no—
209D52—41no—
210D52—41no—
211D52—41no—
212D52—41no—
213D52—82no—
214D52—161no—
215C4×D13—161no—
216C4×D13—161no—
217Dic26—41no—
218Dic26—41no—
219C8×C13—21no—
220C8×C13—21no—
221C8×C13—21no—
222C8×C13C2×#4111yescharacteristic
223C8×C132−1+411yescharacteristic
224#559—261no—
225#554—21no—
226C2×SD32—131no—
227C2×D16—131no—
228C2×D16—131no—
229#500C2×D1311yescharacteristic
230#499C2×D1311yescharacteristic
231#499C2×D1311yescharacteristic
232#495—131no—
233#495—131no—
234#493—131no—
235#478—21no—
236#478—21no—
237#476—21no—
238#463—261no—
239#463—261no—
240#460—261no—
241C8×Q8C2×D1311yescharacteristic
242C4×Q16—131no—
243C4×D8—131no—
244C4×D8—131no—
245C4×D8C2×D1311yescharacteristic
246C4×D8C2×D1311yescharacteristic
247C4×D8C2×D1311yescharacteristic
248#367—131no—
249#366—131no—
250#366—131no—
251C4⋊C16—131no—
252C4⋊C16—131no—
253C4⋊C16—131no—
254#358—131no—
255#358—131no—
256#358—131no—
257#357—131no—
258#357—131no—
259#357—131no—
260#357—131no—
261#357—131no—
262#357—131no—
263#357—131no—
264#346—131no—
265#346—131no—
266C4×C16—131no—
267C22×C13—42no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13C22×D811yescharacteristic
271C2×D13—81no—
272C2×D13—81no—
273C2×D13—81no—
274C2×D13—81no—
275C2×D13—81no—
276C2×D13—81no—
277C4×C13—21no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—81no—
284C4×C13—81no—
285C4×C13—81no—
286C4×C13#54811yescharacteristic
287C4×C13#57711yescharacteristic
288Dic13—81no—
289Dic13—81no—
290C2×Q16—131no—
291C2×SD16—261no—
292C2×SD16—261no—
293C2×D8—131no—
294C2×D8—131no—
295C2×D8—261no—
296C2×D8C22×D1311yescharacteristic
297C4⋊Q8—21no—
298#127—261no—
299#125—21no—
300#125—21no—
301#124—261no—
302#124—261no—
303#124—521no—
304#123—521no—
305#123—521no—
306C22⋊Q8—41no—
307C22⋊Q8—41no—
308C22⋊Q8—41no—
309C4×Q8—261no—
310C4×Q8C22⋊D1311yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—261no—
315C4×D4—261no—
316C4×D4—521no—
317C2×C4⋊C4—41no—
318SD32—262no—
319D16—262no—
320D16—262no—
321C2×C16—131no—
322C2×C16—131no—
323C2×C16—131no—
324C2×C16—131no—
325#107—21no—
326#107—131no—
327#107C22×D1311yescharacteristic
328#107C22×D1311yescharacteristic
329#107C22×D1311yescharacteristic
330#106—21no—
331#106—21no—
332C4⋊C8C22⋊D1311yescharacteristic
333C4⋊C8C22⋊D1311yescharacteristic
334C4⋊C8C22⋊D1311yescharacteristic
335#103—261no—
336#102—21no—
337#102—21no—
338#102—21no—
339#102—261no—
340#102—261no—
341C4×C8C22×D1311yescharacteristic
342C4×C8C22×D1311yescharacteristic
343C4×C8C22×D1311yescharacteristic
344C2×C13—82no—
345C2×C13#335811yescharacteristic
346C2×C13#341411yescharacteristic
347C2×C13#341511yescharacteristic
348D13—161no—
349D13—161no—
350C2×Q8—41no—
351C2×Q8—261no—
352C2×Q8#610411yescharacteristic
353C2×D4—21no—
354C2×D4—261no—
355C2×D4—261no—
356C2×D4—521no—
357C2×D4—521no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—521no—
362C22×C4—521no—
363Q16—261no—
364Q16—261no—
365SD16—1041no—
366SD16—1041no—
367D8—21no—
368D8—261no—
369D8—261no—
370D8—261no—
371D8—261no—
372D8—1041no—
373D8#613112yes—
374C2×C8C2×C22⋊D1311yescharacteristic
375C2×C8C2×C22⋊D1311yescharacteristic
376C2×C8C2×C22⋊D1311yescharacteristic
377C2×C8C23×D1311yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—261no—
387C4⋊C4—521no—
388C4⋊C4#610411yescharacteristic
389C4⋊C4#610411yescharacteristic
390C4⋊C4#610411yescharacteristic
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—521no—
395C22⋊C4—521no—
396C22⋊C4—521no—
397C22⋊C4—521no—
398C22⋊C4—521no—
399C22⋊C4—521no—
400C42—521no—
401C42C2×C22⋊D1311yescharacteristic
402C42C2×C22⋊D1311yescharacteristic
403C42C2×C22⋊D1311yescharacteristic
404C16—261no—
405C16—261no—
406C16—261no—
407C16—261no—
408C13#3393711yescharacteristic, complemented, Sylow
409C23—41no—
410C23—521no—
411C23—521no—
412Q8—41no—
413Q8—161no—
414Q8—521no—
415Q8—521no—
416D4—22no—
417D4—41no—
418D4—521no—
419D4—521no—
420D4—521no—
421D4—521no—
422D4—1042no—
423D4—2081no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—161no—
429C2×C4—161no—
430C2×C4—521no—
431C2×C4—521no—
432C2×C4—2081no—
433C2×C4—2081no—
434C2×C4C2×#610411yescharacteristic
435C2×C4C2×#610411yescharacteristic
436C2×C4C2×#610411yescharacteristic
437C2×C4C2×#610411yescharacteristic
438C2×C4C2×#610411yescharacteristic
439C2×C4C2×#610411yescharacteristic
440C2×C4C22×C22⋊D1311yescharacteristic
441C8—21no—
442C8—21no—
443C8—21no—
444C8C2×#613111yescharacteristic
445C8#8825411yescharacteristic
446C22—42no—
447C22—81no—
448C22—81no—
449C22—1041no—
450C22—1041no—
451C22—1041no—
452C22—1041no—
453C22—1041no—
454C22—1041no—
455C22C22×#610411yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—1041no—
466C4—1041no—
467C4#1171952211yescharacteristic
468C4#1171954211yescharacteristic
469C2—82no—
470C2—2081no—
471C2—2081no—
472C2#1312747111yescharacteristic
473C2#1312797011yescharacteristic
474C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3380C2
socleC22×C13C22×D8
prime radical#13116871C2
hypercenter#3380D13
hypocenterC13#33937
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #13127849C2semidirect
2. #13117079C2semidirect
3. #13117075C2semidirect
4. #13117070C2semidirect
5. #13116997C2semidirect
6. #13116990C2semidirect
7. #13116970C2semidirect
8. #13116891C2semidirect
9. #13116891C2semidirect
11. #13116745C2semidirect
12. #13116710C2semidirect
13. #13116700C2semidirect
14. C4×#88066C2semidirect
15. C13×#3380C2semidirect
173. #3380D13semidirect
408. C13#33937semidirect

Maximal subgroups

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

subgroupindex
#131278492
#131170792
#131170752
#131170702
#131169972
#131169902
#131169702
#131168912
#131168712
#131167452
#131167102
#131167002
C4×#880662
C13×#33802
#3393713