Finite Group Databasebeta

← #16020676

Subgroups — #16020676

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#13127704C211yesmaximal, characteristic, complemented
2#13117077C211yesmaximal, characteristic, complemented
3#13117072C211yesmaximal, characteristic, complemented
4#13117067C211yesmaximal, characteristic, complemented
5#13117000C211yesmaximal, characteristic, complemented
6#13116993C211yesmaximal, characteristic, complemented
7#13116973C211yesmaximal, characteristic, complemented
8#13116888C211yesmaximal, characteristic, complemented
9#13116888C211yesmaximal, characteristic, complemented
10#13116868C211yesmaximal, characteristic
11#13116745C211yesmaximal, characteristic, complemented
12#13116710C211yesmaximal, characteristic, complemented
13#13116698C211yesmaximal, characteristic, complemented
14C4×#88066C211yesmaximal, characteristic, complemented
15C13×#3396C211yesmaximal, characteristic, complemented
16C13×#559—21no—
17#11719284—21no—
18C13×#495C2211yescharacteristic
19C13×#495C2211yescharacteristic
20C13×#493C2211yescharacteristic
21C13×#463—21no—
22C13×#463—21no—
23C13×#460—21no—
24C8×Q8×C13C2211yescharacteristic
25C4×C13×Q16C2211yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C4×C13×D8C2211yescharacteristic
28C2×#88068C2211yescharacteristic
29C2×#88066C2211yescharacteristic
30C2×#88066C2211yescharacteristic
31#11718508—21no—
32#11718508—21no—
33#11718503—21no—
34C4×D104C2211yescharacteristic
35C4×D104C2211yescharacteristic
36C4×D104C2211yescharacteristic
37#11718344C2211yescharacteristic
38#11718344C2211yescharacteristic
39#11718343C2211yescharacteristic
40#11718156C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45#11718154C2211yescharacteristic
46#11718154C2211yescharacteristic
47#11718154C2211yescharacteristic
48#11718154C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718081C2211yescharacteristic
52#11718081C2211yescharacteristic
53C4⋊#6090C2211yescharacteristic
54C4⋊#6090C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56#11718053C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×SD16—21no—
62C2×C13×D8—21no—
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C13×#127—21no—
66C13×#124—21no—
67C13×#124—21no—
68C13×#124—41no—
69C13×#123—41no—
70C13×#123—41no—
71C4×Q8×C13—21no—
72C4×Q8×C13D411yescharacteristic
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13—41no—
76#88200—41no—
77C2×D104C2311yescharacteristic
78#88150—41no—
79#88150—41no—
80C4⋊C4×D13—41no—
81C4×D52—21no—
82C4×D52—21no—
83C4×D52—21no—
84#88124—21no—
85#88124—21no—
86#88123—21no—
87C13×#107C2311yescharacteristic
88C13×C4⋊C8D411yescharacteristic
89C13×C4⋊C8D411yescharacteristic
90C13×C4⋊C8D411yescharacteristic
91C13×#103—21no—
92C13×#102—21no—
93C13×#102—21no—
94C4×C8×C13C2311yescharacteristic
95C4×C8×C13C2311yescharacteristic
96C4×C8×C13C2311yescharacteristic
97#88068—22no—
98#88066—22no—
99#88066—22no—
100#88061—21no—
101#88061—21no—
102#88061—21no—
103#88058—21no—
104#88058C2311yescharacteristic
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88057—21no—
108#88057—21no—
109C2×#6090C2311yescharacteristic
110C2×#6090C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#33937—131nomaximal, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13D811yescharacteristic
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C2×D52—21no—
123C2×C4×D13—41no—
124C2×C4×D13—41no—
125C2×C4×D13—41no—
126C2×Dic26—41no—
127C13×Q16—21no—
128C13×Q16—21no—
129C13×SD16—81no—
130C13×SD16—81no—
131C13×D8—21no—
132C13×D8—21no—
133C13×D8—21no—
134C13×D8—21no—
135C13×D8—81no—
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2411yescharacteristic
140C13×C4⋊C4—21no—
141C13×C4⋊C4—41no—
142C13×C4⋊C4D811yescharacteristic
143C13×C4⋊C4D811yescharacteristic
144C13×C4⋊C4D811yescharacteristic
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C42×C13—41no—
152C42×C13C2×D411yescharacteristic
153C42×C13C2×D411yescharacteristic
154C42×C13C2×D411yescharacteristic
155#6103—41no—
156#6103—41no—
157#6103—41no—
158C4⋊Dic13—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161C4⋊Dic13—41no—
162#6101—41no—
163#6101—41no—
164#6101—41no—
165#6101—41no—
166D104—21no—
167D104#4112yes—
168#6090—21no—
169#6090—21no—
170#6090—21no—
171#6090—21no—
172#3396D1311yescharacteristic, complemented
173#3380—131no—
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—
188C23×C13—41no—
189C22×D13—41no—
190Q8×C13—41no—
191Q8×C13—41no—
192Q8×C13—41no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—82no—
198D4×C13—161no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—161no—
202C2×C4×C13—161no—
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C2×D811yescharacteristic
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213D52—22no—
214D52—41no—
215C4×D13—82no—
216C4×D13—161no—
217C4×D13—161no—
218Dic26—161no—
219C8×C13—21no—
220C8×C13—21no—
221C8×C13—21no—
222C8×C13C2×#4111yescharacteristic
223C8×C132−1+411yescharacteristic
224#559—21no—
225#554—261no—
226C2×SD32—131no—
227C2×D16—131no—
228C2×D16—131no—
229#500—131no—
230#499—131no—
231#499—131no—
232#495C2×D1311yescharacteristic
233#495C2×D1311yescharacteristic
234#493C2×D1311yescharacteristic
235#478—261no—
236#478—261no—
237#476—261no—
238#463—21no—
239#463—21no—
240#460—21no—
241C8×Q8C2×D1311yescharacteristic
242C4×Q16C2×D1311yescharacteristic
243C4×D8—131no—
244C4×D8—131no—
245C4×D8—131no—
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—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13—81no—
273C22×C13C22×D811yescharacteristic
274C2×D13—42no—
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#54811yescharacteristic
286C4×C13#57711yescharacteristic
287Dic13—81no—
288Dic13—81no—
289Dic13—81no—
290C2×Q16C22×D1311yescharacteristic
291C2×SD16—21no—
292C2×SD16—21no—
293C2×D8—21no—
294C2×D8—131no—
295C2×D8C22×D1311yescharacteristic
296C2×D8C22×D1311yescharacteristic
297C4⋊Q8—261no—
298#127—21no—
299#125—261no—
300#125—261no—
301#124—21no—
302#124—21no—
303#124—41no—
304#123—41no—
305#123—41no—
306C22⋊Q8—521no—
307C22⋊Q8—521no—
308C22⋊Q8—521no—
309C4×Q8—21no—
310C4×Q8C22⋊D1311yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—41no—
314C4×D4—261no—
315C4×D4—261no—
316C4×D4—261no—
317C2×C4⋊C4—521no—
318SD32—262no—
319D16—262no—
320D16—262no—
321C2×C16—131no—
322C2×C16—131no—
323C2×C16—131no—
324C2×C16—131no—
325#107—131no—
326#107—131no—
327#107—131no—
328#107—261no—
329#107C22×D1311yescharacteristic
330#106—261no—
331#106—261no—
332C4⋊C8C22⋊D1311yescharacteristic
333C4⋊C8C22⋊D1311yescharacteristic
334C4⋊C8C22⋊D1311yescharacteristic
335#103—21no—
336#102—21no—
337#102—21no—
338#102—261no—
339#102—261no—
340#102—261no—
341C4×C8C22×D1311yescharacteristic
342C4×C8C22×D1311yescharacteristic
343C4×C8C22×D1311yescharacteristic
344C2×C13—161no—
345C2×C13—161no—
346C2×C13#335811yescharacteristic
347C2×C13#341411yescharacteristic
348C2×C13#341511yescharacteristic
349D13—82no—
350C2×Q8—21no—
351C2×Q8—521no—
352C2×Q8#610411yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—261no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—521no—
361C22×C4—521no—
362C22×C4—521no—
363Q16—21no—
364Q16—21no—
365SD16—81no—
366SD16—81no—
367D8—21no—
368D8—21no—
369D8—21no—
370D8—21no—
371D8—81no—
372D8—132no—
373D8—261no—
374C2×C8C2×C22⋊D1311yescharacteristic
375C2×C8C2×C22⋊D1311yescharacteristic
376C2×C8C2×C22⋊D1311yescharacteristic
377C2×C8C23×D1311yescharacteristic
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—261no—
381C4⋊C4—261no—
382C4⋊C4—261no—
383C4⋊C4—521no—
384C4⋊C4—521no—
385C4⋊C4—521no—
386C4⋊C4—521no—
387C4⋊C4—521no—
388C4⋊C4#610411yescharacteristic
389C4⋊C4#610411yescharacteristic
390C4⋊C4#610411yescharacteristic
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—521no—
398C22⋊C4—521no—
399C22⋊C4—521no—
400C42—41no—
401C42C2×C22⋊D1311yescharacteristic
402C42C2×C22⋊D1311yescharacteristic
403C42C2×C22⋊D1311yescharacteristic
404C16—261no—
405C16—261no—
406C16—261no—
407C16—261no—
408C13#3393711yescharacteristic, complemented, Sylow
409C23—41no—
410C23—41no—
411C23—521no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—2081no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—161no—
422D4—262no—
423D4—521no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—521no—
429C2×C4—521no—
430C2×C4—521no—
431C2×C4—1042no—
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—
444C8#41×D1311yescharacteristic
445C8#8825711yescharacteristic
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—522no—
453C22—1041no—
454C22—1041no—
455C22C22×#610411yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—81no—
463C4—81no—
464C4—1041no—
465C4—1041no—
466C4—1041no—
467C4#1171953611yescharacteristic
468C4#1171954111yescharacteristic
469C2—161no—
470C2—161no—
471C2—1042no—
472C2#1312746711yescharacteristic
473C2#1312797011yescharacteristic
474C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3396C2
socleC22×C13C22×D8
prime radical#13116868C2
hypercenter#3396D13
hypocenterC13#33937
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #13127704C2semidirect
2. #13117077C2semidirect
3. #13117072C2semidirect
4. #13117067C2semidirect
5. #13117000C2semidirect
6. #13116993C2semidirect
7. #13116973C2semidirect
8. #13116888C2semidirect
9. #13116888C2semidirect
11. #13116745C2semidirect
12. #13116710C2semidirect
13. #13116698C2semidirect
14. C4×#88066C2semidirect
15. C13×#3396C2semidirect
172. #3396D13semidirect
408. C13#33937semidirect

Maximal subgroups

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

subgroupindex
#131277042
#131170772
#131170722
#131170672
#131170002
#131169932
#131169732
#131168882
#131168682
#131167452
#131167102
#131166982
C4×#880662
C13×#33962
#3393713