Finite Group Databasebeta

← #16019764

Subgroups — #16019764

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127205C211yesmaximal, characteristic, complemented
2#13117067C211yesmaximal, characteristic, complemented
3#13117031C211yesmaximal, characteristic, complemented
4#13117024C211yesmaximal, characteristic, complemented
5#13116993C211yesmaximal, characteristic, complemented
6#13116930C211yesmaximal, characteristic, complemented
7#13116925C211yesmaximal, characteristic, complemented
8#13116895C211yesmaximal, characteristic, complemented
9#13116776C211yesmaximal, characteristic, complemented
10#13116765C211yesmaximal, characteristic, complemented
11C4×#88067C211yesmaximal, characteristic, complemented
12D4×#6090C211yesmaximal, characteristic, complemented
13#13116543C211yesmaximal, characteristic, complemented
14C2×#11718154C211yesmaximal, characteristic, complemented
15C13×#3280C211yesmaximal, characteristic
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#546—21no—
19#11719246—21no—
20C13×#495C2211yescharacteristic
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#463—21no—
24C13×#450—21no—
25C13×#449—21no—
26C4×C13×D8C2211yescharacteristic
27C8×D4×C13C2211yescharacteristic
28C2×#88069C2211yescharacteristic, complemented
29C2×#88067C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31#11718777C2211yescharacteristic
32#11718777C2211yescharacteristic, complemented
33#11718767C2211yescharacteristic, complemented
34C2×#88058C2211yescharacteristic
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic, complemented
37#11718490—21no—
38#11718384—21no—
39#11718382—21no—
40C4×Dic52C2211yescharacteristic, complemented
41#11718344C2211yescharacteristic, complemented
42#11718156C2211yescharacteristic, complemented
43#11718156C2211yescharacteristic, complemented
44#11718156C2211yescharacteristic, complemented
45#11718154C2211yescharacteristic
46#11718154C2211yescharacteristic
47#11718154C2211yescharacteristic
48#11718154C2211yescharacteristic
49#11718154C2211yescharacteristic
50#11718154C2211yescharacteristic
51C22⋊#6090C2211yescharacteristic
52C22⋊#6090C2211yescharacteristic, complemented
53#11718084C2211yescharacteristic, complemented
54#11718082C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718081C2211yescharacteristic, complemented
57C4⋊#6090C2211yescharacteristic, complemented
58C4×#6090C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C22×D4×C13—21no—
61C13×#135—22no—
62C13×#135—41no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×SD16—21no—
65C2×C13×SD16—21no—
66C2×C13×D8—22no—
67C2×C13×D8—21no—
68C2×C13×D8—41no—
69C2×C13×D8C2311yescharacteristic
70C2×C13×D8C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C13×#124—21no—
74C13×#123—41no—
75C13×C22⋊Q8—21no—
76C13×#121—21no—
77C13×#121—41no—
78C13×#120—41no—
79C4×D4×C13—21no—
80C4×D4×C13D411yescharacteristic
81C2×C13×C22⋊C4—41no—
82#88189—41no—
83#88180—21no—
84C2×C4⋊Dic13—21no—
85#88178—21no—
86#88178—21no—
87C2×Dic52C2311yescharacteristic
88#88143—41no—
89#88133—41no—
90#88131—41no—
91#88124—21no—
92C4×Dic26—21no—
93C13×#107C2311yescharacteristic
94C13×C4⋊C8D411yescharacteristic
95C13×#103—21no—
96C13×#102—21no—
97C13×#102—21no—
98C13×C22⋊C8D411yescharacteristic
99C13×C22⋊C8D411yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88069—41no—
102#88067—22no—
103#88067—41no—
104#88058—21no—
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88058C2311yescharacteristic
108#88057—21no—
109#88057—21no—
110#88056—21no—
111#88056—21no—
112#88056—21no—
113C2×#6090—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33863—131nomaximal, Sylow
120C24×C13—41no—
121C13×#41—42no—
122C13×#41—81no—
123C2×Q8×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—42no—
127C2×D4×C13—41no—
128C2×D4×C13—41no—
129C2×D4×C13—41no—
130C2×D4×C13—81no—
131C2×D4×C13D811yescharacteristic
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×Dic13—41no—
137C2×Dic26—21no—
138C13×Q16—21no—
139C13×Q16—21no—
140C13×SD16—42no—
141C13×SD16—81no—
142C13×D8—21no—
143C13×D8—21no—
144C13×D8—21no—
145C13×D8—42no—
146C13×D8#4112yes—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13C2×D411yescharacteristic
152C2×C8×C13C2×D411yescharacteristic
153C2×C8×C13C2×D411yescharacteristic
154C2×C8×C13C2411yescharacteristic
155C13×C4⋊C4—21no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4D811yescharacteristic
164C13×C22⋊C4D811yescharacteristic
165C42×C13C2×D411yescharacteristic
166C22⋊Dic13—41no—
167C22⋊Dic13—41no—
168C22⋊Dic13—41no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—41no—
173#6101—41no—
174#6101—41no—
175#6101—41no—
176#6101—41no—
177#6101—41no—
178C4×Dic13—41no—
179C4×Dic13—41no—
180Dic52—21no—
181Dic52—21no—
182#6090—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#3336—131no—
187#3280D1311yescharacteristic
188#2242—131no—
189#2235—131no—
190#2234—131no—
191#2228—131no—
192#2217—131no—
193#2216—131no—
194#2211—131no—
195#2189—131no—
196#2187—131no—
197C4×SD32—131no—
198D4×C16—131no—
199#2138—131no—
200C2×#357—131no—
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—82no—
204C23×C13—82no—
205C23×C13—161no—
206C23×C13C2×D811yescharacteristic
207C23×C13C2×D811yescharacteristic
208Q8×C13—41no—
209Q8×C13—41no—
210D4×C13—22no—
211D4×C13—22no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—82no—
216D4×C13—82no—
217D4×C13—161no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—82no—
225C2×C4×C13—161no—
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C2×D811yescharacteristic
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C2×D811yescharacteristic
230C2×C4×C13C22×D411yescharacteristic
231C2×Dic13—41no—
232C2×Dic13—41no—
233C2×Dic13—41no—
234C2×Dic13—41no—
235C2×Dic13—82no—
236Dic26—41no—
237Dic26—41no—
238C8×C13—21no—
239C8×C13—21no—
240C8×C13—21no—
241C8×C13C2×#4111yescharacteristic
242C8×C13H(5,𝔽2)11yescharacteristic
243C2×#135C2×D1311yescharacteristic
244C22×D8C2×D1311yescharacteristic
245#552—261no—
246#546—21no—
247C2×Q32—131no—
248C2×SD32—131no—
249C2×SD32—131no—
250C22×C16—131no—
251C22×C16—131no—
252#499—131no—
253#495C2×D1311yescharacteristic
254#485—261no—
255#483—261no—
256#479—261no—
257#467—131no—
258#467—131no—
259#467C2×D1311yescharacteristic
260#466C2×D1311yescharacteristic
261#463—21no—
262#450—21no—
263#449—21no—
264C4×Q16—131no—
265C4×D8C2×D1311yescharacteristic
266C8×D4C2×D1311yescharacteristic
267#427—131no—
268C2×#107—131no—
269#367—131no—
270#367—131no—
271#366—131no—
272C4⋊C16—131no—
273#358—131no—
274#358—131no—
275#358—131no—
276#358—131no—
277#357—131no—
278#357—131no—
279#357—131no—
280#357—131no—
281#357—131no—
282#357—131no—
283C22⋊C16—131no—
284C22⋊C16—131no—
285C4×C16—131no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—42no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13—164no—
298C22×C13#50812yes—
299C22×C13C22×D811yescharacteristic
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—21no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13#54611yescharacteristic
307C4×C13#57711yescharacteristic
308Dic13—81no—
309Dic13—81no—
310Dic13—81no—
311Dic13—81no—
312C2×#41—21no—
313C22×D4—21no—
314#135—22no—
315#135—41no—
316C2×Q16—131no—
317C2×Q16C22×D1311yescharacteristic
318C2×SD16—21no—
319C2×SD16—21no—
320C2×D8—22no—
321C2×D8—21no—
322C2×D8—41no—
323C2×D8C22×D1311yescharacteristic
324C2×D8C22×D1311yescharacteristic
325C22×C8C22×D1311yescharacteristic
326C22×C8C22×D1311yescharacteristic
327#126—521no—
328#125—261no—
329#125—521no—
330#124—21no—
331#123—41no—
332#123—521no—
333C22⋊Q8—21no—
334C22⋊Q8—261no—
335C22⋊Q8—261no—
336#121—21no—
337#121—41no—
338#120—41no—
339C4×Q8—261no—
340C4×D4—21no—
341C4×D4C22⋊D1311yescharacteristic
342#117—261no—
343#117—521no—
344C2×C4⋊C4—261no—
345C2×C22⋊C4—41no—
346Q32—521no—
347SD32—262no—
348SD32—521no—
349C2×C16—131no—
350C2×C16—131no—
351C2×C16—131no—
352C2×C16—131no—
353C2×C16—521no—
354C2×C16—521no—
355#107—131no—
356#107—131no—
357#107—131no—
358#107—261no—
359#107C22×D1311yescharacteristic
360#106—261no—
361#106—261no—
362C4⋊C8C22⋊D1311yescharacteristic
363#103—21no—
364#103—261no—
365#103—261no—
366#103—261no—
367#102—21no—
368#102—21no—
369C22⋊C8C22⋊D1311yescharacteristic
370C22⋊C8C22⋊D1311yescharacteristic
371C4×C8C22×D1311yescharacteristic
372C2×C13—22no—
373C2×C13—41no—
374C2×C13—82no—
375C2×C13—161no—
376C2×C13#329411yescharacteristic
377C2×C13C2×#50811yescharacteristic
378C2×C13#341611yescharacteristic
379C24—41no—
380#41—42no—
381#41—81no—
382C2×Q8—21no—
383C2×Q8—261no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—81no—
391C2×D4#610411yescharacteristic
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—521no—
395C22×C4C2×C22⋊D1311yescharacteristic
396C22×C4C2×C22⋊D1311yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—261no—
400Q16—261no—
401SD16—42no—
402SD16—81no—
403D8—21no—
404D8—21no—
405D8—21no—
406D8—42no—
407D8#612912yes—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8C2×C22⋊D1311yescharacteristic
413C2×C8C2×C22⋊D1311yescharacteristic
414C2×C8C2×C22⋊D1311yescharacteristic
415C2×C8C23×D1311yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—261no—
419C4⋊C4—261no—
420C4⋊C4—261no—
421C4⋊C4—521no—
422C4⋊C4—521no—
423C4⋊C4—521no—
424C4⋊C4—521no—
425C4⋊C4—521no—
426C4⋊C4—521no—
427C4⋊C4#610411yescharacteristic
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—521no—
434C22⋊C4—521no—
435C22⋊C4—521no—
436C22⋊C4#610411yescharacteristic
437C22⋊C4#610411yescharacteristic
438C42—521no—
439C42—521no—
440C42C2×C22⋊D1311yescharacteristic
441C16—261no—
442C16—261no—
443C16—261no—
444C16—261no—
445C13#3386311yescharacteristic, complemented, Sylow
446C23—41no—
447C23—41no—
448C23—82no—
449C23—82no—
450C23—161no—
451C23C2×#610411yescharacteristic
452C23C2×#610411yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—521no—
456Q8—521no—
457D4—22no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—161no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—161no—
473C2×C4—521no—
474C2×C4—521no—
475C2×C4—521no—
476C2×C4—521no—
477C2×C4—1042no—
478C2×C4C2×#610411yescharacteristic
479C2×C4C2×#610411yescharacteristic
480C2×C4C2×#610411yescharacteristic
481C2×C4C2×#610411yescharacteristic
482C2×C4C22×C22⋊D1311yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8C2×#612911yescharacteristic
487C8#8825111yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—164no—
500C22#1171885512yes—
501C22C22×#610411yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—1041no—
509C4—1041no—
510C4—1041no—
511C4—1041no—
512C4#1171951111yescharacteristic
513C4#1171954111yescharacteristic
514C2—22no—
515C2—41no—
516C2—82no—
517C2—161no—
518C2#1312664911yescharacteristic
519C2C2×#1171885511yescharacteristic
520C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3280C2
socleC22×C13C22×D8
hypercenter#3280D13
hypocenterC13#33863
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #13127205C2semidirect
2. #13117067C2semidirect
3. #13117031C2semidirect
4. #13117024C2semidirect
5. #13116993C2semidirect
6. #13116930C2semidirect
7. #13116925C2semidirect
8. #13116895C2semidirect
9. #13116776C2semidirect
10. #13116765C2semidirect
11. C4×#88067C2semidirect
12. D4×#6090C2semidirect
13. #13116543C2semidirect
14. C2×#11718154C2semidirect
28. C2×#88069C22semidirect
32. #11718777C22semidirect
33. #11718767C22semidirect
36. C22×#6090C22semidirect
40. C4×Dic52C22semidirect
41. #11718344C22semidirect
42. #11718156C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
52. C22⋊#6090C22semidirect
53. #11718084C22semidirect
54. #11718082C22semidirect
55. #11718082C22semidirect
56. #11718081C22semidirect
57. C4⋊#6090C22semidirect
58. C4×#6090C22semidirect
445. C13#33863semidirect

Maximal subgroups

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

subgroupindex
#131272052
#131170672
#131170312
#131170242
#131169932
#131169302
#131169252
#131168952
#131167762
#131167652
C4×#880672
D4×#60902
#131165432
C2×#117181542
C13×#32802
#3386313