Finite Group Databasebeta

← #16019758

Subgroups — #16019758

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#13126523C211yesmaximal, characteristic
2#13117070C211yesmaximal, characteristic, complemented
3#13117033C211yesmaximal, characteristic, complemented
4#13117027C211yesmaximal, characteristic, complemented
5#13116990C211yesmaximal, characteristic, complemented
6#13116934C211yesmaximal, characteristic, complemented
7#13116925C211yesmaximal, characteristic, complemented
8#13116898C211yesmaximal, characteristic, complemented
9#13116774C211yesmaximal, characteristic, complemented
10#13116764C211yesmaximal, characteristic, complemented
11C4×#88068C211yesmaximal, characteristic, complemented
12D4×#6090C211yesmaximal, characteristic, complemented
13#13116541C211yesmaximal, characteristic, complemented
14C2×#11718083C211yesmaximal, characteristic, complemented
15C13×#3336C211yesmaximal, characteristic, complemented
16C13×#552—21no—
17C2×#88158C2211yescharacteristic
18C22×D104C2211yescharacteristic
19#11719255—21no—
20C13×#499C2211yescharacteristic, complemented
21C13×#485—21no—
22C13×#483—21no—
23C13×#479—21no—
24C13×#467C2211yescharacteristic
25C13×#467C2211yescharacteristic, complemented
26C4×C13×Q16C2211yescharacteristic, complemented
27C8×D4×C13C2211yescharacteristic
28C13×#427C2211yescharacteristic, complemented
29C2×C13×#107C2211yescharacteristic
30C2×#88069C2211yescharacteristic, complemented
31C2×#88068C2211yescharacteristic
32C2×#88068C2211yescharacteristic
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic, complemented
37#11718505—21no—
38#11718395—21no—
39#11718392—21no—
40#11718357C2211yescharacteristic
41C4×D104C2211yescharacteristic
42#11718156C2211yescharacteristic, complemented
43C22⋊#6090C2211yescharacteristic
44C22⋊#6090C2211yescharacteristic, complemented
45#11718084C2211yescharacteristic, complemented
46#11718084C2211yescharacteristic, complemented
47#11718084C2211yescharacteristic, complemented
48#11718083C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718083C2211yescharacteristic
51#11718083C2211yescharacteristic
52#11718083C2211yescharacteristic
53#11718083C2211yescharacteristic
54#11718082C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718081C2211yescharacteristic, complemented
57C4⋊#6090C2211yescharacteristic, complemented
58C4×#6090C2211yescharacteristic, complemented
59C2×#6127—21no—
60C22×D52—21no—
61C2×C13×Q16C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×#126—41no—
65C13×#125—21no—
66C13×#125—41no—
67C13×#123—41no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—21no—
70C4×Q8×C13—21no—
71C4×D4×C13D411yescharacteristic
72C13×#117—21no—
73C13×#117—41no—
74C2×C13×C4⋊C4—21no—
75#88191—41no—
76#88184—21no—
77#88178—21no—
78C2×Dic52C2311yescharacteristic
79#88158—22no—
80#88158—41no—
81C2×D104—22no—
82C2×D104—21no—
83C2×D104—41no—
84C2×D104C2311yescharacteristic
85C2×D104C2311yescharacteristic
86C2×#6095—21no—
87C2×#6095—21no—
88#88148—41no—
89#88138—41no—
90C22⋊C4×D13—41no—
91#88129—21no—
92C4×D52—21no—
93C13×#107—21no—
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#106—21no—
98C13×#106—21no—
99C13×C4⋊C8D411yescharacteristic
100C13×#103—21no—
101C13×#103—21no—
102C13×#103—21no—
103C13×C22⋊C8D411yescharacteristic
104C13×C22⋊C8D411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88069—41no—
107#88068—22no—
108#88068—41no—
109#88061—21no—
110#88061—21no—
111#88058C2311yescharacteristic
112#88056—21no—
113C2×#6090—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33863—131nomaximal, Sylow
120C23×D13—41no—
121C2×Q8×C13—21no—
122C2×D4×C13D811yescharacteristic
123C22×C4×C13—41no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C2×C22⋊D13—41no—
127C2×C22⋊D13—41no—
128#6127—42no—
129#6127—81no—
130C2×D52—21no—
131C2×D52—21no—
132C2×D52—42no—
133C2×D52—41no—
134C2×D52—81no—
135C2×C4×D13—41no—
136C2×C4×D13—41no—
137C2×Dic26—21no—
138C13×Q16—21no—
139C13×Q16—21no—
140C2×C8×C13—21no—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C2×C8×C13—21no—
144C2×C8×C13C2×D411yescharacteristic
145C2×C8×C13C2×D411yescharacteristic
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2411yescharacteristic
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—41no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4D811yescharacteristic
162C13×C22⋊C4D811yescharacteristic
163C42×C13—41no—
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C22⋊Dic13—41no—
167#6103—41no—
168#6103—41no—
169#6103—41no—
170#6103—41no—
171C4⋊Dic13—21no—
172#6101—41no—
173Dic52—21no—
174Dic52—21no—
175D104—21no—
176D104—21no—
177D104—21no—
178D104—42no—
179D104#4112yes—
180#6095—42no—
181#6095—81no—
182#6090—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#3336D1311yescharacteristic, complemented
187#3280—131no—
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×C13C2×D811yescharacteristic
202C23×C13C2×D811yescharacteristic
203C22×D13—41no—
204C22×D13—41no—
205C22×D13—82no—
206C22×D13—82no—
207C22×D13—161no—
208Q8×C13—41no—
209Q8×C13—41no—
210D4×C13—22no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—82no—
220C2×C4×C13C2×D811yescharacteristic
221C2×C4×C13C2×D811yescharacteristic
222C2×C4×C13C2×D811yescharacteristic
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C22×D411yescharacteristic
225C22⋊D13—82no—
226C22⋊D13—161no—
227C2×Dic13—41no—
228C2×Dic13—41no—
229D52—22no—
230D52—41no—
231D52—41no—
232D52—41no—
233D52—82no—
234C4×D13—82no—
235C4×D13—161no—
236Dic26—41no—
237Dic26—41no—
238C8×C13—21no—
239C8×C13—21no—
240C8×C13—21no—
241C8×C13C2×#4111yescharacteristic
242C8×C13H(5,𝔽2)11yescharacteristic
243C2×#135—131no—
244C22×D8—131no—
245#552—21no—
246#546—261no—
247C2×Q32—131no—
248C2×SD32—131no—
249C2×SD32—131no—
250C22×C16—131no—
251C22×C16—131no—
252#499C2×D1311yescharacteristic, complemented
253#495—131no—
254#485—21no—
255#483—21no—
256#479—21no—
257#467—131no—
258#467C2×D1311yescharacteristic
259#467C2×D1311yescharacteristic, complemented
260#466—131no—
261#463—261no—
262#450—261no—
263#449—261no—
264C4×Q16C2×D1311yescharacteristic, complemented
265C4×D8—131no—
266C8×D4C2×D1311yescharacteristic
267#427C2×D1311yescharacteristic, complemented
268C2×#107C2×D1311yescharacteristic
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#50812yes—
292C22×C13C22×D811yescharacteristic
293C2×D13—42no—
294C2×D13—81no—
295C2×D13—81no—
296C2×D13—81no—
297C2×D13—81no—
298C2×D13—81no—
299C2×D13—164no—
300C4×C13—21no—
301C4×C13—21no—
302C4×C13—21no—
303C4×C13—21no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13—81no—
307C4×C13—81no—
308C4×C13#54611yescharacteristic
309C4×C13#57711yescharacteristic
310Dic13—81no—
311Dic13—81no—
312C2×#41—261no—
313C22×D4—261no—
314#135—262no—
315#135—521no—
316C2×Q16—131no—
317C2×Q16C22×D1311yescharacteristic
318C2×SD16—261no—
319C2×SD16—261no—
320C2×D8—131no—
321C2×D8—131no—
322C2×D8—262no—
323C2×D8—261no—
324C2×D8—521no—
325C22×C8C22×D1311yescharacteristic
326C22×C8C22×D1311yescharacteristic
327#126—41no—
328#125—21no—
329#125—41no—
330#124—261no—
331#123—41no—
332#123—521no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—261no—
336#121—261no—
337#121—521no—
338#120—521no—
339C4×Q8—21no—
340C4×D4—261no—
341C4×D4C22⋊D1311yescharacteristic
342#117—21no—
343#117—41no—
344C2×C4⋊C4—21no—
345C2×C22⋊C4—521no—
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—21no—
356#107—131no—
357#107C22×D1311yescharacteristic
358#107C22×D1311yescharacteristic
359#107C22×D1311yescharacteristic
360#106—21no—
361#106—21no—
362C4⋊C8C22⋊D1311yescharacteristic
363#103—21no—
364#103—21no—
365#103—21no—
366#103—261no—
367#102—261no—
368#102—261no—
369C22⋊C8C22⋊D1311yescharacteristic
370C22⋊C8C22⋊D1311yescharacteristic
371C4×C8C22×D1311yescharacteristic
372C2×C13—22no—
373C2×C13—41no—
374C2×C13#329411yescharacteristic
375C2×C13C2×#50811yescharacteristic
376C2×C13#341611yescharacteristic
377D13—82no—
378D13—161no—
379C24—521no—
380#41—522no—
381#41—1041no—
382C2×Q8—21no—
383C2×Q8—261no—
384C2×D4—261no—
385C2×D4—261no—
386C2×D4—522no—
387C2×D4—521no—
388C2×D4—521no—
389C2×D4—521no—
390C2×D4—1041no—
391C2×D4#610411yescharacteristic
392C22×C4—41no—
393C22×C4—521no—
394C22×C4—521no—
395C22×C4C2×C22⋊D1311yescharacteristic
396C22×C4C2×C22⋊D1311yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—261no—
400Q16—261no—
401SD16—522no—
402SD16—1041no—
403D8—132no—
404D8—261no—
405D8—261no—
406D8—261no—
407D8—522no—
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—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—261no—
426C4⋊C4—521no—
427C4⋊C4#610411yescharacteristic
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—521no—
432C22⋊C4—521no—
433C22⋊C4—521no—
434C22⋊C4—521no—
435C22⋊C4—521no—
436C22⋊C4#610411yescharacteristic
437C22⋊C4#610411yescharacteristic
438C42—41no—
439C42—41no—
440C42C2×C22⋊D1311yescharacteristic
441C16—261no—
442C16—261no—
443C16—261no—
444C16—261no—
445C13#3386311yescharacteristic, complemented, Sylow
446C23—521no—
447C23—521no—
448C23—1042no—
449C23—1042no—
450C23—2081no—
451C23C2×#610411yescharacteristic
452C23C2×#610411yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—521no—
456Q8—521no—
457D4—22no—
458D4—262no—
459D4—521no—
460D4—521no—
461D4—521no—
462D4—1042no—
463D4—1042no—
464D4—2081no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—521no—
475C2×C4—521no—
476C2×C4—1042no—
477C2×C4—2081no—
478C2×C4C2×#610411yescharacteristic
479C2×C4C2×#610411yescharacteristic
480C2×C4C2×#610411yescharacteristic
481C2×C4C2×#610411yescharacteristic
482C2×C4C22×C22⋊D1311yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8#41×D1311yescharacteristic
487C8#8825611yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—522no—
494C22—1041no—
495C22—1041no—
496C22—1041no—
497C22—1041no—
498C22—1041no—
499C22—2084no—
500C22#1171885512yes—
501C22C22×#610411yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—1041no—
511C4—1041no—
512C4#1171953411yescharacteristic
513C4#1171954211yescharacteristic
514C2—22no—
515C2—41no—
516C2—1042no—
517C2—2081no—
518C2#1312664311yescharacteristic
519C2C2×#1171885511yescharacteristic
520C2#1312798011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3336C2
socleC22×C13C22×D8
prime radical#13126523C2
hypercenter#3336D13
hypocenterC13#33863
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3336

Complements

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

NH ≅ G/Ntype
2. #13117070C2semidirect
3. #13117033C2semidirect
4. #13117027C2semidirect
5. #13116990C2semidirect
6. #13116934C2semidirect
7. #13116925C2semidirect
8. #13116898C2semidirect
9. #13116774C2semidirect
10. #13116764C2semidirect
11. C4×#88068C2semidirect
12. D4×#6090C2semidirect
13. #13116541C2semidirect
14. C2×#11718083C2semidirect
15. C13×#3336C2semidirect
20. C13×#499C22semidirect
25. C13×#467C22semidirect
26. C4×C13×Q16C22semidirect
28. C13×#427C22semidirect
30. C2×#88069C22semidirect
36. C22×#6090C22semidirect
42. #11718156C22semidirect
44. C22⋊#6090C22semidirect
45. #11718084C22semidirect
46. #11718084C22semidirect
47. #11718084C22semidirect
54. #11718082C22semidirect
55. #11718082C22semidirect
56. #11718081C22semidirect
57. C4⋊#6090C22semidirect
58. C4×#6090C22semidirect
186. #3336D13semidirect
252. #499C2×D13semidirect
259. #467C2×D13semidirect
264. C4×Q16C2×D13semidirect
267. #427C2×D13semidirect
445. C13#33863semidirect

Maximal subgroups

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

subgroupindex
#131265232
#131170702
#131170332
#131170272
#131169902
#131169342
#131169252
#131168982
#131167742
#131167642
C4×#880682
D4×#60902
#131165412
C2×#117180832
C13×#33362
#3386313