Finite Group Databasebeta

← #16019884

Subgroups — #16019884

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126523C211yesmaximal, characteristic, complemented
2#13117075C211yesmaximal, characteristic, complemented
3#13117033C211yesmaximal, characteristic, complemented
4#13117021C211yesmaximal, characteristic, complemented
5#13116980C211yesmaximal, characteristic, complemented
6#13116937C211yesmaximal, characteristic, complemented
7#13116930C211yesmaximal, characteristic, complemented
8#13116891C211yesmaximal, characteristic, complemented
9#13116757C211yesmaximal, characteristic, complemented
10#13116747C211yesmaximal, characteristic, complemented
11#13116710C211yesmaximal, characteristic, complemented
12#13116662C211yesmaximal, characteristic, complemented
13#13116546C211yesmaximal, characteristic, complemented
14C2×#11718083C211yesmaximal, characteristic, complemented
15C13×#3334C211yesmaximal, characteristic, complemented
16C13×#547—21no—
17C2×#88158C2211yescharacteristic
18C22×D104C2211yescharacteristic
19#11719255—21no—
20C13×#500C2211yescharacteristic, complemented
21C13×#480—21no—
22C13×#480—21no—
23C13×#474—21no—
24C13×#466C2211yescharacteristic
25C13×#466C2211yescharacteristic, complemented
26C4×C13×D8C2211yescharacteristic, complemented
27C8×D4×C13C2211yescharacteristic
28C2×C13×#107C2211yescharacteristic
29C2×C13×#107C2211yescharacteristic, complemented
30C2×#88067C2211yescharacteristic, complemented
31C2×#88066C2211yescharacteristic
32C2×#88066C2211yescharacteristic
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35C2×#88052C2211yescharacteristic, complemented
36C22×#6090C2211yescharacteristic
37#11718505—21no—
38#11718395—21no—
39#11718392—21no—
40#11718357C2211yescharacteristic
41C4×D104C2211yescharacteristic
42#11718154C2211yescharacteristic, 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#11718082C2211yescharacteristic, complemented
57C4⋊#6090C2211yescharacteristic, complemented
58#11718053C2211yescharacteristic, complemented
59C2×C13×#41—41no—
60C2×#6127—21no—
61C22×D52—21no—
62C2×C13×D8C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—21no—
66C13×#123—41no—
67C13×#123—41no—
68C13×C22⋊Q8—41no—
69C13×#121—21no—
70C13×#121—21no—
71C4×D4×C13—21no—
72C4×D4×C13D411yescharacteristic
73C2×C13×C4⋊C4—21no—
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×#107—21no—
95C13×#107—21no—
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#107C2311yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×#102—21no—
101C13×#102—21no—
102C13×#102—21no—
103C13×C22⋊C8D411yescharacteristic
104C13×C22⋊C8D411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88067—41no—
107#88066—22no—
108#88066—41no—
109#88061—21no—
110#88061—21no—
111#88058C2311yescharacteristic
112#88056—21no—
113#88052—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33873—131nomaximal, Sylow
120C23×D13—41no—
121C13×#41—84no—
122C2×Q8×C13—41no—
123C2×D4×C13—21no—
124C2×D4×C13—41no—
125C2×D4×C13—41no—
126C2×D4×C13D811yescharacteristic
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C2×C22⋊D13—41no—
133C2×C22⋊D13—41no—
134#6127—42no—
135#6127—81no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—42no—
139C2×D52—41no—
140C2×D52—81no—
141C2×C4×D13—41no—
142C2×C4×D13—41no—
143C2×Dic26—21no—
144C13×D8—21no—
145C13×D8—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13C2×D411yescharacteristic
151C2×C8×C13C2×D411yescharacteristic
152C2×C8×C13C2×D411yescharacteristic
153C2×C8×C13C2411yescharacteristic
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—41no—
158C13×C4⋊C4—41no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4D811yescharacteristic
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4D811yescharacteristic
165C13×C22⋊C4D811yescharacteristic
166C42×C13C2×D411yescharacteristic
167C22⋊Dic13—41no—
168#6103—41no—
169#6103—41no—
170#6103—41no—
171#6103—41no—
172C4⋊Dic13—21no—
173#6101—41no—
174Dic52—21no—
175Dic52—21no—
176D104—21no—
177D104—21no—
178D104—21no—
179D104—42no—
180D104#4112yescomplemented
181#6095—42no—
182#6095—81no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#6090—21no—
187#3334D1311yescharacteristic, complemented
188#3280—131no—
189#2243—131no—
190#2235—131no—
191#2233—131no—
192#2226—131no—
193#2218—131no—
194#2217—131no—
195#2210—131no—
196#2186—131no—
197#2184—131no—
198#2177—131no—
199#2168—131no—
200#2139—131no—
201C2×#357—131no—
202C23×C13—41no—
203C23×C13C2×D811yescharacteristic
204C23×C13C2×D811yescharacteristic
205C22×D13—41no—
206C22×D13—41no—
207C22×D13—82no—
208C22×D13—82no—
209C22×D13—161no—
210Q8×C13—82no—
211D4×C13—22no—
212D4×C13—41no—
213D4×C13—41no—
214D4×C13—82no—
215D4×C13—82no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—82no—
224C2×C4×C13—82no—
225C2×C4×C13—82no—
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C2×D811yescharacteristic
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C2×D811yescharacteristic
230C2×C4×C13C22×D411yescharacteristic
231C22⋊D13—82no—
232C22⋊D13—161no—
233C2×Dic13—41no—
234C2×Dic13—41no—
235D52—22no—
236D52—41no—
237D52—41no—
238D52—41no—
239D52—82no—
240C4×D13—82no—
241C4×D13—161no—
242Dic26—41no—
243Dic26—41no—
244C8×C13—21no—
245C8×C13—21no—
246C8×C13—21no—
247C8×C13C2×#4111yescharacteristic
248C8×C13H(5,𝔽2)11yescharacteristic
249C2×#135—131no—
250C22×D8—131no—
251#547—21no—
252#546—261no—
253C2×SD32—131no—
254C2×D16—131no—
255C2×D16—131no—
256C2×M32—131no—
257C22×C16—131no—
258#500C2×D1311yescharacteristic, complemented
259#495—131no—
260#480—21no—
261#480—21no—
262#474—21no—
263#467—131no—
264#466—131no—
265#466C2×D1311yescharacteristic
266#466C2×D1311yescharacteristic, complemented
267#463—261no—
268#450—261no—
269#449—261no—
270C4×D8—131no—
271C4×D8C2×D1311yescharacteristic, complemented
272C8×D4C2×D1311yescharacteristic
273C2×#107C2×D1311yescharacteristic
274C2×#107C2×D1311yescharacteristic, complemented
275#367—131no—
276#367—131no—
277#367—131no—
278C4⋊C16—131no—
279#358—131no—
280#358—131no—
281#358—131no—
282#357—131no—
283#357—131no—
284#357—131no—
285#357—131no—
286#357—131no—
287#357—131no—
288#357—131no—
289C22⋊C16—131no—
290C22⋊C16—131no—
291#346—131no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—81no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13#50912yes—
301C22×C13C22×D811yescharacteristic
302C2×D13—42no—
303C2×D13—81no—
304C2×D13—81no—
305C2×D13—81no—
306C2×D13—81no—
307C2×D13—81no—
308C2×D13—164no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—81no—
314C4×C13—81no—
315C4×C13—81no—
316C4×C13#54611yescharacteristic
317C4×C13#57711yescharacteristic
318Dic13—81no—
319Dic13—81no—
320C2×#41—41no—
321C2×#41—261no—
322C22×D4—261no—
323#135—262no—
324#135—521no—
325C2×Q16—131no—
326C2×SD16—261no—
327C2×SD16—261no—
328C2×D8—131no—
329C2×D8—131no—
330C2×D8—262no—
331C2×D8—261no—
332C2×D8—521no—
333C2×D8C22×D1311yescharacteristic
334C22×C8C22×D1311yescharacteristic
335C22×C8C22×D1311yescharacteristic
336C4⋊Q8—21no—
337#124—261no—
338#123—41no—
339#123—41no—
340#123—521no—
341C22⋊Q8—41no—
342C22⋊Q8—261no—
343#121—21no—
344#121—21no—
345#121—261no—
346#121—521no—
347#120—521no—
348C4×D4—21no—
349C4×D4—261no—
350C4×D4C22⋊D1311yescharacteristic
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C22⋊C4—521no—
354SD32—521no—
355D16—262no—
356D16—521no—
357M32—521no—
358C2×C16—131no—
359C2×C16—131no—
360C2×C16—131no—
361C2×C16—131no—
362C2×C16—521no—
363#107—21no—
364#107—21no—
365#107—21no—
366#107—131no—
367#107C22×D1311yescharacteristic
368#107C22×D1311yescharacteristic
369#107C22×D1311yescharacteristic
370C4⋊C8C22⋊D1311yescharacteristic
371#103—261no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—261no—
376#102—261no—
377C22⋊C8C22⋊D1311yescharacteristic
378C22⋊C8C22⋊D1311yescharacteristic
379C4×C8C22×D1311yescharacteristic
380C2×C13—22no—
381C2×C13—41no—
382C2×C13—161no—
383C2×C13#329411yescharacteristic
384C2×C13C2×#50911yescharacteristic
385C2×C13#341611yescharacteristic
386D13—82no—
387D13—161no—
388C24—521no—
389#41—84no—
390#41—522no—
391#41—1041no—
392C2×Q8—41no—
393C2×Q8—261no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—261no—
398C2×D4—261no—
399C2×D4—522no—
400C2×D4—521no—
401C2×D4—521no—
402C2×D4—521no—
403C2×D4—1041no—
404C2×D4#610411yescharacteristic
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—521no—
409C22×C4—521no—
410C22×C4C2×C22⋊D1311yescharacteristic
411C22×C4C2×C22⋊D1311yescharacteristic
412Q16—261no—
413Q16—261no—
414SD16—522no—
415SD16—1041no—
416D8—21no—
417D8—21no—
418D8—132no—
419D8—261no—
420D8—261no—
421D8—261no—
422D8—522no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×C22⋊D1311yescharacteristic
428C2×C8C2×C22⋊D1311yescharacteristic
429C2×C8C2×C22⋊D1311yescharacteristic
430C2×C8C23×D1311yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—261no—
438C4⋊C4—521no—
439C4⋊C4#610411yescharacteristic
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—521no—
444C22⋊C4—521no—
445C22⋊C4—521no—
446C22⋊C4—521no—
447C22⋊C4—521no—
448C22⋊C4#610411yescharacteristic
449C22⋊C4#610411yescharacteristic
450C42C2×C22⋊D1311yescharacteristic
451C16—261no—
452C16—261no—
453C16—261no—
454C16—261no—
455C13#3387311yescharacteristic, complemented, Sylow
456C23—41no—
457C23—521no—
458C23—521no—
459C23—1042no—
460C23—1042no—
461C23—2081no—
462C23C2×#610411yescharacteristic
463C23C2×#610411yescharacteristic
464Q8—82no—
465Q8—521no—
466Q8—521no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—262no—
473D4—521no—
474D4—521no—
475D4—521no—
476D4—1042no—
477D4—1042no—
478D4—2081no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—521no—
490C2×C4—521no—
491C2×C4—1042no—
492C2×C4—2081no—
493C2×C4C2×#610411yescharacteristic
494C2×C4C2×#610411yescharacteristic
495C2×C4C2×#610411yescharacteristic
496C2×C4C2×#610411yescharacteristic
497C2×C4C22×C22⋊D1311yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D1311yescharacteristic
502C8#8825611yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—522no—
512C22—1041no—
513C22—1041no—
514C22—1041no—
515C22—1041no—
516C22—1041no—
517C22—2084no—
518C22#1171880812yes—
519C22C22×#610411yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—1041no—
528C4—1041no—
529C4#1171953411yescharacteristic
530C4#1171954211yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—1042no—
535C2—2081no—
536C2#1312664311yescharacteristic
537C2C2×#1171880811yescharacteristic
538C2#1312798011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3334C2
socleC22×C13C22×D8
hypercenter#3334D13
hypocenterC13#33873
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13126523C2semidirect
2. #13117075C2semidirect
3. #13117033C2semidirect
4. #13117021C2semidirect
5. #13116980C2semidirect
6. #13116937C2semidirect
7. #13116930C2semidirect
8. #13116891C2semidirect
9. #13116757C2semidirect
10. #13116747C2semidirect
11. #13116710C2semidirect
12. #13116662C2semidirect
13. #13116546C2semidirect
14. C2×#11718083C2semidirect
15. C13×#3334C2semidirect
20. C13×#500C22semidirect
25. C13×#466C22semidirect
26. C4×C13×D8C22semidirect
29. C2×C13×#107C22semidirect
30. C2×#88067C22semidirect
35. C2×#88052C22semidirect
42. #11718154C22semidirect
44. C22⋊#6090C22semidirect
45. #11718084C22semidirect
46. #11718084C22semidirect
47. #11718084C22semidirect
54. #11718082C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. C4⋊#6090C22semidirect
58. #11718053C22semidirect
180. D104#41semidirect
187. #3334D13semidirect
258. #500C2×D13semidirect
266. #466C2×D13semidirect
271. C4×D8C2×D13semidirect
274. C2×#107C2×D13semidirect
455. C13#33873semidirect

Maximal subgroups

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

subgroupindex
#131265232
#131170752
#131170332
#131170212
#131169802
#131169372
#131169302
#131168912
#131167572
#131167472
#131167102
#131166622
#131165462
C2×#117180832
C13×#33342
#3387313