Finite Group Databasebeta

← #16019890

Subgroups — #16019890

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#13127184C211yesmaximal, characteristic, complemented
2#13117072C211yesmaximal, characteristic, complemented
3#13117031C211yesmaximal, characteristic, complemented
4#13117019C211yesmaximal, characteristic, complemented
5#13116983C211yesmaximal, characteristic, complemented
6#13116937C211yesmaximal, characteristic, complemented
7#13116934C211yesmaximal, characteristic, complemented
8#13116888C211yesmaximal, characteristic, complemented
9#13116759C211yesmaximal, characteristic, complemented
10#13116748C211yesmaximal, characteristic, complemented
11#13116710C211yesmaximal, characteristic, complemented
12#13116662C211yesmaximal, characteristic, complemented
13#13116548C211yesmaximal, characteristic, complemented
14C2×#11718154C211yesmaximal, characteristic, complemented
15C13×#3280C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#546—21no—
19#11719260—21no—
20C13×#495C2211yescharacteristic
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#463—21no—
24C13×#450—21no—
25C13×#449—21no—
26C4×C13×D8C2211yescharacteristic
27C8×D4×C13C2211yescharacteristic
28C2×#88068C2211yescharacteristic, complemented
29C2×#88066C2211yescharacteristic
30C2×#88066C2211yescharacteristic
31#11718776C2211yescharacteristic
32#11718776C2211yescharacteristic, complemented
33C2×#88058C2211yescharacteristic
34C2×#88058C2211yescharacteristic, complemented
35C2×#88052C2211yescharacteristic, complemented
36C22×#6090C2211yescharacteristic
37#11718507—21no—
38#11718397—21no—
39#11718397—21no—
40C4×D104C2211yescharacteristic, complemented
41#11718343C2211yescharacteristic, 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#11718083C2211yescharacteristic, complemented
54#11718082C2211yescharacteristic, complemented
55#11718082C2211yescharacteristic, complemented
56#11718082C2211yescharacteristic, complemented
57C4⋊#6090C2211yescharacteristic, complemented
58#11718053C2211yescharacteristic, complemented
59C2×C13×#41—21no—
60C22×D4×C13—21no—
61C2×#6129—41no—
62C13×#135—22no—
63C13×#135—41no—
64C2×C13×Q16C2311yescharacteristic
65C2×C13×SD16—21no—
66C2×C13×SD16—21no—
67C2×C13×D8—22no—
68C2×C13×D8—21no—
69C2×C13×D8—41no—
70C2×C13×D8C2311yescharacteristic
71C2×C13×D8C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C13×#124—21no—
75C13×#123—41no—
76C13×C22⋊Q8—21no—
77C13×#121—21no—
78C13×#121—41no—
79C13×#120—41no—
80C4×D4×C13—21no—
81C4×D4×C13D411yescharacteristic
82C2×C13×C22⋊C4—41no—
83#88184—21no—
84#88184—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×D104C2311yescharacteristic
88#88151—41no—
89#88140—41no—
90#88140—41no—
91C4×D52—21no—
92#88123—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#88068—41no—
102#88066—22no—
103#88066—41no—
104#88061—21no—
105#88061—21no—
106#88061—21no—
107#88058—21no—
108#88058—21no—
109#88058—21no—
110#88058C2311yescharacteristic
111#88058C2311yescharacteristic
112#88058C2311yescharacteristic
113#88052—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33873—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
136C2×C22⋊D13—41no—
137C2×C22⋊D13—41no—
138C22×Dic13—41no—
139C22×Dic13—41no—
140#6129—84no—
141C2×D52—21no—
142C2×C4×D13—41no—
143C2×Dic26—41no—
144C13×Q16—21no—
145C13×Q16—21no—
146C13×SD16—42no—
147C13×SD16—81no—
148C13×D8—21no—
149C13×D8—21no—
150C13×D8—21no—
151C13×D8—42no—
152C13×D8#4112yescomplemented
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13C2×D411yescharacteristic
158C2×C8×C13C2×D411yescharacteristic
159C2×C8×C13C2×D411yescharacteristic
160C2×C8×C13C2411yescharacteristic
161C13×C4⋊C4—21no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4D811yescharacteristic
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4—41no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4D811yescharacteristic
170C13×C22⋊C4D811yescharacteristic
171C42×C13C2×D411yescharacteristic
172#6103—41no—
173#6103—41no—
174#6103—41no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—41no—
179C4⋊Dic13—41no—
180C4⋊Dic13—41no—
181D104—21no—
182D104—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#6090—21no—
187#3334—131no—
188#3280D1311yescharacteristic, complemented
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×C13—41no—
204C23×C13—82no—
205C23×C13—82no—
206C23×C13—161no—
207C23×C13C2×D811yescharacteristic
208C23×C13C2×D811yescharacteristic
209C22×D13—41no—
210Q8×C13—41no—
211Q8×C13—41no—
212D4×C13—22no—
213D4×C13—22no—
214D4×C13—41no—
215D4×C13—41no—
216D4×C13—41no—
217D4×C13—82no—
218D4×C13—82no—
219D4×C13—161no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—82no—
227C2×C4×C13—161no—
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C2×D811yescharacteristic
230C2×C4×C13C2×D811yescharacteristic
231C2×C4×C13C2×D811yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C22⋊D13—82no—
234C22⋊D13—82no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—82no—
239C2×Dic13—82no—
240D52—41no—
241D52—41no—
242C4×D13—82no—
243Dic26—82no—
244C8×C13—21no—
245C8×C13—21no—
246C8×C13—21no—
247C8×C13C2×#4111yescharacteristic
248C8×C13H(5,𝔽2)11yescharacteristic
249C2×#135C2×D1311yescharacteristic
250C22×D8C2×D1311yescharacteristic
251#547—261no—
252#546—21no—
253C2×SD32—131no—
254C2×D16—131no—
255C2×D16—131no—
256C2×M32—131no—
257C22×C16—131no—
258#500—131no—
259#495C2×D1311yescharacteristic
260#480—261no—
261#480—261no—
262#474—261no—
263#467C2×D1311yescharacteristic
264#466—131no—
265#466—131no—
266#466C2×D1311yescharacteristic
267#463—21no—
268#450—21no—
269#449—21no—
270C4×D8—131no—
271C4×D8C2×D1311yescharacteristic
272C8×D4C2×D1311yescharacteristic
273C2×#107—131no—
274C2×#107—131no—
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—42no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—81no—
301C22×C13—81no—
302C22×C13—81no—
303C22×C13—164no—
304C22×C13#50912yes—
305C22×C13C22×D811yescharacteristic
306C2×D13—81no—
307C2×D13—81no—
308C2×D13—81no—
309C4×C13—21no—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—81no—
314C4×C13—81no—
315C4×C13#54611yescharacteristic
316C4×C13#57711yescharacteristic
317Dic13—81no—
318Dic13—81no—
319Dic13—81no—
320C2×#41—21no—
321C2×#41—521no—
322C22×D4—21no—
323#135—22no—
324#135—41no—
325C2×Q16C22×D1311yescharacteristic
326C2×SD16—21no—
327C2×SD16—21no—
328C2×D8—22no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8—131no—
332C2×D8C22×D1311yescharacteristic
333C2×D8C22×D1311yescharacteristic
334C22×C8C22×D1311yescharacteristic
335C22×C8C22×D1311yescharacteristic
336C4⋊Q8—261no—
337#124—21no—
338#123—41no—
339#123—521no—
340#123—521no—
341C22⋊Q8—21no—
342C22⋊Q8—521no—
343#121—21no—
344#121—41no—
345#121—261no—
346#121—261no—
347#120—41no—
348C4×D4—21no—
349C4×D4—261no—
350C4×D4C22⋊D1311yescharacteristic
351C2×C4⋊C4—261no—
352C2×C4⋊C4—261no—
353C2×C22⋊C4—41no—
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—131no—
364#107—131no—
365#107—131no—
366#107—261no—
367#107—261no—
368#107—261no—
369#107C22×D1311yescharacteristic
370C4⋊C8C22⋊D1311yescharacteristic
371#103—21no—
372#102—21no—
373#102—21no—
374#102—261no—
375#102—261no—
376#102—261no—
377C22⋊C8C22⋊D1311yescharacteristic
378C22⋊C8C22⋊D1311yescharacteristic
379C4×C8C22×D1311yescharacteristic
380C2×C13—22no—
381C2×C13—41no—
382C2×C13—82no—
383C2×C13—161no—
384C2×C13#329411yescharacteristic
385C2×C13C2×#50911yescharacteristic
386C2×C13#341611yescharacteristic
387D13—161no—
388C24—41no—
389#41—42no—
390#41—81no—
391#41—1044no—
392C2×Q8—21no—
393C2×Q8—521no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—81no—
401C2×D4—261no—
402C2×D4—521no—
403C2×D4—521no—
404C2×D4#610411yescharacteristic
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—521no—
408C22×C4—521no—
409C22×C4—521no—
410C22×C4C2×C22⋊D1311yescharacteristic
411C22×C4C2×C22⋊D1311yescharacteristic
412Q16—21no—
413Q16—21no—
414SD16—42no—
415SD16—81no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—42no—
420D8—261no—
421D8—261no—
422D8#612912yescomplemented
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—41no—
433C4⋊C4—261no—
434C4⋊C4—261no—
435C4⋊C4—261no—
436C4⋊C4—521no—
437C4⋊C4—521no—
438C4⋊C4—521no—
439C4⋊C4#610411yescharacteristic
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
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—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—521no—
462C23C2×#610411yescharacteristic
463C23C2×#610411yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—1042no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—82no—
474D4—161no—
475D4—521no—
476D4—521no—
477D4—1042no—
478D4—1042no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4—521no—
488C2×C4—521no—
489C2×C4—521no—
490C2×C4—1042no—
491C2×C4—1042no—
492C2×C4—1042no—
493C2×C4C2×#610411yescharacteristic
494C2×C4C2×#610411yescharacteristic
495C2×C4C2×#610411yescharacteristic
496C2×C4C2×#610411yescharacteristic
497C2×C4C22×C22⋊D1311yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×#612911yescharacteristic
502C8#8825111yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—1041no—
516C22—1041no—
517C22—1041no—
518C22#1171885412yes—
519C22C22×#610411yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—1041no—
527C4—1041no—
528C4—1041no—
529C4#1171951111yescharacteristic
530C4#1171954111yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—2081no—
536C2#1312664911yescharacteristic
537C2C2×#1171885411yescharacteristic
538C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3280C2
socleC22×C13C22×D8
hypercenter#3280D13
hypocenterC13#33873
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. #13127184C2semidirect
2. #13117072C2semidirect
3. #13117031C2semidirect
4. #13117019C2semidirect
5. #13116983C2semidirect
6. #13116937C2semidirect
7. #13116934C2semidirect
8. #13116888C2semidirect
9. #13116759C2semidirect
10. #13116748C2semidirect
11. #13116710C2semidirect
12. #13116662C2semidirect
13. #13116548C2semidirect
14. C2×#11718154C2semidirect
15. C13×#3280C2semidirect
28. C2×#88068C22semidirect
32. #11718776C22semidirect
34. C2×#88058C22semidirect
35. C2×#88052C22semidirect
40. C4×D104C22semidirect
41. #11718343C22semidirect
42. #11718156C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
52. C22⋊#6090C22semidirect
53. #11718083C22semidirect
54. #11718082C22semidirect
55. #11718082C22semidirect
56. #11718082C22semidirect
57. C4⋊#6090C22semidirect
58. #11718053C22semidirect
152. C13×D8#41semidirect
188. #3280D13semidirect
422. D8#6129semidirect
455. C13#33873semidirect

Maximal subgroups

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

subgroupindex
#131271842
#131170722
#131170312
#131170192
#131169832
#131169372
#131169342
#131168882
#131167592
#131167482
#131167102
#131166622
#131165482
C2×#117181542
C13×#32802
#3387313