Finite Group Databasebeta

← #16019779

Subgroups — #16019779

Order 3328.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127239C211yesmaximal, characteristic, complemented
2#13117067C211yesmaximal, characteristic, complemented
3#13117036C211yesmaximal, characteristic, complemented
4#13117024C211yesmaximal, characteristic, complemented
5#13116993C211yesmaximal, characteristic, complemented
6#13116934C211yesmaximal, characteristic, complemented
7#13116920C211yesmaximal, characteristic, complemented
8#13116888C211yesmaximal, characteristic, complemented
9#13116759C211yesmaximal, characteristic, complemented
10#13116748C211yesmaximal, characteristic, complemented
11C4×#88066C211yesmaximal, characteristic, complemented
12D4×#6090C211yesmaximal, characteristic, complemented
13#13116543C211yesmaximal, characteristic, complemented
14C2×#11718154C211yesmaximal, characteristic, complemented
15C13×#3280C211yesmaximal, characteristic, complemented
16C2×C13×#135C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18C13×#546—21no—
19#11719270—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
33#11718767C2211yescharacteristic, complemented
34C2×#88058C2211yescharacteristic
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic, complemented
37#11718508—21no—
38#11718398—21no—
39#11718396—21no—
40C4×D104C2211yescharacteristic, 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#11718083C2211yescharacteristic, complemented
54#11718082C2211yescharacteristic, complemented
55#11718081C2211yescharacteristic, 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#88193—41no—
83#88184—21no—
84#88184—21no—
85#88180—21no—
86C2×C4⋊Dic13—21no—
87C2×D104C2311yescharacteristic
88#88152—41no—
89#88137—41no—
90#88135—41no—
91C4×D52—21no—
92#88124—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#88058C2311yescharacteristic
109#88058C2311yescharacteristic
110#88058C2311yescharacteristic
111#88057—21no—
112#88057—21no—
113C2×#6090—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33864—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—
139C2×D52—21no—
140C2×C4×D13—41no—
141C13×Q16—21no—
142C13×Q16—21no—
143C13×SD16—42no—
144C13×SD16—81no—
145C13×D8—21no—
146C13×D8—21no—
147C13×D8—21no—
148C13×D8—42no—
149C13×D8#4112yes—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13C2×D411yescharacteristic
155C2×C8×C13C2×D411yescharacteristic
156C2×C8×C13C2×D411yescharacteristic
157C2×C8×C13C2411yescharacteristic
158C13×C4⋊C4—21no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4D811yescharacteristic
161C13×C22⋊C4—41no—
162C13×C22⋊C4—41no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C13×C22⋊C4—41no—
166C13×C22⋊C4D811yescharacteristic
167C13×C22⋊C4D811yescharacteristic
168C42×C13C2×D411yescharacteristic
169C22⋊Dic13—41no—
170#6103—41no—
171#6103—41no—
172#6103—41no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—41no—
177#6101—41no—
178#6101—41no—
179C4×Dic13—41no—
180D104—21no—
181D104—21no—
182#6090—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#3339—131no—
187#3280D1311yescharacteristic, complemented
188#2242—131no—
189#2236—131no—
190#2234—131no—
191#2228—131no—
192#2217—131no—
193#2215—131no—
194#2210—131no—
195#2186—131no—
196#2184—131no—
197C4×D16—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
208C22×D13—41no—
209Q8×C13—41no—
210Q8×C13—41no—
211D4×C13—22no—
212D4×C13—22no—
213D4×C13—41no—
214D4×C13—41no—
215D4×C13—41no—
216D4×C13—82no—
217D4×C13—82no—
218D4×C13—161no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—82no—
226C2×C4×C13—161no—
227C2×C4×C13C2×D811yescharacteristic
228C2×C4×C13C2×D811yescharacteristic
229C2×C4×C13C2×D811yescharacteristic
230C2×C4×C13C2×D811yescharacteristic
231C2×C4×C13C22×D411yescharacteristic
232C22⋊D13—82no—
233C22⋊D13—161no—
234C2×Dic13—41no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—161no—
238D52—41no—
239D52—41no—
240C4×D13—161no—
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135C2×D1311yescharacteristic
247C22×D8C2×D1311yescharacteristic
248#553—261no—
249#546—21no—
250C2×SD32—131no—
251C2×D16—131no—
252C2×D16—131no—
253C22×C16—131no—
254C22×C16—131no—
255#499—131no—
256#495C2×D1311yescharacteristic
257#482—261no—
258#481—261no—
259#478—261no—
260#467C2×D1311yescharacteristic
261#466—131no—
262#466—131no—
263#466C2×D1311yescharacteristic
264#463—21no—
265#450—21no—
266#449—21no—
267C4×D8—131no—
268C4×D8C2×D1311yescharacteristic
269C8×D4C2×D1311yescharacteristic
270#427—131no—
271C2×#107—131no—
272#367—131no—
273#366—131no—
274#366—131no—
275C4⋊C16—131no—
276#358—131no—
277#358—131no—
278#358—131no—
279#357—131no—
280#357—131no—
281#357—131no—
282#357—131no—
283#357—131no—
284#357—131no—
285#357—131no—
286C22⋊C16—131no—
287C22⋊C16—131no—
288C4×C16—131no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—42no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13—81no—
298C22×C13—81no—
299C22×C13—81no—
300C22×C13—164no—
301C22×C13#50812yes—
302C22×C13C22×D811yescharacteristic
303C2×D13—81no—
304C2×D13—81no—
305C2×D13—81no—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—81no—
311C4×C13—81no—
312C4×C13#54611yescharacteristic
313C4×C13#57711yescharacteristic
314Dic13—81no—
315Dic13—81no—
316Dic13—81no—
317C2×#41—21no—
318C22×D4—21no—
319#135—22no—
320#135—41no—
321C2×Q16C22×D1311yescharacteristic
322C2×SD16—21no—
323C2×SD16—21no—
324C2×D8—22no—
325C2×D8—21no—
326C2×D8—41no—
327C2×D8—131no—
328C2×D8C22×D1311yescharacteristic
329C2×D8C22×D1311yescharacteristic
330C22×C8C22×D1311yescharacteristic
331C22×C8C22×D1311yescharacteristic
332#126—521no—
333#125—261no—
334#124—21no—
335#123—41no—
336#123—521no—
337C22⋊Q8—21no—
338#121—21no—
339#121—41no—
340#121—261no—
341#121—261no—
342#121—521no—
343#120—41no—
344C4×D4—21no—
345C4×D4—261no—
346C4×D4—521no—
347C4×D4C22⋊D1311yescharacteristic
348#117—261no—
349C2×C4⋊C4—261no—
350C2×C22⋊C4—41no—
351SD32—521no—
352D16—262no—
353D16—521no—
354C2×C16—131no—
355C2×C16—131no—
356C2×C16—131no—
357C2×C16—131no—
358C2×C16—521no—
359C2×C16—521no—
360#107—131no—
361#107—131no—
362#107—131no—
363#107—261no—
364#107C22×D1311yescharacteristic
365#106—261no—
366#106—261no—
367C4⋊C8C22⋊D1311yescharacteristic
368#103—21no—
369#102—21no—
370#102—21no—
371#102—261no—
372#102—261no—
373#102—261no—
374C22⋊C8C22⋊D1311yescharacteristic
375C22⋊C8C22⋊D1311yescharacteristic
376C4×C8C22×D1311yescharacteristic
377C2×C13—22no—
378C2×C13—41no—
379C2×C13—82no—
380C2×C13—161no—
381C2×C13#329411yescharacteristic
382C2×C13C2×#50811yescharacteristic
383C2×C13#341511yescharacteristic
384D13—161no—
385C24—41no—
386#41—42no—
387#41—81no—
388C2×Q8—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—81no—
396C2×D4—261no—
397C2×D4—521no—
398C2×D4—521no—
399C2×D4#610411yescharacteristic
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—521no—
403C22×C4—521no—
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406Q16—21no—
407Q16—21no—
408SD16—42no—
409SD16—81no—
410D8—21no—
411D8—21no—
412D8—21no—
413D8—42no—
414D8—261no—
415D8—261no—
416D8#612912yes—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×C22⋊D1311yescharacteristic
422C2×C8C2×C22⋊D1311yescharacteristic
423C2×C8C2×C22⋊D1311yescharacteristic
424C2×C8C23×D1311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—261no—
428C4⋊C4—261no—
429C4⋊C4—261no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C4⋊C4—521no—
433C4⋊C4#610411yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—521no—
440C22⋊C4—521no—
441C22⋊C4—521no—
442C22⋊C4—521no—
443C22⋊C4#610411yescharacteristic
444C22⋊C4#610411yescharacteristic
445C42—521no—
446C42C2×C22⋊D1311yescharacteristic
447C16—261no—
448C16—261no—
449C16—261no—
450C16—261no—
451C13#3386411yescharacteristic, complemented, Sylow
452C23—41no—
453C23—41no—
454C23—82no—
455C23—82no—
456C23—161no—
457C23—521no—
458C23C2×#610411yescharacteristic
459C23C2×#610411yescharacteristic
460Q8—41no—
461Q8—41no—
462D4—22no—
463D4—22no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—82no—
468D4—82no—
469D4—161no—
470D4—521no—
471D4—521no—
472D4—1042no—
473D4—2081no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—82no—
481C2×C4—161no—
482C2×C4—521no—
483C2×C4—521no—
484C2×C4—521no—
485C2×C4—2081no—
486C2×C4—2081no—
487C2×C4C2×#610411yescharacteristic
488C2×C4C2×#610411yescharacteristic
489C2×C4C2×#610411yescharacteristic
490C2×C4C2×#610411yescharacteristic
491C2×C4C22×C22⋊D1311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8C2×#612911yescharacteristic
496C8#8825111yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—164no—
509C22—1041no—
510C22—1041no—
511C22—1041no—
512C22#1171885512yes—
513C22C22×#610411yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—1041no—
521C4—1041no—
522C4—1041no—
523C4#1171951111yescharacteristic
524C4#1171954111yescharacteristic
525C2—22no—
526C2—41no—
527C2—82no—
528C2—161no—
529C2—2081no—
530C2#1312664911yescharacteristic
531C2C2×#1171885511yescharacteristic
532C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3280C2
socleC22×C13C22×D8
hypercenter#3280D13
hypocenterC13#33864
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. #13127239C2semidirect
2. #13117067C2semidirect
3. #13117036C2semidirect
4. #13117024C2semidirect
5. #13116993C2semidirect
6. #13116934C2semidirect
7. #13116920C2semidirect
8. #13116888C2semidirect
9. #13116759C2semidirect
10. #13116748C2semidirect
11. C4×#88066C2semidirect
12. D4×#6090C2semidirect
13. #13116543C2semidirect
14. C2×#11718154C2semidirect
15. C13×#3280C2semidirect
28. C2×#88068C22semidirect
32. #11718776C22semidirect
33. #11718767C22semidirect
36. C22×#6090C22semidirect
40. C4×D104C22semidirect
41. #11718344C22semidirect
42. #11718156C22semidirect
43. #11718156C22semidirect
44. #11718156C22semidirect
52. C22⋊#6090C22semidirect
53. #11718083C22semidirect
54. #11718082C22semidirect
55. #11718081C22semidirect
56. #11718081C22semidirect
57. C4⋊#6090C22semidirect
58. C4×#6090C22semidirect
187. #3280D13semidirect
451. C13#33864semidirect

Maximal subgroups

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

subgroupindex
#131272392
#131170672
#131170362
#131170242
#131169932
#131169342
#131169202
#131168882
#131167592
#131167482
C4×#880662
D4×#60902
#131165432
C2×#117181542
C13×#32802
#3386413