Finite Group Databasebeta

← #14745186

Subgroups — #14745186

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4325C211yesmaximal, characteristic, complemented
2#13080967C211yesmaximal, characteristic
3#13080263C211yesmaximal, characteristic
4#13068214C211yesmaximal, characteristic, complemented
5#13068136C211yesmaximal, characteristic, complemented
6#13068110C211yesmaximal, characteristic, complemented
7#13068000C211yesmaximal, characteristic, complemented
8#13067993C211yesmaximal, characteristic, complemented
9#13067837C211yesmaximal, characteristic, complemented
10#13067823C211yesmaximal, characteristic, complemented
11#13067779C211yesmaximal, characteristic, complemented
12#13067765C211yesmaximal, characteristic
13#13067506C211yesmaximal, characteristic, complemented
14SD16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#3385C211yesmaximal, characteristic, complemented
16Q82×C11C2211yescharacteristic
17C11×#554C2211yescharacteristic
18C2×#66968—21no—
19Q8×D44C2211yescharacteristic
20#10623086C2211yescharacteristic
21C11×#501—21no—
22C11×#500C2211yescharacteristic
23C11×#479—21no—
24C11×#477C2211yescharacteristic
25C11×#476C2211yescharacteristic
26C11×#474—21no—
27C11×#446C2211yescharacteristic
28C11×#440—21no—
29C4×C11×SD16C2211yescharacteristic
30#10622697—21no—
31#10622697C2211yescharacteristic
32#10622697C2211yescharacteristic
33#10622694C2211yescharacteristic
34#10622694C2211yescharacteristic
35#10622692—21no—
36#10622692C2211yescharacteristic
37#10622692C2211yescharacteristic
38#10622661—21no—
39#10622656—21no—
40#10622644C2211yescharacteristic
41C4×#4325—21no—
42C4×#4325C2211yescharacteristic
43Q8×C11⋊C8C2211yescharacteristic
44#10622633—21no—
45#10622633C2211yescharacteristic
46#10622633C2211yescharacteristic
47#10622632C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49#10622581—21no—
50C2×#66872—21no—
51#10622481—21no—
52#10622421—21no—
53#10622396—21no—
54#10622312C2211yescharacteristic
55#10622301C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58Q8⋊(C11⋊C8)C2211yescharacteristic
59Q8⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622120C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622095C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11—21no—
68C2×#4341—21no—
69C2×C11×SD16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—41no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#125—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11C2311yescharacteristic
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C2×C11×C4⋊C4—21no—
85C2×#4326—21no—
86C2×#4325D411yescharacteristic
87C2×#4324—21no—
88#66983—21no—
89C2×C4⋊Dic11—21no—
90C22×C11⋊C8—21no—
91#66968—44no—
92C2×Dic44—21no—
93C2×Dic44—21no—
94C2×#4313—21no—
95#66950—21no—
96#66950—21no—
97#66950—41no—
98#66939—41no—
99C4×D44—21no—
100C4×D44C2311yescharacteristic
101#66922—21no—
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#106D411yescharacteristic
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×#103—21no—
112C11×#103D411yescharacteristic
113C11×#102—21no—
114C11×#102D411yescharacteristic
115C11×#97—21no—
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—41no—
120#66899—41no—
121#66899D411yescharacteristic
122C22⋊(C11⋊C8)—21no—
123(C2×D11)⋊C8—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873D411yescharacteristic
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66872D411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19895—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—41no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C2×C22⋊D11—41no—
155C22×Dic11—41no—
156Q8×D11—42no—
157Q8×D11—81no—
158#4341—42no—
159#4341—81no—
160C2×D44C2×D411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11—41no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—41no—
166C11×SD16SD1614yescomplemented
167C2×C8×C11—21no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—41no—
188C42×C11C2411yescharacteristic
189#4326—42no—
190#4325—22no—
191#4324—42no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—41no—
200C4⋊Dic11—41no—
201C4⋊Dic11C2×D411yescharacteristic
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209Dic44—42no—
210Dic44—81no—
211#4313—42no—
212#3385D1111yescharacteristic, complemented
213Q8×SD16—111no—
214#3335—111no—
215#3276—111no—
216#1707—111no—
217#1695—111no—
218#1690—111no—
219#1672—111no—
220#1671—111no—
221#1645—111no—
222#1643—111no—
223#1637—111no—
224#1635—111no—
225#1590—111no—
226C8×SD16—111no—
227C23×C11—21no—
228C22×D11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—81no—
233Q8×C11—81no—
234Q8×C11—161no—
235Q8×C11C2×SD1612yes—
236D4×C11—21no—
237D4×C11C2×SD1612yes—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—161no—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C22⋊D11—82no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—82no—
256D44—21no—
257D44—21no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—82no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—82no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11C2×SD1612yes—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13712yescomplemented
275C2×#137—221no—
276Q82C2×D1111yescharacteristic
277#554C2×D1111yescharacteristic
278D4×Q8—111no—
279#547—111no—
280#501—21no—
281#500C2×D1111yescharacteristic
282#498—111no—
283#498—111no—
284#498—221no—
285#494—111no—
286#487—111no—
287#487—111no—
288#483—221no—
289#481—221no—
290#479—21no—
291#477C2×D1111yescharacteristic
292#476—111no—
293#476—111no—
294#476—221no—
295#476C2×D1111yescharacteristic
296#475—111no—
297#475—111no—
298#475—221no—
299#474—21no—
300#470—221no—
301#465—221no—
302#462—111no—
303#461—111no—
304#452—221no—
305#451—221no—
306#446C2×D1111yescharacteristic
307C8×Q8—111no—
308#440—21no—
309C4×SD16—111no—
310C4×SD16—221no—
311C4×SD16C2×D1111yescharacteristic
312#436—111no—
313C8×D4—111no—
314C2×#106—221no—
315#334—111no—
316#334—111no—
317#333—111no—
318#333—111no—
319#332—111no—
320#332—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325C82—111no—
326C22×C11—22no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11D4211yescharacteristic
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C4×C11—22no—
334C4×C11—21no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11C22×SD1611yescharacteristic
342C4×C11C2×#13711yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—41no—
346Dic11—81no—
347Dic11—81no—
348C2×#41—221no—
349C22×Q8—221no—
350#137—444no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×Q16—221no—
354C2×SD16—111no—
355C2×SD16—221no—
356C2×SD16C22⋊D1111yescharacteristic
357C2×M16—221no—
358C22×C8—221no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8—111no—
363C4⋊Q8—111no—
364C4⋊Q8—221no—
365C4⋊Q8C22×D1111yescharacteristic
366C4⋊Q8C22×D1111yescharacteristic
367#125—21no—
368#123—441no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—221no—
372C22⋊Q8—221no—
373C22⋊Q8—441no—
374#121—221no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8C22×D1111yescharacteristic
378C4×Q8C22×D1111yescharacteristic
379C4×D4—21no—
380C4×D4—111no—
381C4×D4—221no—
382C4×D4C22×D1111yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—221no—
385#107—21no—
386#107—21no—
387#107—21no—
388#106—21no—
389#106—111no—
390#106—221no—
391#106—221no—
392#106—221no—
393#106—221no—
394#106—221no—
395#106—221no—
396#106—221no—
397#106—221no—
398#106C22⋊D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405#103—21no—
406#103—111no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—441no—
412#103—441no—
413#103C22⋊D1111yescharacteristic
414#102—21no—
415#102—111no—
416#102—221no—
417#102—221no—
418#102C22⋊D1111yescharacteristic
419C22⋊C8—221no—
420C22⋊C8—221no—
421#97—21no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C2×C11—42no—
427C2×C11#327611yescharacteristic
428C2×C11D4×SD1611yescharacteristic
429C2×C11#329011yescharacteristic
430D11—81no—
431#41—442no—
432#41—881no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—441no—
439C2×Q8—442no—
440C2×Q8—881no—
441C2×Q8D4×D1111yescharacteristic
442C2×Q8C2×C22⋊D1111yescharacteristic
443C2×D4—111no—
444C2×D4—441no—
445C2×D4C2×C22⋊D1111yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—221no—
449C22×C4—441no—
450C22×C4—441no—
451Q16—442no—
452Q16—442no—
453Q16—881no—
454SD16—222no—
455SD16—442no—
456SD16#432514yescomplemented
457M16—442no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—442no—
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—111no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4D4×D1111yescharacteristic
486C4⋊C4C2×C22⋊D1111yescharacteristic
487C4⋊C4C2×C22⋊D1111yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—41no—
490C22⋊C4—221no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C23×D1111yescharacteristic
497C11#1989511yescharacteristic, complemented, Sylow
498C23—21no—
499C23—221no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—81no—
504Q8—81no—
505Q8—161no—
506Q8—441no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—882no—
511Q8C2×#432512yes—
512D4—21no—
513D4—221no—
514D4—221no—
515D4—882no—
516D4C2×#432512yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—221no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4—882no—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6703711yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—21no—
538C8—41no—
539C8—112no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8C2×#432512yes—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—441no—
550C22—441no—
551C22—441no—
552C22D4×C22⋊D1111yescharacteristic
553C4—21no—
554C4—22no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—441no—
562C4—881no—
563C4—881no—
564C4D11×#13711yescharacteristic
565C4#1062331011yescharacteristic
566C4C22×#432511yescharacteristic
567C4#1062336811yescharacteristic
568C2—42no—
569C2—881no—
570C2#1308025611yescharacteristic
571C2D4×#432511yescharacteristic
572C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3385C2
socleC22×C11D42
prime radical#10623086C22
hypercenter#3385D11
hypocenterC11#19895
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. Q8×#4325C2semidirect
4. #13068214C2semidirect
5. #13068136C2semidirect
6. #13068110C2semidirect
7. #13068000C2semidirect
8. #13067993C2semidirect
9. #13067837C2semidirect
10. #13067823C2semidirect
11. #13067779C2semidirect
13. #13067506C2semidirect
14. SD16×C11⋊C8C2semidirect
15. C11×#3385C2semidirect
166. C11×SD16SD16semidirect
212. #3385D11semidirect
274. C11⋊C8#137semidirect
456. SD16#4325semidirect
497. C11#19895semidirect

Maximal subgroups

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

subgroupindex
Q8×#43252
#130809672
#130802632
#130682142
#130681362
#130681102
#130680002
#130679932
#130678372
#130678232
#130677792
#130677652
#130675062
SD16×C11⋊C82
C11×#33852
#1989511