Finite Group Databasebeta

← #14743646

Subgroups — #14743646

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081393C211yesmaximal, characteristic, complemented
2#13080442C211yesmaximal, characteristic
3#13080434C211yesmaximal, characteristic
4#13068274C211yesmaximal, characteristic, complemented
5#13068158C211yesmaximal, characteristic, complemented
6#13068065C211yesmaximal, characteristic, complemented
7#13068032C211yesmaximal, characteristic, complemented
8#13067988C211yesmaximal, characteristic, complemented
9#13067794C211yesmaximal, characteristic
10#13067750C211yesmaximal, characteristic, complemented
11#13067749C211yesmaximal, characteristic, complemented
12#13067712C211yesmaximal, characteristic, complemented
13#13067453C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15C11×#3381C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17C11×#554C2211yescharacteristic
18#10623110C2211yescharacteristic
19D4×D44C2211yescharacteristic
20C11×#499—21no—
21C11×#498C2211yescharacteristic, complemented
22C11×#479—21no—
23C11×#478—21no—
24C11×#477C2211yescharacteristic, complemented
25C11×#474C2211yescharacteristic
26C8×Q8×C11C2211yescharacteristic, complemented
27C4×C11×SD16—21no—
28C4×C11×SD16C2211yescharacteristic
29#10622782—21no—
30#10622705C2211yescharacteristic, complemented
31#10622701C2211yescharacteristic
32#10622701C2211yescharacteristic
33#10622697C2211yescharacteristic
34#10622696—21no—
35#10622696C2211yescharacteristic
36#10622695—21no—
37#10622694C2211yescharacteristic, complemented
38#10622661—21no—
39#10622659—21no—
40#10622640C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622639—21no—
43C4×#4325C2211yescharacteristic
44#10622637C2211yescharacteristic, complemented
45#10622635—21no—
46#10622634C2211yescharacteristic, complemented
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622581—21no—
50C2×#66873—21no—
51#10622476—21no—
52#10622420—21no—
53D11×#102—21no—
54#10622307C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622184C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11—21no—
68C22×D44—21no—
69C2×C11×SD16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×#125—21no—
75C11×#125—41no—
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—
85#66999—21no—
86C2×#4326—41no—
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325D411yescharacteristic
91#66983—21no—
92C22×C11⋊C8—21no—
93C2×C8×D11—21no—
94#66949—41no—
95#66948—21no—
96C4⋊C4×D11—21no—
97#66935—41no—
98#66927C2311yescharacteristic
99C4×D44—21no—
100C4×D44C2311yescharacteristic
101#66923—21no—
102#66922C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×#106D411yescharacteristic
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103D411yescharacteristic
112C11×#102—21no—
113C11×#102D411yescharacteristic
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899D411yescharacteristic
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123#66885—21no—
124#66885—21no—
125(C2×D11)⋊C8—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—41no—
132#66873D411yescharacteristic
133#66872—21no—
134#66872—21no—
135#66872D411yescharacteristic
136#66871—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19790—111nomaximal, Sylow
145C23×D11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—41no—
153C2×C22⋊D11—41no—
154D4×D11—42no—
155D4×D11—81no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—41no—
160C2×D44—42no—
161C2×D44—81no—
162C2×D44C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—41no—
165C2×Dic22—21no—
166C11×SD16—22no—
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⋊C4—41no—
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—41no—
189C42×C11C2411yescharacteristic
190#4326—82no—
191#4325—22no—
192#4325—42no—
193#4325—81no—
194#4325—81no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D411yescharacteristic
201Dic11⋊C4—41no—
202Dic11⋊C4—41no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C8×D11—81no—
211#3381D1111yescharacteristic, complemented
212#3372—111no—
213#3295—111no—
214#3295—111no—
215#1720—111no—
216#1698—111no—
217#1683—111no—
218#1678—111no—
219#1671—111no—
220#1639—111no—
221#1632—111no—
222#1632—111no—
223#1626—111no—
224#1582—111no—
225SD16⋊C8—111no—
226C23×C11—21no—
227C22×D11—21no—
228C22×D11—41no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—161no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239D4×C11—21no—
240D4×C11#13712yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—161no—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C22⋊D11—82no—
255C2×Dic11—21no—
256C2×Dic11—41no—
257D44—21no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—81no—
263D44—82no—
264D44#13512yes—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—161no—
268Dic22—81no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278#557C2×D1111yescharacteristic, complemented
279#554—111no—
280#554C2×D1111yescharacteristic
281D42—111no—
282#499—21no—
283#498C2×D1111yescharacteristic, complemented
284#494—111no—
285#491—221no—
286#487—111no—
287#486—111no—
288#486—111no—
289#486—111no—
290#481—221no—
291#481—221no—
292#479—21no—
293#479—221no—
294#478—21no—
295#477—111no—
296#477C2×D1111yescharacteristic, complemented
297#476—111no—
298#476—111no—
299#474C2×D1111yescharacteristic
300#465—221no—
301#465—221no—
302#461—111no—
303#461—221no—
304#460—111no—
305#460—111no—
306#450—221no—
307#450—221no—
308#446—111no—
309C8×Q8C2×D1111yescharacteristic, complemented
310#440—221no—
311C4×SD16—21no—
312C4×SD16—111no—
313C4×SD16C2×D1111yescharacteristic
314C8×D4—111no—
315C8×D4—111no—
316C2×#102—221no—
317C2×#102—221no—
318#335—111no—
319#334—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#331—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328#322—111no—
329C22×C11—22no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11D4211yescharacteristic
333C2×D11—22no—
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—164no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11C2×#13511yescharacteristic
349C4×C11C2×#13711yescharacteristic
350C4×C11#57711yescharacteristic
351C4×C11#57711yescharacteristic
352Dic11—41no—
353Dic11—81no—
354C22×D4—221no—
355C22×D4—221no—
356C2×Q16—441no—
357C2×SD16—111no—
358C2×SD16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16C22⋊D1111yescharacteristic
362C22×C8—221no—
363C22×C8—221no—
364C4⋊Q8—21no—
365C4⋊Q8—111no—
366C4⋊Q8C22×D1111yescharacteristic
367C4⋊Q8C22×D1111yescharacteristic
368#127—111no—
369#125—21no—
370#125—21no—
371#125—41no—
372#125—221no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—221no—
376C22⋊Q8—441no—
377#121—221no—
378#121—221no—
379#120—441no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8C22×D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4C22×D1111yescharacteristic
388C2×C4⋊C4—21no—
389C2×C4⋊C4—221no—
390#107—21no—
391#107—21no—
392#107—221no—
393#106—21no—
394#106—21no—
395#106—111no—
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#103C22⋊D1111yescharacteristic
412#102—21no—
413#102—111no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—441no—
423#102C22⋊D1111yescharacteristic
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—221no—
427C4×C8—21no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8C22×D1111yescharacteristic
431C2×C11—42no—
432C2×C11#326611yescharacteristic
433C2×C11#328211yescharacteristic
434C2×C11#328811yescharacteristic
435D11—42no—
436D11—161no—
437C24—441no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—221no—
441C2×Q8D4×D1111yescharacteristic
442C2×Q8C2×C22⋊D1111yescharacteristic
443C2×D4—111no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—441no—
448C2×D4—442no—
449C2×D4—441no—
450C2×D4—442no—
451C2×D4—881no—
452C2×D4—881no—
453C2×D4C2×C22⋊D1111yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—221no—
457C22×C4—441no—
458Q16—882no—
459SD16—22no—
460SD16—222no—
461SD16—442no—
462SD16—881no—
463SD16—881no—
464C2×C8—21no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—881no—
472C2×C8—881no—
473C2×C8C2×C22⋊D1111yescharacteristic
474C2×C8C2×C22⋊D1111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—111no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—441no—
490C4⋊C4—441no—
491C4⋊C4D4×D1111yescharacteristic
492C4⋊C4C2×C22⋊D1111yescharacteristic
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—221no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C23×D1111yescharacteristic
503C11#1979011yescharacteristic, complemented, Sylow
504C23—21no—
505C23—221no—
506C23—441no—
507C23—882no—
508C23—882no—
509C23—1761no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—881no—
518D4—21no—
519D4—112no—
520D4—221no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—881no—
526D4—882no—
527D4—882no—
528D4#6699512yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—161no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—1761no—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C22×C22⋊D1111yescharacteristic
547C8—21no—
548C8—21no—
549C8—41no—
550C8—221no—
551C8—221no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8—441no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—222no—
560C22—441no—
561C22—441no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—1764no—
566C22D4×C22⋊D1111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—441no—
576C4—881no—
577C4D11×#13511yescharacteristic
578C4#1062330111yescharacteristic
579C4C2×#6699511yescharacteristic
580C4#1062336811yescharacteristic
581C2—42no—
582C2—442no—
583C2—1761no—
584C2#1308012711yescharacteristic
585C2#1308031711yescharacteristic
586C2#1308037811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3381C2
socleC22×C11D42
prime radicalD4×D44C22
hypercenter#3381D11
hypocenterC11#19790
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #13081393C2semidirect
4. #13068274C2semidirect
5. #13068158C2semidirect
6. #13068065C2semidirect
7. #13068032C2semidirect
8. #13067988C2semidirect
10. #13067750C2semidirect
11. #13067749C2semidirect
12. #13067712C2semidirect
13. #13067453C2semidirect
14. #13067426C2semidirect
15. C11×#3381C2semidirect
16. C11×#557C22semidirect
21. C11×#498C22semidirect
24. C11×#477C22semidirect
26. C8×Q8×C11C22semidirect
30. #10622705C22semidirect
37. #10622694C22semidirect
44. #10622637C22semidirect
46. #10622634C22semidirect
56. #10622185C22semidirect
57. #10622184C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
211. #3381D11semidirect
278. #557C2×D11semidirect
283. #498C2×D11semidirect
296. #477C2×D11semidirect
309. C8×Q8C2×D11semidirect
503. C11#19790semidirect

Maximal subgroups

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

subgroupindex
#130813932
#130804422
#130804342
#130682742
#130681582
#130680652
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