Finite Group Databasebeta

← #14743256

Subgroups — #14743256

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081533C211yesmaximal, characteristic, complemented
2SD16×D44C211yesmaximal, characteristic
3D4×#4325C211yesmaximal, characteristic
4#13068240C211yesmaximal, characteristic, complemented
5#13068090C211yesmaximal, characteristic, complemented
6#13068036C211yesmaximal, characteristic, complemented
7#13068003C211yesmaximal, characteristic, complemented
8#13067964C211yesmaximal, characteristic, complemented
9#13067879C211yesmaximal, characteristic, complemented
10#13067878C211yesmaximal, characteristic, complemented
11#13067793C211yesmaximal, characteristic
12#13067712C211yesmaximal, characteristic, complemented
13#13067453C211yesmaximal, characteristic, complemented
14#13067426C211yesmaximal, characteristic, complemented
15C11×#3359C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17D4×Q8×C11C2211yescharacteristic
18C22×#4325—21no—
19C2×SD16×D11—21no—
20Q8×D44C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#487—21no—
23C11×#487C2211yescharacteristic, complemented
24C11×#475—21no—
25C11×#475C2211yescharacteristic, complemented
26C11×#461—21no—
27C11×#461C2211yescharacteristic
28C8×Q8×C11C2211yescharacteristic, complemented
29C4×C11×SD16—21no—
30C4×C11×SD16C2211yescharacteristic
31#10622840—21no—
32#10622701C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622698C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622692C2211yescharacteristic, complemented
37#10622691C2211yescharacteristic, complemented
38#10622679—21no—
39#10622678—21no—
40#10622661—21no—
41#10622659—21no—
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622639—21no—
45C4×#4325C2211yescharacteristic
46#10622637C2211yescharacteristic, complemented
47#10622634—21no—
48#10622633C2211yescharacteristic, complemented
49#10622632C2211yescharacteristic
50D4×C11⋊C8C2211yescharacteristic
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622185C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C22×Q8×C11—21no—
68C2×Q8×D11—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16D411yescharacteristic
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#125—21no—
78C11×#125—41no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—41no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×D4×C11—21no—
86C4×D4×C11C2311yescharacteristic
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—44no—
93C2×#4325D411yescharacteristic
94C2×#4324—21no—
95#66983—21no—
96C22×C11⋊C8—21no—
97SD16×D11—44no—
98C2×#4314—21no—
99C2×#4314—21no—
100C2×C8×D11—21no—
101#66950—21no—
102#66950—41no—
103#66948—21no—
104#66935—41no—
105#66927C2311yescharacteristic
106C4×D44—21no—
107C4×D44C2311yescharacteristic
108#66922—21no—
109#66922C2311yescharacteristic
110C11×#106—21no—
111C11×#106D411yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2311yescharacteristic
114C11×#103—21no—
115C11×#103—21no—
116C11×#103—21no—
117C11×#103—21no—
118C11×#103D411yescharacteristic
119C11×#102D411yescharacteristic
120C4×C8×C11—21no—
121C4×C8×C11C2311yescharacteristic
122#66899—21no—
123#66899—21no—
124#66899D411yescharacteristic
125C22⋊(C11⋊C8)—21no—
126(C2×D11)⋊C8—21no—
127#66874—21no—
128#66873—21no—
129#66873—21no—
130#66873—21no—
131#66873—41no—
132#66873D411yescharacteristic
133#66872—21no—
134#66872—41no—
135#66872D411yescharacteristic
136#66871—21no—
137#66871—21no—
138#66871—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#19764—111nomaximal, Sylow
147C23×D11—41no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C2×C22⋊D11—41no—
159Q8×D11—42no—
160Q8×D11—81no—
161D4×D11—42no—
162D4×D11—81no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—41no—
167C2×D44—42no—
168C2×D44—81no—
169C2×D44C2×D411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—41no—
172C2×Dic22—21no—
173C2×Dic22—41no—
174C11×SD16—22no—
175C11×SD16—42no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C22⋊C4—21no—
193C11×C22⋊C4—41no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—41no—
197C42×C11C2411yescharacteristic
198#4325—42no—
199#4325—42no—
200#4325—42no—
201#4325—42no—
202#4325—81no—
203#4325SD1614yescomplemented
204#4324—42no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—41no—
211C4⋊Dic11C2×D411yescharacteristic
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—42no—
217C2×C11⋊C8C2×D411yescharacteristic
218C2×C11⋊C8C2×D411yescharacteristic
219#4314—42no—
220#4314—81no—
221C8×D11—42no—
222#3386—111no—
223#3359D1111yescharacteristic, complemented
224D4×SD16—111no—
225D4×SD16—111no—
226#1714—111no—
227#1686—111no—
228#1679—111no—
229#1673—111no—
230#1666—111no—
231#1651—111no—
232#1651—111no—
233#1639—111no—
234#1626—111no—
235#1582—111no—
236SD16⋊C8—111no—
237C23×C11—21no—
238C22×D11—21no—
239C22×D11—41no—
240C22×D11—82no—
241C22×D11—82no—
242C22×D11—161no—
243Q8×C11—21no—
244Q8×C11—21no—
245Q8×C11—21no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—82no—
251Q8×C11C2×SD1612yescomplemented
252D4×C11—21no—
253D4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—82no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C22⋊D11—82no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270D44—21no—
271D44—41no—
272D44—41no—
273D44—41no—
274D44—41no—
275D44—81no—
276D44—82no—
277D44C2×SD1612yes—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—82no—
281Dic22—41no—
282Dic22—41no—
283Dic22—82no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—41no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8C2×SD1612yescomplemented
293C22×SD16—221no—
294C22×SD16—221no—
295#557C2×D1111yescharacteristic, complemented
296D4×Q8—111no—
297D4×Q8C2×D1111yescharacteristic
298D42—111no—
299#501—221no—
300#500—111no—
301#498—111no—
302#492—111no—
303#492—111no—
304#487—21no—
305#487C2×D1111yescharacteristic, complemented
306#486—111no—
307#478—221no—
308#477—221no—
309#475—21no—
310#475—111no—
311#475C2×D1111yescharacteristic, complemented
312#474—111no—
313#465—221no—
314#465—221no—
315#461—21no—
316#461—111no—
317#461—111no—
318#461C2×D1111yescharacteristic
319#460—111no—
320#460—111no—
321#450—221no—
322#450—221no—
323#448—221no—
324#448—221no—
325#446—111no—
326C8×Q8C2×D1111yescharacteristic, complemented
327#440—221no—
328C4×SD16—21no—
329C4×SD16—111no—
330C4×SD16C2×D1111yescharacteristic
331C8×D4—111no—
332C8×D4—111no—
333#335—111no—
334#334—111no—
335#332—111no—
336#332—111no—
337#332—111no—
338#331—111no—
339Q8⋊C8—111no—
340Q8⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343#322—111no—
344C22×C11—22no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11D4211yescharacteristic
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—164no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11C22×SD1611yescharacteristic
364C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C4×C11#57711yescharacteristic
366C4×C11#57711yescharacteristic
367Dic11—41no—
368Dic11—81no—
369C22×Q8—21no—
370C22×Q8—221no—
371C22×D4—221no—
372C22×D4—221no—
373C2×SD16—21no—
374C2×SD16—111no—
375C2×SD16—221no—
376C2×SD16—221no—
377C2×SD16—221no—
378C2×SD16—221no—
379C2×SD16—221no—
380C2×SD16—221no—
381C2×SD16—221no—
382C2×SD16—221no—
383C2×SD16—444no—
384C2×SD16—444no—
385C2×SD16C22⋊D1111yescharacteristic
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—111no—
391C4⋊Q8—221no—
392C4⋊Q8C22×D1111yescharacteristic
393C4⋊Q8C22×D1111yescharacteristic
394#127—111no—
395#125—21no—
396#125—41no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—221no—
400C22⋊Q8—441no—
401#121—221no—
402#121—221no—
403#120—441no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8C22×D1111yescharacteristic
407C4×Q8C22×D1111yescharacteristic
408C4×D4—21no—
409C4×D4—111no—
410C4×D4—221no—
411C4×D4C22×D1111yescharacteristic
412#107—221no—
413#107—221no—
414#107—221no—
415#106—21no—
416#106—111no—
417#106—221no—
418#106—441no—
419#106C22⋊D1111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—111no—
422C4⋊C8—111no—
423C4⋊C8—111no—
424C4⋊C8—221no—
425C4⋊C8C22×D1111yescharacteristic
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—111no—
431#103—221no—
432#103—221no—
433#103—221no—
434#103C22⋊D1111yescharacteristic
435#102—111no—
436#102—221no—
437#102—221no—
438#102—221no—
439#102—441no—
440#102C22⋊D1111yescharacteristic
441C22⋊C8—221no—
442C22⋊C8—221no—
443#97—221no—
444C4×C8—21no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8C22×D1111yescharacteristic
448C2×C11—42no—
449C2×C11#326511yescharacteristic
450C2×C11D4×SD1611yescharacteristic
451C2×C11#328911yescharacteristic
452D11—42no—
453D11—161no—
454C24—441no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—221no—
461C2×Q8—441no—
462C2×Q8—442no—
463C2×Q8—881no—
464C2×Q8D4×D1111yescharacteristic
465C2×Q8C2×C22⋊D1111yescharacteristic
466C2×D4—111no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—441no—
471C2×D4—442no—
472C2×D4—441no—
473C2×D4—442no—
474C2×D4—881no—
475C2×D4—881no—
476C2×D4C2×C22⋊D1111yescharacteristic
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—221no—
480C22×C4—441no—
481SD16—22no—
482SD16—42no—
483SD16—114no—
484SD16—442no—
485SD16—442no—
486SD16—442no—
487SD16—442no—
488SD16—442no—
489SD16—442no—
490SD16—881no—
491SD16—881no—
492C2×C8—21no—
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—442no—
500C2×C8—442no—
501C2×C8C2×C22⋊D1111yescharacteristic
502C2×C8C2×C22⋊D1111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—111no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—441no—
517C4⋊C4D4×D1111yescharacteristic
518C4⋊C4C2×C22⋊D1111yescharacteristic
519C4⋊C4C2×C22⋊D1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—221no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C42—21no—
526C42—21no—
527C42—41no—
528C42C23×D1111yescharacteristic
529C11#1976411yescharacteristic, complemented, Sylow
530C23—21no—
531C23—221no—
532C23—441no—
533C23—882no—
534C23—882no—
535C23—1761no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—82no—
544Q8—441no—
545Q8—441no—
546Q8—882no—
547Q8SD16×D1112yescomplemented
548D4—21no—
549D4—112no—
550D4—221no—
551D4—441no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—881no—
556D4—882no—
557D4—882no—
558D4#6700212yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—221no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—882no—
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4#6703711yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—21no—
578C8—21no—
579C8—41no—
580C8—112no—
581C8—221no—
582C8—441no—
583C8—441no—
584C8—441no—
585C8—441no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—222no—
590C22—441no—
591C22—441no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—1764no—
596C22D4×C22⋊D1111yescharacteristic
597C4—21no—
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—441no—
606C4—881no—
607C4C2×SD16×D1111yescharacteristic
608C4#1062329311yescharacteristic
609C4C2×#6700211yescharacteristic
610C4#1062336811yescharacteristic
611C2—42no—
612C2—442no—
613C2—1761no—
614C2#1308011211yescharacteristic
615C2SD16×C22⋊D1111yescharacteristic
616C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3359C2
socleC22×C11D42
prime radicalD4×D44C22
hypercenter#3359D11
hypocenterC11#19764
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3359

Complements

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

NH ≅ G/Ntype
1. #13081533C2semidirect
4. #13068240C2semidirect
5. #13068090C2semidirect
6. #13068036C2semidirect
7. #13068003C2semidirect
8. #13067964C2semidirect
9. #13067879C2semidirect
10. #13067878C2semidirect
12. #13067712C2semidirect
13. #13067453C2semidirect
14. #13067426C2semidirect
15. C11×#3359C2semidirect
16. C11×#557C22semidirect
23. C11×#487C22semidirect
25. C11×#475C22semidirect
28. C8×Q8×C11C22semidirect
36. #10622692C22semidirect
37. #10622691C22semidirect
46. #10622637C22semidirect
48. #10622633C22semidirect
56. #10622185C22semidirect
57. #10622185C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622092C22semidirect
203. #4325SD16semidirect
223. #3359D11semidirect
251. Q8×C11C2×SD16semidirect
292. C11⋊C8C2×SD16semidirect
295. #557C2×D11semidirect
305. #487C2×D11semidirect
311. #475C2×D11semidirect
326. C8×Q8C2×D11semidirect
529. C11#19764semidirect
547. Q8SD16×D11semidirect

Maximal subgroups

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

subgroupindex
#130815332
SD16×D442
D4×#43252
#130682402
#130680902
#130680362
#130680032
#130679642
#130678792
#130678782
#130677932
#130677122
#130674532
#130674262
C11×#33592
#1976411