Finite Group Databasebeta

← #14745148

Subgroups — #14745148

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081533C211yesmaximal, characteristic, complemented
2SD16×D44C211yesmaximal, characteristic, complemented
3#13080236C211yesmaximal, characteristic
4#13068206C211yesmaximal, characteristic, complemented
5#13068127C211yesmaximal, characteristic, complemented
6#13068098C211yesmaximal, characteristic, complemented
7#13067964C211yesmaximal, characteristic, complemented
8#13067954C211yesmaximal, characteristic, complemented
9#13067816C211yesmaximal, characteristic, complemented
10#13067793C211yesmaximal, characteristic, complemented
11#13067717C211yesmaximal, characteristic, complemented
12#13067712C211yesmaximal, characteristic, complemented
13#13067507C211yesmaximal, characteristic, complemented
14C8×#4325C211yesmaximal, characteristic, complemented
15C11×#3392C211yesmaximal, characteristic, complemented
16C11×#557C2211yescharacteristic, complemented
17C11×#550C2211yescharacteristic
18C2×#67002—21no—
19C2×SD16×D11—21no—
20Q8×D44C2211yescharacteristic
21D4×D44C2211yescharacteristic
22C11×#492—21no—
23C11×#492C2211yescharacteristic, complemented
24C11×#461—21no—
25C11×#461C2211yescharacteristic
26C11×#460—21no—
27C11×#460C2211yescharacteristic, complemented
28C8×Q8×C11C2211yescharacteristic, complemented
29C4×C11×SD16—21no—
30C4×C11×SD16C2211yescharacteristic
31#10622851—21no—
32#10622701C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622691C2211yescharacteristic, complemented
35#10622686C2211yescharacteristic
36#10622685C2211yescharacteristic
37#10622683C2211yescharacteristic, complemented
38#10622679—21no—
39#10622678—21no—
40#10622652—21no—
41#10622649—21no—
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622639—21no—
45C4×#4325C2211yescharacteristic
46#10622637C2211yescharacteristic, complemented
47#10622634—21no—
48#10622633C2211yescharacteristic, complemented
49#10622632C2211yescharacteristic
50#10622625C2211yescharacteristic
51#10622477—21no—
52#10622419—21no—
53#10622389—21no—
54#10622306C2211yescharacteristic
55C8×D44C2211yescharacteristic
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic, complemented
58Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60D4⋊(C11⋊C8)C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622120C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C2×Q8×D11—21no—
69C2×D4×D11—21no—
70C22×D44—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16D411yescharacteristic
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8C2311yescharacteristic
78C11×#127—21no—
79C11×#127C2311yescharacteristic
80C11×#125—21no—
81C11×#125—41no—
82C11×#121—21no—
83C11×#121—41no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11C2311yescharacteristic
87C4×Q8×C11C2311yescharacteristic
88C4×D4×C11—21no—
89C4×D4×C11C2311yescharacteristic
90#67002—44no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325D411yescharacteristic
94C2×#4324—21no—
95C2×#4323—21no—
96C2×#4323—21no—
97C2×#4323—21no—
98#66983—21no—
99C2×#4318—21no—
100SD16×D11—44no—
101C2×#4314—21no—
102C2×#4314—21no—
103C2×C8×D11—21no—
104#66950—21no—
105#66950—41no—
106#66948—21no—
107#66935—41no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44C2311yescharacteristic
111#66922—21no—
112#66922C2311yescharacteristic
113C11×#106D411yescharacteristic
114C11×C4⋊C8—21no—
115C11×C4⋊C8C2311yescharacteristic
116C11×#103—21no—
117C11×#103D411yescharacteristic
118C11×#102—21no—
119C11×#102D411yescharacteristic
120C4×C8×C11—21no—
121C4×C8×C11C2311yescharacteristic
122#66899—21no—
123#66899D411yescharacteristic
124#66896—21no—
125#66896—41no—
126C22⋊(C11⋊C8)—21no—
127(C2×D11)⋊C8—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66873—21no—
132#66873—41no—
133#66873D411yescharacteristic
134#66872—21no—
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#19892—111nomaximal, Sylow
147C23×D11—41no—
148C11×#41—42no—
149C11×#41—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C2×C22⋊D11—41no—
162Q8×D11—42no—
163Q8×D11—81no—
164D4×D11—42no—
165D4×D11—81no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—41no—
170C2×D44—42no—
171C2×D44—81no—
172C2×D44C2×D411yescharacteristic
173C2×C4×D11—21no—
174C2×C4×D11—41no—
175C2×Dic22—21no—
176C2×Dic22—41no—
177C11×SD16—22no—
178C11×SD16—42no—
179C11×SD16—81no—
180C11×SD16—81no—
181C11×SD16—81no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C22⋊C4—21no—
196C11×C22⋊C4—41no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—41no—
200C42×C11C2411yescharacteristic
201#4325—42no—
202#4325—42no—
203#4325SD1614yescomplemented
204#4324—42no—
205#4323—42no—
206#4323—42no—
207#4323—81no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—41no—
210(C2×D11)⋊C4—41no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—41no—
214C4⋊Dic11C2×D411yescharacteristic
215#4318—42no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#4314—42no—
223#4314—81no—
224C8×D11—42no—
225#3392D1111yescharacteristic, complemented
226#3386—111no—
227D4×SD16—111no—
228#3274—111no—
229#1706—111no—
230#1693—111no—
231#1688—111no—
232#1666—111no—
233#1665—111no—
234#1642—111no—
235#1639—111no—
236#1627—111no—
237#1626—111no—
238#1590—111no—
239C8×SD16—111no—
240C23×C11—21no—
241C23×C11—41no—
242C22×D11—21no—
243C22×D11—41no—
244C22×D11—82no—
245C22×D11—82no—
246C22×D11—161no—
247Q8×C11—21no—
248Q8×C11—21no—
249Q8×C11—21no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11C2×SD1612yescomplemented
253D4×C11—21no—
254D4×C11—21no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—82no—
260D4×C11—81no—
261D4×C11—161no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—82no—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C22⋊D11—82no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277D44—21no—
278D44—41no—
279D44—41no—
280D44—41no—
281D44—41no—
282D44—81no—
283D44—82no—
284D44C2×SD1612yes—
285C4×D11—41no—
286C4×D11—41no—
287C4×D11—82no—
288Dic22—41no—
289Dic22—41no—
290Dic22—82no—
291C8×C11—21no—
292C8×C11—41no—
293C8×C11AGL(1,ℤ/8)12yescomplemented
294C11⋊C8—21no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8C2×SD1612yescomplemented
300C2×AGL(1,ℤ/8)—221no—
301C22×SD16—221no—
302#557C2×D1111yescharacteristic, complemented
303#550C2×D1111yescharacteristic
304D4×Q8—111no—
305D42—111no—
306#501—221no—
307#500—111no—
308#493—111no—
309#492—21no—
310#492—111no—
311#492C2×D1111yescharacteristic, complemented
312#486—111no—
313#486—111no—
314#478—221no—
315#477—221no—
316#475—111no—
317#474—111no—
318#469—221no—
319#465—221no—
320#461—21no—
321#461—111no—
322#461C2×D1111yescharacteristic
323#460—21no—
324#460—111no—
325#460—111no—
326#460C2×D1111yescharacteristic, complemented
327#459—111no—
328#450—221no—
329#449—221no—
330#448—221no—
331#447—221no—
332#446—111no—
333C8×Q8C2×D1111yescharacteristic, complemented
334#440—221no—
335C4×SD16—21no—
336C4×SD16—111no—
337C4×SD16C2×D1111yescharacteristic
338#436—111no—
339C8×D4—111no—
340#334—111no—
341#334—111no—
342#332—111no—
343#332—111no—
344#331—111no—
345#331—111no—
346Q8⋊C8—111no—
347Q8⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350C82—111no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11D4211yescharacteristic
358C2×D11—22no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—164no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—81no—
372C4×C11C22×SD1611yescharacteristic
373C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
374C4×C11#57611yescharacteristic
375C4×C11#57711yescharacteristic
376Dic11—41no—
377Dic11—81no—
378C2×#41—21no—
379C22×Q8—221no—
380C22×D4—221no—
381C22×D4—221no—
382AGL(1,ℤ/8)—444no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—111no—
388C2×SD16—221no—
389C2×SD16—221no—
390C2×SD16—221no—
391C2×SD16—221no—
392C2×SD16—221no—
393C2×SD16—444no—
394C2×SD16C22⋊D1111yescharacteristic
395C2×D8—221no—
396C2×D8—221no—
397C2×D8—221no—
398C2×M16—221no—
399C22×C8—221no—
400C4⋊Q8—21no—
401C4⋊Q8—111no—
402C4⋊Q8—221no—
403C4⋊Q8C22×D1111yescharacteristic
404#127—21no—
405#127—111no—
406#127C22×D1111yescharacteristic
407#125—21no—
408#125—41no—
409C22⋊Q8—221no—
410C22⋊Q8—441no—
411#121—21no—
412#121—41no—
413#121—221no—
414#121—221no—
415#120—441no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8C22×D1111yescharacteristic
419C4×Q8C22×D1111yescharacteristic
420C4×D4—21no—
421C4×D4—111no—
422C4×D4—221no—
423C4×D4C22×D1111yescharacteristic
424#107—221no—
425#107—221no—
426#107—221no—
427#106—111no—
428#106—221no—
429#106C22⋊D1111yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—221no—
435C4⋊C8C22×D1111yescharacteristic
436#103—21no—
437#103—111no—
438#103—221no—
439#103—221no—
440#103C22⋊D1111yescharacteristic
441#102—21no—
442#102—111no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—441no—
448#102—441no—
449#102C22⋊D1111yescharacteristic
450C22⋊C8—221no—
451C22⋊C8—221no—
452#97—221no—
453C4×C8—21no—
454C4×C8—111no—
455C4×C8—111no—
456C4×C8C22×D1111yescharacteristic
457C2×C11—81no—
458C2×C11—161no—
459C2×C11#327411yescharacteristic
460C2×C11D4×SD1611yescharacteristic
461C2×C11#329011yescharacteristic
462D11—42no—
463D11—161no—
464C24—441no—
465#41—42no—
466#41—81no—
467C2×Q8—21no—
468C2×Q8—221no—
469C2×Q8—441no—
470C2×Q8—442no—
471C2×Q8—881no—
472C2×Q8D4×D1111yescharacteristic
473C2×Q8C2×C22⋊D1111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—111no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—441no—
484C2×D4—442no—
485C2×D4—441no—
486C2×D4—442no—
487C2×D4—881no—
488C2×D4—881no—
489C2×D4C2×C22⋊D1111yescharacteristic
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—221no—
493C22×C4—441no—
494SD16—22no—
495SD16—42no—
496SD16—81no—
497SD16—81no—
498SD16—81no—
499SD16—114no—
500SD16—442no—
501SD16—442no—
502SD16—442no—
503SD16—442no—
504SD16—881no—
505D8—442no—
506D8—442no—
507D8—881no—
508M16—442no—
509C2×C8—21no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—442no—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—111no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—441no—
530C4⋊C4D4×D1111yescharacteristic
531C4⋊C4C2×C22⋊D1111yescharacteristic
532C4⋊C4C2×C22⋊D1111yescharacteristic
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—221no—
536C22⋊C4—441no—
537C22⋊C4—441no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42C23×D1111yescharacteristic
542C11#1989211yescharacteristic, complemented, Sylow
543C23—21no—
544C23—41no—
545C23—221no—
546C23—441no—
547C23—882no—
548C23—882no—
549C23—1761no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—41no—
554Q8—41no—
555Q8—441no—
556Q8—441no—
557Q8—882no—
558Q8SD16×D1112yescomplemented
559D4—21no—
560D4—21no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—82no—
566D4—81no—
567D4—112no—
568D4—161no—
569D4—221no—
570D4—441no—
571D4—441no—
572D4—441no—
573D4—441no—
574D4—881no—
575D4—882no—
576D4—882no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—82no—
586C2×C4—221no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—882no—
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—21no—
595C8—41no—
596C8—112no—
597C8—221no—
598C8—441no—
599C8—441no—
600C8—441no—
601C8—441no—
602C8#6700212yescomplemented
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—222no—
610C22—441no—
611C22—441no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—1764no—
616C22D4×C22⋊D1111yescharacteristic
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—441no—
625C4—881no—
626C4C2×SD16×D1111yescharacteristic
627C4#1062329311yescharacteristic
628C4C2×#6700211yescharacteristic
629C4#1062336611yescharacteristic
630C2—81no—
631C2—161no—
632C2—442no—
633C2—1761no—
634C2#1308023611yescharacteristic
635C2SD16×C22⋊D1111yescharacteristic
636C2#1308039611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3392C2
socleC22×C11D42
prime radical#13080236C2
hypercenter#3392D11
hypocenterC11#19892
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3392

Complements

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

NH ≅ G/Ntype
1. #13081533C2semidirect
2. SD16×D44C2semidirect
4. #13068206C2semidirect
5. #13068127C2semidirect
6. #13068098C2semidirect
7. #13067964C2semidirect
8. #13067954C2semidirect
9. #13067816C2semidirect
10. #13067793C2semidirect
11. #13067717C2semidirect
12. #13067712C2semidirect
13. #13067507C2semidirect
14. C8×#4325C2semidirect
15. C11×#3392C2semidirect
16. C11×#557C22semidirect
23. C11×#492C22semidirect
27. C11×#460C22semidirect
28. C8×Q8×C11C22semidirect
34. #10622691C22semidirect
37. #10622683C22semidirect
46. #10622637C22semidirect
48. #10622633C22semidirect
56. #10622185C22semidirect
57. #10622182C22semidirect
58. Q8⋊(C11⋊C8)C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
63. #10622120C22semidirect
64. #10622118C22semidirect
65. #10622095C22semidirect
66. C8×C11⋊C8C22semidirect
203. #4325SD16semidirect
225. #3392D11semidirect
252. Q8×C11C2×SD16semidirect
293. C8×C11AGL(1,ℤ/8)semidirect
299. C11⋊C8C2×SD16semidirect
302. #557C2×D11semidirect
311. #492C2×D11semidirect
326. #460C2×D11semidirect
333. C8×Q8C2×D11semidirect
542. C11#19892semidirect
558. Q8SD16×D11semidirect
602. C8#67002semidirect

Maximal subgroups

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

subgroupindex
#130815332
SD16×D442
#130802362
#130682062
#130681272
#130680982
#130679642
#130679542
#130678162
#130677932
#130677172
#130677122
#130675072
C8×#43252
C11×#33922
#1989211