Finite Group Databasebeta

← #14817213

Subgroups — #14817213

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078476C211yesmaximal, characteristic
2#13078458C211yesmaximal, characteristic, complemented
3#13077209C211yesmaximal, characteristic
4#13070157C211yesmaximal, characteristic, complemented
5#13070129C211yesmaximal, characteristic, complemented
6#13069981C211yesmaximal, characteristic, complemented
7#13069959C211yesmaximal, characteristic, complemented
8#13069396C211yesmaximal, characteristic, complemented
9#13069215C211yesmaximal, characteristic, complemented
10#13069133C211yesmaximal, characteristic
11#13068987C211yesmaximal, characteristic
12#13068893C211yesmaximal, characteristic
13#13068842C211yesmaximal, characteristic
14#13068831C211yesmaximal, characteristic, complemented
15C11×#2947C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C11×#520C2211yescharacteristic
18C11×#519C2211yescharacteristic
19#10623358C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21#10623050C2211yescharacteristic
22C11×#441—21no—
23C11×#440—21no—
24C4×C11×Q16—21no—
25C4×C11×SD16—21no—
26C11×#428C2211yescharacteristic
27C11×#416C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C11×#405C2211yescharacteristic
30C2×#66901C2211yescharacteristic
31#10622845C2211yescharacteristic
32#10622843C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34#10622838C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66883C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38#10622715C2211yescharacteristic
39#10622635—21no—
40#10622635—21no—
41#10622634—21no—
42#10622633—21no—
43#10622612C2211yescharacteristic
44#10622611—21no—
45#10622611C2211yescharacteristic
46#10622608—21no—
47#10622608C2211yescharacteristic
48#10622608C2211yescharacteristic
49#10622608C2211yescharacteristic
50#10622589C2211yescharacteristic
51#10622577—21no—
52#10622577C2211yescharacteristic
53C2×#66872—21no—
54C2×#66872C2211yescharacteristic
55#10622412—21no—
56#10622404—21no—
57#10622376—21no—
58#10622374—21no—
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Q8×C11C2311yescharacteristic
69C11×#137—22no—
70C11×#137Q814yescomplemented
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—41no—
82C11×#117—21no—
83C11×#117—41no—
84C11×#117C2311yescharacteristic
85C11×#117C2311yescharacteristic
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88#67001—22no—
89#67001—22no—
90Q8×Dic11—21no—
91D4×Dic11—21no—
92D4×Dic11—41no—
93#66979—21no—
94#66979C2311yescharacteristic
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—41no—
99C2×C4×Dic11C2311yescharacteristic
100C2×#4318—21no—
101C2×#4318C2311yescharacteristic
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C22×C11⋊C8—21no—
105C22×C11⋊C8C2311yescharacteristic
106#66943—21no—
107#66941—21no—
108#66931—41no—
109#66923—21no—
110#66922—21no—
111C11×#107—21no—
112C11×#106—21no—
113C11×#103—21no—
114C11×#103—21no—
115C11×#103D411yescharacteristic
116C11×#103D411yescharacteristic
117C11×#102D411yescharacteristic
118C11×#102D411yescharacteristic
119C11×#97—21no—
120C4×C8×C11—21no—
121#66901—22no—
122#66900—22no—
123#66899—21no—
124#66899—21no—
125#66899—21no—
126#66899—21no—
127#66899—21no—
128#66896—21no—
129C11⋊#95—41no—
130#66883—22no—
131#66881—21no—
132#66881—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135#66872—21no—
136#66872—21no—
137#66872—21no—
138#66872—21no—
139#66872—21no—
140#66872—21no—
141#66872D411yescharacteristic
142#66872D411yescharacteristic
143#66871—21no—
144#66871—21no—
145#66871—21no—
146#66871—21no—
147#66871D411yescharacteristic
148#66871D411yescharacteristic
149C4⋊(C11⋊C8)—21no—
150C4⋊(C11⋊C8)—21no—
151#26401—111nomaximal, Sylow
152C11×#41—21no—
153C11×#41—21no—
154C11×#41C2×Q812yes—
155C11×#41#4112yes—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C2×D411yescharacteristic
162C2×Q8×C11C2×Q812yes—
163C2×D4×C11—21no—
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—41no—
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—41no—
174C2×Dic22—41no—
175C11×Q16—24no—
176C11×SD16—24no—
177C11×M16—21no—
178C11×M16C2×Q812yes—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
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×C4⋊C4C2×D411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—41no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—41no—
199C42×C11—41no—
200C42×C11—41no—
201C22⋊Dic11—21no—
202C22⋊Dic11—41no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—41no—
208C4⋊Dic11—41no—
209C4⋊Dic11C2×D411yescharacteristic
210C4⋊Dic11C2×D411yescharacteristic
211Dic11⋊C4—41no—
212Dic11⋊C4—41no—
213Dic11⋊C4—82no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—41no—
218#4318—24no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318#4112yes—
225C2×C11⋊C8—24no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C2×D411yescharacteristic
232C2×C11⋊C8C2×D411yescharacteristic
233#3084—111no—
234#3082—111no—
235#2947D1111yescharacteristic
236#2912—111no—
237#2096—111no—
238#2090—111no—
239#2064—111no—
240#2060—111no—
241#1951—111no—
242#1922—111no—
243#1908—111no—
244#1882—111no—
245#1866—111no—
246#1859—111no—
247#1857—111no—
248C23×C11—21no—
249C23×C11H(5,𝔽2)11yescharacteristic
250Q8×C11—21no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11C22⋊Q812yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—21no—
259D4×C11C22⋊Q812yes—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—81no—
272C2×C4×C11—161no—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×Q811yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—81no—
287C2×Dic11—81no—
288C2×Dic11—161no—
289Dic22—161no—
290C8×C11—22no—
291C8×C11—21no—
292C8×C11—21no—
293C11⋊C8—21no—
294C11⋊C8—22no—
295C11⋊C8—21no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×#137C2×D1111yescharacteristic
299C2×#131—111no—
300#544—111no—
301#520—111no—
302#520C2×D1111yescharacteristic
303#519C2×D1111yescharacteristic
304#479—221no—
305#479—221no—
306#479—221no—
307#478—221no—
308#477—221no—
309#476—221no—
310#475—221no—
311#475—221no—
312#441—21no—
313#440—21no—
314C4×Q16—21no—
315C4×SD16—21no—
316C2×#108—111no—
317#428—111no—
318#428—111no—
319#428—111no—
320#428—111no—
321#428—221no—
322#428—221no—
323#428C2×D1111yescharacteristic
324#427—111no—
325#427—221no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—221no—
329#424—111no—
330#424—111no—
331C2×#104—111no—
332#419—111no—
333#417—111no—
334#416C2×D1111yescharacteristic
335C2×#103—111no—
336C2×#103C2×D1111yescharacteristic
337C2×#101—111no—
338#405C2×D1111yescharacteristic
339#391—111no—
340#384—111no—
341#343—111no—
342#343—111no—
343#343—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#336—111no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11#53911yescharacteristic
355C22×C11D4211yescharacteristic
356C22×C11#55411yescharacteristic
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11C2×C22⋊Q811yescharacteristic
365C4×C11#52511yescharacteristic
366C4×C11#54711yescharacteristic
367C4×C11D4×Q811yescharacteristic
368Dic11—42no—
369Dic11—41no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373C2×#41C22×D1111yescharacteristic
374C22×Q8C22×D1111yescharacteristic
375#137—22no—
376#137Dic2214yescomplemented
377C2×Q16—21no—
378C2×SD16—21no—
379#131—222no—
380#131—222no—
381C2×M16—111no—
382C2×M16—111no—
383C2×M16—111no—
384C2×M16—221no—
385C2×M16C22×D1111yescharacteristic
386C22×C8—111no—
387C22×C8—221no—
388C22×C8C22×D1111yescharacteristic
389C4⋊Q8—221no—
390C4⋊Q8—221no—
391#125—221no—
392#125—221no—
393C22⋊Q8—441no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—221no—
400C4×D4—21no—
401C4×D4—41no—
402C4×D4—221no—
403C4×D4—441no—
404#117—21no—
405#117—41no—
406#117—111no—
407#117—221no—
408#117C22×D1111yescharacteristic
409#117C22×D1111yescharacteristic
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C42—111no—
417#108—222no—
418#107—21no—
419#107—111no—
420#107—111no—
421#107—221no—
422#107—221no—
423#107—221no—
424#107—221no—
425#106—21no—
426#106—111no—
427#106—111no—
428#106—221no—
429#106—221no—
430#106—221no—
431#106—221no—
432#106—221no—
433#106—221no—
434#106—221no—
435#106—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440#104—222no—
441#103—21no—
442#103—21no—
443#103—221no—
444#103—221no—
445#103—221no—
446#103—221no—
447#103—221no—
448#103C22⋊D1111yescharacteristic
449#103C22⋊D1111yescharacteristic
450#102—221no—
451#102C22⋊D1111yescharacteristic
452#102C22⋊D1111yescharacteristic
453#101—222no—
454#97—21no—
455C4×C8—21no—
456#95—441no—
457C2×C11—21no—
458C2×C11—21no—
459C2×C11—42no—
460C2×C11#244911yescharacteristic
461C2×C11#328911yescharacteristic
462C2×C11#329111yescharacteristic
463#41—21no—
464#41—21no—
465#41C2×Dic2212yes—
466#41#433912yes—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—441no—
473C2×Q8C2×Dic2212yes—
474C2×Q8C2×C22⋊D1111yescharacteristic
475C2×D4—21no—
476C2×D4C2×C22⋊D1111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—441no—
485C22×C4C23×D1111yescharacteristic
486Q16—24no—
487SD16—24no—
488M16—21no—
489M16—112no—
490M16—224no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16C2×Dic2212yes—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—224no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8C2×C22⋊D1111yescharacteristic
509C2×C8C2×C22⋊D1111yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—111no—
516C4⋊C4—111no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C4⋊C4—441no—
525C4⋊C4—882no—
526C4⋊C4D4×D1111yescharacteristic
527C4⋊C4D4×D1111yescharacteristic
528C4⋊C4C2×C22⋊D1111yescharacteristic
529C4⋊C4C2×C22⋊D1111yescharacteristic
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—221no—
534C22⋊C4—441no—
535C42—21no—
536C42—21no—
537C42—41no—
538C42—41no—
539C42—41no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—441no—
544C11#2640111yescharacteristic, complemented, Sylow
545C23—21no—
546C23#6703711yescharacteristic
547Q8—21no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8—1761no—
553Q8#6697712yes—
554D4—22no—
555D4—22no—
556D4—21no—
557D4#6697712yes—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—161no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—881no—
579C2×C4—881no—
580C2×C4—1761no—
581C2×C4C22×Dic2211yescharacteristic
582C2×C4C2×#433911yescharacteristic
583C2×C4C2×D4×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704311yescharacteristic
586C2×C4C22×C22⋊D1111yescharacteristic
587C8—22no—
588C8—21no—
589C8—21no—
590C8—221no—
591C8—221no—
592C8—222no—
593C8—441no—
594C8—441no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22#1062307011yescharacteristic
601C22#1062309511yescharacteristic
602C22D4×C22⋊D1111yescharacteristic
603C4—22no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—81no—
610C4—442no—
611C4—441no—
612C4—441no—
613C4—881no—
614C4—881no—
615C4D4×Dic2211yescharacteristic
616C4#1062307811yescharacteristic
617C4C2×#6697711yescharacteristic
618C4#1062335511yescharacteristic
619C2—21no—
620C2—21no—
621C2—42no—
622C2#1307241911yescharacteristic
623C2#1308038711yescharacteristic
624C2#1308040711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2947C2
socleC22×C11D42
prime radicalC2×C11×#41C23
hypercenter#2947D11
hypocenterC11#26401
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2947

Complements

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

NH ≅ G/Ntype
2. #13078458C2semidirect
4. #13070157C2semidirect
5. #13070129C2semidirect
6. #13069981C2semidirect
7. #13069959C2semidirect
8. #13069396C2semidirect
9. #13069215C2semidirect
14. #13068831C2semidirect
70. C11×#137Q8semidirect
376. #137Dic22semidirect
544. C11#26401semidirect

Maximal subgroups

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

subgroupindex
#130784762
#130784582
#130772092
#130701572
#130701292
#130699812
#130699592
#130693962
#130692152
#130691332
#130689872
#130688932
#130688422
#130688312
C11×#29472
#2640111