Finite Group Databasebeta

← #14817249

Subgroups — #14817249

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078478C211yesmaximal, characteristic
2#13078461C211yesmaximal, characteristic, complemented
3#13077455C211yesmaximal, characteristic
4#13070161C211yesmaximal, characteristic, complemented
5#13070122C211yesmaximal, characteristic, complemented
6#13069980C211yesmaximal, characteristic, complemented
7#13069964C211yesmaximal, characteristic, complemented
8#13069393C211yesmaximal, characteristic, complemented
9#13069217C211yesmaximal, characteristic, complemented
10#13069131C211yesmaximal, characteristic
11#13068985C211yesmaximal, characteristic
12#13068891C211yesmaximal, characteristic
13#13068849C211yesmaximal, characteristic
14#13068829C211yesmaximal, characteristic, complemented
15C11×#2913C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17C11×#520C2211yescharacteristic
18C11×#520C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20#10623050C2211yescharacteristic
21#10623047C2211yescharacteristic
22C11×#428—21no—
23C11×#428—21no—
24C11×#428C2211yescharacteristic
25C11×#428C2211yescharacteristic
26C11×#427—21no—
27C11×#427C2211yescharacteristic
28C2×C11×#107—21no—
29C2×C11×#107C2211yescharacteristic
30C2×#66901C2211yescharacteristic
31#10622846C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66888C2211yescharacteristic
34C2×#66886C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622715C2211yescharacteristic
37#10622643—21no—
38C4×#4326—21no—
39#10622635—21no—
40#10622633—21no—
41#10622631—21no—
42C4×#4324—21no—
43#10622622—21no—
44#10622621—21no—
45#10622617C2211yescharacteristic
46#10622612C2211yescharacteristic
47#10622610C2211yescharacteristic
48#10622608C2211yescharacteristic
49#10622590C2211yescharacteristic
50#10622587C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52#10622577C2211yescharacteristic
53#10622577C2211yescharacteristic
54C2×#66872C2211yescharacteristic
55#10622490—21no—
56#10622488—21no—
57#10622470—21no—
58#10622467—21no—
59#10622193C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C11×#131—22no—
70C11×#131—22no—
71C2×C11×M16—21no—
72C2×C11×M16C2311yescharacteristic
73C22×C8×C11—21no—
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—41no—
80C4×D4×C11—41no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117C2311yescharacteristic
84C11×#117C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89#67004—22no—
90#67004Q814yescomplemented
91C2×#4326—21no—
92C2×#4324—21no—
93#66979C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66943—21no—
101#66941—21no—
102#66940—21no—
103#66940—21no—
104#66931—41no—
105#66930—41no—
106#66923—21no—
107#66922—21no—
108C4×Dic22—21no—
109C4×Dic22—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#107—21no—
114C11×#107D411yescharacteristic
115C11×#107D411yescharacteristic
116C11×#106—21no—
117C11×#106—21no—
118C11×#106D411yescharacteristic
119C11×#106D411yescharacteristic
120#66901—22no—
121#66899—21no—
122#66899D411yescharacteristic
123#66899D411yescharacteristic
124#66896—21no—
125#66896D411yescharacteristic
126#66896D411yescharacteristic
127C11⋊#95—41no—
128C11⋊#95—41no—
129#66888—22no—
130#66886—22no—
131#66880—21no—
132#66880—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135#66874—21no—
136#66874—21no—
137#66874—21no—
138#66874—21no—
139#66872—21no—
140#66872—21no—
141#66872—21no—
142#66872—21no—
143#66872—21no—
144#66871—21no—
145#66871—21no—
146#66871—21no—
147C4⋊(C11⋊C8)—21no—
148C4⋊(C11⋊C8)—21no—
149#66867—21no—
150C4×C11⋊C8—21no—
151#26403—111nomaximal, Sylow
152C11×#41—21no—
153C11×#41—21no—
154C11×#41C2×Q812yes—
155C11×#41#4112yes—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11C2×D411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—41no—
174C2×Dic22C2×Q812yes—
175C11×M16—24no—
176C11×M16—21no—
177C11×M16#4112yes—
178C2×C8×C11—24no—
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—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4—41no—
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C4⋊C4C2×D411yescharacteristic
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—41no—
201C42×C11—41no—
202C22⋊Dic11—21no—
203#4326—24no—
204#4324—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—41no—
208C4⋊Dic11C2×D411yescharacteristic
209C4⋊Dic11C2×D411yescharacteristic
210Dic11⋊C4—41no—
211Dic11⋊C4—41no—
212Dic11⋊C4—41no—
213Dic11⋊C4—41no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—41no—
218C4×Dic11—41no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318C2×Q812yes—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×D411yescharacteristic
232#3084—111no—
233#3082—111no—
234#2947—111no—
235#2913D1111yescharacteristic
236#2097—111no—
237#2089—111no—
238#2064—111no—
239#2061—111no—
240#1951—111no—
241#1922—111no—
242#1908—111no—
243#1882—111no—
244#1866—111no—
245#1860—111no—
246#1857—111no—
247C23×C11—21no—
248C23×C11H(5,𝔽2)11yescharacteristic
249Q8×C11—21no—
250Q8×C11C22⋊Q812yes—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—21no—
254D4×C11C22⋊Q812yes—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—81no—
265C2×C4×C11—81no—
266C2×C4×C11—161no—
267C2×C4×C11—161no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—81no—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288Dic22—161no—
289C8×C11—21no—
290C8×C11—22no—
291C8×C11—21no—
292C11⋊C8—22no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C2×#137—111no—
298C2×#131C2×D1111yescharacteristic
299#544—111no—
300#520C2×D1111yescharacteristic
301#520C2×D1111yescharacteristic
302#519—111no—
303#479—221no—
304#479—221no—
305#479—221no—
306#478—221no—
307#477—221no—
308#476—221no—
309#475—221no—
310#475—221no—
311#441—221no—
312#440—221no—
313C4×Q16—221no—
314C4×SD16—221no—
315C2×#108—111no—
316#428—21no—
317#428—21no—
318#428—111no—
319#428—111no—
320#428—111no—
321#428C2×D1111yescharacteristic
322#428C2×D1111yescharacteristic
323#427—21no—
324#427C2×D1111yescharacteristic
325C2×#107—21no—
326C2×#107C2×D1111yescharacteristic
327C2×#106—111no—
328#424—111no—
329#424—111no—
330C2×#104—111no—
331#419—111no—
332#417—111no—
333#416—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#101—111no—
337#405—111no—
338#391—111no—
339#382—111no—
340#343—111no—
341#343—111no—
342#343—111no—
343#341—111no—
344#339—111no—
345#339—111no—
346#339—111no—
347#336—111no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11#53911yescharacteristic
354C22×C11D4211yescharacteristic
355C22×C11#55411yescharacteristic
356C4×C11—22no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11C2×C22⋊Q811yescharacteristic
364C4×C11#52511yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11D4×Q811yescharacteristic
367Dic11—42no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372C2×#41C22×D1111yescharacteristic
373C22×Q8—111no—
374#137—114no—
375#137—222no—
376C2×Q16—221no—
377C2×SD16—221no—
378#131—22no—
379#131—22no—
380C2×M16—21no—
381C2×M16—111no—
382C2×M16—111no—
383C2×M16—111no—
384C2×M16C22×D1111yescharacteristic
385C22×C8—21no—
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388C4⋊Q8—221no—
389C4⋊Q8—221no—
390#125—221no—
391#125—221no—
392C22⋊Q8—441no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—221no—
396C4×Q8—221no—
397C4×Q8—221no—
398C4×Q8—221no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—41no—
402C4×D4—41no—
403#117—21no—
404#117—21no—
405#117—111no—
406#117—441no—
407#117C22×D1111yescharacteristic
408#117C22×D1111yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C42—111no—
415#108—222no—
416#107—21no—
417#107—21no—
418#107—21no—
419#107—21no—
420#107—221no—
421#107—221no—
422#107—221no—
423#107C22⋊D1111yescharacteristic
424#107C22⋊D1111yescharacteristic
425#106—21no—
426#106—21no—
427#106—221no—
428#106—221no—
429#106—221no—
430#106—221no—
431#106—221no—
432#106C22⋊D1111yescharacteristic
433#106C22⋊D1111yescharacteristic
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438#104—222no—
439#103—111no—
440#103—111no—
441#103—221no—
442#103—221no—
443#103—221no—
444#103—221no—
445#103—221no—
446#103—221no—
447#103—221no—
448#102—111no—
449#102—111no—
450#102—221no—
451#101—222no—
452#97—221no—
453C4×C8—221no—
454#95—441no—
455#95—441no—
456C2×C11—21no—
457C2×C11—21no—
458C2×C11—42no—
459C2×C11#244911yescharacteristic
460C2×C11#328911yescharacteristic
461C2×C11#329011yescharacteristic
462#41—21no—
463#41—21no—
464#41#433912yes—
465#41Q8×D1112yes—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—441no—
473C2×Q8D4×D1111yescharacteristic
474C2×D4—21no—
475C2×D4D4×D1111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4C23×D1111yescharacteristic
485Q16—224no—
486SD16—224no—
487M16—24no—
488M16—21no—
489M16—112no—
490M16—221no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495M16#433912yes—
496C2×C8—24no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8C2×C22⋊D1111yescharacteristic
508C2×C8C2×C22⋊D1111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—111no—
516C4⋊C4—111no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—441no—
520C4⋊C4—441no—
521C4⋊C4—441no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C4⋊C4C2×C22⋊D1111yescharacteristic
525C4⋊C4C2×C22⋊D1111yescharacteristic
526C4⋊C4C2×C22⋊D1111yescharacteristic
527C4⋊C4C2×C22⋊D1111yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—221no—
533C42—21no—
534C42—21no—
535C42—41no—
536C42—41no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—441no—
541C42—441no—
542C11#2640311yescharacteristic, complemented, Sylow
543C23—21no—
544C23#6703711yescharacteristic
545Q8—21no—
546Q8—222no—
547Q8—222no—
548Q8—441no—
549Q8—441no—
550Q8—1761no—
551Q8#6694912yes—
552D4—22no—
553D4—22no—
554D4—21no—
555D4#6694912yes—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—161no—
568C2×C4—161no—
569C2×C4—222no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—881no—
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4C2×Q8×D1111yescharacteristic
583C2×C4#6704011yescharacteristic
584C2×C4C22×C22⋊D1111yescharacteristic
585C8—21no—
586C8—22no—
587C8—21no—
588C8—221no—
589C8—221no—
590C8—222no—
591C8—441no—
592C8—441no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22#1062304211yescharacteristic
599C22#1062304611yescharacteristic
600C22D4×C22⋊D1111yescharacteristic
601C4—22no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—442no—
609C4—441no—
610C4—441no—
611C4—881no—
612C4—881no—
613C4#1062303811yescharacteristic
614C4C2×#6694911yescharacteristic
615C4#1062332211yescharacteristic
616C4Q8×C22⋊D1111yescharacteristic
617C2—21no—
618C2—21no—
619C2—42no—
620C2#1307242511yescharacteristic
621C2#1308038711yescharacteristic
622C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2913C2
socleC22×C11D42
prime radicalC2×C11×#41C23
hypercenter#2913D11
hypocenterC11#26403
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #13078461C2semidirect
4. #13070161C2semidirect
5. #13070122C2semidirect
6. #13069980C2semidirect
7. #13069964C2semidirect
8. #13069393C2semidirect
9. #13069217C2semidirect
14. #13068829C2semidirect
90. #67004Q8semidirect
542. C11#26403semidirect

Maximal subgroups

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

subgroupindex
#130784782
#130784612
#130774552
#130701612
#130701222
#130699802
#130699642
#130693932
#130692172
#130691312
#130689852
#130688912
#130688492
#130688292
C11×#29132
#2640311