Finite Group Databasebeta

← #14812692

Subgroups — #14812692

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079154C211yesmaximal, characteristic, complemented
2#13078471C211yesmaximal, characteristic
3#13078467C211yesmaximal, characteristic
4#13077214C211yesmaximal, characteristic
5#13070125C211yesmaximal, characteristic, complemented
6#13070124C211yesmaximal, characteristic, complemented
7#13069961C211yesmaximal, characteristic, complemented
8#13069960C211yesmaximal, characteristic, complemented
9#13069400C211yesmaximal, characteristic, complemented
10#13069363C211yesmaximal, characteristic, complemented
11#13068844C211yesmaximal, characteristic
12#13068775C211yesmaximal, characteristic, complemented
13#13068678C211yesmaximal, characteristic
14#13068454C211yesmaximal, characteristic
15C11×#1859C211yesmaximal, characteristic
16C11×#520C2211yescharacteristic
17#10623358C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19#10623050C2211yescharacteristic
20#10623031C2211yescharacteristic
21C11×#428C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#417C2211yescharacteristic
24C11×#384C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622845C2211yescharacteristic
27C2×#66886C2211yescharacteristic
28#10622735C2211yescharacteristic
29#10622734C2211yescharacteristic
30#10622734C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622635—21no—
33#10622634—21no—
34#10622622—21no—
35#10622620—21no—
36#10622612C2211yescharacteristic
37#10622611—21no—
38#10622611C2211yescharacteristic
39#10622608—21no—
40#10622608C2211yescharacteristic
41#10622577—21no—
42#10622577C2211yescharacteristic
43#10622577C2211yescharacteristic
44C2×#66871—21no—
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622548C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622489—21no—
52#10622487—21no—
53#10622471—21no—
54#10622469—21no—
55#10622412—21no—
56#10622407—21no—
57#10622376—21no—
58#10622372—21no—
59C11×#343C2211yescharacteristic
60C11×#339C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622168C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C4×Q8×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—41no—
73C11×#117—21no—
74C11×#117C2311yescharacteristic
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80#67001—22no—
81#67001Q814yescomplemented
82Q8×Dic11—21no—
83D4×Dic11—21no—
84D4×Dic11—41no—
85#66979—21no—
86#66979C2311yescharacteristic
87#66979C2311yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—41no—
93C2×#4318—21no—
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66943—21no—
100#66943—21no—
101#66943—21no—
102#66941—21no—
103#66941—21no—
104#66941—21no—
105#66931—41no—
106#66923—21no—
107#66922—21no—
108C11×#107—21no—
109C11×#106—21no—
110C11×#104Q814yescomplemented
111C11×#103—21no—
112C11×#102—21no—
113#66899—21no—
114#66899D411yescharacteristic
115#66899D411yescharacteristic
116#66896—21no—
117#66896D411yescharacteristic
118#66896D411yescharacteristic
119#66886—22no—
120#66882—21no—
121#66882—21no—
122#66881—21no—
123#66881—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128#66872—21no—
129#66872—21no—
130#66872—21no—
131#66872D411yescharacteristic
132#66872D411yescharacteristic
133#66871—21no—
134#66871—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140#66871—21no—
141#66871—21no—
142#66871—21no—
143#66871—21no—
144#66871D411yescharacteristic
145#66871D411yescharacteristic
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148C4×C11⋊C8—22no—
149#26083—111nomaximal, Sylow
150C11×#41—21no—
151C11×#41—21no—
152C11×#41C2×Q812yes—
153C11×#41C2×Q812yes—
154C2×Q8×C11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—41no—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—41no—
166C2×Dic22—41no—
167C2×Dic22—41no—
168C11×M16—21no—
169C11×M16—21no—
170C11×M16—21no—
171C11×M16C2×Q812yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—82no—
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11C2×Q812yes—
188C22⋊Dic11—21no—
189C22⋊Dic11—21no—
190C22⋊Dic11—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—41no—
196C4⋊Dic11—41no—
197C4⋊Dic11—41no—
198C4⋊Dic11—82no—
199C4⋊Dic11C2×D411yescharacteristic
200C4⋊Dic11C2×D411yescharacteristic
201C4⋊Dic11C2×D411yescharacteristic
202C4⋊Dic11C2×D411yescharacteristic
203Dic11⋊C4—41no—
204Dic11⋊C4—41no—
205Dic11⋊C4—41no—
206Dic11⋊C4—41no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—41no—
210#4318—24no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318C2×Q812yes—
215C2×C11⋊C8—24no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222C2×C11⋊C8C2×D411yescharacteristic
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×Q812yes—
225C2×C11⋊C8#4112yes—
226#3164—111no—
227#3083—111no—
228#3083—111no—
229#2913—111no—
230#2089—111no—
231#2089—111no—
232#2060—111no—
233#2060—111no—
234#1952—111no—
235#1945—111no—
236#1859—111no—
237#1859D1111yescharacteristic
238#1845—111no—
239#1816—111no—
240#1764—111no—
241C23×C11—21no—
242C23×C11H(5,𝔽2)11yescharacteristic
243Q8×C11—21no—
244Q8×C11C4⋊Q812yes—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—21no—
248D4×C11C4⋊Q812yes—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—81no—
260C2×C4×C11—81no—
261C2×C4×C11—161no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C22×Q811yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—81no—
275C2×Dic11—81no—
276C2×Dic11—161no—
277Dic22—161no—
278Dic22—161no—
279C8×C11—22no—
280C8×C11—41no—
281C11⋊C8—22no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8C22⋊Q812yes—
286C11⋊C8C22⋊Q812yes—
287C2×#131—111no—
288#544—111no—
289#544—111no—
290#520—111no—
291#520C2×D1111yescharacteristic
292#501—221no—
293#501—221no—
294#500—221no—
295#499—221no—
296#479—221no—
297#479—221no—
298#478—221no—
299#478—221no—
300#477—221no—
301#477—221no—
302#474—221no—
303#474—221no—
304C2×#108—111no—
305#428—111no—
306#428—111no—
307#428—111no—
308#428—111no—
309#428—111no—
310#428—221no—
311#428—221no—
312#428C2×D1111yescharacteristic
313#427—111no—
314#427—221no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#107—221no—
320#424—111no—
321#424—111no—
322C2×#104C2×D1111yescharacteristic
323#417—111no—
324#417C2×D1111yescharacteristic
325#416—111no—
326#405—111no—
327C2×C4×C8—111no—
328#384—111no—
329#384C2×D1111yescharacteristic
330#343—111no—
331#343—111no—
332#343—111no—
333#343C2×D1111yescharacteristic
334#341—111no—
335#339—111no—
336#339—111no—
337#339C2×D1111yescharacteristic
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11#54411yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11#55411yescharacteristic
346C4×C11—24no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×C22⋊Q811yescharacteristic
353C4×C11C2×C4⋊Q811yescharacteristic
354C4×C11#54711yescharacteristic
355C4×C11D4×Q811yescharacteristic
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—81no—
361Dic11—81no—
362C2×#41C22×D1111yescharacteristic
363#131—114no—
364#131—222no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—221no—
368C2×M16C22×D1111yescharacteristic
369C2×M16C22×D1111yescharacteristic
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C4⋊Q8—221no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376C4⋊Q8—221no—
377#125—221no—
378#125—221no—
379#125—221no—
380#125—221no—
381C22⋊Q8—441no—
382C22⋊Q8—441no—
383C4×Q8—21no—
384C4×Q8—221no—
385C4×D4—21no—
386C4×D4—41no—
387C4×D4—221no—
388C4×D4—441no—
389#117—21no—
390#117—111no—
391#117—111no—
392#117—221no—
393#117C22×D1111yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—441no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403#108—222no—
404#107—21no—
405#107—111no—
406#107—111no—
407#107—221no—
408#107—221no—
409#107—221no—
410#107—221no—
411#107—221no—
412#107—221no—
413#107—221no—
414#107—221no—
415#107—221no—
416#107—221no—
417#107—221no—
418#107—221no—
419#107—221no—
420#106—21no—
421#106—111no—
422#106—111no—
423#106—221no—
424#106—221no—
425#106—221no—
426#106—221no—
427#106—221no—
428C4⋊C8—221no—
429C4⋊C8—221no—
430C4⋊C8—221no—
431C4⋊C8—221no—
432#104Dic2214yescomplemented
433#103—21no—
434#103—111no—
435#103—111no—
436#103—221no—
437#102—21no—
438#102—111no—
439#102—111no—
440#102—221no—
441#97—221no—
442C4×C8—222no—
443C4×C8—221no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—42no—
447C2×C11#244011yescharacteristic
448C2×C11#329211yescharacteristic
449C2×C11#329311yescharacteristic
450#41—21no—
451#41—21no—
452#41C2×Dic2212yes—
453#41Q8×D1112yes—
454C2×Q8—441no—
455C2×Q8—441no—
456C2×Q8D4×D1111yescharacteristic
457C2×D4—21no—
458C2×D4D4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—441no—
467C22×C4C23×D1111yescharacteristic
468M16—21no—
469M16—21no—
470M16—21no—
471M16—112no—
472M16—224no—
473M16—221no—
474M16—221no—
475M16—221no—
476M16C2×Dic2212yes—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—224no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—82no—
496C4⋊C4—111no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C4⋊C4—441no—
506C4⋊C4—441no—
507C4⋊C4—441no—
508C4⋊C4—441no—
509C4⋊C4—441no—
510C4⋊C4—441no—
511C4⋊C4—882no—
512C4⋊C4D4×D1111yescharacteristic
513C4⋊C4D4×D1111yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—441no—
519C42—21no—
520C42—21no—
521C42—41no—
522C42—221no—
523C42—221no—
524C42—441no—
525C42C2×Dic2212yes—
526C11#2608311yescharacteristic, complemented, Sylow
527C23—21no—
528C23#6703711yescharacteristic
529Q8—21no—
530Q8—1761no—
531Q8—1761no—
532Q8#6694112yes—
533D4—22no—
534D4—22no—
535D4—21no—
536D4#6694112yes—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—161no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—881no—
557C2×C4—881no—
558C2×C4—1761no—
559C2×C4C22×Dic2211yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×Q8×D1111yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#6704311yescharacteristic
565C8—22no—
566C8—41no—
567C8—112no—
568C8—112no—
569C8—222no—
570C8—221no—
571C8—221no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22#1062307011yescharacteristic
579C22#1062312111yescharacteristic
580C22#1062315411yescharacteristic
581C4—24no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4—441no—
591C4—881no—
592C4—881no—
593C4C2×#6694111yescharacteristic
594C4D4×Dic2211yescharacteristic
595C4D11×C22⋊Q811yescharacteristic
596C4#1062318611yescharacteristic
597C2—21no—
598C2—21no—
599C2—42no—
600C2#1307231711yescharacteristic
601C2#1308041211yescharacteristic
602C2#1308041711yescharacteristic
subgroupG/H
centerC22#10623121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1859C2
socleC22×C11D42
prime radicalC2×C11×#41C23
hypercenter#1859D11
hypocenterC11#26083
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1859

Complements

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

NH ≅ G/Ntype
1. #13079154C2semidirect
5. #13070125C2semidirect
6. #13070124C2semidirect
7. #13069961C2semidirect
8. #13069960C2semidirect
9. #13069400C2semidirect
10. #13069363C2semidirect
12. #13068775C2semidirect
81. #67001Q8semidirect
110. C11×#104Q8semidirect
432. #104Dic22semidirect
526. C11#26083semidirect

Maximal subgroups

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

subgroupindex
#130791542
#130784712
#130784672
#130772142
#130701252
#130701242
#130699612
#130699602
#130694002
#130693632
#130688442
#130687752
#130686782
#130684542
C11×#18592
#2608311