Finite Group Databasebeta

← #14812698

Subgroups — #14812698

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079156C211yesmaximal, characteristic, complemented
2#13078478C211yesmaximal, characteristic
3#13078467C211yesmaximal, characteristic
4#13070129C211yesmaximal, characteristic, complemented
5#13070124C211yesmaximal, characteristic, complemented
6#13069964C211yesmaximal, characteristic, complemented
7#13069959C211yesmaximal, characteristic, complemented
8#13069394C211yesmaximal, characteristic, complemented
9#13069370C211yesmaximal, characteristic, complemented
10#13068849C211yesmaximal, characteristic
11#13068842C211yesmaximal, characteristic
12#13068781C211yesmaximal, characteristic, complemented
13#13068680C211yesmaximal, characteristic
14#13068458C211yesmaximal, characteristic
15C11×#2912C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17C11×#520C2211yescharacteristic
18C11×#520C2211yescharacteristic
19#10623050C2211yescharacteristic
20#10623050C2211yescharacteristic
21C11×#428—21no—
22C11×#428—21no—
23C11×#428C2211yescharacteristic
24C11×#428C2211yescharacteristic
25C11×#427—21no—
26C11×#427C2211yescharacteristic
27C2×C11×#106—21no—
28C2×C11×#106C2211yescharacteristic
29C2×#66901C2211yescharacteristic
30#10622846C2211yescharacteristic
31#10622845C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66883C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35#10622714C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37#10622635—21no—
38#10622635—21no—
39#10622634—21no—
40#10622633—21no—
41#10622622—21no—
42#10622622—21no—
43#10622621—21no—
44#10622620—21no—
45#10622612C2211yescharacteristic
46#10622612C2211yescharacteristic
47#10622608C2211yescharacteristic
48#10622608C2211yescharacteristic
49#10622590C2211yescharacteristic
50#10622589C2211yescharacteristic
51#10622577C2211yescharacteristic
52#10622577C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622491—21no—
56#10622487—21no—
57#10622469—21no—
58#10622469—21no—
59#10622196C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131Q814yescomplemented
70C2×C11×M16—21no—
71C2×C11×M16C2311yescharacteristic
72C22×C8×C11—21no—
73C22×C8×C11C2311yescharacteristic
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11—41no—
79C4×D4×C11—41no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117C2311yescharacteristic
83C11×#117C2311yescharacteristic
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88#66979C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—41no—
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66943—21no—
98#66943—21no—
99#66941—21no—
100#66941—21no—
101#66931—41no—
102#66931—41no—
103#66923—21no—
104#66923—21no—
105#66922—21no—
106#66922—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×#107D411yescharacteristic
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×#106—21no—
115C11×#106D411yescharacteristic
116C11×#106D411yescharacteristic
117#66901Q814yescomplemented
118#66899—21no—
119#66899—21no—
120#66899D411yescharacteristic
121#66899D411yescharacteristic
122#66896—21no—
123#66896—21no—
124#66896D411yescharacteristic
125#66896D411yescharacteristic
126C11⋊#95—41no—
127#66883—22no—
128#66882—21no—
129#66882—21no—
130#66879—21no—
131#66879—22no—
132C8×Dic11—21no—
133#66872—21no—
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66872—21no—
138#66872—21no—
139#66871—21no—
140#66871—21no—
141#66871—21no—
142#66871—21no—
143#66871—21no—
144#66871—21no—
145C4⋊(C11⋊C8)—21no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148C4⋊(C11⋊C8)—21no—
149#26084—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—41no—
161C22×C4×C11—41no—
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C2×Dic22—41no—
167C2×Dic22—41no—
168C11×M16—24no—
169C11×M16—21no—
170C11×M16C2×Q812yes—
171C2×C8×C11—24no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×Q812yes—
176C2×C8×C11#4112yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D411yescharacteristic
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—41no—
190C11×C22⋊C4—41no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—41no—
194C42×C11—41no—
195C22⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—41no—
201C4⋊Dic11—41no—
202C4⋊Dic11C2×D411yescharacteristic
203C4⋊Dic11C2×D411yescharacteristic
204Dic11⋊C4—41no—
205Dic11⋊C4—41no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208Dic11⋊C4—82no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11C2×Q812yes—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318C2×Q812yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C2×D411yescharacteristic
224C2×C11⋊C8C2×D411yescharacteristic
225#3164—111no—
226#3084—111no—
227#3083—111no—
228#2912D1111yescharacteristic
229#2090—111no—
230#2089—111no—
231#2061—111no—
232#2060—111no—
233#1951—111no—
234#1946—111no—
235#1860—111no—
236#1859—111no—
237#1847—111no—
238#1816—111no—
239#1765—111no—
240C23×C11—21no—
241C23×C11H(5,𝔽2)11yescharacteristic
242Q8×C11—21no—
243Q8×C11C4⋊Q812yes—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—21no—
247D4×C11C4⋊Q812yes—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—81no—
258C2×C4×C11—81no—
259C2×C4×C11—161no—
260C2×C4×C11—161no—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—81no—
275C2×Dic11—81no—
276Dic22—161no—
277Dic22—161no—
278C8×C11—22no—
279C8×C11C22⋊Q812yes—
280C8×C11C22⋊Q812yes—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C2×#131C2×D1111yescharacteristic
287#544—111no—
288#544—111no—
289#520C2×D1111yescharacteristic
290#520C2×D1111yescharacteristic
291#501—221no—
292#501—221no—
293#500—221no—
294#499—221no—
295#479—221no—
296#479—221no—
297#478—221no—
298#478—221no—
299#477—221no—
300#476—221no—
301#475—221no—
302#474—221no—
303C2×#108—111no—
304#428—21no—
305#428—21no—
306#428—111no—
307#428—111no—
308#428—111no—
309#428—111no—
310#428C2×D1111yescharacteristic
311#428C2×D1111yescharacteristic
312#427—21no—
313#427C2×D1111yescharacteristic
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—21no—
317C2×#106—111no—
318C2×#106C2×D1111yescharacteristic
319#424—111no—
320#424—111no—
321C2×#104—111no—
322#417—111no—
323#417—111no—
324#416—111no—
325#405—111no—
326C2×#97—111no—
327#384—111no—
328#382—111no—
329#343—111no—
330#343—111no—
331#343—111no—
332#343—111no—
333#341—111no—
334#339—111no—
335#339—111no—
336#339—111no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11#54411yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11#55411yescharacteristic
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
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—42no—
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361C2×#41C22×D1111yescharacteristic
362#131—22no—
363#131Dic2214yescomplemented
364C2×M16—21no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—111no—
368C2×M16C22×D1111yescharacteristic
369C22×C8—21no—
370C22×C8—111no—
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—221no—
373C4⋊Q8—221no—
374C4⋊Q8—221no—
375C4⋊Q8—221no—
376#125—221no—
377#125—221no—
378#125—221no—
379#125—221no—
380C22⋊Q8—441no—
381C22⋊Q8—441no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—41no—
387C4×D4—41no—
388#117—21no—
389#117—21no—
390#117—111no—
391#117C22×D1111yescharacteristic
392#117C22×D1111yescharacteristic
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—441no—
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C42—111no—
401#108—222no—
402#107—21no—
403#107—21no—
404#107—221no—
405#107—221no—
406#107—221no—
407#107—221no—
408#107—221no—
409#107—221no—
410#107—221no—
411#107—221no—
412#107C22⋊D1111yescharacteristic
413#107C22⋊D1111yescharacteristic
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—221no—
419#106—221no—
420#106—221no—
421#106—221no—
422#106—221no—
423#106—221no—
424#106C22⋊D1111yescharacteristic
425#106C22⋊D1111yescharacteristic
426C4⋊C8—221no—
427C4⋊C8—221no—
428C4⋊C8—221no—
429C4⋊C8—221no—
430#104—114no—
431#103—111no—
432#103—111no—
433#103—221no—
434#103—221no—
435#102—111no—
436#102—111no—
437#102—221no—
438#102—221no—
439#97—222no—
440#97—221no—
441C4×C8—221no—
442#95—441no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—42no—
446C2×C11#244011yescharacteristic
447C2×C11#328811yescharacteristic
448C2×C11#328911yescharacteristic
449#41—21no—
450#41—21no—
451#41C2×Dic2212yes—
452#41Q8×D1112yes—
453C2×Q8—441no—
454C2×Q8—441no—
455C2×Q8D4×D1111yescharacteristic
456C2×D4—21no—
457C2×D4D4×D1111yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C23×D1111yescharacteristic
467M16—21no—
468M16—24no—
469M16—112no—
470M16—221no—
471M16—221no—
472M16—221no—
473M16—221no—
474M16—221no—
475M16C2×Dic2212yes—
476C2×C8—21no—
477C2×C8—24no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8C2×Dic2212yes—
486C2×C8#433912yes—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4—441no—
504C4⋊C4—441no—
505C4⋊C4—441no—
506C4⋊C4—441no—
507C4⋊C4—882no—
508C4⋊C4C2×C22⋊D1111yescharacteristic
509C4⋊C4C2×C22⋊D1111yescharacteristic
510C4⋊C4C2×C22⋊D1111yescharacteristic
511C4⋊C4C2×C22⋊D1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—221no—
517C42—21no—
518C42—21no—
519C42—41no—
520C42—41no—
521C42—112no—
522C42—221no—
523C42—221no—
524C11#2608411yescharacteristic, complemented, Sylow
525C23—21no—
526C23#6703711yescharacteristic
527Q8—21no—
528Q8—1761no—
529Q8—1761no—
530Q8#6694112yes—
531D4—22no—
532D4—22no—
533D4—21no—
534D4#6694112yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—161no—
547C2×C4—161no—
548C2×C4—222no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—881no—
556C2×C4—881no—
557C2×C4C22×Dic2211yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×Q8×D1111yescharacteristic
561C2×C4#6704011yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—22no—
564C8—221no—
565C8—221no—
566C8—222no—
567C8—441no—
568C8—441no—
569C8#6697712yes—
570C8#6697712yes—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22#1062303111yescharacteristic
577C22#1062304211yescharacteristic
578C22D4×C22⋊D1111yescharacteristic
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—442no—
587C4—441no—
588C4—441no—
589C4—881no—
590C4—881no—
591C4C2×#6694111yescharacteristic
592C4#1062303811yescharacteristic
593C4C2×#6697711yescharacteristic
594C4Q8×C22⋊D1111yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2#1307231211yescharacteristic
599C2#1308037811yescharacteristic
600C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2912C2
socleC22×C11D42
prime radicalC2×C11×#41C23
hypercenter#2912D11
hypocenterC11#26084
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2912

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
4. #13070129C2semidirect
5. #13070124C2semidirect
6. #13069964C2semidirect
7. #13069959C2semidirect
8. #13069394C2semidirect
9. #13069370C2semidirect
12. #13068781C2semidirect
69. C11×#131Q8semidirect
117. #66901Q8semidirect
363. #131Dic22semidirect
524. C11#26084semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130784782
#130784672
#130701292
#130701242
#130699642
#130699592
#130693942
#130693702
#130688492
#130688422
#130687812
#130686802
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C11×#29122
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