Finite Group Databasebeta

← #14812700

Subgroups — #14812700

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#13078474C211yesmaximal, characteristic
2#13078463C211yesmaximal, characteristic
3#13077208C211yesmaximal, characteristic
4#13070129C211yesmaximal, characteristic, complemented
5#13070124C211yesmaximal, characteristic, complemented
6#13069963C211yesmaximal, characteristic, complemented
7#13069958C211yesmaximal, characteristic, complemented
8#13069396C211yesmaximal, characteristic, complemented
9#13069370C211yesmaximal, characteristic, complemented
10#13068846C211yesmaximal, characteristic
11#13068839C211yesmaximal, characteristic
12#13068783C211yesmaximal, characteristic, complemented
13#13068681C211yesmaximal, characteristic
14#13068462C211yesmaximal, characteristic
15C11×#3164C211yesmaximal, characteristic, complemented
16C11×#544C2211yescharacteristic
17C11×#544C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623054C2211yescharacteristic
20#10623054C2211yescharacteristic
21C11×#501—21no—
22C11×#501—21no—
23C11×#500—21no—
24C11×#499—21no—
25C11×#428C2211yescharacteristic
26C11×#428C2211yescharacteristic
27C11×#427C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C11×#405C2211yescharacteristic
30C2×#66889C2211yescharacteristic
31C2×#66883C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622707—21no—
35#10622704—21no—
36#10622700—21no—
37#10622697—21no—
38#10622679—21no—
39#10622679—21no—
40#10622676—21no—
41#10622676—21no—
42#10622615C2211yescharacteristic
43#10622612C2211yescharacteristic
44#10622612C2211yescharacteristic
45#10622608C2211yescharacteristic
46#10622608C2211yescharacteristic
47#10622608C2211yescharacteristic
48#10622608C2211yescharacteristic
49#10622590C2211yescharacteristic
50#10622589C2211yescharacteristic
51#10622579C2211yescharacteristic
52#10622579C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55#10622494—21no—
56#10622494—21no—
57#10622473—21no—
58D11×#106—21no—
59#10622196C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622170C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622168C2211yescharacteristic
66#10622168C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×#125—21no—
75C11×#125—21no—
76C11×#125—21no—
77C11×#125—21no—
78C11×C22⋊Q8—41no—
79C11×C22⋊Q8—41no—
80C11×#117C2311yescharacteristic
81C11×#117C2311yescharacteristic
82C11×#117C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—41no—
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318C2311yescharacteristic
90C2×#4318C2311yescharacteristic
91C2×#4318C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66954—22no—
94#66954Q814yescomplemented
95C2×#4313—21no—
96C2×C8×D11—21no—
97#66945—21no—
98#66945—21no—
99C4⋊C4×D11—21no—
100C4⋊C4×D11—21no—
101(C22⋊D11)⋊C4—41no—
102(C22⋊D11)⋊C4—41no—
103C4×D44—21no—
104C4×D44—21no—
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107—21no—
110C11×#107—21no—
111C11×#107D411yescharacteristic
112C11×#107D411yescharacteristic
113C11×#106—21no—
114C11×#106—21no—
115C11×#106D411yescharacteristic
116C11×#106D411yescharacteristic
117C11×#97—21no—
118C4×C8×C11—21no—
119C11⋊#95—41no—
120#66889Q814yescomplemented
121#66883—22no—
122#66881—21no—
123#66881—21no—
124#66879—22no—
125#66874—21no—
126#66874—21no—
127#66874D411yescharacteristic
128#66874D411yescharacteristic
129#66873—21no—
130#66873—21no—
131#66873D411yescharacteristic
132#66873D411yescharacteristic
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
150C2×Q8×C11—41no—
151C2×Q8×C11—41no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159#4339—21no—
160#4339—21no—
161#4339C2×Q812yes—
162#4339C2×Q812yes—
163C2×D44C2×D411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—41no—
166C2×C4×D11—41no—
167C2×Dic22C2×D411yescharacteristic
168C11×M16—21no—
169C11×M16C2×Q812yes—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×Q812yes—
174C2×C8×C11#4112yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—41no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203Dic11⋊C4—41no—
204Dic11⋊C4—41no—
205Dic11⋊C4—82no—
206C4×Dic11—21no—
207C4×Dic11—41no—
208C4×Dic11—41no—
209C4×Dic11C2×Q812yes—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318C2×Q812yes—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C2×D411yescharacteristic
222C2×C11⋊C8C2×D411yescharacteristic
223#4313—24no—
224C8×D11—24no—
225#3164D1111yescharacteristic, complemented
226#3084—111no—
227#3083—111no—
228#2912—111no—
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×C11H(5,𝔽2)11yescharacteristic
241C22×D11—21no—
242Q8×C11—161no—
243Q8×C11—161no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C22⋊D11—22no—
261C22⋊D11—22no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—81no—
269C2×Dic11—81no—
270D44—21no—
271D44C4⋊Q812yes—
272C4×D11—22no—
273C4×D11—22no—
274C4×D11—161no—
275C4×D11—161no—
276Dic22—21no—
277Dic22C4⋊Q812yes—
278C8×C11—22no—
279C8×C11C22⋊Q812yes—
280C8×C11C22⋊Q812yes—
281C11⋊C8—22no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C2×#131—111no—
287#544C2×D1111yescharacteristic
288#544C2×D1111yescharacteristic
289#520—111no—
290#520—111no—
291#501—21no—
292#501—21no—
293#500—21no—
294#499—21no—
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—111no—
305#428—111no—
306#428—111no—
307#428—111no—
308#428—221no—
309#428—221no—
310#428C2×D1111yescharacteristic
311#428C2×D1111yescharacteristic
312#427—221no—
313#427C2×D1111yescharacteristic
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×#106—111no—
317C2×#106—111no—
318C2×#106—221no—
319#424—111no—
320#424—111no—
321C2×#104—111no—
322#417—111no—
323#417—111no—
324#416—111no—
325#405C2×D1111yescharacteristic
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#54411yescharacteristic
340C22×C11D4211yescharacteristic
341C22×C11#55411yescharacteristic
342C2×D11—22no—
343C2×D11—41no—
344C2×D11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11C2×C22⋊Q811yescharacteristic
354C4×C11C2×C4⋊Q811yescharacteristic
355C4×C11#54711yescharacteristic
356C4×C11D4×Q811yescharacteristic
357Dic11—22no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361C2×#41—111no—
362#131—114no—
363#131—222no—
364C2×M16—111no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—221no—
368C2×M16C22×D1111yescharacteristic
369C22×C8—111no—
370C22×C8—221no—
371C22×C8C22×D1111yescharacteristic
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125—21no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382C4×Q8—221no—
383C4×Q8—221no—
384C4×D4—221no—
385C4×D4—221no—
386C4×D4—441no—
387C4×D4—441no—
388#117—221no—
389#117—221no—
390#117C22×D1111yescharacteristic
391#117C22×D1111yescharacteristic
392#117C22×D1111yescharacteristic
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
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—21no—
405#107—21no—
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—221no—
417#106—221no—
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—21no—
440#97—222no—
441C4×C8—21no—
442#95—441no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11#244011yescharacteristic
446C2×C11#328811yescharacteristic
447C2×C11#328911yescharacteristic
448D11—42no—
449#41—112no—
450#41—112no—
451#41—221no—
452#41—221no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—111no—
456C2×D4—111no—
457C2×D4—221no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4C23×D1111yescharacteristic
467M16—21no—
468M16—112no—
469M16—221no—
470M16—224no—
471M16—221no—
472M16—221no—
473M16—221no—
474M16—221no—
475M16Q8×D1112yes—
476C2×C8—21no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—224no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8Q8×D1112yes—
486C2×C8#434312yes—
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—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—441no—
504C4⋊C4—441no—
505C4⋊C4—882no—
506C4⋊C4D4×D1111yescharacteristic
507C4⋊C4D4×D1111yescharacteristic
508C4⋊C4C2×C22⋊D1111yescharacteristic
509C4⋊C4C2×C22⋊D1111yescharacteristic
510C4⋊C4C2×C22⋊D1111yescharacteristic
511C4⋊C4C2×C22⋊D1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—441no—
516C22⋊C4—441no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—112no—
521C42—221no—
522C42—441no—
523C42—441no—
524C11#2608411yescharacteristic, complemented, Sylow
525C23—221no—
526C23#6703711yescharacteristic
527Q8—112no—
528Q8—161no—
529Q8—161no—
530Q8—221no—
531D4—112no—
532D4—222no—
533D4—222no—
534D4—221no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—221no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—881no—
554C2×C4—881no—
555C2×C4—1761no—
556C2×C4—1761no—
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4C2×Q8×D1111yescharacteristic
560C2×C4C2×#434311yescharacteristic
561C2×C4#6704011yescharacteristic
562C2×C4C22×C22⋊D1111yescharacteristic
563C8—22no—
564C8—221no—
565C8—221no—
566C8—222no—
567C8—441no—
568C8—441no—
569C8#6699912yes—
570C8#6699912yes—
571C22—21no—
572C22—21no—
573C22—222no—
574C22—441no—
575C22—441no—
576C22#1062326011yescharacteristic
577C22#1062326111yescharacteristic
578C22D4×C22⋊D1111yescharacteristic
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—222no—
588C4—442no—
589C4—881no—
590C4—881no—
591C4D11×C4⋊Q811yescharacteristic
592C4#1062325711yescharacteristic
593C4C2×#6699911yescharacteristic
594C4Q8×C22⋊D1111yescharacteristic
595C2—21no—
596C2—21no—
597C2—442no—
598C2#1307231411yescharacteristic
599C2#1308038011yescharacteristic
600C2#1308038711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3164C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#3164D11
hypocenterC11#26084
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3164

Complements

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

NH ≅ G/Ntype
4. #13070129C2semidirect
5. #13070124C2semidirect
6. #13069963C2semidirect
7. #13069958C2semidirect
8. #13069396C2semidirect
9. #13069370C2semidirect
12. #13068783C2semidirect
15. C11×#3164C2semidirect
94. #66954Q8semidirect
120. #66889Q8semidirect
225. #3164D11semidirect
524. C11#26084semidirect

Maximal subgroups

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

subgroupindex
#130784742
#130784632
#130772082
#130701292
#130701242
#130699632
#130699582
#130693962
#130693702
#130688462
#130688392
#130687832
#130686812
#130684622
C11×#31642
#2608411