Finite Group Databasebeta

← #14737761

Subgroups — #14737761

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078938C211yesmaximal, characteristic, complemented
2#13078778C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068072C211yesmaximal, characteristic, complemented
5#13068065C211yesmaximal, characteristic, complemented
6#13068058C211yesmaximal, characteristic, complemented
7#13068051C211yesmaximal, characteristic, complemented
8#13068044C211yesmaximal, characteristic, complemented
9#13068037C211yesmaximal, characteristic, complemented
10#13068030C211yesmaximal, characteristic, complemented
11#13068023C211yesmaximal, characteristic, complemented
12#13067377C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067321C211yesmaximal, characteristic, complemented
15C11×#3115C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#482—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C11×#442—21no—
26C11×#440—21no—
27C11×#432C2211yescharacteristic
28#10622852—21no—
29#10622846—21no—
30#10622846—21no—
31#10622694C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622683C2211yescharacteristic
34#10622683C2211yescharacteristic
35#10622669—21no—
36#10622669—21no—
37#10622644C2211yescharacteristic
38#10622643—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622631—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622609—21no—
50#10622539C2211yescharacteristic
51#10622538—21no—
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#124—21no—
74C11×#121—21no—
75C11×#121—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4326—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8D411yescharacteristic
96C22×C11⋊C8D411yescharacteristic
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112#66899—21no—
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66874—21no—
127#66874—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19278—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—42no—
148C11×#41—42no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×SD16—42no—
167C11×D8—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—42no—
190#4324—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—41no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3131—111no—
211#3116—111no—
212#3115D1111yescharacteristic
213C8×#41—111no—
214#1684—111no—
215#1683—111no—
216#1682—111no—
217#1681—111no—
218#1680—111no—
219#1679—111no—
220#1678—111no—
221#1677—111no—
222#1568—111no—
223#1554—111no—
224#1553—111no—
225C23×C11—21no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11#13512yes—
232D4×C11—24no—
233D4×C11—21no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—81no—
239D4×C11—82no—
240D4×C11#13512yes—
241C2×C4×C11—24no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—82no—
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×Dic11—41no—
262C2×Dic11—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—81no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#533—111no—
277#532C2×D1111yescharacteristic
278C4×#41C2×D1111yescharacteristic
279#488—221no—
280#488—221no—
281#487—111no—
282#487—111no—
283#486—111no—
284#486—111no—
285#485—221no—
286#482—21no—
287#477—111no—
288#476—111no—
289#475C2×D1111yescharacteristic
290#474C2×D1111yescharacteristic
291#462—111no—
292#461—111no—
293#460C2×D1111yescharacteristic
294#459C2×D1111yescharacteristic
295#452—221no—
296#449—21no—
297C8×Q8—111no—
298C8×Q8—111no—
299#442—21no—
300#441—221no—
301#440—21no—
302#440—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—221no—
306C8×D4—221no—
307#432—111no—
308#432C2×D1111yescharacteristic
309#431—111no—
310#431—221no—
311#416—221no—
312#416—221no—
313C2×C4×C8—111no—
314C2×C4×C8—221no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319#333—111no—
320#333—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#331—111no—
326#331—111no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—22no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11C2×#12111yescharacteristic
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11C2×#13511yescharacteristic
346C4×C11C2×#13511yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57511yescharacteristic
349Dic11—81no—
350Dic11—81no—
351C2×#41—21no—
352C2×#41C22⋊D1111yescharacteristic
353C2×Q16—221no—
354C2×SD16—21no—
355C2×SD16—221no—
356C2×D8—21no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8C22×D1111yescharacteristic
364#127C22×D1111yescharacteristic
365#125—221no—
366#124—21no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369#121—21no—
370#121—21no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8C22⋊D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C22⋊D1111yescharacteristic
380C4×D4C22×D1111yescharacteristic
381#117—21no—
382#117—221no—
383#117C22⋊D1111yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—21no—
387#107—221no—
388#106—21no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—21no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8—21no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—21no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C2×C11—41no—
429C2×C11—42no—
430C2×C11—161no—
431C2×C11#304011yescharacteristic
432C2×C11#305011yescharacteristic
433C2×C11#306711yescharacteristic
434#41—22no—
435#41—22no—
436#41—42no—
437#41—42no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8C2×C22⋊D1111yescharacteristic
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4C2×C22⋊D1111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456SD16—42no—
457SD16—442no—
458D8—42no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—441no—
470C2×C8—441no—
471C2×C8—442no—
472C2×C8—442no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C4⋊C4C2×C22⋊D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—441no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—441no—
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1927811yescharacteristic, complemented, Sylow
500C23—21no—
501C23—41no—
502C23#6699211yescharacteristic
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—441no—
507Q8—441no—
508Q8—881no—
509Q8#6700312yes—
510D4—24no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4#6700312yes—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—82no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4#6699211yescharacteristic
536C2×C4#6699211yescharacteristic
537C2×C4#6699211yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—41no—
542C8—41no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C2×#6699211yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—881no—
570C4—881no—
571C4#1062330411yescharacteristic
572C4#1062330411yescharacteristic
573C4C2×#6700311yescharacteristic
574C4C2×#6700311yescharacteristic
575C2—41no—
576C2—42no—
577C2—161no—
578C2#1307810811yescharacteristic
579C2#1307819411yescharacteristic
580C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3115C2
socleC22×C11C2×#121
hypercenter#3115D11
hypocenterC11#19278
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13078938C2semidirect
2. #13078778C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068072C2semidirect
5. #13068065C2semidirect
6. #13068058C2semidirect
7. #13068051C2semidirect
8. #13068044C2semidirect
9. #13068037C2semidirect
10. #13068030C2semidirect
11. #13068023C2semidirect
12. #13067377C2semidirect
13. #13067327C2semidirect
14. #13067321C2semidirect
499. C11#19278semidirect

Maximal subgroups

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

subgroupindex
#130789382
#130787782
#41×C11⋊C82
#130680722
#130680652
#130680582
#130680512
#130680442
#130680372
#130680302
#130680232
#130673772
#130673272
#130673212
C11×#31152
#1927811