Finite Group Databasebeta

← #14737759

Subgroups — #14737759

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#13078772C211yesmaximal, characteristic, complemented
2#13078761C211yesmaximal, characteristic
3C8×#4339C211yesmaximal, characteristic, complemented
4#13068071C211yesmaximal, characteristic, complemented
5#13068064C211yesmaximal, characteristic, complemented
6#13068057C211yesmaximal, characteristic, complemented
7#13068050C211yesmaximal, characteristic, complemented
8#13068043C211yesmaximal, characteristic, complemented
9#13068036C211yesmaximal, characteristic, complemented
10#13068029C211yesmaximal, characteristic, complemented
11#13068022C211yesmaximal, characteristic, complemented
12#13067379C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067321C211yesmaximal, characteristic, complemented
15C11×#3131C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#488—21no—
20C11×#488—21no—
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#416—21no—
26C11×#416—21no—
27C2×C4×C8×C11C2211yescharacteristic
28C8×C22⋊D11—21no—
29C8×C22⋊D11—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622703C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622660—21no—
39#10622658—21no—
40#10622650—21no—
41#10622648—21no—
42#10622643—21no—
43#10622639—21no—
44#10622631—21no—
45#10622627—21no—
46#10622539C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622538C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51#10622298—21no—
52C4×C8×D11—21no—
53C8×Dic22C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339D411yescharacteristic
69C22×C8×C11D411yescharacteristic
70C22×C8×C11D411yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#127C2311yescharacteristic
75C11×#125—21no—
76C11×#124—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×#121—21no—
80C11×#121—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C11×#117—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4326—21no—
88C2×#4325—21no—
89C2×#4324—21no—
90C2×#4323—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93#66979D411yescharacteristic
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96C4×D44D411yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99C42×D11—21no—
100C4×Dic22D411yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#103—21no—
103C11×#103—21no—
104C11×#103—21no—
105C11×#103—21no—
106C11×#102—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#102—21no—
110C4×C8×C11D411yescharacteristic
111C4×C8×C11D411yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899—21no—
115#66899—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66872—21no—
132#66872—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142#66867—21no—
143C4×C11⋊C8—21no—
144#19278—111nomaximal, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—21no—
159#4339—22no—
160#4339—22no—
161C2×D44C2×D411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×Dic22C2×D411yescharacteristic
166C2×C8×C11—41no—
167C2×C8×C11—41no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—41no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—21no—
189#4326—42no—
190#4325—42no—
191#4324—42no—
192#4323—42no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C2×D411yescharacteristic
196C4⋊Dic11C2×D411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C8×D11—42no—
209C8×D11—42no—
210#3131D1111yescharacteristic, complemented
211#3116—111no—
212#3115—111no—
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—41no—
226C23×C11#12111yescharacteristic
227C22×D11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—81no—
238D4×C11—82no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—82no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—24no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258D44—21no—
259D44#13512yes—
260C4×D11—24no—
261C4×D11—42no—
262C4×D11—41no—
263C4×D11—41no—
264Dic22—21no—
265Dic22#13512yes—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#533C2×D1111yescharacteristic
277#532C2×D1111yescharacteristic
278C4×#41—111no—
279#488—21no—
280#488—21no—
281#487C2×D1111yescharacteristic
282#487C2×D1111yescharacteristic
283#486C2×D1111yescharacteristic
284#486C2×D1111yescharacteristic
285#485—221no—
286#482—221no—
287#477—111no—
288#476—111no—
289#475—111no—
290#474—111no—
291#462—111no—
292#461—111no—
293#460—111no—
294#459—111no—
295#452—221no—
296#449—221no—
297C8×Q8—111no—
298C8×Q8—111no—
299#442—221no—
300#441—221no—
301#440—221no—
302#440—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—221no—
306C8×D4—221no—
307#432—111no—
308#432—111no—
309#431—111no—
310#431—221no—
311#416—21no—
312#416—21no—
313C2×C4×C8—221no—
314C2×C4×C8C2×D1111yescharacteristic
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—21no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11C2×#12111yescharacteristic
334C2×D11—22no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×#13511yescharacteristic
345C4×C11C2×#13511yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57511yescharacteristic
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—21no—
352C2×#41—111no—
353C2×Q16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×D8—221no—
357C22×C8—221no—
358C22×C8—221no—
359C22×C8C22⋊D1111yescharacteristic
360C22×C8C22⋊D1111yescharacteristic
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363C4⋊Q8C22×D1111yescharacteristic
364#127C22×D1111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—111no—
374C4×Q8—111no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—111no—
378C4×D4—111no—
379C4×D4—221no—
380C4×D4—221no—
381#117—21no—
382#117—111no—
383#117—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—221no—
387#107—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8C22⋊D1111yescharacteristic
425C4×C8C22⋊D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—161no—
430C2×C11#304011yescharacteristic
431C2×C11#305011yescharacteristic
432C2×C11#306711yescharacteristic
433D11—42no—
434#41—42no—
435#41—42no—
436#41—222no—
437#41—222no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—111no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4—111no—
447C2×D4—221no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456SD16—442no—
457SD16—442no—
458D8—442no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C2×C8—442no—
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C42—41no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1927811yescharacteristic, complemented, Sylow
500C23—41no—
501C23—221no—
502C23#6699111yescharacteristic
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—81no—
508Q8—112no—
509Q8—221no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—82no—
516D4—112no—
517D4—224no—
518D4—221no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—224no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—442no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4#6699111yescharacteristic
536C2×C4#6699111yescharacteristic
537C2×C4#6699111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—222no—
558C22—441no—
559C22—441no—
560C22C2×#6699111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4D11×#13511yescharacteristic
572C4D11×#13511yescharacteristic
573C4#1062335311yescharacteristic
574C4#1062335311yescharacteristic
575C2—41no—
576C2—161no—
577C2—442no—
578C2#1307810611yescharacteristic
579C2#1307819311yescharacteristic
580C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3131C2
socleC22×C11C2×#121
prime radical#13078761C2
hypercenter#3131D11
hypocenterC11#19278
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #13078772C2semidirect
3. C8×#4339C2semidirect
4. #13068071C2semidirect
5. #13068064C2semidirect
6. #13068057C2semidirect
7. #13068050C2semidirect
8. #13068043C2semidirect
9. #13068036C2semidirect
10. #13068029C2semidirect
11. #13068022C2semidirect
12. #13067379C2semidirect
13. #13067326C2semidirect
14. #13067321C2semidirect
15. C11×#3131C2semidirect
210. #3131D11semidirect
499. C11#19278semidirect

Maximal subgroups

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

subgroupindex
#130787722
#130787612
C8×#43392
#130680712
#130680642
#130680572
#130680502
#130680432
#130680362
#130680292
#130680222
#130673792
#130673262
#130673212
C11×#31312
#1927811