Finite Group Databasebeta

← #14738785

Subgroups — #14738785

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic, complemented
2#13079623C211yesmaximal, characteristic, complemented
3#13079354C211yesmaximal, characteristic
4#13068184C211yesmaximal, characteristic, complemented
5#13068156C211yesmaximal, characteristic, complemented
6#13068122C211yesmaximal, characteristic, complemented
7#13068100C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13067998C211yesmaximal, characteristic, complemented
11#13067976C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067309C211yesmaximal, characteristic, complemented
14#13067291C211yesmaximal, characteristic, complemented
15C11×#2962C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#446—21no—
20C11×#446—21no—
21C11×#446C2211yescharacteristic
22C11×#446C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C11×#424—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622748—21no—
30#10622748—21no—
31#10622702—21no—
32#10622700—21no—
33#10622699—21no—
34#10622696—21no—
35#10622662—21no—
36#10622662—21no—
37#10622660—21no—
38#10622660—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622640C2211yescharacteristic
42#10622640C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622640C2211yescharacteristic
45#10622634C2211yescharacteristic
46#10622634C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622324—21no—
50#10622324—21no—
51#10622308C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622307C2211yescharacteristic
54#10622293C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622123C2211yescharacteristic
58#10622123C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×C4⋊Q8D411yescharacteristic
73C11×C4⋊Q8D411yescharacteristic
74C11×#125—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×C22⋊Q8D411yescharacteristic
78C4×Q8×C11—21no—
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4326—21no—
84C2×#4326—21no—
85C2×#4325—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89#66983—21no—
90#66983—21no—
91#66983—21no—
92#66983—21no—
93C2×#4318—21no—
94C2×D88—21no—
95C2×D88—21no—
96#66928—21no—
97#66928—21no—
98#66927C2311yescharacteristic
99#66927C2311yescharacteristic
100C4×D44—21no—
101C4×D44—21no—
102C4×D44—21no—
103C4×D44—21no—
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×#97—21no—
114C11×#97—21no—
115C11×#97D411yescharacteristic
116C11×#97D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11—21no—
119C4×C8×C11C2311yescharacteristic
120C4×C8×C11C2311yescharacteristic
121#66899—21no—
122#66899—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66885—21no—
127#66885—21no—
128#66881—21no—
129#66881—21no—
130#66874—21no—
131#66874—21no—
132#66873—21no—
133#66873—21no—
134#66873—21no—
135#66873—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19374—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×Q8×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—41no—
152C2×C22⋊D11—41no—
153#4339—81no—
154#4339—81no—
155#4339—82no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×M16—22no—
167C11×M16—41no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—81no—
193#4326—81no—
194#4325—81no—
195#4325—81no—
196#4325—81no—
197#4325—81no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—41no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206#4318—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211D88—42no—
212D88—42no—
213#3254—111no—
214#3216—111no—
215#3184—111no—
216#2962D1111yescharacteristic, complemented
217#1702—111no—
218#1698—111no—
219#1692—111no—
220#1688—111no—
221#1682—111no—
222#1678—111no—
223#1672—111no—
224#1668—111no—
225#1569—111no—
226#1551—111no—
227#1547—111no—
228C23×C11#12111yescharacteristic
229C22×D11—41no—
230C22×D11—41no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—81no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—82no—
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—81no—
264D44—81no—
265C4×D11—82no—
266C4×D11—82no—
267Dic22—41no—
268Dic22—41no—
269Dic22—81no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11#13712yes—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#533C2×D1111yescharacteristic
281#532—111no—
282#532—111no—
283#498—111no—
284#497—221no—
285#493—111no—
286#489—221no—
287#486—111no—
288#486—111no—
289#477—111no—
290#477—111no—
291#474—221no—
292#469—221no—
293#469—221no—
294#468—221no—
295#468—221no—
296#462—111no—
297#462—111no—
298#461—221no—
299#460—111no—
300#460—111no—
301#460—111no—
302#460—111no—
303#452—221no—
304#452—221no—
305#446—21no—
306#446—21no—
307#446C2×D1111yescharacteristic
308#446C2×D1111yescharacteristic
309C8×Q8C2×D1111yescharacteristic
310C8×Q8C2×D1111yescharacteristic
311#442—221no—
312#442—221no—
313#432—111no—
314#424—21no—
315#423—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317#405—21no—
318C4×M16C2×D1111yescharacteristic
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323#333—111no—
324#333—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329#331—111no—
330#331—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×#12111yescharacteristic
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11C2×#13711yescharacteristic
350C4×C11#57511yescharacteristic
351C4×C11#57611yescharacteristic
352C4×C11#57711yescharacteristic
353Dic11—81no—
354Dic11—81no—
355C2×#41—221no—
356C2×#41—221no—
357C2×Q16—221no—
358C2×Q16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—221no—
364C2×D8—221no—
365C2×M16—221no—
366C2×M16C22⋊D1111yescharacteristic
367C2×M16C22⋊D1111yescharacteristic
368C22×C8—21no—
369C4⋊Q8—111no—
370C4⋊Q8—111no—
371C4⋊Q8D4411yescharacteristic
372C4⋊Q8D4411yescharacteristic
373#127—111no—
374#127—111no—
375#125—21no—
376#124—221no—
377#124—221no—
378C22⋊Q8—21no—
379C22⋊Q8D4411yescharacteristic
380C22⋊Q8D4411yescharacteristic
381#121—221no—
382#121—221no—
383#121—221no—
384#121—221no—
385C4×Q8—21no—
386C4×Q8C22×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—221no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4—221no—
392#117—21no—
393C2×C42C22×D1111yescharacteristic
394#107—221no—
395#107—221no—
396#106—221no—
397#106—221no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—221no—
411#103—221no—
412#103—221no—
413#103—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422C22⋊C8—221no—
423#97—21no—
424#97—21no—
425#97—221no—
426#97C22⋊D1111yescharacteristic
427#97C22⋊D1111yescharacteristic
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11#303711yescharacteristic
434C2×C11#306211yescharacteristic
435C2×C11#306811yescharacteristic
436D11—161no—
437D11—161no—
438#41—881no—
439#41—881no—
440#41—882no—
441C2×Q8—21no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8C2×D4411yescharacteristic
445C2×Q8C2×D4411yescharacteristic
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4—441no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4C2×D4411yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459Q16—881no—
460Q16—881no—
461SD16—881no—
462SD16—881no—
463SD16—881no—
464SD16—881no—
465D8—442no—
466D8—442no—
467M16—22no—
468M16—41no—
469M16—881no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C2×C8C2×C22⋊D1111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4C2×D4411yescharacteristic
493C4⋊C4C2×D4411yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C42—21no—
501C42—21no—
502C42C2×D4411yescharacteristic
503C42#433911yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1937411yescharacteristic, complemented, Sylow
507C23—441no—
508C23—441no—
509C23#6698311yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—81no—
515Q8—441no—
516Q8—441no—
517Q8—881no—
518D4—441no—
519D4—441no—
520D4—441no—
521D4—441no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—881no—
527D4—881no—
528D4—882no—
529D4—882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—882no—
542C2×C4—882no—
543C2×C4#6698311yescharacteristic
544C2×C4#6698311yescharacteristic
545C2×C4#6698311yescharacteristic
546C2×C4C22×D4411yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—441no—
555C8—441no—
556C8—441no—
557C8—441no—
558C8#6699512yes—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22C2×#6698311yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—881no—
578C4—881no—
579C4#1062328211yescharacteristic
580C4#1062328311yescharacteristic
581C4C2×#6699511yescharacteristic
582C4#1062335311yescharacteristic
583C2—41no—
584C2—1761no—
585C2—1761no—
586C2#1307808811yescharacteristic
587C2#1307829611yescharacteristic
588C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#13079354C2
hypercenter#2962D11
hypocenterC11#19374
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #13079999C2semidirect
2. #13079623C2semidirect
4. #13068184C2semidirect
5. #13068156C2semidirect
6. #13068122C2semidirect
7. #13068100C2semidirect
8. #13068060C2semidirect
9. #13068032C2semidirect
10. #13067998C2semidirect
11. #13067976C2semidirect
12. #13067383C2semidirect
13. #13067309C2semidirect
14. #13067291C2semidirect
15. C11×#2962C2semidirect
216. #2962D11semidirect
506. C11#19374semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130796232
#130793542
#130681842
#130681562
#130681222
#130681002
#130680602
#130680322
#130679982
#130679762
#130673832
#130673092
#130672912
C11×#29622
#1937411