Finite Group Databasebeta

← #14725720

Subgroups — #14725720

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079207C211yesmaximal, characteristic
2#13077779C211yesmaximal, characteristic, complemented
3#13077681C211yesmaximal, characteristic, complemented
4#13067500C211yesmaximal, characteristic, complemented
5#13067491C211yesmaximal, characteristic, complemented
6#13067477C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067441C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067367C211yesmaximal, characteristic, complemented
12#13067023C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic, complemented
14#13066914C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17#10623079C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622789C411yescharacteristic
22#10622787C411yescharacteristic
23#10622742—21no—
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622478C411yescharacteristic
30#10622469C411yescharacteristic
31#10622452—21no—
32#10622451C2211yescharacteristic
33#10622451C2211yescharacteristic
34#10622447—21no—
35#10622446C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622425C411yescharacteristic
38#10622408C411yescharacteristic
39#10622395C411yescharacteristic
40#10622377C411yescharacteristic
41#10622340—21no—
42(C22⋊D11)⋊C8—21no—
43#10622322—21no—
44#10622319—21no—
45C4×D88C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#67000C2×C411yescharacteristic
73#66999C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×D88C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313C2×C411yescharacteristic
84C2×#4313C2×C411yescharacteristic
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66951—21no—
89#66948C2×C411yescharacteristic
90#66948C2×C411yescharacteristic
91#66947—21no—
92#66943C2×C411yescharacteristic
93#66941C2×C411yescharacteristic
94#66938—21no—
95#66937—21no—
96C4×D44—21no—
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100C42×D11C2311yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8D411yescharacteristic
124(C2×D11)⋊C8D411yescharacteristic
125#66882C2×C411yescharacteristic
126#66879C2×C411yescharacteristic
127#66879C2×C411yescharacteristic
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8D411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132C8×Dic11—21no—
133#66873C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18082—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151#4339—81no—
152#4339—81no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C11×SD16—22no—
164C11×M16—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179#4325—41no—
180#4323—41no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11C22×C411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11#4111yescharacteristic
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205D88—22no—
206#4313—22no—
207#4313—41no—
208#4313—81no—
209#4313—81no—
210C8×D11—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3171—111no—
214#2994—111no—
215#2979—111no—
216#1592D1111yescharacteristic, complemented
217#1589—111no—
218#1588—111no—
219#1586—111no—
220#1582—111no—
221#1581—111no—
222#1580—111no—
223C8×SD16—111no—
224#1565—111no—
225#1482—111no—
226#1480—111no—
227#1453—111no—
228C23×C11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—42no—
245C22⋊D11—81no—
246C22⋊D11—81no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252D44—21no—
253D44—21no—
254D44—21no—
255D44—21no—
256D44—42no—
257D44—81no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267Dic22—81no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11#13112yes—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282#532—111no—
283#529—111no—
284#501—111no—
285#496—111no—
286#490—111no—
287#489—111no—
288#469—111no—
289#469—111no—
290#468—111no—
291#468—111no—
292#446C2×D1111yescharacteristic
293C8×Q8—111no—
294C4×SD16—111no—
295C4×SD16C2×D1111yescharacteristic
296C4×D8—111no—
297C4×D8—111no—
298#436—111no—
299#436—111no—
300#436—221no—
301#436C2×D1111yescharacteristic
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—221no—
307C8×D4—221no—
308#433—221no—
309#431—111no—
310#431—111no—
311#431—111no—
312#424—221no—
313C2×C4⋊C8—111no—
314#408—221no—
315#408—221no—
316C4×M16—111no—
317#335—111no—
318#335C2×D1111yescharacteristic
319#334—111no—
320#334—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329#322—111no—
330#322—111no—
331#322C2×D1111yescharacteristic
332C82—111no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11C2×#13111yescharacteristic
351C4×C11#56811yescharacteristic
352C4×C11#57611yescharacteristic
353C4×C11#57711yescharacteristic
354Dic11—21no—
355Dic11—21no—
356Dic11—21no—
357Dic11—41no—
358Dic11—41no—
359C2×#41—221no—
360C2×SD16—111no—
361C2×SD16C4×D1111yescharacteristic
362C2×D8—111no—
363C2×D8—111no—
364C2×M16—21no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—221no—
368C2×M16—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C4⋊Q8—111no—
374#127—111no—
375#126—221no—
376#125—111no—
377#124—111no—
378#124—221no—
379#123—221no—
380C22⋊Q8—111no—
381#121—111no—
382#121—111no—
383#121—111no—
384#121—221no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391#117—221no—
392C2×C42—111no—
393#107—111no—
394#107—111no—
395#106—111no—
396#106C4×D1111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8C22×D1111yescharacteristic
406C4⋊C8C22×D1111yescharacteristic
407#103—111no—
408#103C4×D1111yescharacteristic
409#102—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102C4×D1111yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—111no—
417C22⋊C8—111no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—21no—
426#97—111no—
427#97—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—81no—
437C2×C11#293511yescharacteristic
438C2×C11#294611yescharacteristic
439C2×C11#295511yescharacteristic
440D11—41no—
441D11—81no—
442D11—81no—
443#41—881no—
444#41—881no—
445C2×Q8—221no—
446C2×Q8C2×C4×D1111yescharacteristic
447C2×D4—111no—
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—221no—
460C22×C4—221no—
461SD16—22no—
462SD16—441no—
463D8—222no—
464D8—441no—
465M16—81no—
466M16—222no—
467M16—441no—
468M16—881no—
469M16—881no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—881no—
481C2×C8—881no—
482C2×C8—881no—
483C2×C8—881no—
484C2×C8C2×C4×D1111yescharacteristic
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8D4×D1111yescharacteristic
487C2×C8D4×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—111no—
490C4⋊C4—111no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4C2×C4×D1111yescharacteristic
496C4⋊C4C2×C4×D1111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—21no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42C23×D1111yescharacteristic
511C11#1808211yescharacteristic, complemented, Sylow
512C23—21no—
513C23—111no—
514C23—221no—
515C23—221no—
516Q8—21no—
517Q8—21no—
518Q8—881no—
519D4—21no—
520D4—21no—
521D4—221no—
522D4—221no—
523D4—221no—
524D4—221no—
525D4—442no—
526D4—442no—
527D4—881no—
528D4—881no—
529D4—881no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—441no—
563C8—441no—
564C8—441no—
565C8#6696012yes—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—221no—
570C22—221no—
571C22—221no—
572C22—441no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22C4×D4×D1111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—221no—
584C4—221no—
585C4—221no—
586C4—441no—
587C4—441no—
588C4C2×#6696011yescharacteristic
589C4#1062328111yescharacteristic
590C4#1062330511yescharacteristic
591C4#1062330911yescharacteristic
592C2—81no—
593C2—441no—
594C2—881no—
595C2—881no—
596C2#1307736111yescharacteristic
597C2#1307744711yescharacteristic
598C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radical#13079207C2
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#18082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #13077779C2semidirect
3. #13077681C2semidirect
4. #13067500C2semidirect
5. #13067491C2semidirect
6. #13067477C2semidirect
7. #13067450C2semidirect
8. #13067443C2semidirect
9. #13067441C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067367C2semidirect
12. #13067023C2semidirect
13. #13067013C2semidirect
14. #13066914C2semidirect
15. C11×#1592C2semidirect
216. #1592D11semidirect
511. C11#18082semidirect

Maximal subgroups

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

subgroupindex
#130792072
#130777792
#130776812
#130675002
#130674912
#130674772
#130674502
#130674432
#130674412
SD16×C11⋊C82
#130673672
#130670232
#130670132
#130669142
C11×#15922
#1808211