Finite Group Databasebeta

← #14723969

Subgroups — #14723969

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078645C211yesmaximal, characteristic
2D11×#446C211yesmaximal, characteristic, complemented
3#13077323C211yesmaximal, characteristic
4#13067509C211yesmaximal, characteristic, complemented
5#13067507C211yesmaximal, characteristic, complemented
6#13067505C211yesmaximal, characteristic, complemented
7#13067503C211yesmaximal, characteristic, complemented
8#13067454C211yesmaximal, characteristic, complemented
9#13067452C211yesmaximal, characteristic, complemented
10#13067450C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic, complemented
12#13067043C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic
14#13066901C211yesmaximal, characteristic, complemented
15C11×#1582C211yesmaximal, characteristic, complemented
16C2×#66954—21no—
17C4×Q8×D11C2211yescharacteristic
18#10623079C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622783C411yescharacteristic
23#10622776C411yescharacteristic
24C8×C22⋊D11—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622476C411yescharacteristic
30#10622467C411yescharacteristic
31#10622451C2211yescharacteristic
32#10622450C2211yescharacteristic
33D11×C4⋊C8—21no—
34D11×C4⋊C8C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622441—21no—
37#10622419C411yescharacteristic
38#10622404C411yescharacteristic
39#10622390C411yescharacteristic
40#10622375C411yescharacteristic
41#10622342—21no—
42#10622340—21no—
43D11×#97—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80C2×#4314C2×C411yescharacteristic
81#66954—44no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11D411yescharacteristic
87C2×C8×D11D411yescharacteristic
88#66948C2×C411yescharacteristic
89C4⋊C4×D11—21no—
90C4⋊C4×D11C2×C411yescharacteristic
91#66941C2×C411yescharacteristic
92#66940—21no—
93#66940C2×C411yescharacteristic
94#66938—21no—
95#66937—21no—
96C4×D44C2311yescharacteristic
97C42×D11—21no—
98C42×D11C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22C2311yescharacteristic
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(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8C2×C411yescharacteristic
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8C2×C411yescharacteristic
132C8×Dic11D411yescharacteristic
133C8×Dic11D411yescharacteristic
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17929—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152Q8×D11—41no—
153Q8×D11—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11C22×C411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11#4111yescharacteristic
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C22×C411yescharacteristic
167C11×SD16—41no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4325—41no—
184#4324—41no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4314—41no—
209#4313—42no—
210#4313—42no—
211C8×D11—22no—
212C8×D11—42no—
213C8×D11—42no—
214C8×D11SD1614yescomplemented
215#3103—111no—
216C2×#446—111no—
217#2931—111no—
218#1590—111no—
219#1590—111no—
220#1590—111no—
221#1590—111no—
222#1582—111no—
223#1582—111no—
224#1582—111no—
225#1582D1111yescharacteristic, complemented
226#1570—111no—
227#1487—111no—
228#1480—111no—
229#1450—111no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—42no—
246C22⋊D11—42no—
247C22⋊D11—42no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254D44—21no—
255D44—21no—
256D44—42no—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—41no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—41no—
263C4×D11—41no—
264C4×D11C2×SD1612yes—
265C4×D11#13512yes—
266Dic22—21no—
267Dic22—21no—
268Dic22—42no—
269Dic22—42no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11C2×SD1612yes—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8C2×SD1612yes—
284C2×#131—221no—
285#532—111no—
286C2×C4×Q8—111no—
287#481—111no—
288#481—111no—
289#475—111no—
290#475—111no—
291#460—111no—
292#460—111no—
293#448—111no—
294#448—111no—
295#446—111no—
296#446—111no—
297#446—111no—
298#446—221no—
299#446—221no—
300#446C2×D1111yescharacteristic
301C4×SD16—111no—
302C4×SD16—111no—
303C4×SD16—111no—
304C4×SD16C2×D1111yescharacteristic
305#436—111no—
306#436—111no—
307#436—221no—
308C8×D4—111no—
309C8×D4—221no—
310C8×D4C2×D1111yescharacteristic
311#431—111no—
312#431—111no—
313#423—111no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8—221no—
316#408—221no—
317C2×#97—221no—
318C2×C4×C8—111no—
319#334—111no—
320#334—111no—
321#334—111no—
322#334C2×D1111yescharacteristic
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326Q8⋊C8C2×D1111yescharacteristic
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic
331#322—111no—
332#322C2×D1111yescharacteristic
333C82—111no—
334C82—111no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×C4×D411yescharacteristic
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11C4×SD1612yes—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11#56811yescharacteristic
350C4×C11#56811yescharacteristic
351C4×C11C22×SD1611yescharacteristic
352C4×C11C2×#13511yescharacteristic
353Dic11—21no—
354Dic11—21no—
355Dic11—41no—
356Dic11—41no—
357Dic11—41no—
358Dic11C4×SD1612yes—
359C2×#41—221no—
360C22×Q8—111no—
361C2×SD16—111no—
362C2×SD16—111no—
363C2×SD16—111no—
364C2×SD16C4×D1111yescharacteristic
365#131—444no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C22×C8—21no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C4⋊Q8—111no—
375#127—111no—
376#124—221no—
377#121—111no—
378#121—111no—
379#121—221no—
380C4×Q8—111no—
381C4×Q8—111no—
382C4×Q8—111no—
383C4×Q8—221no—
384C4×Q8—221no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—111no—
387C4×D4—221no—
388C4×D4C22×D1111yescharacteristic
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C42—111no—
392C2×C42—221no—
393#106—111no—
394#106—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⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#103—111no—
413#103C4×D1111yescharacteristic
414#102—111no—
415#102—111no—
416#102—111no—
417#102C4×D1111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—21no—
426#97—221no—
427#97—221no—
428#97—221no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—81no—
438C2×C11#293011yescharacteristic
439C2×C11C2×C4×SD1611yescharacteristic
440C2×C11#295511yescharacteristic
441D11—22no—
442D11—81no—
443#41—442no—
444#41—442no—
445C2×Q8—111no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—441no—
449C2×Q8—441no—
450C2×Q8C2×C4×D1111yescharacteristic
451C2×D4—111no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4C2×C4×D1111yescharacteristic
457C22×C4—21no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464SD16—41no—
465SD16—441no—
466SD16—441no—
467SD16—441no—
468M16—442no—
469M16—442no—
470M16—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—42no—
475C2×C8—111no—
476C2×C8—114no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—222no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—442no—
485C2×C8—442no—
486C2×C8C2×C4×D1111yescharacteristic
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8D4×D1111yescharacteristic
489C2×C8D4×D1111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4C2×C4×D1111yescharacteristic
499C4⋊C4C2×C4×D1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C42—21no—
505C42—111no—
506C42—111no—
507C42—111no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42C23×D1111yescharacteristic
512C11#1792911yescharacteristic, complemented, Sylow
513C23—21no—
514C23—111no—
515C23—221no—
516Q8—21no—
517Q8—21no—
518Q8—221no—
519Q8—221no—
520Q8—442no—
521Q8—442no—
522D4—21no—
523D4—21no—
524D4—221no—
525D4—221no—
526D4—442no—
527D4—442no—
528D4—442no—
529D4—442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—111no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—441no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4C22×C4×D1111yescharacteristic
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—112no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—441no—
564C8—441no—
565C8—441no—
566C8SD16×D1112yes—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—112no—
571C22—221no—
572C22—221no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22C4×D4×D1111yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—112no—
582C4—221no—
583C4—221no—
584C4—441no—
585C4—441no—
586C4—441no—
587C4#1062327611yescharacteristic
588C4#1062328111yescharacteristic
589C4C2×SD16×D1111yescharacteristic
590C4D11×#13511yescharacteristic
591C2—81no—
592C2—222no—
593C2—881no—
594C2#1307731411yescharacteristic
595C2C4×SD16×D1111yescharacteristic
596C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1582C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1582D11
hypocenterC11#17929
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. D11×#446C2semidirect
4. #13067509C2semidirect
5. #13067507C2semidirect
6. #13067505C2semidirect
7. #13067503C2semidirect
8. #13067454C2semidirect
9. #13067452C2semidirect
10. #13067450C2semidirect
11. #13067385C2semidirect
12. #13067043C2semidirect
14. #13066901C2semidirect
15. C11×#1582C2semidirect
214. C8×D11SD16semidirect
225. #1582D11semidirect
512. C11#17929semidirect

Maximal subgroups

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

subgroupindex
#130786452
D11×#4462
#130773232
#130675092
#130675072
#130675052
#130675032
#130674542
#130674522
#130674502
#130673852
#130670432
#130670132
#130669012
C11×#15822
#1792911