Finite Group Databasebeta

← #14725144

Subgroups — #14725144

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078645C211yesmaximal, characteristic
2#13077702C211yesmaximal, characteristic, complemented
3#13077681C211yesmaximal, characteristic
4#13067503C211yesmaximal, characteristic, complemented
5#13067493C211yesmaximal, characteristic, complemented
6#13067474C211yesmaximal, characteristic, complemented
7#13067457C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10#13067419C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic, complemented
12#13067083C211yesmaximal, characteristic
13#13067009C211yesmaximal, characteristic, complemented
14#13066917C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16C4×Q8×D11C2211yescharacteristic
17#10623079C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622783C411yescharacteristic
22#10622776C411yescharacteristic
23#10622742—21no—
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622476C411yescharacteristic
30#10622467C411yescharacteristic
31#10622451C2211yescharacteristic
32#10622448C2211yescharacteristic
33#10622446—21no—
34#10622446C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622419C411yescharacteristic
38#10622404C411yescharacteristic
39#10622390C411yescharacteristic
40#10622375C411yescharacteristic
41#10622340—21no—
42(C22⋊D11)⋊C8—21no—
43#10622318—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
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#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—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—
79C22×C11⋊C8—21no—
80C2×#4314C2×C411yescharacteristic
81C2×#4313—21no—
82C2×C8×D11—21no—
83#66948C2×C411yescharacteristic
84C4⋊C4×D11—21no—
85C4⋊C4×D11C2×C411yescharacteristic
86#66941C2×C411yescharacteristic
87#66940—21no—
88#66940C2×C411yescharacteristic
89#66938—21no—
90#66937—21no—
91C4×D44C2311yescharacteristic
92C42×D11—21no—
93C42×D11C2311yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C11×#106C2×C411yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#102C2×C411yescharacteristic
102C11×C22⋊C8—21no—
103C11×#97—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109C22⋊(C11⋊C8)—21no—
110#66885C2×C411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8C2×C411yescharacteristic
117(C2×D11)⋊C8C2×C411yescharacteristic
118(C2×D11)⋊C8D411yescharacteristic
119(C2×D11)⋊C8D411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8D411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11—21no—
133#66874C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18030—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—
151Q8×D11—22no—
152Q8×D11—41no—
153#4339—81no—
154#4339—81no—
155C2×D44—21no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11#4111yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C22×C411yescharacteristic
166C11×SD16—41no—
167C11×M16—81no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4325—41no—
183#4324—22no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#4314—22no—
208#4313—81no—
209C8×D11—81no—
210#3103—111no—
211#2984—111no—
212#2979—111no—
213#1592D1111yescharacteristic, complemented
214#1590—111no—
215#1588—111no—
216#1585—111no—
217#1583—111no—
218#1582—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221#1572—111no—
222#1496—111no—
223#1479—111no—
224#1454—111no—
225C23×C11—21no—
226C22×D11—21no—
227C22×D11C4×D411yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—42no—
241C22⋊D11—81no—
242C22⋊D11—81no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249D44—21no—
250D44—21no—
251D44—81no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257C4×D11—42no—
258C4×D11—42no—
259C4×D11—41no—
260C4×D11—41no—
261Dic22—21no—
262Dic22—42no—
263Dic22—81no—
264Dic22#13112yes—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#532—111no—
280C2×C4×Q8—111no—
281#481—111no—
282#481—111no—
283#475—111no—
284#475—111no—
285#460—111no—
286#460—111no—
287#448—111no—
288#448—111no—
289#446—111no—
290#446—221no—
291#446—221no—
292#446C2×D1111yescharacteristic
293C8×Q8—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16C2×D1111yescharacteristic
299#436—111no—
300#436—221no—
301#436C2×D1111yescharacteristic
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305#432—111no—
306#432—221no—
307#431—111no—
308#431—111no—
309#431—111no—
310#431—111no—
311#431—221no—
312#408—221no—
313#408—221no—
314#335—111no—
315#335C2×D1111yescharacteristic
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8C2×D1111yescharacteristic
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8C2×D1111yescharacteristic
326#322—111no—
327#322—111no—
328#322C2×D1111yescharacteristic
329C82—111no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×#13111yescharacteristic
345C4×C11#56811yescharacteristic
346C4×C11#57711yescharacteristic
347C4×C11#57711yescharacteristic
348Dic11—22no—
349Dic11—21no—
350Dic11—21no—
351Dic11—21no—
352Dic11—41no—
353Dic11—41no—
354C2×#41—221no—
355C22×Q8—111no—
356C2×SD16—111no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16C4×D1111yescharacteristic
360C2×M16—21no—
361C2×M16—221no—
362C22×C8—221no—
363C22×C8—221no—
364C4⋊Q8—111no—
365#127—111no—
366#124—221no—
367#121—111no—
368#121—111no—
369#121—221no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—221no—
374C4×Q8—221no—
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—221no—
378C4×D4C22×D1111yescharacteristic
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C42—111no—
382C2×C42—221no—
383#106—111no—
384#106—111no—
385#106—111no—
386#106C4×D1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—111no—
401#103—111no—
402#103—111no—
403#103C4×D1111yescharacteristic
404#102—111no—
405#102—111no—
406#102—111no—
407#102C4×D1111yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—21no—
420#97—221no—
421#97—221no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—81no—
432C2×C11#293311yescharacteristic
433C2×C11#294911yescharacteristic
434C2×C11#295511yescharacteristic
435D11—41no—
436D11—81no—
437#41—881no—
438#41—881no—
439C2×Q8—111no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—222no—
443C2×Q8—441no—
444C2×Q8C2×C4×D1111yescharacteristic
445C2×D4—111no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4C2×C4×D1111yescharacteristic
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458SD16—41no—
459SD16—222no—
460SD16—222no—
461SD16—441no—
462M16—81no—
463M16—881no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—881no—
475C2×C8—881no—
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8C2×C4×D1111yescharacteristic
478C2×C8D4×D1111yescharacteristic
479C2×C8D4×D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4C2×C4×D1111yescharacteristic
489C4⋊C4C2×C4×D1111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C23×D1111yescharacteristic
502C11#1803011yescharacteristic, complemented, Sylow
503C23—21no—
504C23—111no—
505C23—221no—
506Q8—21no—
507Q8—21no—
508Q8—112no—
509Q8—221no—
510Q8—442no—
511Q8—881no—
512D4—21no—
513D4—21no—
514D4—221no—
515D4—221no—
516D4—442no—
517D4—881no—
518D4—881no—
519D4—881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—441no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C2×D4×D1111yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—441no—
555C8—441no—
556C8—441no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—221no—
561C22—221no—
562C22—221no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22C4×D4×D1111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—221no—
572C4—221no—
573C4—222no—
574C4—221no—
575C4—441no—
576C4—441no—
577C4#1062327611yescharacteristic
578C4D11×#13111yescharacteristic
579C4#1062330611yescharacteristic
580C4#1062330911yescharacteristic
581C2—81no—
582C2—441no—
583C2—881no—
584C2#1307734511yescharacteristic
585C2#1307747211yescharacteristic
586C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#18030
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. #13077702C2semidirect
4. #13067503C2semidirect
5. #13067493C2semidirect
6. #13067474C2semidirect
7. #13067457C2semidirect
8. #13067450C2semidirect
9. #13067430C2semidirect
10. #13067419C2semidirect
11. #13067395C2semidirect
13. #13067009C2semidirect
14. #13066917C2semidirect
15. C11×#1592C2semidirect
213. #1592D11semidirect
502. C11#18030semidirect

Maximal subgroups

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

subgroupindex
#130786452
#130777022
#130776812
#130675032
#130674932
#130674742
#130674572
#130674502
#130674302
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