Finite Group Databasebeta

← #14723903

Subgroups — #14723903

Order 2816.

626 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#13078645C211yesmaximal, characteristic
2#13077695C211yesmaximal, characteristic, complemented
3#13077693C211yesmaximal, characteristic
4#13067494C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067461C211yesmaximal, characteristic, complemented
7#13067431C211yesmaximal, characteristic, complemented
8#13067425C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067393C211yesmaximal, characteristic, complemented
12#13067061C211yesmaximal, characteristic, complemented
13#13067031C211yesmaximal, characteristic
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1583C211yesmaximal, characteristic, complemented
16C4×Q8×D11C2211yescharacteristic
17#10623079C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622783C411yescharacteristic
22#10622776C411yescharacteristic
23#10622742—21no—
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622476C411yescharacteristic
30#10622467C411yescharacteristic
31#10622448C2211yescharacteristic
32#10622447C2211yescharacteristic
33#10622446—21no—
34#10622446C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622419C411yescharacteristic
38#10622404C411yescharacteristic
39#10622390C411yescharacteristic
40#10622375C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43C4×#4314C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×#4313C2211yescharacteristic
46#10622298—21no—
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
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×#4313—21no—
83C2×C8×D11—21no—
84#66948C2×C411yescharacteristic
85C4⋊C4×D11—21no—
86C4⋊C4×D11C2×C411yescharacteristic
87#66941C2×C411yescharacteristic
88#66940—21no—
89#66940C2×C411yescharacteristic
90#66938—21no—
91#66937—21no—
92C4×D44C2311yescharacteristic
93C42×D11—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C11×#106C2×C411yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×#103C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×C22⋊C8—21no—
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111#66885C2×C411yescharacteristic
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—
123#66879—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
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17923—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—22no—
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—22no—
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—22no—
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—42no—
209#4313—81no—
210C8×D11—81no—
211#3103—111no—
212#2982—111no—
213#2981—111no—
214#1588—111no—
215#1588—111no—
216#1583—111no—
217#1583D1111yescharacteristic, complemented
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221C8×SD16—111no—
222#1572—111no—
223#1491—111no—
224#1484—111no—
225#1453—111no—
226C23×C11—21no—
227C22×D11—21no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11#13112yes—
231D4×C11—21no—
232D4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C22⋊D11—81no—
242C22⋊D11—81no—
243C22⋊D11—81no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249C2×Dic11C4×D411yescharacteristic
250D44—21no—
251D44—21no—
252D44—81no—
253C4×D11—24no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—81no—
262Dic22—24no—
263Dic22—21no—
264Dic22—81no—
265Dic22#13112yes—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—22no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280#532—111no—
281C2×C4×Q8—111no—
282#481—111no—
283#481—111no—
284#475—111no—
285#475—111no—
286#460—111no—
287#460—111no—
288#448—111no—
289#448—111no—
290C8×Q8—111no—
291C8×Q8—111no—
292C8×Q8—111no—
293C8×Q8—221no—
294C8×Q8—221no—
295C8×Q8C2×D1111yescharacteristic
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×SD16C2×D1111yescharacteristic
300#436—111no—
301#436C2×D1111yescharacteristic
302#435—221no—
303#435—221no—
304C8×D4—111no—
305C8×D4—111no—
306#432—111no—
307#431—111no—
308#431—111no—
309#431—111no—
310#431—221no—
311#431—221no—
312#408—221no—
313#408—221no—
314C4×M16—111no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334C2×D1111yescharacteristic
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8C2×D1111yescharacteristic
327#322—111no—
328#322—111no—
329#322C2×D1111yescharacteristic
330C82—111no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—41no—
341C4×C11—22no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11C2×#13111yescharacteristic
346C4×C11C2×#13111yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57711yescharacteristic
349Dic11—21no—
350Dic11—22no—
351Dic11—21no—
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355C2×#41—221no—
356C22×Q8—111no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16C4×D1111yescharacteristic
361C2×M16—21no—
362C2×M16—221no—
363C2×M16—221no—
364C22×C8—221no—
365C22×C8—221no—
366C4⋊Q8—111no—
367#127—111no—
368#124—221no—
369#121—111no—
370#121—111no—
371#121—221no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8—111no—
375C4×Q8—221no—
376C4×Q8—221no—
377C4×Q8C22×D1111yescharacteristic
378C4×D4—111no—
379C4×D4—221no—
380C4×D4C22×D1111yescharacteristic
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C42—111no—
384C2×C42—221no—
385#106—111no—
386#106—111no—
387#106—111no—
388#106C4×D1111yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103C4×D1111yescharacteristic
405#102—111no—
406#102—111no—
407#102—111no—
408#102C4×D1111yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—111no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—221no—
420#97—221no—
421C4×C8—21no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—81no—
433C2×C11#292911yescharacteristic
434C2×C11#294911yescharacteristic
435C2×C11#295611yescharacteristic
436D11—41no—
437D11—81no—
438#41—881no—
439#41—881no—
440C2×Q8—111no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—222no—
444C2×Q8—222no—
445C2×Q8C2×C4×D1111yescharacteristic
446C2×D4—111no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4C2×C4×D1111yescharacteristic
452C22×C4—21no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459SD16—22no—
460SD16—222no—
461SD16—222no—
462SD16—222no—
463M16—81no—
464M16—442no—
465M16—881no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—881no—
477C2×C8—881no—
478C2×C8C2×C4×D1111yescharacteristic
479C2×C8C2×C4×D1111yescharacteristic
480C2×C8D4×D1111yescharacteristic
481C2×C8D4×D1111yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—111no—
484C4⋊C4—111no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4C2×C4×D1111yescharacteristic
491C4⋊C4C2×C4×D1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—221no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C42—21no—
497C42—111no—
498C42—111no—
499C42—111no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42C23×D1111yescharacteristic
504C11#1792311yescharacteristic, complemented, Sylow
505C23—21no—
506C23—111no—
507C23—221no—
508Q8—21no—
509Q8—112no—
510Q8—224no—
511Q8—221no—
512Q8—881no—
513Q8#6696012yes—
514D4—21no—
515D4—21no—
516D4—221no—
517D4—221no—
518D4—881no—
519D4—881no—
520D4—881no—
521D4—881no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—111no—
528C2×C4—111no—
529C2×C4—111no—
530C2×C4—224no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—881no—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—222no—
553C8—221no—
554C8—221no—
555C8—221no—
556C8—221no—
557C8—441no—
558C8—441no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—221no—
563C22—221no—
564C22—221no—
565C22—441no—
566C22—441no—
567C22—441no—
568C22C4×D4×D1111yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—221no—
574C4—221no—
575C4—222no—
576C4—221no—
577C4—441no—
578C4—441no—
579C4C2×#6696011yescharacteristic
580C4D11×#13111yescharacteristic
581C4#1062329311yescharacteristic
582C4#1062330111yescharacteristic
583C2—81no—
584C2—441no—
585C2—881no—
586C2#1307730711yescharacteristic
587C2#1307747011yescharacteristic
588C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1583C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1583D11
hypocenterC11#17923
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13077695C2semidirect
4. #13067494C2semidirect
5. #13067492C2semidirect
6. #13067461C2semidirect
7. #13067431C2semidirect
8. #13067425C2semidirect
9. SD16×C11⋊C8C2semidirect
10. #13067415C2semidirect
11. #13067393C2semidirect
12. #13067061C2semidirect
14. #13066912C2semidirect
15. C11×#1583C2semidirect
217. #1583D11semidirect
504. C11#17923semidirect

Maximal subgroups

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

subgroupindex
#130786452
#130776952
#130776932
#130674942
#130674922
#130674612
#130674312
#130674252
SD16×C11⋊C82
#130674152
#130673932
#130670612
#130670312
#130669122
C11×#15832
#1792311