Finite Group Databasebeta

← #14725795

Subgroups — #14725795

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079172C211yesmaximal, characteristic
2#13077714C211yesmaximal, characteristic, complemented
3#13077681C211yesmaximal, characteristic
4#13067517C211yesmaximal, characteristic, complemented
5#13067457C211yesmaximal, characteristic, complemented
6#13067456C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067449C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11#13067363C211yesmaximal, characteristic, complemented
12#13067035C211yesmaximal, characteristic, complemented
13#13067031C211yesmaximal, characteristic
14#13066902C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623079C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622788C411yescharacteristic
22#10622784C411yescharacteristic
23#10622742—21no—
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622468C411yescharacteristic
31#10622453—21no—
32#10622451C2211yescharacteristic
33#10622446C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622443—21no—
37#10622420C411yescharacteristic
38#10622405C411yescharacteristic
39#10622391C411yescharacteristic
40#10622373C411yescharacteristic
41#10622340—21no—
42(C22⋊D11)⋊C8—21no—
43#10622322—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
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#10622093C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×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—
84C2×C8×D11C2×C411yescharacteristic
85C2×C8×D11C2×C411yescharacteristic
86#66950C2×C411yescharacteristic
87#66949—21no—
88#66948C2×C411yescharacteristic
89#66942—21no—
90#66941C2×C411yescharacteristic
91#66941C2×C411yescharacteristic
92#66938—21no—
93#66937—21no—
94C4×D44C2311yescharacteristic
95#66925—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C11×#97—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
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⋊C8D411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
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#18089—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×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11C22×C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11#4111yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C11×SD16—22no—
163C11×M16—81no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C411yescharacteristic
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11C2411yescharacteristic
177C22⋊Dic11—21no—
178#4325—41no—
179#4324—41no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—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
205#4314—22no—
206#4313—42no—
207#4313—81no—
208C8×D11—22no—
209C8×D11—41no—
210C8×D11—81no—
211#3167—111no—
212#2986—111no—
213#2979—111no—
214#1592—111no—
215#1592D1111yescharacteristic, complemented
216#1583—111no—
217#1583—111no—
218#1582—111no—
219#1582—111no—
220SD16⋊C8—111no—
221SD16⋊C8—111no—
222#1564—111no—
223#1485—111no—
224#1484—111no—
225#1451—111no—
226C23×C11—21no—
227C22×D11—21no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
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—42no—
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—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—22no—
258C4×D11—41no—
259C4×D11—41no—
260Dic22—21no—
261Dic22—21no—
262Dic22—42no—
263Dic22—81no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#13112yes—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278#533—111no—
279#532—111no—
280#498—111no—
281#492—111no—
282#487—111no—
283#486—111no—
284#465—111no—
285#465—111no—
286#465—111no—
287#465—111no—
288#446—111no—
289#446—221no—
290#446C2×D1111yescharacteristic
291C8×Q8—111no—
292C8×Q8—111no—
293C8×Q8—221no—
294C4×SD16—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16C2×D1111yescharacteristic
298#436—111no—
299#436—221no—
300#436C2×D1111yescharacteristic
301C8×D4—111no—
302C8×D4—111no—
303C8×D4—221no—
304#433—221no—
305#433—221no—
306#431—111no—
307#431—111no—
308#431—111no—
309#408—221no—
310#408—221no—
311C4×M16—111no—
312C2×C4×C8—111no—
313#335—111no—
314#335C2×D1111yescharacteristic
315#334—111no—
316#334—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8C2×D1111yescharacteristic
321D4⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8C2×D1111yescharacteristic
325#322—111no—
326#322—111no—
327#322—111no—
328#322C2×D1111yescharacteristic
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11C2×#13111yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57711yescharacteristic
347Dic11—21no—
348Dic11—21no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11#44412yes—
353C2×#41—221no—
354C2×SD16—111no—
355C2×SD16—111no—
356C2×SD16—111no—
357C2×SD16C4×D1111yescharacteristic
358C2×M16—21no—
359C2×M16—221no—
360C2×M16—221no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—221no—
364C22×C8—221no—
365C4⋊Q8—111no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368#127—111no—
369#125—221no—
370#124—221no—
371C22⋊Q8—111no—
372C22⋊Q8—111no—
373C22⋊Q8—221no—
374#121—111no—
375#121—111no—
376#121—221no—
377C4×Q8—111no—
378C4×Q8—221no—
379C4×Q8C22×D1111yescharacteristic
380C4×D4—111no—
381C4×D4—221no—
382C4×D4C22×D1111yescharacteristic
383#117—221no—
384C2×C42—111no—
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—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103C4×D1111yescharacteristic
403#102—111no—
404#102—111no—
405#102—111no—
406#102C4×D1111yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—21no—
416#97—221no—
417#97—221no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C2×C11—81no—
431C2×C11#293511yescharacteristic
432C2×C11#294911yescharacteristic
433C2×C11C2×#44411yescharacteristic
434D11—41no—
435D11—81no—
436#41—881no—
437#41—881no—
438C2×Q8—111no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8C2×C4×D1111yescharacteristic
442C2×D4—111no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4C2×C4×D1111yescharacteristic
448C22×C4—21no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—221no—
453SD16—22no—
454SD16—222no—
455SD16—441no—
456SD16—441no—
457M16—81no—
458M16—442no—
459M16—881no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—222no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—441no—
472C2×C8—881no—
473C2×C8—881no—
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8D4×D1111yescharacteristic
477C2×C8D4×D1111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—221no—
482C4⋊C4—221no—
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—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C42—21no—
497C42—111no—
498C42—111no—
499C42—111no—
500C42—221no—
501C42C23×D1111yescharacteristic
502C11#1808911yescharacteristic, complemented, Sylow
503C23—21no—
504C23—111no—
505C23—221no—
506Q8—21no—
507Q8—21no—
508Q8—221no—
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—222no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—221no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8#6696012yes—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—221no—
559C22—221no—
560C22—221no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22C4×D4×D1111yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—112no—
570C4—221no—
571C4—221no—
572C4—441no—
573C4—441no—
574C4—441no—
575C4C2×#6696011yescharacteristic
576C4#1062328111yescharacteristic
577C4#1062330611yescharacteristic
578C4#1062330911yescharacteristic
579C2—81no—
580C2—441no—
581C2—881no—
582C2#1307736111yescharacteristic
583C2#1307747211yescharacteristic
584C2D11×#44411yescharacteristic
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#18089
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. #13077714C2semidirect
4. #13067517C2semidirect
5. #13067457C2semidirect
6. #13067456C2semidirect
7. #13067450C2semidirect
8. #13067449C2semidirect
9. #13067430C2semidirect
10. SD16⋊(C11⋊C8)C2semidirect
11. #13067363C2semidirect
12. #13067035C2semidirect
14. #13066902C2semidirect
15. C11×#1592C2semidirect
215. #1592D11semidirect
502. C11#18089semidirect

Maximal subgroups

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

subgroupindex
#130791722
#130777142
#130776812
#130675172
#130674572
#130674562
#130674502
#130674492
#130674302
SD16⋊(C11⋊C8)2
#130673632
#130670352
#130670312
#130669022
C11×#15922
#1808911