Finite Group Databasebeta

← #14725141

Subgroups — #14725141

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#13078648C211yesmaximal, characteristic
2#13077703C211yesmaximal, characteristic, complemented
3#13077682C211yesmaximal, characteristic
4#13067520C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067475C211yesmaximal, characteristic, complemented
8#13067461C211yesmaximal, characteristic, complemented
9#13067454C211yesmaximal, characteristic, complemented
10#13067430C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067086C211yesmaximal, characteristic
14#13067012C211yesmaximal, characteristic, complemented
15C11×#1454C211yesmaximal, characteristic, complemented
16#10623008C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622464C411yescharacteristic
24#10622464C411yescharacteristic
25#10622461C411yescharacteristic
26#10622461C411yescharacteristic
27#10622451—21no—
28#10622447—21no—
29#10622441—21no—
30#10622441—21no—
31#10622351C411yescharacteristic
32#10622351C411yescharacteristic
33#10622348C411yescharacteristic
34#10622348C411yescharacteristic
35#10622340—21no—
36#10622340—21no—
37#10622332—21no—
38#10622331—21no—
39C4×#4314C2211yescharacteristic
40C4×#4314C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45C8×D44C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339—21no—
68C22×Dic22C2×C411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#66983—21no—
71#66983C2×C411yescharacteristic
72#66983C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×#4314C2×C411yescharacteristic
77C2×#4314C2×C411yescharacteristic
78C2×#4314C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4313—21no—
81C2×#4313—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84#66928—21no—
85#66927C2×C411yescharacteristic
86C4×D44—21no—
87C4×D44C2311yescharacteristic
88C4×D44C2311yescharacteristic
89#66922C2×C411yescharacteristic
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8—21no—
97C11×C4⋊C8C2×C411yescharacteristic
98C11×C4⋊C8C2×C411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8C2×C411yescharacteristic
103C11×C22⋊C8C2×C411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C11×C22⋊C8D411yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66881C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66881C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66880C2×C411yescharacteristic
128#66880C2×C411yescharacteristic
129#66880C2×C411yescharacteristic
130#66879—21no—
131#66879—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#18030—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—81no—
153#4339—81no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×Dic22—22no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—41no—
164C2×Dic22C22×C411yescharacteristic
165C2×Dic22C22×C411yescharacteristic
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
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×Dic11—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202#4314—22no—
203#4314—22no—
204#4314—41no—
205#4314—41no—
206#4313—81no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
210#3103—111no—
211#2984—111no—
212#2979—111no—
213#1592—111no—
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#1454D1111yescharacteristic, complemented
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—81no—
240C22⋊D11—81no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249D44—21no—
250D44—21no—
251D44—21no—
252D44—21no—
253D44—42no—
254D44—81no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259Dic22—21no—
260Dic22—21no—
261Dic22—21no—
262Dic22—42no—
263Dic22—81no—
264Dic22#13112yes—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—41no—
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—111no—
291#446—221no—
292#446—221no—
293C8×Q8—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—111no—
300#436—111no—
301#436—221no—
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305#432—111no—
306#432—221no—
307#431—111no—
308#431—221no—
309#431C2×D1111yescharacteristic
310#431C2×D1111yescharacteristic
311#431C2×D1111yescharacteristic
312#408—221no—
313#408—221no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326#322C2×D1111yescharacteristic
327#322C2×D1111yescharacteristic
328#322C2×D1111yescharacteristic
329C82C2×D1111yescharacteristic
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11C2×#13111yescharacteristic
345C4×C11#56811yescharacteristic
346C4×C11#57711yescharacteristic
347C4×C11#57711yescharacteristic
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354C2×#41—221no—
355C22×Q8—111no—
356C2×SD16—111no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—221no—
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—111no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#106—111no—
384#106—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C4×D1111yescharacteristic
397C4⋊C8C4×D1111yescharacteristic
398C4⋊C8D4411yescharacteristic
399C4⋊C8D4411yescharacteristic
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#102—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408C22⋊C8—21no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8C4×D1111yescharacteristic
416C22⋊C8C4×D1111yescharacteristic
417C22⋊C8D4411yescharacteristic
418C22⋊C8D4411yescharacteristic
419#97—221no—
420#97—221no—
421#97—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11#293311yescharacteristic
433C2×C11#294911yescharacteristic
434C2×C11#295511yescharacteristic
435D11—81no—
436D11—81no—
437#41—881no—
438#41—881no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—222no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—441no—
445C2×D4—111no—
446C2×D4—111no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×D4411yescharacteristic
457C22×C4#433911yescharacteristic
458SD16—222no—
459SD16—222no—
460SD16—441no—
461SD16—441no—
462M16—881no—
463M16—881no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—881no—
471C2×C8—881no—
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8C2×D4411yescharacteristic
477C2×C8C2×D4411yescharacteristic
478C2×C8C2×D4411yescharacteristic
479C2×C8C2×D4411yescharacteristic
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42C2×C4×D1111yescharacteristic
499C42C2×D4411yescharacteristic
500C42#433911yescharacteristic
501C42C23×D1111yescharacteristic
502C11#1803011yescharacteristic, complemented, Sylow
503C23—221no—
504C23—221no—
505C23C4×D4411yescharacteristic
506Q8—112no—
507Q8—221no—
508Q8—221no—
509Q8—221no—
510Q8—442no—
511Q8—881no—
512D4—221no—
513D4—221no—
514D4—221no—
515D4—221no—
516D4—442no—
517D4—881no—
518D4—881no—
519D4—881no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4C4×D4411yescharacteristic
538C2×C4C4×D4411yescharacteristic
539C2×C4C4×D4411yescharacteristic
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—441no—
554C8—441no—
555C8—441no—
556C8—441no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22C2×C4×D4411yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—222no—
572C4—441no—
573C4—441no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4D11×#13111yescharacteristic
578C4#1062328111yescharacteristic
579C4#1062328211yescharacteristic
580C4#1062328211yescharacteristic
581C2—41no—
582C2—881no—
583C2—881no—
584C2#1307734411yescharacteristic
585C2#1307747711yescharacteristic
586C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1454C2
socleC22×C11C2×C4×D4
prime radical#10623008C22
cosocleC42×C11C24
hypercenter#1454D11
hypocenterC11#18030
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #13077703C2semidirect
4. #13067520C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067475C2semidirect
8. #13067461C2semidirect
9. #13067454C2semidirect
10. #13067430C2semidirect
11. C8×#4314C2semidirect
12. #13067396C2semidirect
14. #13067012C2semidirect
15. C11×#1454C2semidirect
224. #1454D11semidirect
502. C11#18030semidirect

Maximal subgroups

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

subgroupindex
#130786482
#130777032
#130776822
#130675202
#130675082
#130674962
#130674752
#130674612
#130674542
#130674302
C8×#43142
#130673962
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C11×#14542
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