Finite Group Databasebeta

← #14724646

Subgroups — #14724646

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079180C211yesmaximal, characteristic
2#13077765C211yesmaximal, characteristic, complemented
3#13077761C211yesmaximal, characteristic, complemented
4#13067490C211yesmaximal, characteristic, complemented
5#13067484C211yesmaximal, characteristic, complemented
6#13067483C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067462C211yesmaximal, characteristic, complemented
9#13067456C211yesmaximal, characteristic, complemented
10#13067455C211yesmaximal, characteristic, complemented
11#13067449C211yesmaximal, characteristic, complemented
12#13067371C211yesmaximal, characteristic, complemented
13#13067082C211yesmaximal, characteristic, complemented
14#13066909C211yesmaximal, characteristic, complemented
15C11×#1495C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20#10622741—21no—
21#10622740—21no—
22#10622681C411yescharacteristic
23#10622677C411yescharacteristic
24#10622672C411yescharacteristic
25#10622669C411yescharacteristic
26#10622664C411yescharacteristic
27#10622661C411yescharacteristic
28#10622654C411yescharacteristic
29#10622651C411yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4325C2211yescharacteristic
32#10622637C2211yescharacteristic
33Q8×C11⋊C8C2211yescharacteristic
34C4×#4324C2211yescharacteristic
35C4×#4323C2211yescharacteristic
36#10622625—21no—
37#10622625C2211yescharacteristic
38#10622624—21no—
39D4×C11⋊C8C2211yescharacteristic
40#10622613—21no—
41#10622612—21no—
42#10622538C2211yescharacteristic
43#10622537C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622453—21no—
46#10622452—21no—
47#10622451C2211yescharacteristic
48#10622447C2211yescharacteristic
49#10622444C2211yescharacteristic
50#10622443C2211yescharacteristic
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622118C2211yescharacteristic
58#10622118C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×M16—21no—
68C11×#126—21no—
69C11×#125C2×C411yescharacteristic
70C11×#124C2×C411yescharacteristic
71C11×#123—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×#121C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11C2311yescharacteristic
77C11×#117—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4324C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83#66983C2×C411yescharacteristic
84#66982—21no—
85C4×C22⋊D11—21no—
86#66977C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318—21no—
89C22×C11⋊C8—21no—
90C22×C11⋊C8C2×C411yescharacteristic
91C22×C11⋊C8C2×C411yescharacteristic
92C2×#4313—21no—
93C2×C8×D11—21no—
94#66929—21no—
95#66928C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117#66879—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120C8×Dic11—21no—
121#66874C2×C411yescharacteristic
122#66874C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66873C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66871C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8C2×C411yescharacteristic
139C4×C11⋊C8C2×C411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17993—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—21no—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×Dic22C22×C411yescharacteristic
156C11×M16—81no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11C22×C411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11#4111yescharacteristic
176C42×C11C2411yescharacteristic
177C22⋊Dic11—21no—
178#4326—41no—
179#4325—41no—
180#4324—41no—
181#4323—41no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193#4318—81no—
194#4318—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8—81no—
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4313—81no—
209C8×D11—81no—
210#3168—111no—
211#2993—111no—
212#2993—111no—
213#1587—111no—
214#1587—111no—
215#1586—111no—
216#1586—111no—
217#1583—111no—
218#1583—111no—
219#1582—111no—
220#1582—111no—
221#1566—111no—
222#1495—111no—
223#1495D1111yescharacteristic, complemented
224#1452—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—81no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253D44—21no—
254D44—21no—
255C4×D11—41no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259C8×C11—41no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#529—111no—
274#529C2×D1111yescharacteristic
275#499—111no—
276#495—111no—
277#488—111no—
278#488—111no—
279#467—111no—
280#466—111no—
281#465—111no—
282#465—111no—
283#446—111no—
284#446—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C4×Q16—111no—
288C4×SD16—111no—
289C4×SD16—111no—
290C4×D8—111no—
291#436—111no—
292#436—111no—
293#436—221no—
294#436—221no—
295#435—221no—
296#435—221no—
297C8×D4—111no—
298C8×D4—111no—
299#433—221no—
300#433—221no—
301#431—111no—
302#431C2×D1111yescharacteristic
303#424—221no—
304#424—221no—
305#423—111no—
306#423C2×D1111yescharacteristic
307C2×C4×C8—111no—
308#334—111no—
309#334—111no—
310#334—111no—
311#334—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8C2×D1111yescharacteristic
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8—111no—
317D4⋊C8—111no—
318D4⋊C8C2×D1111yescharacteristic
319D4⋊C8C2×D1111yescharacteristic
320#322—111no—
321#322—111no—
322#322—111no—
323#322—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×C4×D411yescharacteristic
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#56811yescharacteristic
342C4×C11#56811yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57711yescharacteristic
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C2×Q16—111no—
349C2×SD16—111no—
350C2×SD16—111no—
351C2×D8—111no—
352C2×M16—21no—
353C2×M16—221no—
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—221no—
359C22×C8—221no—
360#126—21no—
361#126—221no—
362#125—111no—
363#125C4×D1111yescharacteristic
364#124—111no—
365#124C4×D1111yescharacteristic
366#123—21no—
367#123—221no—
368C22⋊Q8—111no—
369C22⋊Q8C4×D1111yescharacteristic
370#121—111no—
371#121C4×D1111yescharacteristic
372C4×Q8—111no—
373C4×Q8C22×D1111yescharacteristic
374C4×D4—21no—
375C4×D4—111no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8C22×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398#103—111no—
399#103—111no—
400#103—111no—
401#103—111no—
402#102—111no—
403#102—111no—
404#102—111no—
405#102—111no—
406C22⋊C8—21no—
407C22⋊C8—111no—
408C22⋊C8—111no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—221no—
414#97—221no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—81no—
427C2×C11#293211yescharacteristic
428C2×C11#295211yescharacteristic
429C2×C11#295711yescharacteristic
430D11—81no—
431C2×Q8—111no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—21no—
434C2×D4—111no—
435C2×D4—221no—
436C2×D4C2×C4×D1111yescharacteristic
437C22×C4—21no—
438C22×C4—221no—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4D4×D1111yescharacteristic
441C22×C4#434111yescharacteristic
442Q16—441no—
443SD16—441no—
444SD16—441no—
445D8—441no—
446M16—81no—
447M16—881no—
448M16—881no—
449M16—881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—441no—
465C2×C8—441no—
466C2×C8—881no—
467C2×C8—881no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C4×D1111yescharacteristic
479C4⋊C4C2×C4×D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—221no—
492C42C2×C4×D1111yescharacteristic
493C42D4×D1111yescharacteristic
494C42#434111yescharacteristic
495C42C23×D1111yescharacteristic
496C11#1799311yescharacteristic, complemented, Sylow
497C23—21no—
498C23—221no—
499C23(C22⋊D11)⋊C411yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—221no—
503Q8—221no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—221no—
508D4—221no—
509D4—881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4(C22⋊D11)⋊C411yescharacteristic
526C2×C4(C22⋊D11)⋊C411yescharacteristic
527C2×C4(C22⋊D11)⋊C411yescharacteristic
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434111yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—221no—
536C8—221no—
537C8—221no—
538C8—221no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—221no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22C2×(C22⋊D11)⋊C411yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4#1062328111yescharacteristic
566C4#1062328111yescharacteristic
567C4#1062330611yescharacteristic
568C4#1062330911yescharacteristic
569C2—41no—
570C2—81no—
571C2—881no—
572C2#1307733111yescharacteristic
573C2#1307749511yescharacteristic
574C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1495C2
socleC22×C11C2×C4×D4
prime radical#10622651C4
cosocleC42×C11C24
hypercenter#1495D11
hypocenterC11#17993
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #13077765C2semidirect
3. #13077761C2semidirect
4. #13067490C2semidirect
5. #13067484C2semidirect
6. #13067483C2semidirect
7. #13067477C2semidirect
8. #13067462C2semidirect
9. #13067456C2semidirect
10. #13067455C2semidirect
11. #13067449C2semidirect
12. #13067371C2semidirect
13. #13067082C2semidirect
14. #13066909C2semidirect
15. C11×#1495C2semidirect
223. #1495D11semidirect
496. C11#17993semidirect

Maximal subgroups

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

subgroupindex
#130791802
#130777652
#130777612
#130674902
#130674842
#130674832
#130674772
#130674622
#130674562
#130674552
#130674492
#130673712
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