Finite Group Databasebeta

← #14724683

Subgroups — #14724683

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078634C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3#13067511C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067464C211yesmaximal, characteristic, complemented
6#13067452C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067445C211yesmaximal, characteristic, complemented
9C8×#4324C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067397C211yesmaximal, characteristic, complemented
12#13067074C211yesmaximal, characteristic, complemented
13#13066998C211yesmaximal, characteristic, complemented
14M16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#2970C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C11×#435—21no—
21C11×#435—21no—
22C8×D4×C11C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24C11×#432—21no—
25C11×#432C2211yescharacteristic
26C4×C11×M16C2211yescharacteristic
27C2×C11×#97—21no—
28#10622852C411yescharacteristic
29#10622851C411yescharacteristic
30#10622741—21no—
31#10622740—21no—
32C4×#4326C2211yescharacteristic
33#10622641C411yescharacteristic
34C4×#4325C2211yescharacteristic
35#10622635C411yescharacteristic
36C4×#4324C2211yescharacteristic
37#10622629C411yescharacteristic
38C4×#4323C2211yescharacteristic
39#10622622C411yescharacteristic
40#10622616C411yescharacteristic
41#10622609C411yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622322—21no—
46#10622321—21no—
47#10622301C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11C2×C411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117C2×C411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87#66982—21no—
88C4×C22⋊D11—21no—
89#66977C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93#66929—21no—
94#66928C2×C411yescharacteristic
95C4×D44C2311yescharacteristic
96#66925—21no—
97#66923C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×#97—21no—
107C11×#97—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66899C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66879—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17996—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×Dic22C22×C411yescharacteristic
160C11×M16—22no—
161C11×M16—22no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11—42no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—41no—
186#4325—41no—
187#4324—22no—
188#4323—22no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209#4313—42no—
210C8×D11—42no—
211#3102—111no—
212#2970D1111yescharacteristic, complemented
213#2969—111no—
214#1591—111no—
215#1590—111no—
216#1584—111no—
217#1582—111no—
218#1582—111no—
219#1581—111no—
220C8×SD16—111no—
221C8×D8—111no—
222#1572—111no—
223#1494—111no—
224#1476—111no—
225C8×M16—111no—
226C23×C11—21no—
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231D4×C11—21no—
232D4×C11—42no—
233D4×C11#13112yes—
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—21no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—81no—
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—81no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256D44—21no—
257D44—21no—
258C4×D11—41no—
259C4×D11—41no—
260Dic22—21no—
261Dic22—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11#13512yes—
267C8×C11#13512yes—
268C11⋊C8—22no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#529—111no—
277C4×#41C2×D1111yescharacteristic
278#485—111no—
279#482—111no—
280#479—111no—
281#478—111no—
282#464—111no—
283#463—111no—
284#452—111no—
285#449—111no—
286#446—111no—
287#446C2×D1111yescharacteristic
288#446C2×D1111yescharacteristic
289C8×Q8—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8—111no—
294#436—111no—
295#436—221no—
296#435—21no—
297#435—21no—
298#435—221no—
299C8×D4—111no—
300C8×D4C2×D1111yescharacteristic
301C8×D4C2×D1111yescharacteristic
302#433—221no—
303#432—21no—
304#432C2×D1111yescharacteristic
305#431—111no—
306#431—111no—
307#405—221no—
308C4×M16C2×D1111yescharacteristic
309C2×#97—21no—
310C2×C4×C8—111no—
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324#322—111no—
325C82—111no—
326C82—111no—
327C22×C11—21no—
328C22×C11—22no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×#13111yescharacteristic
345C4×C11#56811yescharacteristic
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×#13511yescharacteristic
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351C2×#41C4×D1111yescharacteristic
352C2×Q16—111no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8—111no—
356C2×M16—221no—
357C2×M16C22⋊D1111yescharacteristic
358C2×M16C22⋊D1111yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—221no—
362C22×C8—221no—
363#126—221no—
364#125—111no—
365#124—111no—
366#123—221no—
367C22⋊Q8—111no—
368#121—111no—
369C4×Q8—111no—
370C4×Q8C4×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4C4×D1111yescharacteristic
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—221no—
380#117C4×D1111yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397#103—111no—
398#103—111no—
399#103—111no—
400#103—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404#102—111no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—21no—
415#97—21no—
416#97—221no—
417#97C22⋊D1111yescharacteristic
418#97C22⋊D1111yescharacteristic
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—42no—
430C2×C11#293311yescharacteristic
431C2×C11C4×#13511yescharacteristic
432C2×C11#295611yescharacteristic
433D11—81no—
434#41—22no—
435#41—41no—
436C2×Q8—111no—
437C2×Q8C2×C4×D1111yescharacteristic
438C2×D4—21no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4C2×C4×D1111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—221no—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4#433911yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449Q16—441no—
450SD16—222no—
451SD16—441no—
452D8—222no—
453M16—22no—
454M16—22no—
455M16—442no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—42no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—442no—
469C2×C8—442no—
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C2×C8C2×C22⋊D1111yescharacteristic
473C2×C8C2×C22⋊D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—221no—
496C42C2×C4×D1111yescharacteristic
497C42#433911yescharacteristic
498C42C2×C22⋊D1111yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1799611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—221no—
503C23C4×C22⋊D1111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—221no—
507Q8—221no—
508D4—21no—
509D4—42no—
510D4—221no—
511D4—221no—
512D4—881no—
513D4#6696012yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4C4×C22⋊D1111yescharacteristic
532C2×C4C4×C22⋊D1111yescharacteristic
533C2×C4C4×C22⋊D1111yescharacteristic
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×#433911yescharacteristic
536C2×C4C22×C22⋊D1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—222no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8#6700312yes—
550C8#6700312yes—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22C2×C4×C22⋊D1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—441no—
569C4—441no—
570C4—441no—
571C4C2×#6696011yescharacteristic
572C4#1062327611yescharacteristic
573C4C2×#6700311yescharacteristic
574C4C2×#6700311yescharacteristic
575C2—41no—
576C2—42no—
577C2—881no—
578C2#1307734111yescharacteristic
579C2C4×#6700311yescharacteristic
580C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C2×C4×D4
prime radical#10622851C4
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#17996
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13067511C2semidirect
4. #13067506C2semidirect
5. #13067464C2semidirect
6. #13067452C2semidirect
7. #13067450C2semidirect
8. #13067445C2semidirect
9. C8×#4324C2semidirect
10. C8×#4323C2semidirect
11. #13067397C2semidirect
12. #13067074C2semidirect
13. #13066998C2semidirect
14. M16×C11⋊C8C2semidirect
15. C11×#2970C2semidirect
212. #2970D11semidirect
500. C11#17996semidirect

Maximal subgroups

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

subgroupindex
#130786342
#130776202
#130675112
#130675062
#130674642
#130674522
#130674502
#130674452
C8×#43242
C8×#43232
#130673972
#130670742
#130669982
M16×C11⋊C82
C11×#29702
#1799611