Finite Group Databasebeta

← #14725182

Subgroups — #14725182

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078634C211yesmaximal, characteristic
2#13077778C211yesmaximal, characteristic, complemented
3#13067518C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067494C211yesmaximal, characteristic, complemented
6#13067492C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067392C211yesmaximal, characteristic, complemented
12#13067079C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2991C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623010C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#436C2211yescharacteristic
24C11×#431—21no—
25C11×#431C2211yescharacteristic
26C11×#423—21no—
27C11×#423C2211yescharacteristic
28#10622852C411yescharacteristic
29#10622851C411yescharacteristic
30C4×#4326C2211yescharacteristic
31#10622641C411yescharacteristic
32C4×#4325C2211yescharacteristic
33#10622635C411yescharacteristic
34C4×#4324C2211yescharacteristic
35#10622629C411yescharacteristic
36C4×#4323C2211yescharacteristic
37#10622622C411yescharacteristic
38#10622616C411yescharacteristic
39#10622609C411yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622453—21no—
44#10622452—21no—
45#10622343—21no—
46(C22⋊D11)⋊C8—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#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C11×#117—21no—
78C11×#117C2×C411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86#66982—21no—
87C4×C22⋊D11—21no—
88#66977C2×C411yescharacteristic
89C22×C11⋊C8—21no—
90C2×#4313—21no—
91C2×C8×D11—21no—
92#66929—21no—
93#66928C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95#66925—21no—
96#66923C2×C411yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8D411yescharacteristic
102C11×C4⋊C8D411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8D411yescharacteristic
108C11×C22⋊C8D411yescharacteristic
109C4×C8×C11—21no—
110C4×C8×C11—21no—
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)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18033—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—81no—
161C11×M16—81no—
162C11×M16—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184#4326—22no—
185#4325—22no—
186#4324—41no—
187#4323—41no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208#4313—81no—
209C8×D11—81no—
210#3102—111no—
211#2994—111no—
212#2991D1111yescharacteristic, complemented
213#1592—111no—
214#1589—111no—
215#1588—111no—
216#1588—111no—
217#1584—111no—
218#1581—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221#1571—111no—
222#1495—111no—
223#1477—111no—
224#1454—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11#13112yes—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—42no—
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—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—42no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255D44—21no—
256D44—21no—
257C4×D11—41no—
258C4×D11—41no—
259Dic22—21no—
260Dic22—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#529—111no—
276C4×#41C2×D1111yescharacteristic
277#485—111no—
278#482—111no—
279#479—111no—
280#478—111no—
281#464—111no—
282#463—111no—
283#452—111no—
284#449—111no—
285#446—111no—
286C8×Q8—111no—
287C8×Q8C2×D1111yescharacteristic
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C4×D8—111no—
293#436—21no—
294#436—21no—
295#436—111no—
296#436C2×D1111yescharacteristic
297#436C2×D1111yescharacteristic
298#435—221no—
299C8×D4—111no—
300C8×D4—221no—
301#433—221no—
302#431—21no—
303#431—111no—
304#431—111no—
305#431C2×D1111yescharacteristic
306#424—221no—
307#423—21no—
308#423C2×D1111yescharacteristic
309C2×C4⋊C8—111no—
310#335—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322#322—111no—
323#322—111no—
324#322—111no—
325C82—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—21no—
337C4×C11—22no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11C2×#13111yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41C4×D1111yescharacteristic
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—221no—
359C22×C8—221no—
360C22×C8—221no—
361#126—221no—
362#125—111no—
363#124—111no—
364#123—221no—
365C22⋊Q8—111no—
366#121—111no—
367C4×Q8—111no—
368C4×Q8C4×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4C4×D1111yescharacteristic
375C4×D4C22×D1111yescharacteristic
376#117—21no—
377#117—221no—
378#117C4×D1111yescharacteristic
379C2×C42—21no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—21no—
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⋊C8C22⋊D1111yescharacteristic
397C4⋊C8C22⋊D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
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—21no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8C22⋊D1111yescharacteristic
416C22⋊C8C22⋊D1111yescharacteristic
417#97—221no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11—81no—
429C2×C11#293311yescharacteristic
430C2×C11#295111yescharacteristic
431C2×C11#295511yescharacteristic
432D11—81no—
433#41—22no—
434#41—41no—
435C2×Q8—111no—
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—21no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4C2×C4×D1111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—221no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4#433911yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448Q16—222no—
449SD16—222no—
450SD16—441no—
451D8—441no—
452M16—81no—
453M16—81no—
454M16—81no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—881no—
467C2×C8—881no—
468C2×C8C2×C22⋊D1111yescharacteristic
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C4×D1111yescharacteristic
481C4⋊C4C2×C4×D1111yescharacteristic
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—21no—
492C42—21no—
493C42—221no—
494C42C2×C4×D1111yescharacteristic
495C42#433911yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1803311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—221no—
501C23C4×C22⋊D1111yescharacteristic
502Q8—21no—
503Q8—221no—
504Q8—221no—
505Q8#6696012yes—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4C4×C22⋊D1111yescharacteristic
530C2×C4C4×C22⋊D1111yescharacteristic
531C2×C4C4×C22⋊D1111yescharacteristic
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—221no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×C4×C22⋊D1111yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—22no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4C2×#6696011yescharacteristic
570C4#1062327611yescharacteristic
571C4#1062336611yescharacteristic
572C4#1062336911yescharacteristic
573C2—41no—
574C2—81no—
575C2—881no—
576C2#1307734111yescharacteristic
577C2#1307748911yescharacteristic
578C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2991C2
socleC22×C11C2×C4×D4
prime radical#10622851C4
cosocleC42×C11C24
hypercenter#2991D11
hypocenterC11#18033
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #13077778C2semidirect
3. #13067518C2semidirect
4. #13067499C2semidirect
5. #13067494C2semidirect
6. #13067492C2semidirect
7. #13067466C2semidirect
8. #13067443C2semidirect
9. #13067426C2semidirect
10. C8×#4326C2semidirect
11. #13067392C2semidirect
12. #13067079C2semidirect
13. #13067003C2semidirect
14. #13066916C2semidirect
15. C11×#2991C2semidirect
212. #2991D11semidirect
498. C11#18033semidirect

Maximal subgroups

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

subgroupindex
#130786342
#130777782
#130675182
#130674992
#130674942
#130674922
#130674662
#130674432
#130674262
C8×#43262
#130673922
#130670792
#130670032
#130669162
C11×#29912
#1803311