Finite Group Databasebeta

← #14723724

Subgroups — #14723724

Order 2816.

626 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#13077585C211yesmaximal, characteristic, complemented
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13067491C211yesmaximal, characteristic, complemented
5#13067484C211yesmaximal, characteristic, complemented
6#13067477C211yesmaximal, characteristic, complemented
7#13067470C211yesmaximal, characteristic, complemented
8#13067437C211yesmaximal, characteristic, complemented
9#13067432C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067425C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13067025C211yesmaximal, characteristic, complemented
14#13066909C211yesmaximal, characteristic, complemented
15C11×#1488C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622852C411yescharacteristic
21#10622851C411yescharacteristic
22C4×#4326C2211yescharacteristic
23#10622641C411yescharacteristic
24C4×#4325C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622635C411yescharacteristic
28C4×#4324C2211yescharacteristic
29#10622629C411yescharacteristic
30C4×#4323C2211yescharacteristic
31D4×C11⋊C8—21no—
32D4×C11⋊C8—21no—
33D4×C11⋊C8C2211yescharacteristic
34D4×C11⋊C8C2211yescharacteristic
35#10622622C411yescharacteristic
36#10622616C411yescharacteristic
37#10622609C411yescharacteristic
38#10622538—21no—
39#10622538C2211yescharacteristic
40#10622538C2211yescharacteristic
41C2×C4×C11⋊C8—21no—
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622447C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622343—21no—
48(C22⋊D11)⋊C8—21no—
49#10622322—21no—
50#10622321—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C4×Q8×C11C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2311yescharacteristic
74C11×#117—21no—
75C11×#117C2×C411yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×#4326C2×C411yescharacteristic
79C2×#4325C2×C411yescharacteristic
80C2×#4324C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82#66983C2×C411yescharacteristic
83#66982—21no—
84C4×C22⋊D11—21no—
85#66977C2×C411yescharacteristic
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8D411yescharacteristic
89C22×C11⋊C8D411yescharacteristic
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⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×#97—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66899C2×C411yescharacteristic
107#66899C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
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)C2×C411yescharacteristic
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4×C11⋊C8—21no—
136C4×C11⋊C8—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8D411yescharacteristic
139C4×C11⋊C8D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17909—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
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
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C4⋊C4C22×C411yescharacteristic
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C22×C411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11#4111yescharacteristic
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179#4326—22no—
180#4325—22no—
181#4324—22no—
182#4323—22no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—42no—
199C2×C11⋊C8—42no—
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—42no—
209C8×D11—42no—
210#3102—111no—
211#2966—111no—
212C8×#41—111no—
213#1588—111no—
214#1587—111no—
215#1586—111no—
216#1585—111no—
217#1580—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221#1572—111no—
222#1488D1111yescharacteristic, complemented
223#1482—111no—
224#1452—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11#13112yes—
230D4×C11—24no—
231D4×C11—21no—
232D4×C11#13112yes—
233C2×C4×C11—24no—
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×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—41no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
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×Q8—111no—
288C8×Q8—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C4×D8—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—111no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4—221no—
301#433—221no—
302#432C2×D1111yescharacteristic
303#431—111no—
304#431—111no—
305#431—221no—
306#431C2×D1111yescharacteristic
307#405—221no—
308C2×C4×C8—111no—
309C2×C4×C8—221no—
310#335—111no—
311#335—111no—
312#334—111no—
313#334—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8C2×D1111yescharacteristic
317Q8⋊C8C2×D1111yescharacteristic
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8C2×D1111yescharacteristic
321D4⋊C8C2×D1111yescharacteristic
322#322—111no—
323#322—111no—
324#322—111no—
325#322—111no—
326C22×C11—21no—
327C22×C11—22no—
328C22×C11—21no—
329C22×C11—21no—
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×C11C2×#13111yescharacteristic
345C4×C11#57511yescharacteristic
346C4×C11#57511yescharacteristic
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41C4×D1111yescharacteristic
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—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—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103—111no—
399#103—111no—
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—111no—
407C22⋊C8—111no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
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×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11—41no—
428C2×C11—42no—
429C2×C11#292911yescharacteristic
430C2×C11#294311yescharacteristic
431C2×C11#295511yescharacteristic
432D11—81no—
433#41—22no—
434#41—22no—
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×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448Q16—222no—
449SD16—222no—
450SD16—222no—
451D8—222no—
452M16—442no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C2×C8—441no—
469C2×C8—441no—
470C2×C8—442no—
471C2×C8—442no—
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
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1790911yescharacteristic, complemented, Sylow
499C23—21no—
500C23—221no—
501C23(C22⋊D11)⋊C411yescharacteristic
502Q8—21no—
503Q8—221no—
504Q8—221no—
505Q8#6696012yes—
506D4—24no—
507D4—21no—
508D4—221no—
509D4—221no—
510D4—442no—
511D4#6696012yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
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×C4(C22⋊D11)⋊C411yescharacteristic
530C2×C4(C22⋊D11)⋊C411yescharacteristic
531C2×C4(C22⋊D11)⋊C411yescharacteristic
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×#434111yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—221no—
540C8—221no—
541C8—221no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—22no—
552C22—21no—
553C22—41no—
554C22—41no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×(C22⋊D11)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—22no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—441no—
567C4—441no—
568C4—441no—
569C4C2×#6696011yescharacteristic
570C4C2×#6696011yescharacteristic
571C4#1062329911yescharacteristic
572C4#1062329911yescharacteristic
573C2—41no—
574C2—42no—
575C2—881no—
576C2#1307730611yescharacteristic
577C2#1307741211yescharacteristic
578C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1488C2
socleC22×C11C2×C4×D4
prime radical#10622851C4
cosocleC42×C11C24
hypercenter#1488D11
hypocenterC11#17909
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #13077585C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13067491C2semidirect
5. #13067484C2semidirect
6. #13067477C2semidirect
7. #13067470C2semidirect
8. #13067437C2semidirect
9. #13067432C2semidirect
10. #13067431C2semidirect
11. #13067425C2semidirect
12. #13067397C2semidirect
13. #13067025C2semidirect
14. #13066909C2semidirect
15. C11×#1488C2semidirect
222. #1488D11semidirect
498. C11#17909semidirect

Maximal subgroups

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

subgroupindex
#130786342
#130775852
#41×C11⋊C82
#130674912
#130674842
#130674772
#130674702
#130674372
#130674322
#130674312
#130674252
#130673972
#130670252
#130669092
C11×#14882
#1790911