Finite Group Databasebeta

← #14724409

Subgroups — #14724409

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079212C211yesmaximal, characteristic
2#13077765C211yesmaximal, characteristic, complemented
3#13077694C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067521C211yesmaximal, characteristic, complemented
6#13067503C211yesmaximal, characteristic, complemented
7#13067498C211yesmaximal, characteristic, complemented
8#13067437C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067068C211yesmaximal, characteristic, complemented
14C8×#4318C211yesmaximal, characteristic, complemented
15C11×#1494C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622680C411yescharacteristic
21#10622678C411yescharacteristic
22#10622671C411yescharacteristic
23#10622668C411yescharacteristic
24#10622662C411yescharacteristic
25#10622662C411yescharacteristic
26#10622652C411yescharacteristic
27#10622652C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637C2211yescharacteristic
31Q8×C11⋊C8C2211yescharacteristic
32C4×#4323C2211yescharacteristic
33C4×#4323C2211yescharacteristic
34#10622625—21no—
35#10622625C2211yescharacteristic
36#10622624—21no—
37D4×C11⋊C8C2211yescharacteristic
38#10622613—21no—
39#10622612—21no—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622340—21no—
48#10622340—21no—
49#10622319—21no—
50#10622319—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#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622092C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C22×C8×C11—21no—
69C11×#126—21no—
70C11×#125C2×C411yescharacteristic
71C11×#124C2×C411yescharacteristic
72C11×#123—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×#121C2×C411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84#66983—21no—
85#66983C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318C2×C411yescharacteristic
90C2×#4318C2×C411yescharacteristic
91C22×C11⋊C8—21no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96#66928—21no—
97#66927C2×C411yescharacteristic
98C4×D44—21no—
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101#66922C2×C411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×#97—21no—
106C4×C8×C11—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66899C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66873C2×C411yescharacteristic
122#66873C2×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—
137#66867C2×C411yescharacteristic
138#66867C2×C411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17968—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×C22⋊D11—21no—
154#4339—81no—
155#4339—81no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×Dic22—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—42no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
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—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184#4325—22no—
185#4325—22no—
186#4323—22no—
187#4323—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195#4318—22no—
196#4318—22no—
197#4318—81no—
198#4318—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4313—81no—
211#4313—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3171—111no—
215#2993—111no—
216#2981—111no—
217#1594—111no—
218#1592—111no—
219#1590—111no—
220#1589—111no—
221#1580—111no—
222SD16⋊C8—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1569—111no—
226#1494D1111yescharacteristic, complemented
227#1492—111no—
228C8×M16—111no—
229C23×C11—21no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—81no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—81no—
255C22⋊D11—81no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—81no—
263D44—81no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268Dic22—81no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8#13112yes—
282C11⋊C8#13112yes—
283#532—111no—
284#529C2×D1111yescharacteristic
285#501—111no—
286#496—111no—
287#490—111no—
288#489—111no—
289#469—111no—
290#469—111no—
291#468—111no—
292#468—111no—
293#446—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×D8—111no—
298C4×D8—111no—
299#436—111no—
300#436—111no—
301#436—111no—
302#436—221no—
303#435—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309#433—221no—
310#432C2×D1111yescharacteristic
311#431—111no—
312#424—221no—
313#423—111no—
314#408—221no—
315#408—221no—
316C4×M16—111no—
317C2×C4×C8C2×D1111yescharacteristic
318#335—111no—
319#335—111no—
320#334—111no—
321#334—111no—
322Q8⋊C8C2×D1111yescharacteristic
323Q8⋊C8C2×D1111yescharacteristic
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329D4⋊C8C2×D1111yescharacteristic
330#322—111no—
331#322—111no—
332C82—111no—
333C82—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×C4×D411yescharacteristic
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11C2×#13111yescharacteristic
355C4×C11C2×#13111yescharacteristic
356C4×C11#57611yescharacteristic
357C4×C11#57711yescharacteristic
358Dic11—41no—
359Dic11—41no—
360C2×#41—221no—
361C2×SD16—111no—
362C2×SD16—111no—
363C2×D8—111no—
364C2×D8—111no—
365C2×M16—111no—
366C2×M16—111no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—21no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376#127—111no—
377#126—21no—
378#125C4×D1111yescharacteristic
379#124—221no—
380#124C4×D1111yescharacteristic
381#123—21no—
382C22⋊Q8C4×D1111yescharacteristic
383#121—111no—
384#121—111no—
385#121—221no—
386#121C4×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4C22×D1111yescharacteristic
393#117—21no—
394C2×C42C22×D1111yescharacteristic
395#107—111no—
396#107—111no—
397#106—111no—
398#106—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—111no—
409#103—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416C22⋊C8—21no—
417C22⋊C8—111no—
418C22⋊C8—111no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—21no—
426#97—111no—
427#97—111no—
428#97—221no—
429C4×C8—21no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—41no—
438C2×C11—81no—
439C2×C11#293111yescharacteristic
440C2×C11#294611yescharacteristic
441C2×C11#295611yescharacteristic
442D11—81no—
443D11—81no—
444#41—881no—
445#41—881no—
446C2×Q8—221no—
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—21no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4#434111yescharacteristic
462SD16—222no—
463SD16—222no—
464D8—222no—
465D8—222no—
466M16—222no—
467M16—222no—
468M16—881no—
469M16—881no—
470M16—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8—881no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C42—21no—
509C42C2×C4×D1111yescharacteristic
510C42D4×D1111yescharacteristic
511C42#434111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—221no—
516C23—221no—
517C23(C22⋊D11)⋊C411yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—881no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—221no—
525D4—221no—
526D4—221no—
527D4—221no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4(C22⋊D11)⋊C411yescharacteristic
549C2×C4(C22⋊D11)⋊C411yescharacteristic
550C2×C4(C22⋊D11)⋊C411yescharacteristic
551C2×C4C22×C4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—112no—
559C8—112no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—441no—
567C8—441no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22C2×(C22⋊D11)⋊C411yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—441no—
589C4—441no—
590C4D11×#13111yescharacteristic
591C4D11×#13111yescharacteristic
592C4#1062330011yescharacteristic
593C4#1062330111yescharacteristic
594C2—41no—
595C2—81no—
596C2—881no—
597C2—881no—
598C2#1307732411yescharacteristic
599C2#1307745111yescharacteristic
600C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1494C2
socleC22×C11C2×C4×D4
prime radical#13079212C2
cosocleC42×C11C24
hypercenter#1494D11
hypocenterC11#17968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #13077765C2semidirect
3. #13077694C2semidirect
4. #13067527C2semidirect
5. #13067521C2semidirect
6. #13067503C2semidirect
7. #13067498C2semidirect
8. #13067437C2semidirect
9. #13067431C2semidirect
10. #13067413C2semidirect
11. #13067408C2semidirect
12. #13067384C2semidirect
13. #13067068C2semidirect
14. C8×#4318C2semidirect
15. C11×#1494C2semidirect
226. #1494D11semidirect
513. C11#17968semidirect

Maximal subgroups

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

subgroupindex
#130792122
#130777652
#130776942
#130675272
#130675212
#130675032
#130674982
#130674372
#130674312
#130674132
#130674082
#130673842
#130670682
C8×#43182
C11×#14942
#1796811