Finite Group Databasebeta

← #14725711

Subgroups — #14725711

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079212C211yesmaximal, characteristic
2#13077776C211yesmaximal, characteristic, complemented
3#13077682C211yesmaximal, characteristic, complemented
4#13067521C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067483C211yesmaximal, characteristic, complemented
8#13067455C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067016C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
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#10622625C2211yescharacteristic
35#10622624—21no—
36D4×C11⋊C8—21no—
37D4×C11⋊C8C2211yescharacteristic
38#10622613—21no—
39#10622612—21no—
40#10622538C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622340—21no—
48#10622340—21no—
49#10622301—21no—
50C8×D44—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#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—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×#4325C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83#66983—21no—
84#66983C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318C2×C411yescharacteristic
88C2×#4318C2×C411yescharacteristic
89C22×C11⋊C8—21no—
90C22×C11⋊C8—21no—
91C2×#4313—21no—
92C2×#4313—21no—
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95#66928—21no—
96#66927C2×C411yescharacteristic
97C4×D44—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100#66922C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—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#18082—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—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
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—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183#4325—22no—
184#4325—41no—
185#4323—22no—
186#4323—41no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194#4318—22no—
195#4318—41no—
196#4318—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—81no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#4313—81no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3171—111no—
214#2994—111no—
215#2979—111no—
216#1592—111no—
217#1589—111no—
218#1588—111no—
219#1586—111no—
220#1582—111no—
221#1581—111no—
222#1580—111no—
223C8×SD16—111no—
224#1565—111no—
225#1482D1111yescharacteristic, complemented
226#1480—111no—
227#1453—111no—
228C23×C11—21no—
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237C2×C4×C11—21no—
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—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—81no—
254C22⋊D11—81no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—42no—
262D44—81no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267Dic22—81no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
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—
282#532—111no—
283#529C2×D1111yescharacteristic
284#501—111no—
285#496—111no—
286#490—111no—
287#489—111no—
288#469—111no—
289#469—111no—
290#468—111no—
291#468—111no—
292#446—111no—
293C8×Q8—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296C4×D8—111no—
297C4×D8—111no—
298#436—111no—
299#436—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—221no—
307C8×D4—221no—
308#433—221no—
309#431—111no—
310#431C2×D1111yescharacteristic
311#431C2×D1111yescharacteristic
312#424—221no—
313C2×C4⋊C8—111no—
314#408—221no—
315#408—221no—
316C4×M16—111no—
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321Q8⋊C8C2×D1111yescharacteristic
322Q8⋊C8C2×D1111yescharacteristic
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8C2×D1111yescharacteristic
328D4⋊C8C2×D1111yescharacteristic
329#322—111no—
330#322—111no—
331#322—111no—
332C82—111no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11C2×#13111yescharacteristic
354C4×C11#56811yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357Dic11—41no—
358Dic11—41no—
359C2×#41—221no—
360C2×SD16—111no—
361C2×SD16—111no—
362C2×D8—111no—
363C2×D8—111no—
364C2×M16—111no—
365C2×M16—111no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C4⋊Q8—111no—
374#127—111no—
375#126—21no—
376#125C4×D1111yescharacteristic
377#124—221no—
378#124C4×D1111yescharacteristic
379#123—21no—
380C22⋊Q8C4×D1111yescharacteristic
381#121—111no—
382#121—111no—
383#121—221no—
384#121C4×D1111yescharacteristic
385C4×Q8C22×D1111yescharacteristic
386C4×D4—21no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391#117—21no—
392C2×C42C22×D1111yescharacteristic
393#107—111no—
394#107—111no—
395#106—111no—
396#106—111no—
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8C22×D1111yescharacteristic
406C4⋊C8C22×D1111yescharacteristic
407#103—111no—
408#103—111no—
409#102—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415C22⋊C8—21no—
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—111no—
426#97—111no—
427#97—221no—
428C4×C8—21no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—41no—
437C2×C11—81no—
438C2×C11#293511yescharacteristic
439C2×C11#294611yescharacteristic
440C2×C11#295511yescharacteristic
441D11—81no—
442D11—81no—
443#41—881no—
444#41—881no—
445C2×Q8—221no—
446C2×Q8C2×C4×D1111yescharacteristic
447C2×D4—21no—
448C2×D4—111no—
449C2×D4—111no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4#434111yescharacteristic
461SD16—222no—
462SD16—441no—
463D8—222no—
464D8—441no—
465M16—222no—
466M16—441no—
467M16—881no—
468M16—881no—
469M16—881no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8—881no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4C2×C4×D1111yescharacteristic
496C4⋊C4C2×C4×D1111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—21no—
507C42C2×C4×D1111yescharacteristic
508C42D4×D1111yescharacteristic
509C42#434111yescharacteristic
510C42C23×D1111yescharacteristic
511C11#1808211yescharacteristic, complemented, Sylow
512C23—21no—
513C23—221no—
514C23—221no—
515C23(C22⋊D11)⋊C411yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—881no—
519D4—21no—
520D4—21no—
521D4—42no—
522D4—221no—
523D4—221no—
524D4—221no—
525D4—221no—
526D4—442no—
527D4—881no—
528D4—881no—
529D4—881no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4(C22⋊D11)⋊C411yescharacteristic
547C2×C4(C22⋊D11)⋊C411yescharacteristic
548C2×C4(C22⋊D11)⋊C411yescharacteristic
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434111yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—112no—
557C8—221no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—441no—
565C8—441no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—441no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22C2×(C22⋊D11)⋊C411yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—441no—
587C4—441no—
588C4D11×#13111yescharacteristic
589C4#1062328111yescharacteristic
590C4#1062330011yescharacteristic
591C4#1062330111yescharacteristic
592C2—41no—
593C2—81no—
594C2—881no—
595C2—881no—
596C2#1307735611yescharacteristic
597C2#1307745111yescharacteristic
598C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1482C2
socleC22×C11C2×C4×D4
prime radical#13079212C2
cosocleC42×C11C24
hypercenter#1482D11
hypocenterC11#18082
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #13077776C2semidirect
3. #13077682C2semidirect
4. #13067521C2semidirect
5. #13067498C2semidirect
6. #13067491C2semidirect
7. #13067483C2semidirect
8. #13067455C2semidirect
9. #13067442C2semidirect
10. #13067437C2semidirect
11. #13067413C2semidirect
12. #13067369C2semidirect
13. #13067016C2semidirect
14. #13066911C2semidirect
15. C11×#1482C2semidirect
225. #1482D11semidirect
511. C11#18082semidirect

Maximal subgroups

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

subgroupindex
#130792122
#130777762
#130776822
#130675212
#130674982
#130674912
#130674832
#130674552
#130674422
#130674372
#130674132
#130673692
#130670162
#130669112
C11×#14822
#1808211