Finite Group Databasebeta

← #14725188

Subgroups — #14725188

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#13078628C211yesmaximal, characteristic
2#13077776C211yesmaximal, characteristic, complemented
3#13077746C211yesmaximal, characteristic, complemented
4#13067521C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067491C211yesmaximal, characteristic, complemented
8#13067469C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067425C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067392C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1495C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20#10622741—21no—
21#10622741—21no—
22#10622679C411yescharacteristic
23#10622676C411yescharacteristic
24#10622670C411yescharacteristic
25#10622667C411yescharacteristic
26#10622660C411yescharacteristic
27#10622658C411yescharacteristic
28#10622650C411yescharacteristic
29#10622648C411yescharacteristic
30C4×#4326C2211yescharacteristic
31C4×#4325C2211yescharacteristic
32#10622637C2211yescharacteristic
33Q8×C11⋊C8C2211yescharacteristic
34C4×#4324C2211yescharacteristic
35C4×#4323C2211yescharacteristic
36#10622625C2211yescharacteristic
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8C2211yescharacteristic
40#10622613—21no—
41#10622612—21no—
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622451C2211yescharacteristic
46#10622451C2211yescharacteristic
47#10622450—21no—
48#10622446—21no—
49#10622443C2211yescharacteristic
50#10622443C2211yescharacteristic
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622117C2211yescharacteristic
56#10622117C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C2×C11×M16—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×#4326C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4324C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84C4×C22⋊D11—21no—
85C4×C22⋊D11—21no—
86#66979C2×C411yescharacteristic
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C2×#4313—21no—
91C2×#4313—21no—
92C4×D44C2×C411yescharacteristic
93C4×D44C2311yescharacteristic
94#66925—21no—
95C42×D11—21no—
96C4×Dic22C2×C411yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C4×C8×C11C2311yescharacteristic
104C4×C8×C11C2311yescharacteristic
105#66899C2×C411yescharacteristic
106#66899C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)C2×C411yescharacteristic
112C22⋊(C11⋊C8)C2×C411yescharacteristic
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119C8×Dic11—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)—21no—
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18033—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—
153#4339—22no—
154#4339—41no—
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×Dic22C22×C411yescharacteristic
160C11×M16—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182#4326—22no—
183#4325—41no—
184#4324—22no—
185#4323—41no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195#4318—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—81no—
199C2×C11⋊C8—81no—
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—81no—
209#4313—81no—
210#3102—111no—
211#2994—111no—
212#2991—111no—
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#1495D1111yescharacteristic, complemented
223#1477—111no—
224#1454—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
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—41no—
242C2×C4×C11—41no—
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—42no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253D44—21no—
254D44—21no—
255C4×D11—42no—
256C4×D11—42no—
257C4×D11—41no—
258C4×D11—41no—
259Dic22—21no—
260Dic22#13112yes—
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#529C2×D1111yescharacteristic
276C4×#41—111no—
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#436—111no—
295#436—111no—
296#436—221no—
297#436—221no—
298#435—221no—
299C8×D4—111no—
300C8×D4—221no—
301#433—221no—
302#431—111no—
303#431—111no—
304#431—221no—
305#431C2×D1111yescharacteristic
306#424—221no—
307#423—221no—
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⋊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—
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—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11C2×#13111yescharacteristic
344C4×C11#56811yescharacteristic
345C4×C11#57611yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16—111no—
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—21no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C22×C8—221no—
360C22×C8—221no—
361#126—21no—
362#125C4×D1111yescharacteristic
363#124C4×D1111yescharacteristic
364#123—21no—
365C22⋊Q8C4×D1111yescharacteristic
366#121C4×D1111yescharacteristic
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8C22×D1111yescharacteristic
370C4×D4—21no—
371C4×D4—111no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4C22×D1111yescharacteristic
376#117—21no—
377#117—111no—
378#117—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
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—111no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#97—221no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
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—222no—
434#41—441no—
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—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448Q16—222no—
449SD16—222no—
450SD16—441no—
451D8—441no—
452M16—81no—
453M16—881no—
454M16—881no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—881no—
471C2×C8—881no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—111no—
477C4⋊C4—111no—
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—21no—
486C22⋊C4—21no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42C2×C4×D1111yescharacteristic
495C42D4×D1111yescharacteristic
496C42#434111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1803311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—221no—
501C23(C22⋊D11)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—112no—
505Q8—221no—
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—41no—
521C2×C4—41no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—442no—
526C2×C4—442no—
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—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C2×(C22⋊D11)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—222no—
567C4—441no—
568C4—441no—
569C4D11×#13111yescharacteristic
570C4#1062328111yescharacteristic
571C4#1062330511yescharacteristic
572C4#1062331011yescharacteristic
573C2—41no—
574C2—81no—
575C2—881no—
576C2#1307734611yescharacteristic
577C2#1307748711yescharacteristic
578C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1495C2
socleC22×C11C2×C4×D4
prime radical#10622650C4
cosocleC42×C11C24
hypercenter#1495D11
hypocenterC11#18033
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #13077776C2semidirect
3. #13077746C2semidirect
4. #13067521C2semidirect
5. #13067498C2semidirect
6. #13067497C2semidirect
7. #13067491C2semidirect
8. #13067469C2semidirect
9. #13067442C2semidirect
10. #13067425C2semidirect
11. #13067420C2semidirect
12. #13067392C2semidirect
13. #13067004C2semidirect
14. #13066916C2semidirect
15. C11×#1495C2semidirect
222. #1495D11semidirect
498. C11#18033semidirect

Maximal subgroups

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

subgroupindex
#130786282
#130777762
#130777462
#130675212
#130674982
#130674972
#130674912
#130674692
#130674422
#130674252
#130674202
#130673922
#130670042
#130669162
C11×#14952
#1803311