Finite Group Databasebeta

← #14725556

Subgroups — #14725556

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079180C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3#13067511C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067459C211yesmaximal, characteristic, complemented
6#13067457C211yesmaximal, characteristic, complemented
7#13067452C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067362C211yesmaximal, characteristic, complemented
12#13067024C211yesmaximal, characteristic, complemented
13#13067022C211yesmaximal, characteristic, complemented
14M16×C11⋊C8C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623010C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#405—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622681C411yescharacteristic
31#10622677C411yescharacteristic
32#10622672C411yescharacteristic
33#10622669C411yescharacteristic
34#10622664C411yescharacteristic
35#10622661C411yescharacteristic
36#10622654C411yescharacteristic
37#10622651C411yescharacteristic
38C4×#4326C2211yescharacteristic
39C4×#4325C2211yescharacteristic
40C4×#4324C2211yescharacteristic
41C4×#4323C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622322—21no—
46#10622321—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#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622093C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×M16—21no—
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C22×C8×C11—21no—
71C11×#126—21no—
72C11×#125C2×C411yescharacteristic
73C11×#124C2×C411yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4325C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87#66982—21no—
88C4×C22⋊D11—21no—
89#66977C2×C411yescharacteristic
90C22×C11⋊C8C2×C411yescharacteristic
91C22×C11⋊C8C2×C411yescharacteristic
92C2×#4313—21no—
93C2×C8×D11—21no—
94#66929—21no—
95#66928C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98#66923C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C11×#97D411yescharacteristic
109C11×#97D411yescharacteristic
110C4×C8×C11—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
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)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4×C11⋊C8—21no—
138C4×C11⋊C8C2×C411yescharacteristic
139C4×C11⋊C8C2×C411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18069—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×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×Dic22C22×C411yescharacteristic
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—42no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—42no—
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4326—22no—
184#4325—41no—
185#4324—41no—
186#4323—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208#4313—42no—
209C8×D11—42no—
210#3168—111no—
211#2969—111no—
212#2969D1111yescharacteristic, complemented
213#1591—111no—
214#1589—111no—
215#1583—111no—
216#1583—111no—
217#1582—111no—
218#1582—111no—
219C8×Q16—111no—
220C8×D8—111no—
221#1564—111no—
222#1482—111no—
223#1482—111no—
224C8×M16—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227C22×D11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—81no—
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—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253D44—21no—
254D44—21no—
255C4×D11—41no—
256C4×D11—41no—
257Dic22—21no—
258Dic22—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11#13512yes—
264C8×C11#13512yes—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8#13112yes—
273#529—111no—
274#529C2×D1111yescharacteristic
275#499—111no—
276#495—111no—
277#488—111no—
278#488—111no—
279#467—111no—
280#466—111no—
281#465—111no—
282#465—111no—
283#446—111no—
284#446C2×D1111yescharacteristic
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C4×Q16—111no—
288C4×SD16—111no—
289C4×SD16—111no—
290C4×D8—111no—
291#436—21no—
292#436—111no—
293#436—221no—
294#436C2×D1111yescharacteristic
295#435—21no—
296#435—221no—
297C8×D4—111no—
298C8×D4C2×D1111yescharacteristic
299#433—21no—
300#433—221no—
301#431—111no—
302#431—111no—
303#431C2×D1111yescharacteristic
304#405—21no—
305#405—221no—
306C4×M16C2×D1111yescharacteristic
307C2×C4×C8—111no—
308#335—111no—
309#335—111no—
310#334—111no—
311#334—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318D4⋊C8—111no—
319D4⋊C8—111no—
320#322—111no—
321#322—111no—
322C82—111no—
323C82—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×C4×D411yescharacteristic
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#13111yescharacteristic
342C4×C11#56811yescharacteristic
343C4×C11C2×#13511yescharacteristic
344C4×C11C2×#13511yescharacteristic
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C2×Q16—111no—
349C2×SD16—111no—
350C2×SD16—111no—
351C2×D8—111no—
352C2×M16—21no—
353C2×M16—221no—
354C2×M16C22⋊D1111yescharacteristic
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—21no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—221no—
360#126—21no—
361#126—221no—
362#125—111no—
363#125C4×D1111yescharacteristic
364#124—111no—
365#124C4×D1111yescharacteristic
366#123—21no—
367#123—221no—
368C22⋊Q8—111no—
369C22⋊Q8C4×D1111yescharacteristic
370#121—111no—
371#121C4×D1111yescharacteristic
372C4×Q8—111no—
373C4×Q8C22×D1111yescharacteristic
374C4×D4—21no—
375C4×D4—111no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—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—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400#102—111no—
401#102—111no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409#97—21no—
410#97—221no—
411#97C22⋊D1111yescharacteristic
412#97C22⋊D1111yescharacteristic
413C4×C8—21no—
414C4×C8—21no—
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×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—81no—
427C2×C11#293511yescharacteristic
428C2×C11C4×#13511yescharacteristic
429C2×C11#295711yescharacteristic
430D11—81no—
431C2×Q8—111no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—21no—
434C2×D4—111no—
435C2×D4—221no—
436C2×D4C2×C4×D1111yescharacteristic
437C22×C4—21no—
438C22×C4—221no—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4#433911yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442Q16—222no—
443SD16—441no—
444SD16—441no—
445D8—222no—
446M16—22no—
447M16—22no—
448M16—42no—
449M16—442no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—441no—
463C2×C8—442no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C4×D1111yescharacteristic
479C4⋊C4C2×C4×D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
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—221no—
492C42C2×C4×D1111yescharacteristic
493C42#433911yescharacteristic
494C42C2×C22⋊D1111yescharacteristic
495C42C23×D1111yescharacteristic
496C11#1806911yescharacteristic, complemented, Sylow
497C23—21no—
498C23—221no—
499C23C4×C22⋊D1111yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—221no—
503Q8—221no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—221no—
508D4—221no—
509D4—881no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4C4×C22⋊D1111yescharacteristic
526C2×C4C4×C22⋊D1111yescharacteristic
527C2×C4C4×C22⋊D1111yescharacteristic
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×#433911yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—112no—
536C8—221no—
537C8—221no—
538C8—221no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C8#6700312yes—
544C8#6700312yes—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22C2×C4×C22⋊D1111yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4D11×#13111yescharacteristic
566C4#1062328111yescharacteristic
567C4C2×#6700311yescharacteristic
568C4C2×#6700311yescharacteristic
569C2—41no—
570C2—81no—
571C2—881no—
572C2#1307735811yescharacteristic
573C2C4×#6700311yescharacteristic
574C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×C4×D4
prime radical#10622651C4
cosocleC42×C11C24
hypercenter#2969D11
hypocenterC11#18069
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13067511C2semidirect
4. #13067499C2semidirect
5. #13067459C2semidirect
6. #13067457C2semidirect
7. #13067452C2semidirect
8. #13067450C2semidirect
9. C8×#4326C2semidirect
10. C8×#4323C2semidirect
11. #13067362C2semidirect
12. #13067024C2semidirect
13. #13067022C2semidirect
14. M16×C11⋊C8C2semidirect
15. C11×#2969C2semidirect
212. #2969D11semidirect
496. C11#18069semidirect

Maximal subgroups

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

subgroupindex
#130791802
#130776202
#130675112
#130674992
#130674592
#130674572
#130674522
#130674502
C8×#43262
C8×#43232
#130673622
#130670242
#130670222
M16×C11⋊C82
C11×#29692
#1806911