Finite Group Databasebeta

← #14724726

Subgroups — #14724726

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078628C211yesmaximal, characteristic
2#13077633C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13067503C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067469C211yesmaximal, characteristic, complemented
7#13067462C211yesmaximal, characteristic, complemented
8#13067456C211yesmaximal, characteristic, complemented
9#13067442C211yesmaximal, characteristic, complemented
10#13067420C211yesmaximal, characteristic, complemented
11#13067419C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13066999C211yesmaximal, characteristic, complemented
14C8×#4318C211yesmaximal, characteristic, complemented
15C11×#1494C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20#10622679C411yescharacteristic
21#10622676C411yescharacteristic
22#10622670C411yescharacteristic
23#10622667C411yescharacteristic
24#10622660C411yescharacteristic
25#10622658C411yescharacteristic
26#10622650C411yescharacteristic
27#10622648C411yescharacteristic
28C4×#4326C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637C2211yescharacteristic
31Q8×C11⋊C8C2211yescharacteristic
32C4×#4324C2211yescharacteristic
33C4×#4323C2211yescharacteristic
34#10622625—21no—
35#10622625C2211yescharacteristic
36#10622624—21no—
37D4×C11⋊C8C2211yescharacteristic
38#10622613—21no—
39#10622610—21no—
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622443C2211yescharacteristic
46#10622443C2211yescharacteristic
47#10622342—21no—
48#10622342—21no—
49#10622320—21no—
50#10622318—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#10622092C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
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×#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—
88C2×#4318D411yescharacteristic
89C2×#4318D411yescharacteristic
90C22×C11⋊C8—21no—
91C2×#4313—21no—
92C2×#4313—21no—
93C4×D44C2×C411yescharacteristic
94C4×D44C2311yescharacteristic
95#66925—21no—
96C42×D11—21no—
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×#97—21no—
103C4×C8×C11—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—
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)C2×C411yescharacteristic
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867D411yescharacteristic
137#66867D411yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17999—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
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
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—22no—
196#4318—22no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—42no—
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—42no—
210#4313—42no—
211#3102—111no—
212#2971—111no—
213#2969—111no—
214#1590—111no—
215#1589—111no—
216#1584—111no—
217#1583—111no—
218#1583—111no—
219#1581—111no—
220C8×Q16—111no—
221C8×SD16—111no—
222#1572—111no—
223#1494D1111yescharacteristic, complemented
224#1476—111no—
225C8×M16—111no—
226C23×C11—21no—
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—81no—
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—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—42no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254D44—21no—
255D44—21no—
256C4×D11—42no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—81no—
260Dic22—21no—
261Dic22#13112yes—
262C8×C11—22no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13512yes—
275C11⋊C8#13512yes—
276#529C2×D1111yescharacteristic
277C4×#41—111no—
278#485—111no—
279#482—111no—
280#479—111no—
281#478—111no—
282#464—111no—
283#463—111no—
284#452—111no—
285#449—111no—
286#446—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8—111no—
294#436—111no—
295#436—111no—
296#436—111no—
297#436—221no—
298#436—221no—
299#436—221no—
300#435—221no—
301C8×D4—111no—
302#433—221no—
303#432—221no—
304#432C2×D1111yescharacteristic
305#431—111no—
306#431—111no—
307#405—221no—
308C4×M16—111no—
309C4×M16—221no—
310C2×C4×C8C2×D1111yescharacteristic
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8C2×D1111yescharacteristic
318Q8⋊C8C2×D1111yescharacteristic
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8C2×D1111yescharacteristic
322D4⋊C8C2×D1111yescharacteristic
323#322—111no—
324#322—111no—
325C82—111no—
326C82—111no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C2×#13111yescharacteristic
345C4×C11#56811yescharacteristic
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×#13511yescharacteristic
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—111no—
352C2×Q16—111no—
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8—111no—
356C2×M16—111no—
357C2×M16—111no—
358C2×M16—221no—
359C2×M16—221no—
360C2×M16—221no—
361C22×C8—21no—
362C22×C8—221no—
363#126—21no—
364#125C4×D1111yescharacteristic
365#124C4×D1111yescharacteristic
366#123—21no—
367C22⋊Q8C4×D1111yescharacteristic
368#121C4×D1111yescharacteristic
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—111no—
380#117—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—111no—
384#107—111no—
385#106—111no—
386#106—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397#103—111no—
398#103—111no—
399#103—111no—
400#103—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404#102—111no—
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—111no—
415#97—111no—
416#97—221no—
417C4×C8—21no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—81no—
430C2×C11#293311yescharacteristic
431C2×C11C4×#13511yescharacteristic
432C2×C11#295611yescharacteristic
433D11—81no—
434#41—222no—
435#41—441no—
436C2×Q8—111no—
437C2×Q8C2×C4×D1111yescharacteristic
438C2×D4—21no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4C2×C4×D1111yescharacteristic
442C22×C4—21no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4C2×C4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4#434111yescharacteristic
449Q16—222no—
450SD16—222no—
451SD16—441no—
452D8—441no—
453M16—222no—
454M16—222no—
455M16—442no—
456M16—442no—
457M16—442no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—42no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—442no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—111no—
479C4⋊C4—111no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42C2×C4×D1111yescharacteristic
497C42D4×D1111yescharacteristic
498C42#434111yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1799911yescharacteristic, complemented, Sylow
501C23—21no—
502C23—221no—
503C23(C22⋊D11)⋊C411yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—112no—
507Q8—221no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—221no—
512D4—221no—
513D4—442no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—881no—
531C2×C4(C22⋊D11)⋊C411yescharacteristic
532C2×C4(C22⋊D11)⋊C411yescharacteristic
533C2×C4(C22⋊D11)⋊C411yescharacteristic
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434111yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—112no—
542C8—112no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22C2×(C22⋊D11)⋊C411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4D11×#13111yescharacteristic
572C4#1062328111yescharacteristic
573C4D11×#13511yescharacteristic
574C4D11×#13511yescharacteristic
575C2—41no—
576C2—81no—
577C2—881no—
578C2#1307734611yescharacteristic
579C2#1307738411yescharacteristic
580C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1494C2
socleC22×C11C2×C4×D4
prime radical#10622650C4
cosocleC42×C11C24
hypercenter#1494D11
hypocenterC11#17999
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. #13077633C2semidirect
3. #13077621C2semidirect
4. #13067503C2semidirect
5. #13067498C2semidirect
6. #13067469C2semidirect
7. #13067462C2semidirect
8. #13067456C2semidirect
9. #13067442C2semidirect
10. #13067420C2semidirect
11. #13067419C2semidirect
12. #13067397C2semidirect
13. #13066999C2semidirect
14. C8×#4318C2semidirect
15. C11×#1494C2semidirect
223. #1494D11semidirect
500. C11#17999semidirect

Maximal subgroups

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

subgroupindex
#130786282
#130776332
#130776212
#130675032
#130674982
#130674692
#130674622
#130674562
#130674422
#130674202
#130674192
#130673972
#130669992
C8×#43182
C11×#14942
#1799911