Finite Group Databasebeta

← #14723737

Subgroups — #14723737

Order 2816.

626 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#13078640C211yesmaximal, characteristic
2#13077590C211yesmaximal, characteristic, complemented
3C8×#4343C211yesmaximal, characteristic, complemented
4#13067494C211yesmaximal, characteristic, complemented
5#13067482C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067439C211yesmaximal, characteristic, complemented
8#13067435C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067393C211yesmaximal, characteristic, complemented
12#13067049C211yesmaximal, characteristic, complemented
13#13067023C211yesmaximal, characteristic, complemented
14#13066907C211yesmaximal, characteristic, complemented
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17C4×#4343C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622800C411yescharacteristic
22#10622798C411yescharacteristic
23C4×#4325C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622504C411yescharacteristic
28#10622498C411yescharacteristic
29#10622453—21no—
30#10622448C2211yescharacteristic
31#10622447—21no—
32#10622447—21no—
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446—21no—
36#10622446C2211yescharacteristic
37#10622432C411yescharacteristic
38#10622427C411yescharacteristic
39#10622424C411yescharacteristic
40#10622409C411yescharacteristic
41#10622321—21no—
42#10622319—21no—
43C4×D88C2211yescharacteristic
44#10622301C2211yescharacteristic
45C8×D44—21no—
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11—21no—
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×D88C2×C411yescharacteristic
77C2×#4313—21no—
78C2×C8×D11—21no—
79C2×C8×D11—21no—
80C2×C8×D11—21no—
81C2×C8×D11D411yescharacteristic
82C2×C8×D11D411yescharacteristic
83#66951—21no—
84#66948C2×C411yescharacteristic
85#66947—21no—
86#66946—21no—
87#66946C2×C411yescharacteristic
88#66945—21no—
89#66945C2×C411yescharacteristic
90#66943C2×C411yescharacteristic
91C4×D44—21no—
92C4×D44—21no—
93C4×D44C2311yescharacteristic
94C4×D44C2311yescharacteristic
95#66925—21no—
96C42×D11—21no—
97C42×D11C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#97—21no—
106C4×C8×C11—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66885C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123#66882C2×C411yescharacteristic
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8C2×C411yescharacteristic
127Dic11⋊C8C2×C411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11D411yescharacteristic
130C8×Dic11D411yescharacteristic
131#66873C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66872C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17909—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147#4343—22no—
148#4343—22no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44C22×C411yescharacteristic
152C2×D44C22×C411yescharacteristic
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11C22×C411yescharacteristic
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11#4111yescharacteristic
160C11×Q16—22no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C2411yescharacteristic
175#4325—22no—
176#4325—22no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203D88—22no—
204#4313—42no—
205C8×D11—41no—
206C8×D11—41no—
207C8×D11—42no—
208C8×D11—42no—
209C8×D11—42no—
210#3102—111no—
211#2966—111no—
212C8×#41—111no—
213#1588—111no—
214#1587D1111yescharacteristic, complemented
215#1586—111no—
216#1585—111no—
217#1580—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221#1572—111no—
222#1488—111no—
223#1482—111no—
224#1452—111no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11C4×D411yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11#13112yes—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244D44—24no—
245D44—21no—
246D44—21no—
247D44—21no—
248D44—42no—
249D44#13112yes—
250C4×D11—24no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—41no—
256C4×D11—42no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—41no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#529—111no—
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#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16C2×D1111yescharacteristic
290C4×SD16—111no—
291C4×SD16—111no—
292C4×D8—111no—
293#436—111no—
294#435—221no—
295C8×D4—111no—
296C8×D4—111no—
297C8×D4—111no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4—221no—
301#433—221no—
302#432—111no—
303#431—111no—
304#431—111no—
305#431—111no—
306#431—221no—
307#405—221no—
308C2×C4×C8—111no—
309C2×C4×C8—221no—
310#335—111no—
311#335—111no—
312#334—111no—
313#334C2×D1111yescharacteristic
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8C2×D1111yescharacteristic
317Q8⋊C8C2×D1111yescharacteristic
318D4⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322#322—111no—
323#322—111no—
324#322—111no—
325#322C2×D1111yescharacteristic
326C22×C11C2×C4×D411yescharacteristic
327C2×D11—22no—
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#13111yescharacteristic
342C4×C11C2×#13111yescharacteristic
343C4×C11#57511yescharacteristic
344C4×C11#57511yescharacteristic
345Dic11—21no—
346Dic11—21no—
347Dic11—21no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C2×Q16C4×D1111yescharacteristic
352C2×SD16—111no—
353C2×SD16—111no—
354C2×D8—111no—
355C2×M16—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—221no—
359C22×C8—221no—
360C22×C8—221no—
361#126—221no—
362#125—111no—
363#124—111no—
364#123—221no—
365C22⋊Q8—111no—
366#121—111no—
367C4×Q8—111no—
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—111no—
371C4×D4—111no—
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4—221no—
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C42—111no—
380C2×C42—221no—
381#107—111no—
382#107C4×D1111yescharacteristic
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—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—111no—
397#103—111no—
398#103C4×D1111yescharacteristic
399#103C4×D1111yescharacteristic
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404C22⋊C8—111no—
405C22⋊C8—111no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—221no—
415C4×C8—21no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C2×C11#292911yescharacteristic
428C2×C11#294311yescharacteristic
429C2×C11#295511yescharacteristic
430D11—41no—
431D11—42no—
432D11—81no—
433#41—222no—
434#41—222no—
435C2×Q8C2×C4×D1111yescharacteristic
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—111no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4—221no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448Q16—22no—
449SD16—222no—
450SD16—222no—
451D8—222no—
452M16—442no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—441no—
464C2×C8—441no—
465C2×C8—442no—
466C2×C8—442no—
467C2×C8—442no—
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8D4×D1111yescharacteristic
471C2×C8D4×D1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C4×D1111yescharacteristic
481C4⋊C4C2×C4×D1111yescharacteristic
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—21no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—221no—
496C42—221no—
497C42C23×D1111yescharacteristic
498C11#1790911yescharacteristic, complemented, Sylow
499C23—111no—
500C23—221no—
501C23—221no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8#6696012yes—
506D4—112no—
507D4—224no—
508D4—221no—
509D4—221no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—224no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—441no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—221no—
550C22—222no—
551C22—221no—
552C22—221no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C4×D4×D1111yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—221no—
565C4—221no—
566C4—221no—
567C4—441no—
568C4—441no—
569C4C2×#6696011yescharacteristic
570C4D11×#13111yescharacteristic
571C4#1062330811yescharacteristic
572C4#1062330811yescharacteristic
573C2—441no—
574C2—442no—
575C2—881no—
576C2#1307730711yescharacteristic
577C2#1307741511yescharacteristic
578C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radical#10622424C4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17909
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
2. #13077590C2semidirect
3. C8×#4343C2semidirect
4. #13067494C2semidirect
5. #13067482C2semidirect
6. #13067471C2semidirect
7. #13067439C2semidirect
8. #13067435C2semidirect
9. #13067431C2semidirect
10. #13067431C2semidirect
11. #13067393C2semidirect
12. #13067049C2semidirect
13. #13067023C2semidirect
14. #13066907C2semidirect
15. C11×#1587C2semidirect
214. #1587D11semidirect
498. C11#17909semidirect

Maximal subgroups

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

subgroupindex
#130786402
#130775902
C8×#43432
#130674942
#130674822
#130674712
#130674392
#130674352
#130674312
#130673932
#130670492
#130670232
#130669072
C11×#15872
#1790911