Finite Group Databasebeta

← #14723936

Subgroups — #14723936

Order 2816.

620 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#13078640C211yesmaximal, characteristic
2#13077768C211yesmaximal, characteristic, complemented
3#13077726C211yesmaximal, characteristic, complemented
4#13067494C211yesmaximal, characteristic, complemented
5#13067471C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067431C211yesmaximal, characteristic, complemented
8#13067431C211yesmaximal, characteristic, complemented
9Q16×C11⋊C8C211yesmaximal, characteristic, complemented
10#13067410C211yesmaximal, characteristic, complemented
11#13067389C211yesmaximal, characteristic, complemented
12#13067054C211yesmaximal, characteristic, complemented
13#13067028C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1584C211yesmaximal, 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#10622452—21no—
30#10622451—21no—
31#10622450C2211yescharacteristic
32#10622447—21no—
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35D11×C4⋊C8—21no—
36D11×C4⋊C8C2211yescharacteristic
37#10622432C411yescharacteristic
38#10622427C411yescharacteristic
39#10622424C411yescharacteristic
40#10622409C411yescharacteristic
41#10622322—21no—
42#10622319—21no—
43C4×D88C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×#4313C2211yescharacteristic
46C8×D44—21no—
47C8×D44C2211yescharacteristic
48#10622298—21no—
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic
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#10622096C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
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×#4313—21no—
79C2×#4313—21no—
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84#66951—21no—
85#66948C2×C411yescharacteristic
86#66947—21no—
87#66946—21no—
88#66946C2×C411yescharacteristic
89#66945—21no—
90#66945C2×C411yescharacteristic
91#66943C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44—21no—
94C4×D44C2311yescharacteristic
95C4×D44C2311yescharacteristic
96#66925—21no—
97C42×D11—21no—
98C42×D11C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#97—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8C2×C411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122(C2×D11)⋊C8D411yescharacteristic
123#66882C2×C411yescharacteristic
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
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#17926—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—
205#4313—81no—
206#4313—81no—
207C8×D11—81no—
208C8×D11—81no—
209C8×D11—81no—
210C8×D11—81no—
211#3102—111no—
212#2993—111no—
213#2988—111no—
214#1588—111no—
215#1585—111no—
216#1584D1111yescharacteristic, complemented
217#1581—111no—
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221C8×D8—111no—
222#1571—111no—
223#1489—111no—
224#1483—111no—
225#1453—111no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11#13112yes—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244C2×Dic11C4×D411yescharacteristic
245D44—24no—
246D44—21no—
247D44—21no—
248D44—21no—
249D44—81no—
250D44#13112yes—
251C4×D11—24no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—81no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—41no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—22no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#529—111no—
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#446C2×D1111yescharacteristic
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8C2×D1111yescharacteristic
290C4×Q16C2×D1111yescharacteristic
291C4×SD16—111no—
292C4×SD16—111no—
293C4×D8—111no—
294#436—111no—
295#436—221no—
296#435—221no—
297C8×D4—111no—
298C8×D4—111no—
299C8×D4—111no—
300C8×D4—221no—
301C8×D4—221no—
302#433—221no—
303#431—111no—
304#431—111no—
305#431—221no—
306#424—221no—
307#423—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—221no—
310C4×M16—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#335C2×D1111yescharacteristic
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8C2×D1111yescharacteristic
318Q8⋊C8C2×D1111yescharacteristic
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324#322—111no—
325#322C2×D1111yescharacteristic
326C82—111no—
327C22×C11C2×C4×D411yescharacteristic
328C2×D11—22no—
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—41no—
337C4×C11—22no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C2×#13111yescharacteristic
343C4×C11C2×#13111yescharacteristic
344C4×C11#57611yescharacteristic
345C4×C11#57811yescharacteristic
346Dic11—21no—
347Dic11—21no—
348Dic11—21no—
349Dic11—41no—
350Dic11—41no—
351C2×#41—111no—
352C2×Q16C4×D1111yescharacteristic
353C2×SD16—111no—
354C2×SD16—111no—
355C2×D8—111no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363#126—221no—
364#125—111no—
365#124—111no—
366#123—221no—
367C22⋊Q8—111no—
368#121—111no—
369C4×Q8—111no—
370C4×Q8C22×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—111no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4—221no—
378#117—111no—
379#117—221no—
380#117—221no—
381C2×C42—111no—
382C2×C42—221no—
383#107—111no—
384#107C4×D1111yescharacteristic
385#106—111no—
386#106—111no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103C4×D1111yescharacteristic
404#103C4×D1111yescharacteristic
405#102—111no—
406#102—111no—
407#102—111no—
408#102—111no—
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—21no—
418#97—221no—
419C4×C8—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11#292911yescharacteristic
429C2×C11#295111yescharacteristic
430C2×C11#295611yescharacteristic
431D11—41no—
432D11—42no—
433D11—81no—
434#41—222no—
435#41—222no—
436C2×Q8C2×C4×D1111yescharacteristic
437C2×Q8C2×C4×D1111yescharacteristic
438C2×D4—111no—
439C2×D4—111no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449Q16—22no—
450SD16—222no—
451SD16—222no—
452D8—222no—
453M16—442no—
454M16—881no—
455M16—881no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—881no—
467C2×C8—881no—
468C2×C8—881no—
469C2×C8—881no—
470C2×C8C2×C4×D1111yescharacteristic
471C2×C8C2×C4×D1111yescharacteristic
472C2×C8D4×D1111yescharacteristic
473C2×C8D4×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C4×D1111yescharacteristic
483C4⋊C4C2×C4×D1111yescharacteristic
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—21no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42—221no—
498C42—221no—
499C42C23×D1111yescharacteristic
500C11#1792611yescharacteristic, complemented, Sylow
501C23—111no—
502C23—221no—
503C23—221no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#6696012yes—
508D4—112no—
509D4—224no—
510D4—221no—
511D4—221no—
512D4—221no—
513D4—881no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—111no—
521C2×C4—224no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—881no—
534C2×C4C22×C4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4#41×D1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—222no—
545C8—221no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C22—221no—
552C22—222no—
553C22—221no—
554C22—221no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22C4×D4×D1111yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—221no—
567C4—221no—
568C4—221no—
569C4—441no—
570C4—441no—
571C4C2×#6696011yescharacteristic
572C4D11×#13111yescharacteristic
573C4#1062329711yescharacteristic
574C4#1062330011yescharacteristic
575C2—441no—
576C2—442no—
577C2—881no—
578C2#1307730711yescharacteristic
579C2#1307749111yescharacteristic
580C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radical#10622424C4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11#17926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. #13077768C2semidirect
3. #13077726C2semidirect
4. #13067494C2semidirect
5. #13067471C2semidirect
6. #13067447C2semidirect
7. #13067431C2semidirect
8. #13067431C2semidirect
9. Q16×C11⋊C8C2semidirect
10. #13067410C2semidirect
11. #13067389C2semidirect
12. #13067054C2semidirect
13. #13067028C2semidirect
14. #13066912C2semidirect
15. C11×#1584C2semidirect
216. #1584D11semidirect
500. C11#17926semidirect

Maximal subgroups

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

subgroupindex
#130786402
#130777682
#130777262
#130674942
#130674712
#130674472
#130674312
Q16×C11⋊C82
#130674102
#130673892
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