Finite Group Databasebeta

← #14725320

Subgroups — #14725320

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077631C211yesmaximal, characteristic
2C4×#66995C211yesmaximal, characteristic
3#13067523C211yesmaximal, characteristic, complemented
4#13067511C211yesmaximal, characteristic, complemented
5#13067487C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067381C211yesmaximal, characteristic, complemented
12#13067063C211yesmaximal, characteristic, complemented
13#13067053C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15Q8×C11×M16C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66995C411yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#446—21no—
20C11×#446—21no—
21C11×#446C2211yescharacteristic
22C11×#446C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C11×#423—21no—
26C11×#423C2211yescharacteristic
27C4×C11×M16—21no—
28C4×C11×M16C2211yescharacteristic
29#10622838C411yescharacteristic
30#10622740—21no—
31#10622740—21no—
32#10622643C411yescharacteristic
33#10622643C411yescharacteristic
34C4×#4326C2211yescharacteristic
35C4×#4326C2211yescharacteristic
36#10622639C411yescharacteristic
37#10622639C411yescharacteristic
38C4×#4325C2211yescharacteristic
39C4×#4325C2211yescharacteristic
40#10622579C411yescharacteristic
41#10622577C411yescharacteristic
42#10622539C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622318—21no—
46D11×#97—21no—
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Q8×C11C2×C411yescharacteristic
68C2×#4339C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11C2×C411yescharacteristic
75C4×Q8×C11C2×C411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2×C411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4326C2×C411yescharacteristic
84#66995—24no—
85C2×#4325C2×C411yescharacteristic
86C2×#4325C2×C411yescharacteristic
87C4×C22⋊D11—21no—
88C4×C22⋊D11—21no—
89#66979C2×C411yescharacteristic
90C2×#4318—21no—
91C2×#4318C2×C411yescharacteristic
92C2×#4318C2×C411yescharacteristic
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C4×D44C2×C411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11—21no—
99C4×Dic22C2×C411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#97—21no—
109C11×#97—21no—
110C11×#97D411yescharacteristic
111C11×#97D411yescharacteristic
112C4×C8×C11—21no—
113C4×C8×C11—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119#66899C2×C411yescharacteristic
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867—21no—
139#66867C2×C411yescharacteristic
140#66867C2×C411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18047—111nomaximal, Sylow
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11C22×C411yescharacteristic
150C2×Q8×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157#4339—22no—
158#4339—41no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—21no—
189#4326—22no—
190#4326—22no—
191#4325—22no—
192#4325M1614yescomplemented
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202#4318—22no—
203#4318—41no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C22×C411yescharacteristic
213C8×D11—42no—
214C8×D11—42no—
215#2970—111no—
216Q8×M16D1111yescharacteristic, complemented
217C4×#137—111no—
218#1593—111no—
219#1591—111no—
220#1587—111no—
221#1585—111no—
222#1584—111no—
223#1582—111no—
224SD16⋊C8—111no—
225C8×SD16—111no—
226#1569—111no—
227#1491—111no—
228#1489—111no—
229#1455—111no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—42no—
236Q8×C11C2×M1612yes—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—81no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—42no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258D44—21no—
259D44C2×M1612yes—
260C4×D11—42no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—81no—
264Dic22—21no—
265Dic22—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11#13712yescomplemented
272C11⋊C8—22no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8C2×M1612yes—
280C2×#137—111no—
281C4×#41—111no—
282C2×C4×Q8C2×D1111yescharacteristic
283#446—21no—
284#446—21no—
285#446—111no—
286#446—111no—
287#446C2×D1111yescharacteristic
288#446C2×D1111yescharacteristic
289C8×Q8C2×D1111yescharacteristic
290C8×Q8C2×D1111yescharacteristic
291#441—111no—
292#441—111no—
293#440—111no—
294#440—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#435—221no—
300#435—221no—
301C8×D4—111no—
302C8×D4—111no—
303#432—111no—
304#432—221no—
305#428—111no—
306#423—21no—
307#423C2×D1111yescharacteristic
308#419—111no—
309#417—111no—
310C4×M16—21no—
311C4×M16—111no—
312C4×M16—111no—
313C4×M16C2×D1111yescharacteristic
314C2×#97—221no—
315#335—111no—
316#335—111no—
317#334—111no—
318#334—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327#322—111no—
328#322—111no—
329#322—111no—
330C82—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—22no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C22×M1611yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11C2×#13711yescharacteristic
349C4×C11#57511yescharacteristic
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41—111no—
354C22×Q8C4×D1111yescharacteristic
355#137—224no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—21no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—221no—
364C2×M16C22⋊D1111yescharacteristic
365C2×M16C22⋊D1111yescharacteristic
366C22×C8—221no—
367C22×C8—221no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8C4×D1111yescharacteristic
373C4×Q8C4×D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—111no—
381#117—221no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C4×D1111yescharacteristic
384C2×C42—21no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—111no—
388#107—111no—
389#106—111no—
390#106—111no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—111no—
403#103—111no—
404#103—111no—
405#103—111no—
406#103—111no—
407#103—111no—
408#102—111no—
409#102—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—21no—
415#97—111no—
416#97—111no—
417#97—221no—
418#97—221no—
419#97—221no—
420#97—221no—
421#97C22⋊D1111yescharacteristic
422#97C22⋊D1111yescharacteristic
423C4×C8—21no—
424C4×C8—21no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11D4×M1611yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#295611yescharacteristic
435D11—42no—
436#41—222no—
437#41—441no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8—111no—
442C2×Q8C2×C4×D1111yescharacteristic
443C2×Q8C2×C4×D1111yescharacteristic
444C2×D4—111no—
445C2×D4—221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4#433911yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454Q16—222no—
455Q16—222no—
456SD16—114no—
457SD16—222no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—222no—
462M16—441no—
463M16—442no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
475C2×C8—442no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—111no—
486C4⋊C4—111no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C2×C4×D1111yescharacteristic
502C42#433911yescharacteristic
503C42C2×C22⋊D1111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804711yescharacteristic, complemented, Sylow
506C23—221no—
507C23C4×C22⋊D1111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—42no—
512Q8—221no—
513Q8—221no—
514Q8M16×D1112yes—
515D4—112no—
516D4—221no—
517D4—442no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—442no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—881no—
536C2×C4C4×C22⋊D1111yescharacteristic
537C2×C4C4×C22⋊D1111yescharacteristic
538C2×C4C4×C22⋊D1111yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×#433911yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—112no—
548C8—222no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—441no—
553C8—441no—
554C8—441no—
555C8#6699512yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—222no—
560C22—441no—
561C22—441no—
562C22C2×C4×C22⋊D1111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C2×M16×D1111yescharacteristic
575C4#1062327611yescharacteristic
576C4C2×#6699511yescharacteristic
577C4#1062335311yescharacteristic
578C2—41no—
579C2—442no—
580C2M16×C22⋊D1111yescharacteristic
581C2C4×#6699511yescharacteristic
582C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingQ8×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenterQ8×M16D11
hypocenterC11#18047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
3. #13067523C2semidirect
4. #13067511C2semidirect
5. #13067487C2semidirect
6. #13067471C2semidirect
7. #13067466C2semidirect
8. #13067450C2semidirect
9. #13067426C2semidirect
10. C8×#4325C2semidirect
11. #13067381C2semidirect
12. #13067063C2semidirect
14. #13066919C2semidirect
15. Q8×C11×M16C2semidirect
192. #4325M16semidirect
216. Q8×M16D11semidirect
271. C8×C11#137semidirect
505. C11#18047semidirect
555. C8#66995semidirect

Maximal subgroups

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

subgroupindex
#130776312
C4×#669952
#130675232
#130675112
#130674872
#130674712
#130674662
#130674502
#130674262
C8×#43252
#130673812
#130670632
#130670532
#130669192
Q8×C11×M162
#1804711