Finite Group Databasebeta

← #14725346

Subgroups — #14725346

Order 2816.

640 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
1M16×Dic22C211yesmaximal, characteristic, complemented
2C4×#67004C211yesmaximal, characteristic
3#13067518C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067487C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067457C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067384C211yesmaximal, characteristic, complemented
12#13067062C211yesmaximal, characteristic, complemented
13#13067055C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67004C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436—21no—
23C11×#436C2211yescharacteristic
24C11×#436C2211yescharacteristic
25C11×#432—21no—
26C11×#432C2211yescharacteristic
27C4×C11×M16—21no—
28C4×C11×M16C2211yescharacteristic
29#10622845C411yescharacteristic
30#10622731—21no—
31M16×Dic11—21no—
32#10622643C411yescharacteristic
33#10622643C411yescharacteristic
34C4×#4326C2211yescharacteristic
35C4×#4326C2211yescharacteristic
36#10622631C411yescharacteristic
37#10622631C411yescharacteristic
38C4×#4324C2211yescharacteristic
39C4×#4324C2211yescharacteristic
40#10622617C411yescharacteristic
41#10622608C411yescharacteristic
42#10622537C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622314—21no—
46#10622314—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C4×Q8×C11C2×C411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11C2×C411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117C2×C411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83#67004—24no—
84C2×#4326C2×C411yescharacteristic
85C2×#4326C2×C411yescharacteristic
86C2×#4324C2×C411yescharacteristic
87C2×#4324C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318C2×C411yescharacteristic
94C2×#4318C2×C411yescharacteristic
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66879—21no—
120#66879—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66874C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139#66867C2×C411yescharacteristic
140#66867C2×C411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18049—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×Dic22—22no—
160C2×Dic22—21no—
161C2×Dic22—41no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—42no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C22×C411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188#4326—22no—
189#4326M1614yescomplemented
190#4324—22no—
191#4324—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203#4318—22no—
204#4318—41no—
205#4318—42no—
206#4318—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C22×C411yescharacteristic
212C2×C11⋊C8C22×C411yescharacteristic
213C2×C11⋊C8C22×C411yescharacteristic
214C2×C11⋊C8C22×C411yescharacteristic
215#2971D1111yescharacteristic
216Q8×M16—111no—
217C4×#137—111no—
218#1592—111no—
219#1590—111no—
220#1588—111no—
221#1587—111no—
222#1584—111no—
223#1583—111no—
224#1579—111no—
225C8×Q16—111no—
226#1569—111no—
227#1491—111no—
228#1489—111no—
229#1455—111no—
230C23×C11—21no—
231C23×C11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11C2×M1612yes—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
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—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—81no—
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—42no—
260C2×Dic11—81no—
261Dic22—21no—
262Dic22—21no—
263Dic22—21no—
264Dic22—42no—
265Dic22C2×M1612yes—
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×#41C2×D1111yescharacteristic
282C2×C4×Q8—111no—
283#446—111no—
284#446—111no—
285#446—221no—
286#446—221no—
287C8×Q8—111no—
288C8×Q8—111no—
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#436—21no—
300#436—21no—
301#436C2×D1111yescharacteristic
302#436C2×D1111yescharacteristic
303#432—21no—
304#432C2×D1111yescharacteristic
305#428—111no—
306#423—111no—
307#423—221no—
308#419—111no—
309#417—111no—
310C4×M16—21no—
311C4×M16—111no—
312C4×M16—111no—
313C4×M16—221no—
314C4×M16C2×D1111yescharacteristic
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×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C4×C11—21no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11C22×M1611yescharacteristic
346C4×C11#56811yescharacteristic
347C4×C11C2×#13711yescharacteristic
348C4×C11#57511yescharacteristic
349Dic11—22no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41C4×D1111yescharacteristic
354C22×Q8—111no—
355#137—224no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16C22⋊D1111yescharacteristic
367C2×M16C22⋊D1111yescharacteristic
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—221no—
373C4×Q8—221no—
374C4×Q8C4×D1111yescharacteristic
375C4×Q8C22×D1111yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C4×D1111yescharacteristic
379C4×D4C22×D1111yescharacteristic
380#117—21no—
381#117C4×D1111yescharacteristic
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
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—111no—
394C4⋊C8—111no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
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—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—111no—
415#97—111no—
416#97—221no—
417#97—221no—
418#97—221no—
419#97C22⋊D1111yescharacteristic
420#97C22⋊D1111yescharacteristic
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11—81no—
433C2×C11D4×M1611yescharacteristic
434C2×C11C4×#13711yescharacteristic
435C2×C11#295611yescharacteristic
436#41—22no—
437#41—41no—
438C2×Q8—111no—
439C2×Q8—111no—
440C2×Q8—222no—
441C2×Q8—221no—
442C2×Q8—441no—
443C2×Q8C2×C4×D1111yescharacteristic
444C2×D4—21no—
445C2×D4C2×C4×D1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4#433911yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454Q16—114no—
455Q16—222no—
456SD16—222no—
457SD16—222no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—42no—
462M16—222no—
463M16—441no—
464M16—442no—
465M16—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C22⋊D1111yescharacteristic
477C2×C8C2×C22⋊D1111yescharacteristic
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C2×C4×D1111yescharacteristic
502C42#433911yescharacteristic
503C42C2×C22⋊D1111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804911yescharacteristic, complemented, Sylow
506C23—21no—
507C23C4×C22⋊D1111yescharacteristic
508Q8—21no—
509Q8—112no—
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—442no—
514Q8M16×D1112yes—
515D4—21no—
516D4—21no—
517D4—42no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—81no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—442no—
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#6700412yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22C2×C4×C22⋊D1111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—222no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C2×M16×D1111yescharacteristic
575C4#1062327611yescharacteristic
576C4#1062335311yescharacteristic
577C4C2×#6700411yescharacteristic
578C2—41no—
579C2—81no—
580C2M16×C22⋊D1111yescharacteristic
581C2C4×#6700411yescharacteristic
582C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2971D11
hypocenterC11#18049
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. M16×Dic22C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067487C2semidirect
7. #13067466C2semidirect
8. #13067457C2semidirect
9. #13067433C2semidirect
10. C8×#4326C2semidirect
11. #13067384C2semidirect
12. #13067062C2semidirect
14. #13066919C2semidirect
189. #4326M16semidirect
271. C8×C11#137semidirect
505. C11#18049semidirect
555. C8#67004semidirect

Maximal subgroups

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

subgroupindex
M16×Dic222
C4×#670042
#130675182
#130675042
#130674922
#130674872
#130674662
#130674572
#130674332
C8×#43262
#130673842
#130670622
#130670552
#130669192
C11×#29712
#1804911