Finite Group Databasebeta

← #14725356

Subgroups — #14725356

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
1#13077636C211yesmaximal, characteristic
2#13077567C211yesmaximal, characteristic, complemented
3C4×#67004C211yesmaximal, characteristic
4#13067515C211yesmaximal, characteristic, complemented
5#13067509C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067484C211yesmaximal, characteristic, complemented
8#13067463C211yesmaximal, characteristic, complemented
9#13067462C211yesmaximal, characteristic, complemented
10#13067432C211yesmaximal, characteristic, complemented
11#13067420C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067064C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1489C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C2×#67004C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#423C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21#10622845C411yescharacteristic
22#10622731—21no—
23M16×Dic11—21no—
24#10622643C411yescharacteristic
25#10622643C411yescharacteristic
26C4×#4326C2211yescharacteristic
27C4×#4326C2211yescharacteristic
28Q8×C11⋊C8C2211yescharacteristic
29Q8×C11⋊C8C2211yescharacteristic
30#10622631C411yescharacteristic
31#10622631C411yescharacteristic
32C4×#4324C2211yescharacteristic
33C4×#4324C2211yescharacteristic
34#10622625—21no—
35#10622625—21no—
36#10622625C2211yescharacteristic
37#10622625C2211yescharacteristic
38#10622617C411yescharacteristic
39#10622608C411yescharacteristic
40#10622539—21no—
41#10622539C2211yescharacteristic
42C4×#4318—21no—
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622444C2211yescharacteristic
46#10622444C2211yescharacteristic
47#10622443C2211yescharacteristic
48#10622443C2211yescharacteristic
49#10622441—21no—
50#10622441—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622094C2211yescharacteristic
60#10622094C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C11×#117—21no—
78C11×#117C2×C411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81#67004—24no—
82C2×#4326C2×C411yescharacteristic
83C2×#4326C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4318C2×C411yescharacteristic
92C2×#4318C2×C411yescharacteristic
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2×C411yescharacteristic
99C4×Dic22C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#97—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66879—21no—
115#66879—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120C8×Dic11—21no—
121C8×Dic11—21no—
122#66874C2×C411yescharacteristic
123#66874C2×C411yescharacteristic
124#66874C2×C411yescharacteristic
125#66874C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134#66867—21no—
135#66867C2×C411yescharacteristic
136#66867C2×C411yescharacteristic
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
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—42no—
165C11×M16—42no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11C22×C411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184#4326—22no—
185#4326M1614yescomplemented
186#4324—22no—
187#4324—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199#4318—22no—
200#4318—22no—
201#4318—41no—
202#4318—41no—
203#4318—42no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#2971—111no—
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#1489D1111yescharacteristic
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—22no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8C2×M1612yes—
279C11⋊C8#13712yescomplemented
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×Q8—111no—
290C8×Q8—111no—
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—111no—
300#436—111no—
301#436—221no—
302#436—221no—
303#432—111no—
304#432—221no—
305#428—111no—
306#423—221no—
307#423C2×D1111yescharacteristic
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C4×M16—111no—
312C4×M16—221no—
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⋊C8C2×D1111yescharacteristic
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8C2×D1111yescharacteristic
326D4⋊C8C2×D1111yescharacteristic
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—111no—
365C2×M16—111no—
366C2×M16—221no—
367C2×M16—221no—
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—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
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—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—111no—
415#97—111no—
416#97—111no—
417#97—111no—
418#97—221no—
419#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
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×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454Q16—114no—
455Q16—222no—
456SD16—222no—
457SD16—222no—
458M16—42no—
459M16—42no—
460M16—222no—
461M16—222no—
462M16—442no—
463M16—441no—
464M16—441no—
465M16—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—221no—
479C2×C8—221no—
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
502C42D4×D1111yescharacteristic
503C42#434111yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804911yescharacteristic, complemented, Sylow
506C23—21no—
507C23(C22⋊D11)⋊C411yescharacteristic
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×C4(C22⋊D11)⋊C411yescharacteristic
537C2×C4(C22⋊D11)⋊C411yescharacteristic
538C2×C4(C22⋊D11)⋊C411yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C8—22no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—112no—
547C8—112no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—441no—
555C8—441no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22C2×(C22⋊D11)⋊C411yescharacteristic
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#1062330411yescharacteristic
577C4D11×#13711yescharacteristic
578C2—41no—
579C2—81no—
580C2#1307734811yescharacteristic
581C2#1307744011yescharacteristic
582C2#1307752211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1489C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#1489D11
hypocenterC11#18049
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #13077567C2semidirect
4. #13067515C2semidirect
5. #13067509C2semidirect
6. #13067497C2semidirect
7. #13067484C2semidirect
8. #13067463C2semidirect
9. #13067462C2semidirect
10. #13067432C2semidirect
11. #13067420C2semidirect
12. #13067381C2semidirect
13. #13067064C2semidirect
14. #13066919C2semidirect
185. #4326M16semidirect
279. C11⋊C8#137semidirect
505. C11#18049semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130775672
C4×#670042
#130675152
#130675092
#130674972
#130674842
#130674632
#130674622
#130674322
#130674202
#130673812
#130670642
#130669192
C11×#14892
#1804911