Finite Group Databasebeta

← #14725384

Subgroups — #14725384

Order 2816.

626 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077737C211yesmaximal, characteristic
2#13077703C211yesmaximal, characteristic, complemented
3C4×#66962C211yesmaximal, characteristic
4#13067526C211yesmaximal, characteristic, complemented
5#13067514C211yesmaximal, characteristic, complemented
6#13067489C211yesmaximal, characteristic, complemented
7#13067475C211yesmaximal, characteristic, complemented
8#13067468C211yesmaximal, characteristic, complemented
9#13067454C211yesmaximal, characteristic, complemented
10#13067430C211yesmaximal, characteristic, complemented
11C8×#4314C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067051C211yesmaximal, characteristic
14#13067046C211yesmaximal, characteristic, complemented
15C11×#1453C211yesmaximal, characteristic, complemented
16C2×#66962C411yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622746C411yescharacteristic
23#10622734C411yescharacteristic
24#10622733C411yescharacteristic
25#10622539C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622448—21no—
28D11×C4⋊C8—21no—
29#10622441—21no—
30#10622441—21no—
31#10622341—21no—
32#10622341—21no—
33#10622332—21no—
34#10622331—21no—
35#10622329C411yescharacteristic
36#10622329C411yescharacteristic
37#10622323C411yescharacteristic
38#10622323C411yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43C8×D44C2211yescharacteristic
44C8×D44C2211yescharacteristic
45#10622292C2211yescharacteristic
46#10622292C2211yescharacteristic
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622096C2211yescharacteristic
58#10622096C2211yescharacteristic
59#10622095C2211yescharacteristic
60#10622095C2211yescharacteristic
61#10622094C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622094C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16C2×C411yescharacteristic
70C2×C11×M16C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C4×C22⋊D11—21no—
73C4×C22⋊D11—21no—
74#66979C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—21no—
78C2×#4318—21no—
79#66962—24no—
80C2×Dic44C2×C411yescharacteristic
81C2×Dic44C2×C411yescharacteristic
82C2×#4314C2×C411yescharacteristic
83C2×#4314C2×C411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C4×D44C2×C411yescharacteristic
87C4×D44C2311yescharacteristic
88#66925—21no—
89C42×D11—21no—
90C4×Dic22—21no—
91C4×Dic22—21no—
92C4×Dic22C2×C411yescharacteristic
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2×C411yescharacteristic
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×C4⋊C8—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8D411yescharacteristic
103C11×C22⋊C8D411yescharacteristic
104C11×#97C2×C411yescharacteristic
105C11×#97C2×C411yescharacteristic
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117#66882C2×C411yescharacteristic
118#66882C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66879—21no—
128#66879—21no—
129#66879—21no—
130#66879—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11—21no—
138C8×Dic11—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144#66867—21no—
145#18051—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11#4111yescharacteristic
179C42×C11C2411yescharacteristic
180C22⋊Dic11—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201#4318—81no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206Dic44—22no—
207Dic44—22no—
208#4314—22no—
209#4314M1614yescomplemented
210C8×D11—81no—
211C8×D11—81no—
212#2990—111no—
213#2984—111no—
214C4×#137—111no—
215#1593—111no—
216#1591—111no—
217#1587—111no—
218#1585—111no—
219#1584—111no—
220#1582—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223#1569—111no—
224#1488—111no—
225#1487—111no—
226#1453D1111yescharacteristic, complemented
227C23×C11C4×D411yescharacteristic
228C22×D11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C22⋊D11—42no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—21no—
251D44C2×M1612yes—
252C4×D11—42no—
253C4×D11—42no—
254C4×D11—41no—
255C4×D11—41no—
256Dic22—21no—
257Dic22—21no—
258Dic22—21no—
259Dic22—21no—
260Dic22—21no—
261Dic22—42no—
262Dic22C2×M1612yes—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11C2×M1612yes—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#137—111no—
278C4×#41—111no—
279C2×C4×Q8—111no—
280#446—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288#441—111no—
289#441—111no—
290#440—111no—
291#440—111no—
292C4×Q16—111no—
293C4×Q16—111no—
294C4×SD16—111no—
295C4×SD16—111no—
296#435—221no—
297#435—221no—
298C8×D4—111no—
299C8×D4—111no—
300#432—111no—
301#432—221no—
302#432—221no—
303#431—221no—
304#431C2×D1111yescharacteristic
305#431C2×D1111yescharacteristic
306#428—111no—
307#423—111no—
308C2×C4⋊C8—221no—
309#419—111no—
310#417—111no—
311C4×M16C2×D1111yescharacteristic
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324#322C2×D1111yescharacteristic
325#322C2×D1111yescharacteristic
326#322C2×D1111yescharacteristic
327C82C2×D1111yescharacteristic
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C2×C4×D411yescharacteristic
332C2×D11—22no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11C22×M1611yescharacteristic
340C4×C11#56811yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C2×#41—111no—
351C22×Q8—111no—
352#137—224no—
353C2×Q16—111no—
354C2×Q16—111no—
355C2×SD16—111no—
356C2×SD16—111no—
357C2×M16—221no—
358C2×M16C4×D1111yescharacteristic
359C2×M16C4×D1111yescharacteristic
360C22×C8—221no—
361C22×C8—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×D4—111no—
371C4×D4—111no—
372C4×D4—221no—
373C4×D4—221no—
374#117—111no—
375#117—221no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#107—111no—
382#107—111no—
383#106—111no—
384#106—111no—
385C4⋊C8—21no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8D4411yescharacteristic
398C4⋊C8D4411yescharacteristic
399#103—111no—
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407C22⋊C8—21no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8D4411yescharacteristic
412C22⋊C8D4411yescharacteristic
413#97—221no—
414#97—221no—
415#97—221no—
416#97—221no—
417#97—221no—
418#97C4×D1111yescharacteristic
419#97C4×D1111yescharacteristic
420C4×C8—221no—
421C4×C8—221no—
422C4×C8C22×D1111yescharacteristic
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11D4×M1611yescharacteristic
430C2×C11#294711yescharacteristic
431C2×C11#295511yescharacteristic
432D11—42no—
433#41—222no—
434#41—441no—
435C2×Q8—111no—
436C2×Q8—111no—
437C2×Q8—111no—
438C2×Q8—222no—
439C2×Q8—221no—
440C2×Q8—441no—
441C2×D4—111no—
442C2×D4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4#433911yescharacteristic
451Q16—222no—
452Q16—222no—
453SD16—114no—
454SD16—222no—
455M16—22no—
456M16—41no—
457M16—881no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—881no—
465C2×C8—881no—
466C2×C8C2×C4×D1111yescharacteristic
467C2×C8C2×C4×D1111yescharacteristic
468C2×C8C2×C4×D1111yescharacteristic
469C2×C8C2×C4×D1111yescharacteristic
470C2×C8C2×D4411yescharacteristic
471C2×C8C2×D4411yescharacteristic
472C2×C8C2×D4411yescharacteristic
473C2×C8C2×D4411yescharacteristic
474C4⋊C4—111no—
475C4⋊C4—111no—
476C4⋊C4—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42C2×C4×D1111yescharacteristic
496C42C2×D4411yescharacteristic
497C42#433911yescharacteristic
498C42C23×D1111yescharacteristic
499C11#1805111yescharacteristic, complemented, Sylow
500C23—221no—
501C23C4×D4411yescharacteristic
502Q8—112no—
503Q8—221no—
504Q8—221no—
505Q8—221no—
506Q8—221no—
507Q8—221no—
508Q8—442no—
509D4—112no—
510D4—221no—
511D4—442no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C4×D4411yescharacteristic
531C2×C4C4×D4411yescharacteristic
532C2×C4C4×D4411yescharacteristic
533C2×C4C22×C4×D1111yescharacteristic
534C2×C4C22×D4411yescharacteristic
535C2×C4C2×#433911yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—41no—
544C8—41no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8M16×D1112yes—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—222no—
554C22—441no—
555C22—441no—
556C22C2×C4×D4411yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—222no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4—441no—
566C4—441no—
567C4—441no—
568C4C2×M16×D1111yescharacteristic
569C4#1062327611yescharacteristic
570C4#1062328211yescharacteristic
571C4#1062328411yescharacteristic
572C2—41no—
573C2—442no—
574C2M16×D4411yescharacteristic
575C2#1307746111yescharacteristic
576C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1453C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1453D11
hypocenterC11#18051
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13077703C2semidirect
4. #13067526C2semidirect
5. #13067514C2semidirect
6. #13067489C2semidirect
7. #13067475C2semidirect
8. #13067468C2semidirect
9. #13067454C2semidirect
10. #13067430C2semidirect
11. C8×#4314C2semidirect
12. #13067383C2semidirect
14. #13067046C2semidirect
15. C11×#1453C2semidirect
209. #4314M16semidirect
226. #1453D11semidirect
499. C11#18051semidirect

Maximal subgroups

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

subgroupindex
#130777372
#130777032
C4×#669622
#130675262
#130675142
#130674892
#130674752
#130674682
#130674542
#130674302
C8×#43142
#130673832
#130670512
#130670462
C11×#14532
#1805111