Finite Group Databasebeta

← #14723221

Subgroups — #14723221

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077726C211yesmaximal, characteristic
2#13077695C211yesmaximal, characteristic, complemented
3C4×#66971C211yesmaximal, characteristic
4#13067432C211yesmaximal, characteristic, complemented
5#13067431C211yesmaximal, characteristic, complemented
6#13067430C211yesmaximal, characteristic, complemented
7Q16×C11⋊C8C211yesmaximal, characteristic, complemented
8C8×#4326C211yesmaximal, characteristic, complemented
9C8×#4325C211yesmaximal, characteristic, complemented
10#13067415C211yesmaximal, characteristic, complemented
11#13067365C211yesmaximal, characteristic, complemented
12#13066997C211yesmaximal, characteristic
13D11×Q8⋊C8C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C2×#66971C411yescharacteristic
17C4×#4343C2211yescharacteristic
18C4×Q8×D11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22#10622797C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622502C411yescharacteristic
28#10622494C411yescharacteristic
29#10622447—21no—
30#10622447C2211yescharacteristic
31#10622446—21no—
32#10622446C2211yescharacteristic
33D11×C4⋊C8—21no—
34D11×C4⋊C8C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622430C411yescharacteristic
38#10622416C411yescharacteristic
39#10622415C411yescharacteristic
40#10622402C411yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4313C2211yescharacteristic
43C8×D44—21no—
44C8×D44C2211yescharacteristic
45#10622298—21no—
46#10622298—21no—
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×Q8×D11C2×C411yescharacteristic
69C2×C11×Q16C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72Q8×Dic11C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76#66971C818yescomplemented
77C2×#4314C2×C411yescharacteristic
78C2×#4313C2×C411yescharacteristic
79C2×#4313C2×C411yescharacteristic
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84#66946—21no—
85#66946C2×C411yescharacteristic
86#66945—21no—
87#66945C2×C411yescharacteristic
88C4⋊C4×D11—21no—
89C4⋊C4×D11C2×C411yescharacteristic
90#66940—21no—
91#66940C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44C2311yescharacteristic
94C42×D11—21no—
95C42×D11—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8D411yescharacteristic
118(C2×D11)⋊C8D411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66879C2×C411yescharacteristic
122#66879C2×C411yescharacteristic
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8D411yescharacteristic
127Dic11⋊C8D411yescharacteristic
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132#66874C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66872C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17853—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148#4343—22no—
149#4343C2×C814yes—
150Q8×D11—22no—
151Q8×D11C2×C814yescomplemented
152C2×D44—21no—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×Q16C2×C814yescomplemented
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179#4326C2×C814yescomplemented
180#4325C2×C814yescomplemented
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#4314C2×C814yescomplemented
207#4313—22no—
208#4313C2×C814yescomplemented
209C8×D11—42no—
210C8×D11—81no—
211C8×D11—81no—
212C8×D11—81no—
213#2988—111no—
214#2982—111no—
215C4×#137—111no—
216#1579—111no—
217#1579D1111yescharacteristic, complemented
218SD16⋊C8—111no—
219SD16⋊C8—111no—
220C8×Q16—111no—
221C8×Q16—111no—
222C8×SD16—111no—
223C8×SD16—111no—
224#1565—111no—
225#1476—111no—
226C2×Q8⋊C8—111no—
227C8×M16—111no—
228C22×D11—21no—
229C22×D11C4×D411yescharacteristic
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11C22×C812yes—
233Q8×C11C22×C812yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11C4×D411yescharacteristic
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247D44—24no—
248D44—21no—
249D44C22×C812yes—
250C4×D11—24no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—24no—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—81no—
258C4×D11—81no—
259C4×D11C22×C812yes—
260C4×D11#13112yes—
261Dic22—21no—
262Dic22—24no—
263Dic22C22×C812yes—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11C22×C812yes—
271C11⋊C8—22no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8C22×C812yes—
278C2×#137—111no—
279C4×#41—111no—
280C2×C4×Q8—111no—
281C8×Q8—111no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—221no—
286C8×Q8—221no—
287C8×Q8C2×D1111yescharacteristic
288C8×Q8C2×D1111yescharacteristic
289#441—111no—
290#441—111no—
291#440—111no—
292#440—111no—
293C4×Q16—111no—
294C4×Q16C2×D1111yescharacteristic
295C4×SD16—111no—
296C4×SD16—111no—
297C8×D4—111no—
298C8×D4—111no—
299C8×D4—221no—
300C8×D4—221no—
301#431—111no—
302#431—111no—
303#431—221no—
304#431—221no—
305#431—221no—
306#428—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—221no—
309#419—111no—
310#417—111no—
311C4×M16—111no—
312C2×C4×C8—111no—
313#335—111no—
314#335—111no—
315#334—111no—
316#334C2×D1111yescharacteristic
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8C2×D1111yescharacteristic
322Q8⋊C8C2×D1111yescharacteristic
323D4⋊C8—111no—
324D4⋊C8—111no—
325#322—111no—
326#322C2×D1111yescharacteristic
327C82—111no—
328C82—111no—
329C22×C11C2×C4×D411yescharacteristic
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—22no—
333C2×D11—41no—
334C2×D11—41no—
335C2×D11C8×D412yes—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C23×C811yescharacteristic
342C4×C11C2×#13111yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—22no—
346Dic11—21no—
347Dic11—21no—
348Dic11—41no—
349Dic11—41no—
350Dic11C8×D412yes—
351C2×#41—111no—
352C22×Q8—111no—
353#137—118no—
354C2×Q16—111no—
355C2×Q16C4×D1111yescharacteristic
356C2×SD16—111no—
357C2×SD16—111no—
358C2×M16—111no—
359C2×M16—111no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363C22×C8—221no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—221no—
369C4×Q8—221no—
370C4×Q8C22×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—111no—
373C4×D4—111no—
374C4×D4—221no—
375C4×D4—221no—
376#117—111no—
377#117—221no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—221no—
380C2×C42—111no—
381C2×C42—221no—
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—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400#103—111no—
401#103—111no—
402#103—111no—
403#103—111no—
404#103C4×D1111yescharacteristic
405#103C4×D1111yescharacteristic
406#102—111no—
407#102—111no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—111no—
420C4×C8—221no—
421C4×C8—221no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C2×C11C2×C8×D411yescharacteristic
430C2×C11#294711yescharacteristic
431C2×C11#295611yescharacteristic
432D11—22no—
433D11—42no—
434#41—114no—
435#41—222no—
436C2×Q8—114no—
437C2×Q8—111no—
438C2×Q8—221no—
439C2×Q8—222no—
440C2×Q8C2×C4×D1111yescharacteristic
441C2×Q8C2×C4×D1111yescharacteristic
442C2×D4—111no—
443C2×D4—221no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452Q16—114no—
453Q16C8×D1114yescomplemented
454SD16—114no—
455SD16—114no—
456M16—114no—
457M16—222no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—442no—
469C2×C8—881no—
470C2×C8—881no—
471C2×C8—881no—
472C2×C8C2×C4×D1111yescharacteristic
473C2×C8C2×C4×D1111yescharacteristic
474C2×C8D4×D1111yescharacteristic
475C2×C8D4×D1111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—111no—
479C4⋊C4—111no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4C2×C4×D1111yescharacteristic
486C4⋊C4C2×C4×D1111yescharacteristic
487C22⋊C4—221no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—21no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42C23×D1111yescharacteristic
501C11#1785311yescharacteristic, complemented, Sylow
502C23—111no—
503C23—221no—
504Q8—21no—
505Q8—21no—
506Q8—112no—
507Q8—224no—
508Q8—221no—
509Q8C2×C8×D1112yes—
510Q8C2×C8×D1112yes—
511D4—112no—
512D4—224no—
513D4—221no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—111no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—111no—
522C2×C4—111no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—881no—
534C2×C4—881no—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4#41×D1111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—112no—
545C8—222no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8C2×C8×D1112yes—
552C22—112no—
553C22—221no—
554C22—221no—
555C22—222no—
556C22—441no—
557C22—441no—
558C22C4×D4×D1111yescharacteristic
559C4—21no—
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—112no—
565C4—221no—
566C4—222no—
567C4—221no—
568C4—441no—
569C4—441no—
570C4C22×C8×D1111yescharacteristic
571C4D11×#13111yescharacteristic
572C4#1062330911yescharacteristic
573C4#1062331011yescharacteristic
574C2—222no—
575C2—442no—
576C2C8×D4×D1111yescharacteristic
577C2#1307745811yescharacteristic
578C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1579C2
socleC22×C11C2×C4×D4
prime radicalC2×#4343C2×C4
cosocleC42×C11C24
hypercenter#1579D11
hypocenterC11#17853
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
2. #13077695C2semidirect
4. #13067432C2semidirect
5. #13067431C2semidirect
6. #13067430C2semidirect
7. Q16×C11⋊C8C2semidirect
8. C8×#4326C2semidirect
9. C8×#4325C2semidirect
10. #13067415C2semidirect
11. #13067365C2semidirect
13. D11×Q8⋊C8C2semidirect
14. #13066895C2semidirect
15. C11×#1579C2semidirect
76. #66971C8semidirect
151. Q8×D11C2×C8semidirect
164. C11×Q16C2×C8semidirect
179. #4326C2×C8semidirect
180. #4325C2×C8semidirect
206. #4314C2×C8semidirect
208. #4313C2×C8semidirect
217. #1579D11semidirect
453. Q16C8×D11semidirect
501. C11#17853semidirect

Maximal subgroups

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

subgroupindex
#130777262
#130776952
C4×#669712
#130674322
#130674312
#130674302
Q16×C11⋊C82
C8×#43262
C8×#43252
#130674152
#130673652
#130669972
D11×Q8⋊C82
#130668952
C11×#15792
#1785311