Finite Group Databasebeta

← #14723219

Subgroups — #14723219

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#13077723C211yesmaximal, characteristic
2#13077695C211yesmaximal, characteristic, complemented
3C4×#66968C211yesmaximal, characteristic
4#13067436C211yesmaximal, characteristic, complemented
5#13067432C211yesmaximal, characteristic, complemented
6#13067425C211yesmaximal, characteristic, complemented
7#13067422C211yesmaximal, characteristic, complemented
8C8×#4326C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11#13067367C211yesmaximal, characteristic, complemented
12#13066995C211yesmaximal, characteristic
13D11×Q8⋊C8C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#66968C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C8×D4×C11C2211yescharacteristic
22#10622777C411yescharacteristic
23C8×C22⋊D11—21no—
24C2×Dic11⋊C8—21no—
25C4×#4326C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622474C411yescharacteristic
30#10622466C411yescharacteristic
31#10622446—21no—
32#10622446C2211yescharacteristic
33D11×C4⋊C8C2211yescharacteristic
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622415C411yescharacteristic
38#10622402C411yescharacteristic
39#10622384C411yescharacteristic
40#10622370C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42#10622331—21no—
43C4×Dic44C2211yescharacteristic
44C4×#4313C2211yescharacteristic
45#10622298—21no—
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48C8×Dic22—21no—
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4341C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C22×C8×C11—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—21no—
80#66968C818yescomplemented
81C2×Dic44C2×C411yescharacteristic
82C2×#4313C2×C411yescharacteristic
83C2×#4313C2×C411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86#66945C2×C411yescharacteristic
87C4⋊C4×D11—21no—
88C4⋊C4×D11C2×C411yescharacteristic
89#66940—21no—
90#66940C2×C411yescharacteristic
91#66940C2×C411yescharacteristic
92(C22⋊D11)⋊C4—21no—
93#66930—21no—
94C42×D11—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×#106C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#102C2×C411yescharacteristic
105C11×C22⋊C8—21no—
106C4×C8×C11—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112C22⋊(C11⋊C8)—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8D411yescharacteristic
115(C2×D11)⋊C8D411yescharacteristic
116#66882C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66879C2×C411yescharacteristic
120#66879C2×C411yescharacteristic
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
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—
132C8×Dic11—21no—
133C8×Dic11—21no—
134#66874C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17853—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152Q8×D11—22no—
153Q8×D11C2×C814yescomplemented
154#4341—22no—
155#4341C2×C814yes—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11C22×C411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11#4111yescharacteristic
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×SD16C2×C814yescomplemented
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—81no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4326C2×C814yescomplemented
181#4324C2×C814yescomplemented
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
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×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208Dic44C2×C814yescomplemented
209#4313—22no—
210#4313C2×C814yescomplemented
211C8×D11—42no—
212C8×D11—81no—
213#2988—111no—
214#2982—111no—
215C4×#137—111no—
216#1579—111no—
217#1579—111no—
218SD16⋊C8—111no—
219SD16⋊C8D1111yescharacteristic, complemented
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—
228C23×C11—21no—
229C22×D11C4×D411yescharacteristic
230Q8×C11—21no—
231Q8×C11C22×C812yes—
232D4×C11—21no—
233D4×C11C22×C812yes—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C22⋊D11—24no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—24no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—81no—
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C4×D11—24no—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—41no—
256C4×D11—81no—
257C4×D11C22×C812yes—
258C4×D11#13112yes—
259Dic22—21no—
260Dic22—21no—
261Dic22—24no—
262Dic22C22×C812yes—
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—111no—
286C8×Q8—221no—
287C8×Q8—221no—
288C8×Q8C2×D1111yescharacteristic
289#441—111no—
290#441—111no—
291#440—111no—
292#440—111no—
293C4×Q16—111no—
294C4×Q16—111no—
295C4×SD16—111no—
296C4×SD16C2×D1111yescharacteristic
297C8×D4—111no—
298C8×D4—221no—
299C8×D4—221no—
300C8×D4C2×D1111yescharacteristic
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#335C2×D1111yescharacteristic
315#334—111no—
316#334—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic
323D4⋊C8—111no—
324D4⋊C8C2×D1111yescharacteristic
325#322—111no—
326#322C2×D1111yescharacteristic
327C82—111no—
328C82—111no—
329C22×C11—22no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C2×D11—21no—
334C2×D11—21no—
335C2×D11C8×D412yes—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11C23×C811yescharacteristic
341C4×C11C2×#13111yescharacteristic
342C4×C11#57711yescharacteristic
343C4×C11#57811yescharacteristic
344Dic11—22no—
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×Q16—111no—
356C2×SD16—111no—
357C2×SD16C4×D1111yescharacteristic
358C2×M16—111no—
359C2×M16—111no—
360C22×C8—21no—
361C22×C8—221no—
362C22×C8—221no—
363C22×C8—221no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8—221no—
370C4×Q8—221no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—111no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4C22×D1111yescharacteristic
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#107—111no—
385#106—111no—
386#106C4×D1111yescharacteristic
387C4⋊C8—21no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
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#103—111no—
405#103C4×D1111yescharacteristic
406#102—111no—
407#102C4×D1111yescharacteristic
408C22⋊C8—21no—
409C22⋊C8—111no—
410C22⋊C8—111no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—111no—
414#97—111no—
415C4×C8—21no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
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×C11—42no—
430C2×C11C2×C8×D411yescharacteristic
431C2×C11#294711yescharacteristic
432C2×C11#295611yescharacteristic
433D11—22no—
434#41—114no—
435#41—222no—
436C2×Q8—114no—
437C2×Q8—111no—
438C2×Q8—111no—
439C2×Q8—221no—
440C2×Q8—222no—
441C2×Q8C2×C4×D1111yescharacteristic
442C2×D4—221no—
443C2×D4C2×C4×D1111yescharacteristic
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452Q16—114no—
453Q16—114no—
454SD16—114no—
455SD16C8×D1114yescomplemented
456M16—114no—
457M16—222no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—442no—
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—111no—
478C4⋊C4—111no—
479C4⋊C4—221no—
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—21no—
488C22⋊C4—221no—
489C22⋊C4—221no—
490C42—21no—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42C23×D1111yescharacteristic
501C11#1785311yescharacteristic, complemented, Sylow
502C23—21no—
503C23—111no—
504Q8—21no—
505Q8—112no—
506Q8—112no—
507Q8—224no—
508Q8—221no—
509Q8—221no—
510Q8C2×C8×D1112yes—
511D4—21no—
512D4—224no—
513D4C2×C8×D1112yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—111no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—111no—
523C2×C4—111no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
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—22no—
553C22—41no—
554C22—41no—
555C22—112no—
556C22—221no—
557C22—221no—
558C22C4×D4×D1111yescharacteristic
559C4—21no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—112no—
564C4—221no—
565C4—222no—
566C4—222no—
567C4—221no—
568C4—441no—
569C4—441no—
570C4C22×C8×D1111yescharacteristic
571C4D11×#13111yescharacteristic
572C4#1062330611yescharacteristic
573C4#1062331011yescharacteristic
574C2—42no—
575C2—222no—
576C2C8×D4×D1111yescharacteristic
577C2#1307745611yescharacteristic
578C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×#4341C2×C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#17853
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #13077695C2semidirect
4. #13067436C2semidirect
5. #13067432C2semidirect
6. #13067425C2semidirect
7. #13067422C2semidirect
8. C8×#4326C2semidirect
9. SD16×C11⋊C8C2semidirect
10. C8×#4324C2semidirect
11. #13067367C2semidirect
13. D11×Q8⋊C8C2semidirect
14. #13066895C2semidirect
15. C11×SD16⋊C8C2semidirect
80. #66968C8semidirect
153. Q8×D11C2×C8semidirect
164. C11×SD16C2×C8semidirect
180. #4326C2×C8semidirect
181. #4324C2×C8semidirect
208. Dic44C2×C8semidirect
210. #4313C2×C8semidirect
219. SD16⋊C8D11semidirect
455. SD16C8×D11semidirect
501. C11#17853semidirect

Maximal subgroups

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

subgroupindex
#130777232
#130776952
C4×#669682
#130674362
#130674322
#130674252
#130674222
C8×#43262
SD16×C11⋊C82
C8×#43242
#130673672
#130669952
D11×Q8⋊C82
#130668952
C11×SD16⋊C82
#1785311