Finite Group Databasebeta

← C8×#66971 #14723199

Subgroups — C8×#66971 #14723199

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#4343C211yesmaximal, characteristic
2C8×Q8×D11C211yesmaximal, characteristic, complemented
3C4×#66971C211yesmaximal, characteristic
4#13067435C211yesmaximal, characteristic, complemented
5#13067432C211yesmaximal, characteristic, complemented
6#13067431C211yesmaximal, characteristic, complemented
7#13067427C211yesmaximal, characteristic, complemented
8C8×#4326C211yesmaximal, characteristic, complemented
9C8×#4314C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067367C211yesmaximal, characteristic, complemented
12#13067009C211yesmaximal, characteristic, complemented
13#13067002C211yesmaximal, characteristic
14C8×#4313C211yesmaximal, characteristic, complemented
15C8×C11×Q16C211yesmaximal, 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#10622298C2211yescharacteristic
46C4×C8×D11—21no—
47C4×C8×D11—21no—
48C4×C8×D11C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
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#66971C818yesdirect product factor
77C2×#4314C2×C411yescharacteristic
78C2×#4313C2×C411yescharacteristic
79C2×#4313C2×C411yescharacteristic
80C2×C8×D11—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11D411yescharacteristic
84C2×C8×D11D411yescharacteristic
85#66946—21no—
86#66946C2×C411yescharacteristic
87#66945—21no—
88#66945C2×C411yescharacteristic
89C4⋊C4×D11—21no—
90C4⋊C4×D11C2×C411yescharacteristic
91#66940—21no—
92#66940C2×C411yescharacteristic
93C4×D44—21no—
94C4×D44C2311yescharacteristic
95C42×D11—21no—
96C42×D11—21no—
97C42×D11C2311yescharacteristic
98C4×Dic22—21no—
99C4×Dic22C2311yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C4×C8×C11—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66899C2×C411yescharacteristic
113#66899C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66879C2×C411yescharacteristic
122#66879C2×C411yescharacteristic
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11D411yescharacteristic
131C8×Dic11D411yescharacteristic
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
145C8×#137—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—22no—
210C8×D11—41no—
211C8×D11—42no—
212C8×D11—42no—
213C8×D11—42no—
214C8×#41—111no—
215C2×C8×Q8—111no—
216C4×#137—111no—
217#1579—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221C8×Q16—111no—
222C8×Q16D1111yescharacteristic, complemented
223C8×SD16—111no—
224C8×SD16—111no—
225#1565—111no—
226#1479—111no—
227#1477—111no—
228C8×M16—111no—
229C22×D11—21no—
230C22×D11C4×D411yescharacteristic
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11C22×C812yes—
234Q8×C11C22×C812yes—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248D44—24no—
249D44—21no—
250D44C22×C812yes—
251C4×D11—24no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—24no—
255C4×D11—41no—
256C4×D11—42no—
257C4×D11—42no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11C22×C812yes—
261C4×D11#13112yes—
262Dic22—21no—
263Dic22—24no—
264Dic22C22×C812yes—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11C22×C812yes—
271C8×C11#13712yescomplemented
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8C22×C812yes—
279C2×#137—111no—
280C4×#41—111no—
281C2×C4×Q8—111no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—221no—
287C8×Q8—221no—
288C8×Q8C2×D1111yescharacteristic
289C8×Q8C2×D1111yescharacteristic
290#441—111no—
291#441—111no—
292#440—111no—
293#440—111no—
294C4×Q16—111no—
295C4×Q16C2×D1111yescharacteristic
296C4×SD16—111no—
297C4×SD16—111no—
298C8×D4—111no—
299C8×D4—111no—
300C8×D4—221no—
301C8×D4—221no—
302#431—111no—
303#431—111no—
304#431—221no—
305#428—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—221no—
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C2×C4×C8—111no—
312C2×C4×C8—221no—
313C2×C4×C8—221no—
314#335—111no—
315#335C2×D1111yescharacteristic
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8C2×D1111yescharacteristic
323Q8⋊C8C2×D1111yescharacteristic
324D4⋊C8—111no—
325D4⋊C8—111no—
326#322—111no—
327#322—111no—
328C82—111no—
329C82C2×D1111yescharacteristic
330C22×C11C2×C4×D411yescharacteristic
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—22no—
334C2×D11—41no—
335C2×D11—41no—
336C2×D11C8×D412yes—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C23×C811yescharacteristic
343C4×C11C2×#13111yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346Dic11—22no—
347Dic11—21no—
348Dic11—21no—
349Dic11—41no—
350Dic11—41no—
351Dic11C8×D412yes—
352C2×#41—111no—
353C22×Q8—111no—
354#137—118no—
355C2×Q16—111no—
356C2×Q16C4×D1111yescharacteristic
357C2×SD16—111no—
358C2×SD16—111no—
359C2×M16—111no—
360C2×M16—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—221no—
364C22×C8—221no—
365C22×C8—221no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—221no—
371C4×Q8—221no—
372C4×Q8C22×D1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×D4—111no—
375C4×D4—111no—
376C4×D4—221no—
377C4×D4—221no—
378#117—111no—
379#117—221no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385#107—111no—
386#107C4×D1111yescharacteristic
387#106—111no—
388#106—111no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#103C4×D1111yescharacteristic
406#103C4×D1111yescharacteristic
407#102—111no—
408#102—111no—
409C22⋊C8—221no—
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—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C2×C11C2×C8×D411yescharacteristic
431C2×C11C4×#13711yescharacteristic
432C2×C11#295511yescharacteristic
433D11—22no—
434D11—42no—
435#41—114no—
436#41—222no—
437C2×Q8—114no—
438C2×Q8—111no—
439C2×Q8—221no—
440C2×Q8—222no—
441C2×Q8C2×C4×D1111yescharacteristic
442C2×Q8C2×C4×D1111yescharacteristic
443C2×D4—111no—
444C2×D4—221no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453Q16—114no—
454Q16C8×D1114yescomplemented
455SD16—114no—
456SD16—114no—
457M16—114no—
458M16—222no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—111no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—222no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—441no—
471C2×C8—442no—
472C2×C8—442no—
473C2×C8—442no—
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8D4×D1111yescharacteristic
477C2×C8D4×D1111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4C2×C4×D1111yescharacteristic
488C4⋊C4C2×C4×D1111yescharacteristic
489C22⋊C4—221no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—21no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42C23×D1111yescharacteristic
503C11C8×#13711yescharacteristic, complemented, Sylow
504C23—111no—
505C23—221no—
506Q8—21no—
507Q8—21no—
508Q8—112no—
509Q8—224no—
510Q8—221no—
511Q8C2×C8×D1112yes—
512Q8C2×C8×D1112yes—
513D4—112no—
514D4—224no—
515D4—221no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—111no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4C22×C4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—112no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8C2×C8×D1112yes—
553C8#6697112yesdirect product factor
554C22—112no—
555C22—221no—
556C22—221no—
557C22—222no—
558C22—441no—
559C22—441no—
560C22C4×D4×D1111yescharacteristic
561C4—21no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—112no—
567C4—221no—
568C4—222no—
569C4—221no—
570C4—441no—
571C4—441no—
572C4C22×C8×D1111yescharacteristic
573C4D11×#13111yescharacteristic
574C4C2×#6697111yescharacteristic
575C4#1062329911yescharacteristic
576C2—222no—
577C2—442no—
578C2C8×D4×D1111yescharacteristic
579C2C4×#6697111yescharacteristic
580C2#1307751411yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC8×C11×Q16C2
socleC22×C11C2×C4×D4
prime radicalC2×#4343C2×C4
cosocleC42×C11C24
hypercenterC8×Q16D11
hypocenterC11C8×#137
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D11C2semidirect
4. #13067435C2semidirect
5. #13067432C2semidirect
6. #13067431C2semidirect
7. #13067427C2semidirect
8. C8×#4326C2semidirect
9. C8×#4314C2semidirect
10. C8×#4325C2semidirect
11. #13067367C2semidirect
12. #13067009C2semidirect
14. C8×#4313C2semidirect
15. C8×C11×Q16C2semidirect
76. #66971C8direct (N × H)
151. Q8×D11C2×C8semidirect
164. C11×Q16C2×C8semidirect
179. #4326C2×C8semidirect
180. #4325C2×C8semidirect
206. #4314C2×C8semidirect
208. #4313C2×C8semidirect
222. C8×Q16D11semidirect
271. C8×C11#137semidirect
454. Q16C8×D11semidirect
503. C11C8×#137semidirect
553. C8#66971direct (N × H)

Maximal subgroups

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

subgroupindex
C8×#43432
C8×Q8×D112
C4×#669712
#130674352
#130674322
#130674312
#130674272
C8×#43262
C8×#43142
C8×#43252
#130673672
#130670092
#130670022
C8×#43132
C8×C11×Q162
C8×#13711