Finite Group Databasebeta

← C8×#13094056 #26185704

Subgroups — C8×#13094056 #26185704

Order 12032.

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×#10625354C211yesmaximal, characteristic
2C8×Q8×D47C211yesmaximal, characteristic, complemented
3C4×#13094056C211yesmaximal, characteristic
4#20242207C211yesmaximal, characteristic, complemented
5#20242204C211yesmaximal, characteristic, complemented
6#20242203C211yesmaximal, characteristic, complemented
7#20242199C211yesmaximal, characteristic, complemented
8C8×#10625337C211yesmaximal, characteristic, complemented
9C8×#10625325C211yesmaximal, characteristic, complemented
10C8×#10625336C211yesmaximal, characteristic, complemented
11#20242139C211yesmaximal, characteristic, complemented
12#20241781C211yesmaximal, characteristic, complemented
13#20241774C211yesmaximal, characteristic
14C8×#10625324C211yesmaximal, characteristic, complemented
15C8×Q16×C47C211yesmaximal, characteristic, complemented
16C2×#13094056C411yescharacteristic
17C4×#10625354C2211yescharacteristic
18C4×Q8×D47C2211yescharacteristic
19Q8×C47⋊C8C2211yescharacteristic
20Q8×C47⋊C8C2211yescharacteristic
21C8×Dic94—21no—
22C8×Dic94C2211yescharacteristic
23#15689247—21no—
24#15689247C2211yescharacteristic
25#15689230C411yescharacteristic
26#15689227C411yescharacteristic
27#15689226C411yescharacteristic
28#15689222C411yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625325C2211yescharacteristic
31C4×#10625336C2211yescharacteristic
32C8×D188—21no—
33C8×D188C2211yescharacteristic
34#15689188—21no—
35#15689188C2211yescharacteristic
36#15689175—21no—
37#15689175C2211yescharacteristic
38#15689174C2211yescharacteristic
39#15689164C411yescharacteristic
40C4⋊C8×D47—21no—
41C4⋊C8×D47C2211yescharacteristic
42#15689130C411yescharacteristic
43#15689123C411yescharacteristic
44C4×#10625324C2211yescharacteristic
45C4×C8×D47—21no—
46C4×C8×D47—21no—
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688874C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54#15688853C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625354C2×C411yescharacteristic
68C2×Q8×D47C2×C411yescharacteristic
69#13094056C818yesdirect product factor
70C2×#10625337C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625336C2×C411yescharacteristic
73C2×#10625324C2×C411yescharacteristic
74C2×#10625324C2×C411yescharacteristic
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47D411yescharacteristic
79C2×C8×D47D411yescharacteristic
80Q8×Dic47C2×C411yescharacteristic
81Q8×Dic47C2×C411yescharacteristic
82C4×Dic94—21no—
83C4×Dic94C2311yescharacteristic
84#13093989—21no—
85#13093989C2×C411yescharacteristic
86C4×D188—21no—
87C4×D188C2311yescharacteristic
88#13093986—21no—
89#13093986C2×C411yescharacteristic
90#13093982—21no—
91#13093982C2×C411yescharacteristic
92C4⋊C4×D47—21no—
93C4⋊C4×D47C2×C411yescharacteristic
94C42×D47—21no—
95C42×D47—21no—
96C42×D47C2311yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093956C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)C2311yescharacteristic
103C4⋊(C47⋊C8)C2311yescharacteristic
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108#13093949C2×C411yescharacteristic
109#13093948C2×C411yescharacteristic
110#13093948C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093944C2×C411yescharacteristic
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118#13093934C2×C411yescharacteristic
119#13093934C2×C411yescharacteristic
120C4×C47⋊C8—21no—
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47—21no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
130C2×Q16×C47C2×C411yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133#107×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#103×C47C2×C411yescharacteristic
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147#10625354—22no—
148#10625354C2×C814yes—
149Q8×D47—22no—
150Q8×D47C2×C814yescomplemented
151C2×D188—21no—
152C2×D188C22×C411yescharacteristic
153C2×C4×D47—21no—
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47C22×C411yescharacteristic
159C2×C4×D47C2×D411yescharacteristic
160C2×C4×D47#4111yescharacteristic
161C2×Dic94—21no—
162C2×Dic94C22×C411yescharacteristic
163Q16×C47C2×C814yescomplemented
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C2×D411yescharacteristic
170C2×C8×C47C2×D411yescharacteristic
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C411yescharacteristic
174C4⋊C4×C47C22×C411yescharacteristic
175C42×C47—21no—
176C42×C47—21no—
177C42×C47C2411yescharacteristic
178#10625337C2×C814yescomplemented
179#10625336C2×C814yescomplemented
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47C22×C411yescharacteristic
196C4×Dic47C2×D411yescharacteristic
197C4×Dic47#4111yescharacteristic
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205#10625325C2×C814yescomplemented
206#10625324—22no—
207#10625324C2×C814yescomplemented
208C8×D47—22no—
209C8×D47—41no—
210C8×D47—42no—
211C8×D47—42no—
212C8×D47—42no—
213C22×D47—21no—
214C22×D47C4×D411yescharacteristic
215Q8×C47—21no—
216Q8×C47—21no—
217Q8×C47C22×C812yes—
218Q8×C47C22×C812yes—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47C23×C411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C47C2×#4111yescharacteristic
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47C4×D411yescharacteristic
230C2×Dic47C4×D411yescharacteristic
231C2×Dic47C4×D411yescharacteristic
232D188—24no—
233D188—21no—
234D188C22×C812yes—
235C4×D47—24no—
236C4×D47—21no—
237C4×D47—21no—
238C4×D47—24no—
239C4×D47—41no—
240C4×D47—42no—
241C4×D47—42no—
242C4×D47—41no—
243C4×D47—41no—
244C4×D47C22×C812yes—
245C4×D47#13112yes—
246Dic94—21no—
247Dic94—24no—
248Dic94C22×C812yes—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47C22×C812yes—
255C8×C47#13712yescomplemented
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8C22×C812yes—
263C8×#137—471nomaximal, Sylow
264C22×C47C2×C4×D411yescharacteristic
265C2×D47—21no—
266C2×D47—21no—
267C2×D47—22no—
268C2×D47—41no—
269C2×D47—41no—
270C2×D47C8×D412yes—
271C4×C47—22no—
272C4×C47—22no—
273C4×C47—21no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47C23×C811yescharacteristic
277C4×C47C2×#13111yescharacteristic
278C4×C47C2×#13711yescharacteristic
279C4×C47#57511yescharacteristic
280Dic47—22no—
281Dic47—21no—
282Dic47—21no—
283Dic47—41no—
284Dic47—41no—
285Dic47C8×D412yes—
286C8×#41—471no—
287C2×C8×Q8—471no—
288C4×#137—471no—
289#1579—471no—
290#1579—471no—
291SD16⋊C8—471no—
292SD16⋊C8—471no—
293C8×Q16—471no—
294C8×Q16D4711yescharacteristic, complemented
295C8×SD16—471no—
296C8×SD16—471no—
297#1565—471no—
298#1479—471no—
299#1477—471no—
300C8×M16—471no—
301C2×C47C2×C8×D411yescharacteristic
302C2×C47C4×#13711yescharacteristic
303C2×C47#295511yescharacteristic
304D47—22no—
305D47—42no—
306C2×#137—471no—
307C4×#41—471no—
308C2×C4×Q8—471no—
309C8×Q8—471no—
310C8×Q8—471no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—941no—
314C8×Q8—941no—
315C8×Q8C2×D4711yescharacteristic
316C8×Q8C2×D4711yescharacteristic
317#441—471no—
318#441—471no—
319#440—471no—
320#440—471no—
321C4×Q16—471no—
322C4×Q16C2×D4711yescharacteristic
323C4×SD16—471no—
324C4×SD16—471no—
325C8×D4—471no—
326C8×D4—471no—
327C8×D4—941no—
328C8×D4—941no—
329#431—471no—
330#431—471no—
331#431—941no—
332#428—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—941no—
335#419—471no—
336#417—471no—
337C4×M16—471no—
338C2×C4×C8—471no—
339C2×C4×C8—941no—
340C2×C4×C8—941no—
341#335—471no—
342#335C2×D4711yescharacteristic
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349Q8⋊C8C2×D4711yescharacteristic
350Q8⋊C8C2×D4711yescharacteristic
351D4⋊C8—471no—
352D4⋊C8—471no—
353#322—471no—
354#322—471no—
355C82—471no—
356C82C2×D4711yescharacteristic
357C47C8×#13711yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C22×Q8—471no—
360#137—478no—
361C2×Q16—471no—
362C2×Q16C4×D4711yescharacteristic
363C2×SD16—471no—
364C2×SD16—471no—
365C2×M16—471no—
366C2×M16—471no—
367C22×C8—471no—
368C22×C8—471no—
369C22×C8—941no—
370C22×C8—941no—
371C22×C8—941no—
372C4×Q8—471no—
373C4×Q8—471no—
374C4×Q8—471no—
375C4×Q8—471no—
376C4×Q8—941no—
377C4×Q8—941no—
378C4×Q8C22×D4711yescharacteristic
379C4×Q8C22×D4711yescharacteristic
380C4×D4—471no—
381C4×D4—471no—
382C4×D4—941no—
383C4×D4—941no—
384#117—471no—
385#117—941no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—941no—
388C2×C42—471no—
389C2×C42—941no—
390C2×C42—941no—
391#107—471no—
392#107C4×D4711yescharacteristic
393#106—471no—
394#106—471no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8C22×D4711yescharacteristic
406C4⋊C8C22×D4711yescharacteristic
407#103—471no—
408#103—471no—
409#103—471no—
410#103—471no—
411#103C4×D4711yescharacteristic
412#103C4×D4711yescharacteristic
413#102—471no—
414#102—471no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419#97—471no—
420#97—471no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—471no—
424C4×C8—471no—
425C4×C8—471no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—941no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435C4×C8C22×D4711yescharacteristic
436#41—474no—
437#41—942no—
438C2×Q8—474no—
439C2×Q8—471no—
440C2×Q8—941no—
441C2×Q8—942no—
442C2×Q8C2×C4×D4711yescharacteristic
443C2×Q8C2×C4×D4711yescharacteristic
444C2×D4—471no—
445C2×D4—941no—
446C22×C4—471no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454Q16—474no—
455Q16C8×D4714yescomplemented
456SD16—474no—
457SD16—474no—
458M16—474no—
459M16—942no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—471no—
467C2×C8—942no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—1881no—
472C2×C8—1882no—
473C2×C8—1882no—
474C2×C8—1882no—
475C2×C8C2×C4×D4711yescharacteristic
476C2×C8C2×C4×D4711yescharacteristic
477C2×C8D4×D4711yescharacteristic
478C2×C8D4×D4711yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—471no—
482C4⋊C4—471no—
483C4⋊C4—941no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4C2×C4×D4711yescharacteristic
489C4⋊C4C2×C4×D4711yescharacteristic
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—21no—
495C42—471no—
496C42—471no—
497C42—471no—
498C42—941no—
499C42—941no—
500C42—941no—
501C42—941no—
502C42—941no—
503C42C23×D4711yescharacteristic
504C23—471no—
505C23—941no—
506Q8—21no—
507Q8—21no—
508Q8—472no—
509Q8—944no—
510Q8—941no—
511Q8C2×C8×D4712yes—
512Q8C2×C8×D4712yes—
513D4—472no—
514D4—944no—
515D4—941no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—471no—
521C2×C4—472no—
522C2×C4—472no—
523C2×C4—471no—
524C2×C4—471no—
525C2×C4—944no—
526C2×C4—944no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—1881no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4C22×C4×D4711yescharacteristic
538C2×C4C2×D4×D4711yescharacteristic
539C2×C4#41×D4711yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—472no—
546C8—941no—
547C8—941no—
548C8—941no—
549C8—1881no—
550C8—1881no—
551C8—1881no—
552C8C2×C8×D4712yes—
553C8#1309405612yesdirect product factor
554C22—472no—
555C22—941no—
556C22—941no—
557C22—942no—
558C22—1881no—
559C22—1881no—
560C22C4×D4×D4711yescharacteristic
561C4—21no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—472no—
567C4—941no—
568C4—941no—
569C4—942no—
570C4—1881no—
571C4—1881no—
572C4C22×C8×D4711yescharacteristic
573C4#131×D4711yescharacteristic
574C4C2×#1309405611yescharacteristic
575C4#1568992011yescharacteristic
576C2—942no—
577C2—1882no—
578C2C8×D4×D4711yescharacteristic
579C2C4×#1309405611yescharacteristic
580C2#2025228611yescharacteristic
subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC8×Q16×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625354C2×C4
cosocleC42×C47C24
hypercenterC8×Q16D47
hypocenterC47C8×#137
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D47C2semidirect
4. #20242207C2semidirect
5. #20242204C2semidirect
6. #20242203C2semidirect
7. #20242199C2semidirect
8. C8×#10625337C2semidirect
9. C8×#10625325C2semidirect
10. C8×#10625336C2semidirect
11. #20242139C2semidirect
12. #20241781C2semidirect
14. C8×#10625324C2semidirect
15. C8×Q16×C47C2semidirect
69. #13094056C8direct (N × H)
150. Q8×D47C2×C8semidirect
163. Q16×C47C2×C8semidirect
178. #10625337C2×C8semidirect
179. #10625336C2×C8semidirect
205. #10625325C2×C8semidirect
207. #10625324C2×C8semidirect
255. C8×C47#137semidirect
294. C8×Q16D47semidirect
357. C47C8×#137semidirect
455. Q16C8×D47semidirect
553. C8#13094056direct (N × H)

Maximal subgroups

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

subgroupindex
C8×#106253542
C8×Q8×D472
C4×#130940562
#202422072
#202422042
#202422032
#202421992
C8×#106253372
C8×#106253252
C8×#106253362
#202421392
#202417812
#202417742
C8×#106253242
C8×Q16×C472
C8×#13747