Finite Group Databasebeta

← C8×#13063357 #25066023

Subgroups — C8×#13063357 #25066023

Order 11008.

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×#10621902C211yesmaximal, characteristic
2C8×Q8×D43C211yesmaximal, characteristic, complemented
3C4×#13063357C211yesmaximal, characteristic
4#19133414C211yesmaximal, characteristic, complemented
5#19133411C211yesmaximal, characteristic, complemented
6#19133410C211yesmaximal, characteristic, complemented
7#19133406C211yesmaximal, characteristic, complemented
8C8×#10621885C211yesmaximal, characteristic, complemented
9C8×#10621873C211yesmaximal, characteristic, complemented
10C8×#10621884C211yesmaximal, characteristic, complemented
11#19133346C211yesmaximal, characteristic, complemented
12#19132988C211yesmaximal, characteristic, complemented
13#19132981C211yesmaximal, characteristic
14C8×#10621872C211yesmaximal, characteristic, complemented
15C8×Q16×C43C211yesmaximal, characteristic, complemented
16C2×#13063357C411yescharacteristic
17C4×#10621902C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19Q8×C43⋊C8C2211yescharacteristic
20Q8×C43⋊C8C2211yescharacteristic
21C8×Dic86—21no—
22C8×Dic86C2211yescharacteristic
23#14583023—21no—
24#14583023C2211yescharacteristic
25#14583006C411yescharacteristic
26#14583003C411yescharacteristic
27#14583002C411yescharacteristic
28#14582998C411yescharacteristic
29C4×#10621885C2211yescharacteristic
30C4×#10621873C2211yescharacteristic
31C4×#10621884C2211yescharacteristic
32C8×D172—21no—
33C8×D172C2211yescharacteristic
34#14582964—21no—
35#14582964C2211yescharacteristic
36#14582951—21no—
37#14582951C2211yescharacteristic
38#14582950C2211yescharacteristic
39#14582940C411yescharacteristic
40C4⋊C8×D43—21no—
41C4⋊C8×D43C2211yescharacteristic
42#14582906C411yescharacteristic
43#14582899C411yescharacteristic
44C4×#10621872C2211yescharacteristic
45C4×C8×D43—21no—
46C4×C8×D43—21no—
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582650C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×Q8×D43C2×C411yescharacteristic
69#13063357C818yesdirect product factor
70C2×#10621885C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621872C2×C411yescharacteristic
74C2×#10621872C2×C411yescharacteristic
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43D411yescharacteristic
79C2×C8×D43D411yescharacteristic
80Q8×Dic43C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290C2×C411yescharacteristic
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88#13063287—21no—
89#13063287C2×C411yescharacteristic
90#13063283—21no—
91#13063283C2×C411yescharacteristic
92C4⋊C4×D43—21no—
93C4⋊C4×D43C2×C411yescharacteristic
94C42×D43—21no—
95C42×D43—21no—
96C42×D43C2311yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108#13063250C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118#13063235C2×C411yescharacteristic
119#13063235C2×C411yescharacteristic
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×Q16×C43C2×C411yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#103×C43C2×C411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147#10621902—22no—
148#10621902C2×C814yes—
149Q8×D43—22no—
150Q8×D43C2×C814yescomplemented
151C2×D172—21no—
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43C22×C411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86C22×C411yescharacteristic
163Q16×C43C2×C814yescomplemented
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C22×C411yescharacteristic
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C42×C43—21no—
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178#10621885C2×C814yescomplemented
179#10621884C2×C814yescomplemented
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C411yescharacteristic
186C4⋊Dic43C22×C411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621873C2×C814yescomplemented
206#10621872—22no—
207#10621872C2×C814yescomplemented
208C8×D43—22no—
209C8×D43—41no—
210C8×D43—42no—
211C8×D43—42no—
212C8×D43—42no—
213C22×D43—21no—
214C22×D43C4×D411yescharacteristic
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43C22×C812yes—
218Q8×C43C22×C812yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43C4×D411yescharacteristic
230C2×Dic43C4×D411yescharacteristic
231C2×Dic43C4×D411yescharacteristic
232D172—24no—
233D172—21no—
234D172C22×C812yes—
235C4×D43—24no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—24no—
239C4×D43—41no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43C22×C812yes—
245C4×D43#13112yes—
246Dic86—21no—
247Dic86—24no—
248Dic86C22×C812yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43C22×C812yes—
255C8×C43#13712yescomplemented
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8C22×C812yes—
263C8×#137—431nomaximal, Sylow
264C22×C43C2×C4×D411yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43C8×D412yes—
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43C23×C811yescharacteristic
277C4×C43C2×#13111yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57511yescharacteristic
280Dic43—22no—
281Dic43—21no—
282Dic43—21no—
283Dic43—41no—
284Dic43—41no—
285Dic43C8×D412yes—
286C8×#41—431no—
287C2×C8×Q8—431no—
288C4×#137—431no—
289#1579—431no—
290#1579—431no—
291SD16⋊C8—431no—
292SD16⋊C8—431no—
293C8×Q16—431no—
294C8×Q16D4311yescharacteristic, complemented
295C8×SD16—431no—
296C8×SD16—431no—
297#1565—431no—
298#1479—431no—
299#1477—431no—
300C8×M16—431no—
301C2×C43C2×C8×D411yescharacteristic
302C2×C43C4×#13711yescharacteristic
303C2×C43#295511yescharacteristic
304D43—22no—
305D43—42no—
306C2×#137—431no—
307C4×#41—431no—
308C2×C4×Q8—431no—
309C8×Q8—431no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8—861no—
315C8×Q8C2×D4311yescharacteristic
316C8×Q8C2×D4311yescharacteristic
317#441—431no—
318#441—431no—
319#440—431no—
320#440—431no—
321C4×Q16—431no—
322C4×Q16C2×D4311yescharacteristic
323C4×SD16—431no—
324C4×SD16—431no—
325C8×D4—431no—
326C8×D4—431no—
327C8×D4—861no—
328C8×D4—861no—
329#431—431no—
330#431—431no—
331#431—861no—
332#428—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—861no—
335#419—431no—
336#417—431no—
337C4×M16—431no—
338C2×C4×C8—431no—
339C2×C4×C8—861no—
340C2×C4×C8—861no—
341#335—431no—
342#335C2×D4311yescharacteristic
343#334—431no—
344#334—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8C2×D4311yescharacteristic
350Q8⋊C8C2×D4311yescharacteristic
351D4⋊C8—431no—
352D4⋊C8—431no—
353#322—431no—
354#322—431no—
355C82—431no—
356C82C2×D4311yescharacteristic
357C43C8×#13711yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C22×Q8—431no—
360#137—438no—
361C2×Q16—431no—
362C2×Q16C4×D4311yescharacteristic
363C2×SD16—431no—
364C2×SD16—431no—
365C2×M16—431no—
366C2×M16—431no—
367C22×C8—431no—
368C22×C8—431no—
369C22×C8—861no—
370C22×C8—861no—
371C22×C8—861no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×Q8C22×D4311yescharacteristic
379C4×Q8C22×D4311yescharacteristic
380C4×D4—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384#117—431no—
385#117—861no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C42—431no—
389C2×C42—861no—
390C2×C42—861no—
391#107—431no—
392#107C4×D4311yescharacteristic
393#106—431no—
394#106—431no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—431no—
408#103—431no—
409#103—431no—
410#103—431no—
411#103C4×D4311yescharacteristic
412#103C4×D4311yescharacteristic
413#102—431no—
414#102—431no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—431no—
420#97—431no—
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—434no—
437#41—862no—
438C2×Q8—434no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—862no—
442C2×Q8C2×C4×D4311yescharacteristic
443C2×Q8C2×C4×D4311yescharacteristic
444C2×D4—431no—
445C2×D4—861no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454Q16—434no—
455Q16C8×D4314yescomplemented
456SD16—434no—
457SD16—434no—
458M16—434no—
459M16—862no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—862no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—1721no—
472C2×C8—1722no—
473C2×C8—1722no—
474C2×C8—1722no—
475C2×C8C2×C4×D4311yescharacteristic
476C2×C8C2×C4×D4311yescharacteristic
477C2×C8D4×D4311yescharacteristic
478C2×C8D4×D4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—431no—
482C4⋊C4—431no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4C2×C4×D4311yescharacteristic
489C4⋊C4C2×C4×D4311yescharacteristic
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—21no—
494C42—21no—
495C42—431no—
496C42—431no—
497C42—431no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42—861no—
502C42—861no—
503C42C23×D4311yescharacteristic
504C23—431no—
505C23—861no—
506Q8—21no—
507Q8—21no—
508Q8—432no—
509Q8—864no—
510Q8—861no—
511Q8C2×C8×D4312yes—
512Q8C2×C8×D4312yes—
513D4—432no—
514D4—864no—
515D4—861no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—431no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—431no—
524C2×C4—431no—
525C2×C4—864no—
526C2×C4—864no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—1721no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4C22×C4×D4311yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4#41×D4311yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—432no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8C2×C8×D4312yes—
553C8#1306335712yesdirect product factor
554C22—432no—
555C22—861no—
556C22—861no—
557C22—862no—
558C22—1721no—
559C22—1721no—
560C22C4×D4×D4311yescharacteristic
561C4—21no—
562C4—22no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—432no—
567C4—861no—
568C4—862no—
569C4—861no—
570C4—1721no—
571C4—1721no—
572C4C22×C8×D4311yescharacteristic
573C4#131×D4311yescharacteristic
574C4C2×#1306335711yescharacteristic
575C4#1458369611yescharacteristic
576C2—862no—
577C2—1722no—
578C2C8×D4×D4311yescharacteristic
579C2C4×#1306335711yescharacteristic
580C2#1914349311yescharacteristic
subgroupG/H
centerC2×C8D4×D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC8×Q16×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621902C2×C4
cosocleC42×C43C24
hypercenterC8×Q16D43
hypocenterC43C8×#137
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
2. C8×Q8×D43C2semidirect
4. #19133414C2semidirect
5. #19133411C2semidirect
6. #19133410C2semidirect
7. #19133406C2semidirect
8. C8×#10621885C2semidirect
9. C8×#10621873C2semidirect
10. C8×#10621884C2semidirect
11. #19133346C2semidirect
12. #19132988C2semidirect
14. C8×#10621872C2semidirect
15. C8×Q16×C43C2semidirect
69. #13063357C8direct (N × H)
150. Q8×D43C2×C8semidirect
163. Q16×C43C2×C8semidirect
178. #10621885C2×C8semidirect
179. #10621884C2×C8semidirect
205. #10621873C2×C8semidirect
207. #10621872C2×C8semidirect
255. C8×C43#137semidirect
294. C8×Q16D43semidirect
357. C43C8×#137semidirect
455. Q16C8×D43semidirect
553. C8#13063357direct (N × H)

Maximal subgroups

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

subgroupindex
C8×#106219022
C8×Q8×D432
C4×#130633572
#191334142
#191334112
#191334102
#191334062
C8×#106218852
C8×#106218732
C8×#106218842
#191333462
#191329882
#191329812
C8×#106218722
C8×Q16×C432
C8×#13743