Finite Group Databasebeta

← C4×#125×D47 #26374763

Subgroups — C4×#125×D47 #26374763

Order 12032.

2622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C211yesmaximal, characteristic
2#125×Dic47C211yesmaximal, characteristic, complemented
3C4×#13094016C211yesmaximal, characteristic, complemented
4#20245947C212yesmaximal, complemented
5C4×#13094015C212yesmaximal, complemented
6#20245945C214yesmaximal, complemented
7C4×#13094014C214yesmaximal, complemented
8#20245943C211yesmaximal, characteristic, complemented
9#389×D47C212yesmaximal
10#387×D47C214yesmaximal
11#382×D47C211yesmaximal, characteristic
12C4×C4⋊C4×D47C214yesmaximal
13C4×C4⋊C4×D47C212yesmaximal
14C43×D47C211yesmaximal, characteristic
15C4×#125×C47C211yesmaximal, characteristic, complemented
16C2×#13094016C2211yescharacteristic
17C2×#13094015C2212yes—
18C2×#13094014C2214yes—
19#125×D47C4116yesdirect product factor
20C2×C4⋊C4×D47C2212yes—
21C2×C4⋊C4×D47C2214yes—
22C2×C4⋊C4×D47C2214yes—
23C2×C4⋊C4×D47C2212yes—
24C2×C42×D47C2212yes—
25C2×C42×D47C2211yescharacteristic
26C2×C42×D47C2212yes—
27C2×C42×D47C2214yes—
28C2×C42×D47C2211yescharacteristic
29C2×C42×D47C2211yescharacteristic
30#15689022C2212yes—
31#15689021C2212yes—
32#15689020C2214yes—
33#15689019C2212yes—
34#15689018C2214yes—
35#15689010C2214yes—
36#15689009C2214yes—
37#15689008C2214yes—
38#15689007C2214yes—
39#15689006C2214yes—
40#15689005C2214yes—
41#15689004C2214yes—
42#15688989C2211yescharacteristic
43#15688988C2212yes—
44#15688987C2214yes—
45C4⋊C4×Dic47C2212yes—
46C4⋊C4×Dic47C2214yes—
47C4⋊C4×Dic47C2214yes—
48C4⋊C4×Dic47C2212yes—
49C4×Dic47⋊C4C2214yes—
50C4×Dic47⋊C4C2214yes—
51C4×Dic47⋊C4C2214yes—
52C4×C4⋊Dic47C2214yes—
53C4×C4⋊Dic47C2212yes—
54#15688974C2214yes—
55#15688974C2214yes—
56#15688974C2214yes—
57#95×D47C2214yes—
58#95×D47C2214yes—
59#95×D47C2214yes—
60C42×Dic47C2211yescharacteristic
61C42×Dic47C2212yes—
62C42×Dic47C2212yes—
63C42×Dic47C2211yescharacteristic
64C42×Dic47C2211yescharacteristic
65C2×#125×C47C2211yescharacteristic
66C47×#389C2212yes—
67C47×#387C2214yes—
68C47×#382C2211yescharacteristic
69C4×C4⋊C4×C47C2214yes—
70C4×C4⋊C4×C47C2212yes—
71C43×C47C2211yescharacteristic
72C22×C4×D47C2314yes—
73C22×C4×D47C2312yes—
74C22×C4×D47C2314yes—
75C22×C4×D47C2311yescharacteristic
76C22×C4×D47C2312yes—
77C22×C4×D47C2311yescharacteristic
78C22×C4×D47C2311yescharacteristic
79#13094016C2×C418yescomplemented
80#13094015C2×C4116yescomplemented
81#13094014C2×C4132yescomplemented
82C2×C4⋊Dic47C2312yes—
83C2×C4⋊Dic47C2314yes—
84C2×C4⋊Dic47C2314yes—
85C2×C4⋊Dic47C2312yes—
86C2×Dic47⋊C4C2314yes—
87C2×Dic47⋊C4C2314yes—
88C2×Dic47⋊C4C2314yes—
89C2×Dic47⋊C4C2314yes—
90C2×Dic47⋊C4C2314yes—
91C2×Dic47⋊C4C2314yes—
92C4⋊C4×D47—216no—
93C4⋊C4×D47—28no—
94C4⋊C4×D47C2×C4116yes—
95C4⋊C4×D47C2×C4132yes—
96C2×C4×Dic47C2312yes—
97C2×C4×Dic47C2312yes—
98C2×C4×Dic47C2312yes—
99C2×C4×Dic47C2312yes—
100C2×C4×Dic47C2312yes—
101C2×C4×Dic47C2312yes—
102C2×C4×Dic47C2312yes—
103C2×C4×Dic47C2311yescharacteristic
104C2×C4×Dic47C2314yes—
105C2×C4×Dic47C2314yes—
106C2×C4×Dic47C2314yes—
107C2×C4×Dic47C2312yes—
108C2×C4×Dic47C2311yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C42×D47—28no—
113C42×D47—24no—
114C42×D47—28no—
115C42×D47—216no—
116C42×D47C2×C418yes—
117C42×D47Q818yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127#125×C47C2×C418yescomplemented
128C2×C4⋊C4×C47C2312yes—
129C2×C4⋊C4×C47C2314yes—
130C2×C4⋊C4×C47C2314yes—
131C2×C4⋊C4×C47C2312yes—
132C2×C42×C47C2312yes—
133C2×C42×C47C2312yes—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2314yes—
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138#95×C47C2314yes—
139#95×C47C2314yes—
140#95×C47C2314yes—
141C23×D47C2411yescharacteristic
142C22×C4×C47C2414yes—
143C22×C4×C47C2412yes—
144C22×C4×C47C2414yes—
145C22×C4×C47C2411yescharacteristic
146C22×C4×C47C2412yes—
147C22×C4×C47C2411yescharacteristic
148C22×C4×C47C2411yescharacteristic
149C22×Dic47C2414yes—
150C22×Dic47C2412yes—
151C22×Dic47C2414yes—
152C22×Dic47C2411yescharacteristic
153C22×Dic47C2412yes—
154C22×Dic47C2411yescharacteristic
155C22×Dic47C2411yescharacteristic
156C2×C4×D47—24no—
157C2×C4×D47—28no—
158C2×C4×D47—24no—
159C2×C4×D47—24no—
160C2×C4×D47—24no—
161C2×C4×D47—24no—
162C2×C4×D47—28no—
163C2×C4×D47—28no—
164C2×C4×D47—28no—
165C2×C4×D47—28no—
166C2×C4×D47C22×C418yes—
167C2×C4×D47C22×C4116yes—
168C2×C4×D47C22×C414yes—
169C2×C4×D47C2×Q814yes—
170C2×C4×D47C2×Q814yes—
171C2×C4×D47C2×Q814yes—
172C2×C4×D47#4118yes—
173C2×C4×D47#4114yes—
174C2×C4×D47#4118yes—
175C4⋊C4×C47—28no—
176C4⋊C4×C47—24no—
177C4⋊C4×C47C22×C4116yes—
178C4⋊C4×C47C22×C418yes—
179C42×C47—24no—
180C42×C47—22no—
181C42×C47—24no—
182C42×C47—28no—
183C42×C47C22×C414yes—
184C42×C47C2×Q814yes—
185C4⋊Dic47—24no—
186C4⋊Dic47—28no—
187C4⋊Dic47C22×C4116yes—
188C4⋊Dic47C22×C418yes—
189Dic47⋊C4—28no—
190Dic47⋊C4—28no—
191Dic47⋊C4—28no—
192Dic47⋊C4C22×C4116yes—
193Dic47⋊C4C22×C4116yes—
194Dic47⋊C4C22×C4116yes—
195C4×Dic47—24no—
196C4×Dic47—22no—
197C4×Dic47—24no—
198C4×Dic47—28no—
199C4×Dic47—24no—
200C4×Dic47—24no—
201C4×Dic47—24no—
202C4×Dic47—24no—
203C4×Dic47—24no—
204C4×Dic47—28no—
205C4×Dic47—28no—
206C4×Dic47C22×C418yes—
207C4×Dic47C22×C414yes—
208C4×Dic47C2×Q814yes—
209C4×Dic47C2×Q814yes—
210C4×Dic47C2×Q814yes—
211C23×C47C2511yescharacteristic
212C22×D47C23×C412yes—
213C22×D47C22×Q812yes—
214C22×D47C2×#4112yes—
215C22×D47C2×#4114yes—
216C22×D47C2×#4114yes—
217C2×C4×C47—22no—
218C2×C4×C47—24no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—24no—
226C2×C4×C47—24no—
227C2×C4×C47C23×C414yes—
228C2×C4×C47C23×C418yes—
229C2×C4×C47C23×C412yes—
230C2×C4×C47C22×Q812yes—
231C2×C4×C47C22×Q812yes—
232C2×C4×C47C22×Q812yes—
233C2×C4×C47C2×#4114yes—
234C2×C4×C47C2×#4112yes—
235C2×C4×C47C2×#4114yes—
236C2×Dic47—22no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47C23×C414yes—
247C2×Dic47C23×C418yes—
248C2×Dic47C23×C412yes—
249C2×Dic47C22×Q812yes—
250C2×Dic47C22×Q812yes—
251C2×Dic47C22×Q812yes—
252C2×Dic47C2×#4114yes—
253C2×Dic47C2×#4112yes—
254C2×Dic47C2×#4114yes—
255C4×D47—216no—
256C4×D47—232no—
257C4×D47—216no—
258C4×D47—28no—
259C4×D47—416no—
260C4×D47C4×Q8116yes—
261C4×D47#125116yesdirect product factor
262C2×C4×#125—471nomaximal, Sylow
263C22×C47C24×C411yescharacteristic
264C22×C47C23×Q811yescharacteristic
265C22×C47C22×#4111yescharacteristic
266C22×C47C22×#4112yes—
267C22×C47C22×#4112yes—
268C2×D47C2×C4×Q814yes—
269C2×D47C4×#4118yes—
270C2×D47C2×#12514yes—
271C2×D47#52918yes—
272C2×D47#53314yes—
273C4×C47—24no—
274C4×C47—28no—
275C4×C47—24no—
276C4×C47—22no—
277C4×C47—44no—
278C4×C47C2×C4×Q814yes—
279C4×C47C2×#12514yescomplemented
280Dic47—24no—
281Dic47—28no—
282Dic47—24no—
283Dic47—22no—
284Dic47—44no—
285Dic47C2×C4×Q814yes—
286Dic47C2×#12514yescomplemented
287C22×#125—471no—
288C4×#125—472no—
289C4×#125—474no—
290C4×#125—471no—
291C4×#125—474no—
292C4×#125—472no—
293C4×#125—471no—
294C4×#125—471no—
295C4×#125D4711yescharacteristic, direct product factor
296C2×#389—472no—
297C2×#387—474no—
298C2×#382—471no—
299C2×C4×C4⋊C4—474no—
300C2×C4×C4⋊C4—472no—
301C2×C43—471no—
302C2×C47C22×C4×Q811yescharacteristic
303C2×C47C2×C4×#4112yes—
304C2×C47C22×#12511yescharacteristic
305C2×C47C2×#52912yes—
306C2×C47C2×#53311yescharacteristic
307D47C4×#12518yesdirect product factor
308C2×#125—4716no—
309C2×#125—474no—
310C2×#125—472no—
311C2×#125—471no—
312C2×#125C2×D4711yescharacteristic
313C22×C4⋊C4—474no—
314C22×C4⋊C4—472no—
315C22×C4⋊C4—472no—
316C22×C4⋊C4—474no—
317C22×C42—471no—
318C22×C42—471no—
319C22×C42—472no—
320C22×C42—472no—
321C22×C42—471no—
322C22×C42—474no—
323#389—474no—
324#389—472no—
325#389—472no—
326#389—472no—
327#389—474no—
328#389C2×D4712yes—
329#387—474no—
330#387—474no—
331#387—474no—
332#387—474no—
333#387—474no—
334#387—474no—
335#387—474no—
336#387C2×D4714yes—
337#382—472no—
338#382—471no—
339#382—474no—
340#382C2×D4711yescharacteristic
341C4×C4⋊C4—474no—
342C4×C4⋊C4—474no—
343C4×C4⋊C4—472no—
344C4×C4⋊C4—472no—
345C4×C4⋊C4—474no—
346C4×C4⋊C4—472no—
347C4×C4⋊C4—474no—
348C4×C4⋊C4—474no—
349C4×C4⋊C4—474no—
350C4×C4⋊C4—474no—
351C4×C4⋊C4—474no—
352C4×C4⋊C4—474no—
353C4×C4⋊C4C2×D4714yes—
354C4×C4⋊C4C2×D4712yes—
355C2×#95—474no—
356C2×#95—474no—
357C2×#95—474no—
358C43—471no—
359C43—472no—
360C43—472no—
361C43—471no—
362C43—471no—
363C43C2×D4711yescharacteristic
364C47C2×C4×#12511yescharacteristic, complemented, Sylow
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—474no—
368C23×C4—472no—
369C23×C4—472no—
370C23×C4—471no—
371C23×C4—474no—
372#125—4732no—
373#125—4716no—
374#125—478no—
375#125C4×D4718yesdirect product factor
376C2×C4⋊C4—474no—
377C2×C4⋊C4—474no—
378C2×C4⋊C4—474no—
379C2×C4⋊C4—474no—
380C2×C4⋊C4—472no—
381C2×C4⋊C4—4716no—
382C2×C4⋊C4—4732no—
383C2×C4⋊C4—474no—
384C2×C4⋊C4—474no—
385C2×C4⋊C4—474no—
386C2×C4⋊C4—472no—
387C2×C4⋊C4—474no—
388C2×C4⋊C4—948no—
389C2×C4⋊C4—9416no—
390C2×C4⋊C4C22×D4712yes—
391C2×C4⋊C4C22×D4714yes—
392C2×C4⋊C4C22×D4714yes—
393C2×C4⋊C4C22×D4712yes—
394C2×C42—472no—
395C2×C42—471no—
396C2×C42—471no—
397C2×C42—471no—
398C2×C42—471no—
399C2×C42—478no—
400C2×C42—478no—
401C2×C42—472no—
402C2×C42—472no—
403C2×C42—472no—
404C2×C42—472no—
405C2×C42—472no—
406C2×C42—472no—
407C2×C42—471no—
408C2×C42—474no—
409C2×C42—474no—
410C2×C42—472no—
411C2×C42—474no—
412C2×C42—948no—
413C2×C42—9416no—
414C2×C42—944no—
415C2×C42—948no—
416C2×C42C22×D4712yes—
417C2×C42C22×D4711yescharacteristic
418C2×C42C22×D4712yes—
419C2×C42C22×D4714yes—
420C2×C42C22×D4711yescharacteristic
421C2×C42C22×D4711yescharacteristic
422#95—474no—
423#95—474no—
424#95—474no—
425#95—474no—
426#95—474no—
427#95—474no—
428#95—474no—
429#95—474no—
430#95—474no—
431#95C22×D4714yes—
432#95C22×D4714yes—
433#95C22×D4714yes—
434C24—471no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—474no—
438C22×C4—474no—
439C22×C4—474no—
440C22×C4—478no—
441C22×C4—474no—
442C22×C4—471no—
443C22×C4—472no—
444C22×C4—472no—
445C22×C4—474no—
446C22×C4—478no—
447C22×C4—4716no—
448C22×C4—474no—
449C22×C4—478no—
450C22×C4—474no—
451C22×C4—948no—
452C22×C4—944no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—944no—
456C22×C4—944no—
457C22×C4—948no—
458C22×C4—948no—
459C22×C4—948no—
460C22×C4—948no—
461C22×C4C23×D4714yes—
462C22×C4C23×D4712yes—
463C22×C4C23×D4714yes—
464C22×C4C23×D4711yescharacteristic
465C22×C4C23×D4712yes—
466C22×C4C23×D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468C4⋊C4—28no—
469C4⋊C4—24no—
470C4⋊C4—4716no—
471C4⋊C4—4716no—
472C4⋊C4—4716no—
473C4⋊C4—4716no—
474C4⋊C4—478no—
475C4⋊C4—948no—
476C4⋊C4—948no—
477C4⋊C4—948no—
478C4⋊C4—948no—
479C4⋊C4—944no—
480C4⋊C4C2×C4×D47116yes—
481C4⋊C4C2×C4×D4718yes—
482C42—24no—
483C42—22no—
484C42—24no—
485C42—28no—
486C42—478no—
487C42—474no—
488C42—474no—
489C42—474no—
490C42—474no—
491C42—944no—
492C42—944no—
493C42—948no—
494C42—944no—
495C42—944no—
496C42—944no—
497C42—948no—
498C42—944no—
499C42—942no—
500C42—944no—
501C42—948no—
502C42C2×C4×D4714yes—
503C42Q8×D4714yes—
504C23—472no—
505C23—472no—
506C23—472no—
507C23—474no—
508C23—474no—
509C23C24×D4711yescharacteristic
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—472no—
521C2×C4—472no—
522C2×C4—472no—
523C2×C4—474no—
524C2×C4—472no—
525C2×C4—4716no—
526C2×C4—4716no—
527C2×C4—474no—
528C2×C4—478no—
529C2×C4—472no—
530C2×C4—474no—
531C2×C4—9416no—
532C2×C4—9432no—
533C2×C4—9416no—
534C2×C4—948no—
535C2×C4—942no—
536C2×C4—944no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—944no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—18816no—
546C2×C4C22×C4×D4714yes—
547C2×C4C22×C4×D4718yes—
548C2×C4C22×C4×D4712yes—
549C2×C4C2×Q8×D4712yes—
550C2×C4C2×Q8×D4712yes—
551C2×C4C2×Q8×D4712yes—
552C2×C4#41×D4714yes—
553C2×C4#41×D4712yes—
554C2×C4#41×D4714yes—
555C22—474no—
556C22—478no—
557C22—474no—
558C22—478no—
559C22—474no—
560C22C23×C4×D4711yescharacteristic
561C22C22×Q8×D4711yescharacteristic
562C22C2×#41×D4711yescharacteristic
563C22C2×#41×D4712yes—
564C22C2×#41×D4712yes—
565C4—24no—
566C4—28no—
567C4—24no—
568C4—22no—
569C4—44no—
570C4—474no—
571C4—474no—
572C4—944no—
573C4—948no—
574C4—944no—
575C4—942no—
576C4—1884no—
577C4C4×Q8×D4714yes—
578C4#125×D4714yesdirect product factor
579C2—478no—
580C2C2×C4×Q8×D4711yescharacteristic
581C2C4×#41×D4712yes—
582C2C2×#125×D4711yescharacteristic
583C2#529×D4712yes—
584C2#533×D4711yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC4×#125×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D47C24
hypercenterC4×#125D47
hypocenterC47C2×C4×#125
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #125×Dic47C2semidirect
3. C4×#13094016C2semidirect
4. #20245947C2semidirect
5. C4×#13094015C2semidirect
6. #20245945C2semidirect
7. C4×#13094014C2semidirect
8. #20245943C2semidirect
15. C4×#125×C47C2semidirect
19. #125×D47C4direct (N × H)
79. #13094016C2×C4semidirect
80. #13094015C2×C4semidirect
81. #13094014C2×C4semidirect
127. #125×C47C2×C4semidirect
261. C4×D47#125direct (N × H)
279. C4×C47C2×#125semidirect
286. Dic47C2×#125semidirect
295. C4×#125D47direct (N × H)
307. D47C4×#125direct (N × H)
364. C47C2×C4×#125semidirect
375. #125C4×D47direct (N × H)
578. C4#125×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D472
#125×Dic472
C4×#130940162
#202459472
C4×#130940152
#202459452
C4×#130940142
#202459432
#389×D472
#387×D472
#382×D472
C4×C4⋊C4×D472
C43×D472
C4×#125×C472
C2×C4×#12547