Finite Group Databasebeta

← D47×#1515 #26183540

Subgroups — D47×#1515 #26183540

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#432×D47C211yesmaximal, characteristic
3#383×D47C211yesmaximal, characteristic
4#20241940C211yesmaximal, characteristic, complemented
5#20241939C211yesmaximal, characteristic, complemented
6#20241938C211yesmaximal, characteristic, complemented
7#20241937C214yesmaximal, complemented
8#328×D47C214yesmaximal
9C47×#1515C211yesmaximal, characteristic, complemented
10#15689680C2211yescharacteristic
11#15689679—21no—
12#15689678C411yescharacteristic, complemented
13#15689678C411yescharacteristic, complemented
14#15689677—21no—
15#15689677C412yescomplemented
16#15689676—21no—
17#15689675—21no—
18#15689675C2212yes—
19C4⋊Q8×D47C411yescharacteristic, complemented
20C4⋊Q8×D47C411yescharacteristic, complemented
21#125×D47—21no—
22C22⋊Q8×D47—21no—
23C22⋊Q8×D47C2212yes—
24C4×Q8×D47—21no—
25C4×Q8×D47C412yescomplemented
26#117×D47—21no—
27C2×C42×D47C2211yescharacteristic
28#15689180C2211yescharacteristic
29#15689179—21no—
30#15689178—21no—
31#15689177C2212yes—
32C4⋊C8×D47—21no—
33C22⋊C8×D47C2212yes—
34#97×D47—21no—
35#15688991C2211yescharacteristic
36#15688990—21no—
37#15688990—21no—
38#15688990C2212yes—
39#95×D47—21no—
40#95×D47—21no—
41#95×D47C2212yes—
42#15688861C2214yes—
43#15688860C2214yes—
44#15688859C2214yes—
45C47×#533C2211yescharacteristic
46C47×#432C2211yescharacteristic
47C47×#383C2211yescharacteristic
48C47×#328C2214yes—
49C2×Q8×D47—21no—
50C2×Q8×D47C2×C412yes—
51C22×C4×D47—22no—
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47C2311yescharacteristic
55C2×C8×D47—22no—
56#13094024C2×C411yescharacteristic, complemented
57#13094024C2×C411yescharacteristic, complemented
58#13094023—21no—
59#13094023—21no—
60#13094023—21no—
61#13094023C2×C412yescomplemented
62#13094022—21no—
63#13094022C2×C412yescomplemented
64#13094016—21no—
65#13094015—21no—
66#13094015—21no—
67#13094014—22no—
68#13094014—22no—
69#13094004—21no—
70#13094004C2×C412yes—
71#13094003—21no—
72#13094003C2312yes—
73#13094002—22no—
74#13094002—22no—
75#13094001—22no—
76#13094001—22no—
77#13094000—21no—
78#13094000C2×C412yes—
79Q8×Dic47—21no—
80Q8×Dic47C2×C412yescomplemented
81C4×Dic94—21no—
82C4×Dic94—22no—
83C4×Dic94—22no—
84C4×Dic94C2×C412yescomplemented
85#13093989—21no—
86#13093989—22no—
87#13093989—22no—
88#13093989C2×C412yescomplemented
89#13093983—21no—
90#13093982—21no—
91#13093982—21no—
92#13093981—22no—
93#13093980—22no—
94C4⋊C4×D47—21no—
95C4⋊C4×D47—21no—
96C4⋊C4×D47—21no—
97C4⋊C4×D47—22no—
98C4⋊C4×D47—22no—
99C4⋊C4×D47C2×C412yes—
100C22⋊C4×D47—22no—
101C2×C4×Dic47D411yescharacteristic
102C2×C4×Dic47D411yescharacteristic
103C2×C4×Dic47C2311yescharacteristic
104C42×D47—22no—
105C42×D47C2×C411yescharacteristic
106C42×D47C2×C411yescharacteristic
107C42×D47C2×C411yescharacteristic
108C42×D47C2×C411yescharacteristic
109C42×D47D411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47D411yescharacteristic
112C42×D47D411yescharacteristic
113C4⋊(C47⋊C8)—21no—
114Dic47⋊C8—22no—
115C22⋊(C47⋊C8)C2312yes—
116(C2×D47)⋊C8—22no—
117#13093935—21no—
118#13093934—22no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—22no—
122C47⋊#95—22no—
123C47⋊#95—22no—
124C47⋊#95C2312yes—
125C4⋊Q8×C47C2×C411yescharacteristic, complemented
126C4⋊Q8×C47C2×C411yescharacteristic, complemented
127#125×C47—21no—
128C22⋊Q8×C47—21no—
129C22⋊Q8×C47C2312yes—
130C4×Q8×C47—21no—
131C4×Q8×C47C2×C412yescomplemented
132#117×C47—21no—
133C2×C42×C47C2311yescharacteristic
134C4⋊C8×C47—21no—
135C22⋊C8×C47C2312yes—
136#97×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47C2312yes—
140C23×D47C2×D411yescharacteristic
141C2×Q8×C47—21no—
142C2×Q8×C47C22×C412yes—
143C22×C4×C47—22no—
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2411yescharacteristic
147C22×Dic47—22no—
148C22×Dic47C2×D411yescharacteristic
149C22×Dic47C2×D411yescharacteristic
150C22×Dic47C2×D411yescharacteristic
151Q8×D47—44no—
152Q8×D47—44no—
153C2×C4×D47—24no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—42no—
157C2×C4×D47—42no—
158C2×C4×D47—44no—
159C2×C4×D47—44no—
160C2×C4×D47—44no—
161C2×C4×D47C22⋊C411yescharacteristic
162C2×C4×D47C22⋊C411yescharacteristic
163C2×C4×D47C22⋊C411yescharacteristic
164C2×C4×D47C22⋊C411yescharacteristic
165C2×C4×D47C22⋊C411yescharacteristic
166C2×C4×D47C22⋊C411yescharacteristic
167C2×C4×D47C22⋊C411yescharacteristic
168C2×C4×D47C22⋊C411yescharacteristic
169C2×C4×D47C22×C411yescharacteristic
170C2×C4×D47C22×C411yescharacteristic
171C2×C4×D47C2×D411yescharacteristic
172C2×C4×D47C2×D411yescharacteristic
173C2×Dic94—21no—
174C2×Dic94—22no—
175C2×Dic94—22no—
176C2×Dic94C22×C412yes—
177C2×C8×C47—22no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47C22×C412yes—
184C22⋊C4×C47—22no—
185C42×C47—22no—
186C42×C47C22×C411yescharacteristic
187C42×C47C22×C411yescharacteristic
188C42×C47C2×D411yescharacteristic
189C42×C47C2×D411yescharacteristic
190C22⋊Dic47—22no—
191(C2×D47)⋊C4—22no—
192(C2×D47)⋊C4—22no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—22no—
197C4⋊Dic47—22no—
198C4⋊Dic47C22×C412yes—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47—22no—
210C4×Dic47C22⋊C411yescharacteristic
211C4×Dic47C22⋊C411yescharacteristic
212C4×Dic47C22⋊C411yescharacteristic
213C4×Dic47C22⋊C411yescharacteristic
214C4×Dic47C22⋊C411yescharacteristic
215C4×Dic47C22⋊C411yescharacteristic
216C4×Dic47C22⋊C411yescharacteristic
217C4×Dic47C22⋊C411yescharacteristic
218C4×Dic47C22×C411yescharacteristic
219C4×Dic47C22×C411yescharacteristic
220C4×Dic47C2×D411yescharacteristic
221C4×Dic47C2×D411yescharacteristic
222C2×C47⋊C8—22no—
223C8×D47—44no—
224C23×C47C22×D411yescharacteristic
225C22×D47—22no—
226C22×D47—22no—
227C22×D47C2×C22⋊C411yescharacteristic
228C22×D47C2×C22⋊C411yescharacteristic
229C22×D47#13714yes—
230Q8×C47—42no—
231Q8×C47—42no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C2×C22⋊C411yescharacteristic
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47C2×C22⋊C411yescharacteristic
255C2×Dic47C2×C22⋊C411yescharacteristic
256C2×Dic47C2×C22⋊C411yescharacteristic
257C2×Dic47C2×C22⋊C411yescharacteristic
258C2×Dic47C2×C22⋊C411yescharacteristic
259C2×Dic47C2×C22⋊C411yescharacteristic
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—22no—
268C4×D47—41no—
269C4×D47—41no—
270C4×D47—41no—
271C4×D47—41no—
272C4×D47—44no—
273C4×D47—44no—
274C4×D47—88no—
275Dic94—44no—
276Dic94—44no—
277Dic94—42no—
278Dic94—42no—
279C8×C47—42no—
280C47⋊C8—42no—
281C2×#1515—471nomaximal, Sylow
282C22×C47—21no—
283C22×C47—21no—
284C22×C47C22×C22⋊C411yescharacteristic
285C22×C47C2×#13712yes—
286C2×D47—21no—
287C2×D47—21no—
288C2×D47—28no—
289C2×D47#41012yes—
290C2×D47#41912yes—
291C2×D47#41912yes—
292C2×D47#42112yes—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—42no—
300C4×C47—42no—
301C4×C47—82no—
302Dic47—21no—
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—21no—
307Dic47—21no—
308Dic47—42no—
309Dic47—42no—
310Dic47—82no—
311C2×#533—471no—
312C2×#432—471no—
313C2×#383—471no—
314#1515—471no—
315#1515—471no—
316#1515—474no—
317#1515—471no—
318#1515D4711yescharacteristic, direct product factor
319C2×#328—474no—
320C2×C47—22no—
321C2×C47C2×#41011yescharacteristic
322C2×C47C2×#41911yescharacteristic
323C2×C47C2×#42111yescharacteristic
324D47—22no—
325D47#151514yesdirect product factor
326#533—471no—
327#533—471no—
328#533—472no—
329#533—472no—
330#533—471no—
331#533—941no—
332#533—941no—
333#533—941no—
334#533—941no—
335#533C2×D4711yescharacteristic
336C2×C4⋊Q8—471no—
337C2×C4⋊Q8—471no—
338C2×#125—941no—
339C2×C22⋊Q8—472no—
340C2×C22⋊Q8—941no—
341C2×C4×Q8—472no—
342C2×C4×Q8—941no—
343C2×#117—941no—
344C22×C42—471no—
345#432—471no—
346#432—472no—
347#432—941no—
348#432—941no—
349#432C2×D4711yescharacteristic
350C2×C4⋊C8—941no—
351C2×C22⋊C8—472no—
352C2×#97—941no—
353#383—471no—
354#383—472no—
355#383—941no—
356#383—941no—
357#383C2×D4711yescharacteristic
358C2×#95—472no—
359C2×#95—941no—
360C2×#95—941no—
361#328—474no—
362#328—474no—
363#328—474no—
364#328C2×D4714yes—
365C47C2×#151511yescharacteristic, complemented, Sylow
366C22×Q8—472no—
367C22×Q8—941no—
368C23×C4—471no—
369C23×C4—471no—
370C23×C4—471no—
371C23×C4—942no—
372C22×C8—942no—
373C4⋊Q8—472no—
374C4⋊Q8—472no—
375C4⋊Q8—471no—
376C4⋊Q8—471no—
377C4⋊Q8—941no—
378C4⋊Q8—941no—
379C4⋊Q8—941no—
380C4⋊Q8—941no—
381C4⋊Q8C4×D4711yescharacteristic, complemented
382C4⋊Q8C4×D4711yescharacteristic, complemented
383#125—21no—
384#125—942no—
385#125—942no—
386#125—941no—
387#125—941no—
388#125—941no—
389C22⋊Q8—21no—
390C22⋊Q8—472no—
391C22⋊Q8—472no—
392C22⋊Q8—472no—
393C22⋊Q8—942no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396C22⋊Q8—942no—
397C22⋊Q8—941no—
398C22⋊Q8—941no—
399C22⋊Q8—941no—
400C22⋊Q8C22×D4712yes—
401C4×Q8—21no—
402C4×Q8—472no—
403C4×Q8—472no—
404C4×Q8—472no—
405C4×Q8—942no—
406C4×Q8—942no—
407C4×Q8—942no—
408C4×Q8—941no—
409C4×Q8—942no—
410C4×Q8—941no—
411C4×Q8—941no—
412C4×Q8C4×D4712yescomplemented
413#117—21no—
414#117—942no—
415#117—942no—
416#117—941no—
417#117—941no—
418#117—941no—
419C2×C4⋊C4—472no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4—942no—
424C2×C4⋊C4—941no—
425C2×C22⋊C4—942no—
426C2×C42—471no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—471no—
430C2×C42—471no—
431C2×C42—471no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—942no—
438C2×C42C22×D4711yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—942no—
441C4⋊C8—941no—
442C22⋊C8—472no—
443C22⋊C8—942no—
444C22⋊C8C22×D4712yes—
445#97—21no—
446#97—942no—
447#97—941no—
448#95—21no—
449#95—21no—
450#95—472no—
451#95—942no—
452#95—942no—
453#95—942no—
454#95—941no—
455#95—941no—
456#95C22×D4712yes—
457C24—471no—
458C2×Q8—21no—
459C2×Q8—472no—
460C2×Q8—942no—
461C2×Q8—942no—
462C2×Q8—941no—
463C2×Q8—1884no—
464C2×Q8—1884no—
465C2×Q8C2×C4×D4712yes—
466C22×C4—22no—
467C22×C4—471no—
468C22×C4—471no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—471no—
482C22×C4—944no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—1882no—
487C22×C4—1882no—
488C22×C4—1884no—
489C22×C4—1884no—
490C22×C4—1884no—
491C22×C4D4×D4711yescharacteristic
492C22×C4D4×D4711yescharacteristic
493C22×C4C23×D4711yescharacteristic
494C2×C8—22no—
495C2×C8—942no—
496C2×C8—1884no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—472no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—941no—
515C4⋊C4—942no—
516C4⋊C4C2×C4×D4712yes—
517C22⋊C4—22no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C42—22no—
522C42—471no—
523C42—471no—
524C42—471no—
525C42—471no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—471no—
534C42—942no—
535C42—942no—
536C42—942no—
537C42C2×C4×D4711yescharacteristic
538C42C2×C4×D4711yescharacteristic
539C42D4×D4711yescharacteristic
540C42D4×D4711yescharacteristic
541C23—471no—
542C23—471no—
543C23—474no—
544C23—942no—
545C23—942no—
546C23C2×D4×D4711yescharacteristic
547Q8—42no—
548Q8—42no—
549Q8—1882no—
550Q8—1882no—
551Q8—1884no—
552Q8—1884no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—471no—
564C2×C4—471no—
565C2×C4—471no—
566C2×C4—471no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—3768no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1884no—
584C2×C4—1884no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1882no—
588C2×C4—1882no—
589C2×C4—1882no—
590C2×C4C22⋊C4×D4711yescharacteristic
591C2×C4C22⋊C4×D4711yescharacteristic
592C2×C4C22⋊C4×D4711yescharacteristic
593C2×C4C22⋊C4×D4711yescharacteristic
594C2×C4C22×C4×D4711yescharacteristic
595C2×C4C2×D4×D4711yescharacteristic
596C8—42no—
597C8—1882no—
598C22—21no—
599C22—21no—
600C22—472no—
601C22—472no—
602C22—472no—
603C22—472no—
604C22—948no—
605C22—941no—
606C22—941no—
607C22C2×C22⋊C4×D4711yescharacteristic
608C22#137×D4712yes—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—42no—
616C4—42no—
617C4—82no—
618C4—941no—
619C4—941no—
620C4—941no—
621C4—941no—
622C4—941no—
623C4—941no—
624C4—3762no—
625C4—1882no—
626C4—1882no—
627C2—22no—
628C2—474no—
629C2—942no—
630C2#410×D4711yescharacteristic
631C2#419×D4711yescharacteristic
632C2#421×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1515C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1515D47
hypocenterC47C2×#1515
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
4. #20241940C2semidirect
5. #20241939C2semidirect
6. #20241938C2semidirect
7. #20241937C2semidirect
9. C47×#1515C2semidirect
12. #15689678C4semidirect
13. #15689678C4semidirect
15. #15689677C4semidirect
19. C4⋊Q8×D47C4semidirect
20. C4⋊Q8×D47C4semidirect
25. C4×Q8×D47C4semidirect
56. #13094024C2×C4semidirect
57. #13094024C2×C4semidirect
61. #13094023C2×C4semidirect
63. #13094022C2×C4semidirect
80. Q8×Dic47C2×C4semidirect
84. C4×Dic94C2×C4semidirect
88. #13093989C2×C4semidirect
125. C4⋊Q8×C47C2×C4semidirect
126. C4⋊Q8×C47C2×C4semidirect
131. C4×Q8×C47C2×C4semidirect
318. #1515D47direct (N × H)
325. D47#1515direct (N × H)
365. C47C2×#1515semidirect
381. C4⋊Q8C4×D47semidirect
382. C4⋊Q8C4×D47semidirect
412. C4×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#432×D472
#383×D472
#202419402
#202419392
#202419382
#202419372
#328×D472
C47×#15152
C2×#151547