Finite Group Databasebeta

← D47×#1485 #26182798

Subgroups — D47×#1485 #26182798

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#431×D47C211yesmaximal, characteristic
3C4×M16×D47C211yesmaximal, characteristic
4#20241810C211yesmaximal, characteristic, complemented
5#20241809C211yesmaximal, characteristic, complemented
6#20241808C211yesmaximal, characteristic, complemented
7#20241807C214yesmaximal, complemented
8Q8⋊C8×D47C214yesmaximal, complemented
9C47×#1485C211yesmaximal, characteristic, complemented
10C2×M16×D47—21no—
11#15689680C2211yescharacteristic
12#15689679—21no—
13#15689678C411yescharacteristic
14#15689678C411yescharacteristic
15#15689677—21no—
16#15689677C2212yes—
17#15689676—21no—
18#15689675—21no—
19#15689675C412yes—
20C4⋊Q8×D47C411yescharacteristic
21C4⋊Q8×D47C411yescharacteristic
22#125×D47—21no—
23C22⋊Q8×D47—21no—
24C22⋊Q8×D47C412yes—
25C4×Q8×D47—21no—
26C4×Q8×D47C2212yes—
27#117×D47—21no—
28C2×C42×D47C2211yescharacteristic
29#15689176C2211yescharacteristic
30#15689175C2212yes—
31#15689174—21no—
32#15689173—21no—
33C4⋊C8×D47C2212yes—
34C22⋊C8×D47—21no—
35C4×#10625329C2211yescharacteristic
36#15689075—21no—
37M16×Dic47—21no—
38C4×#10625324C2212yes—
39#97×D47—21no—
40C4×C8×D47—21no—
41C4×C8×D47C2212yes—
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C47×#533C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C4×M16×C47C2211yescharacteristic
48C47×Q8⋊C8C2214yescomplemented
49C2×Q8×D47—21no—
50C2×Q8×D47C2×C412yes—
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C2×#10625329—21no—
55C2×#10625324—22no—
56M16×D47—28no—
57C2×C8×D47—22no—
58C2×C8×D47—22no—
59#13094024C2×C411yescharacteristic
60#13094024C2×C411yescharacteristic
61#13094023—21no—
62#13094023—21no—
63#13094023—21no—
64#13094023C2×C412yes—
65#13094022—21no—
66#13094022C2×C412yes—
67#13094016—21no—
68#13094015—21no—
69#13094015—21no—
70#13094014—22no—
71#13094014—22no—
72#13094004—21no—
73#13094004C2×C412yes—
74#13094003—21no—
75#13094003C2×C412yes—
76#13094002—22no—
77#13094002—22no—
78#13094001—22no—
79#13094001—22no—
80#13094000—21no—
81#13094000C2×C412yes—
82Q8×Dic47—21no—
83Q8×Dic47C2×C412yes—
84C4×Dic94—21no—
85C4×Dic94—22no—
86C4×Dic94—22no—
87C4×Dic94C2312yes—
88#13093989—21no—
89#13093989—22no—
90#13093989—22no—
91#13093989C2×C412yes—
92#13093983—21no—
93#13093982—21no—
94#13093982—21no—
95#13093981—22no—
96#13093980—22no—
97C4⋊C4×D47—21no—
98C4⋊C4×D47—21no—
99C4⋊C4×D47—21no—
100C4⋊C4×D47—22no—
101C4⋊C4×D47—22no—
102C4⋊C4×D47C2×C412yes—
103C22⋊C4×D47—22no—
104C2×C4×Dic47C2×C411yescharacteristic
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C42×D47—22no—
108C42×D47C2×C411yescharacteristic
109C42×D47C2×C411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47D411yescharacteristic
112C42×D47D411yescharacteristic
113C42×D47D411yescharacteristic
114C42×D47C2311yescharacteristic
115C42×D47C2311yescharacteristic
116C4⋊(C47⋊C8)C2312yes—
117Dic47⋊C8—22no—
118C22⋊(C47⋊C8)—21no—
119(C2×D47)⋊C8—22no—
120#13093935—21no—
121#13093934—22no—
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2312yes—
124C8×Dic47—22no—
125C8×Dic47—22no—
126C2×M16×C47—21no—
127C4⋊Q8×C47C2×C411yescharacteristic
128C4⋊Q8×C47C2×C411yescharacteristic
129#125×C47—21no—
130C22⋊Q8×C47—21no—
131C22⋊Q8×C47C2×C412yes—
132C4×Q8×C47—21no—
133C4×Q8×C47C2312yes—
134#117×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47C2312yes—
137C22⋊C8×C47—21no—
138#97×C47—21no—
139C4×C8×C47—21no—
140C4×C8×C47C2312yes—
141C23×D47C22⋊C411yescharacteristic
142C2×Q8×C47—21no—
143C2×Q8×C47C22×C412yes—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×Dic47C22⋊C411yescharacteristic
148C22×Dic47C22⋊C411yescharacteristic
149C22×Dic47C22⋊C411yescharacteristic
150Q8×D47—28no—
151Q8×D47—44no—
152C2×C4×D47—24no—
153C2×C4×D47—24no—
154C2×C4×D47—24no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47C22⋊C411yescharacteristic
158C2×C4×D47C22⋊C411yescharacteristic
159C2×C4×D47C22⋊C411yescharacteristic
160C2×C4×D47C22⋊C411yescharacteristic
161C2×C4×D47C22⋊C411yescharacteristic
162C2×C4×D47C22⋊C411yescharacteristic
163C2×C4×D47C22×C411yescharacteristic
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C2×D411yescharacteristic
166C2×C4×D47C2×D411yescharacteristic
167C2×C4×D47C2×D411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×Dic94—21no—
170C2×Dic94—22no—
171C2×Dic94—22no—
172C2×Dic94C22×C412yes—
173M16×C47—24no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—22no—
180C4⋊C4×C47—22no—
181C4⋊C4×C47C22×C412yes—
182C22⋊C4×C47—22no—
183C42×C47—22no—
184C42×C47C22×C411yescharacteristic
185C42×C47C2×D411yescharacteristic
186C42×C47C2×D411yescharacteristic
187C42×C47C2411yescharacteristic
188C22⋊Dic47—22no—
189(C2×D47)⋊C4—22no—
190(C2×D47)⋊C4—22no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—22no—
195C4⋊Dic47—22no—
196C4⋊Dic47C22×C412yes—
197Dic47⋊C4—22no—
198Dic47⋊C4—22no—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205C4×Dic47—22no—
206C4×Dic47—22no—
207C4×Dic47—22no—
208C4×Dic47C22⋊C411yescharacteristic
209C4×Dic47C22⋊C411yescharacteristic
210C4×Dic47C22⋊C411yescharacteristic
211C4×Dic47C22⋊C411yescharacteristic
212C4×Dic47C22⋊C411yescharacteristic
213C4×Dic47C22⋊C411yescharacteristic
214C4×Dic47C22×C411yescharacteristic
215C4×Dic47C22×C411yescharacteristic
216C4×Dic47C2×D411yescharacteristic
217C4×Dic47C2×D411yescharacteristic
218C4×Dic47C2×D411yescharacteristic
219C4×Dic47C2×D411yescharacteristic
220#10625329—24no—
221C2×C47⋊C8—22no—
222C2×C47⋊C8—22no—
223#10625324—28no—
224C8×D47—28no—
225C8×D47—44no—
226C23×C47C2×C22⋊C411yescharacteristic
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47C2×C22⋊C411yescharacteristic
231C22×D47C2×C22⋊C411yescharacteristic
232Q8×C47—24no—
233Q8×C47—42no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47C2×C22⋊C411yescharacteristic
251C2×Dic47C2×C22⋊C411yescharacteristic
252C2×Dic47C2×C22⋊C411yescharacteristic
253C2×Dic47C2×C22⋊C411yescharacteristic
254C2×Dic47C2×C22⋊C411yescharacteristic
255C2×Dic47C2×C22⋊C411yescharacteristic
256C4×D47—22no—
257C4×D47—22no—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—44no—
266C4×D47—44no—
267C4×D47#10414yes—
268C4×D47#13114yes—
269C4×D47#13714yes—
270Dic94—24no—
271Dic94—42no—
272Dic94—44no—
273Dic94—44no—
274C8×C47—24no—
275C8×C47—42no—
276C47⋊C8—24no—
277C47⋊C8—42no—
278C2×#1485—471nomaximal, Sylow
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47C22×C22⋊C411yescharacteristic
283C2×D47—21no—
284C2×D47—21no—
285C2×D47—21no—
286C2×D47—44no—
287C2×D47#40812yes—
288C2×D47#41912yes—
289C2×D47C2×#10412yes—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—21no—
293C4×C47—42no—
294C4×C47—42no—
295C4×C47C2×#10412yes—
296C4×C47C2×#13112yes—
297C4×C47C2×#13712yes—
298Dic47—21no—
299Dic47—21no—
300Dic47—21no—
301Dic47—42no—
302Dic47—42no—
303Dic47#40812yes—
304Dic47#41912yes—
305Dic47C2×#10412yes—
306C2×#533—471no—
307C2×#431—471no—
308C2×C4×M16—471no—
309#1485—471no—
310#1485—471no—
311#1485—474no—
312#1485—471no—
313#1485D4711yescharacteristic, direct product factor
314C2×Q8⋊C8—474no—
315C2×C47—41no—
316C2×C47C2×#40811yescharacteristic
317C2×C47C2×#41911yescharacteristic
318C2×C47C22×#10411yescharacteristic
319D47—41no—
320D47#148514yesdirect product factor
321C22×M16—941no—
322#533—471no—
323#533—471no—
324#533—472no—
325#533—472no—
326#533—471no—
327#533—941no—
328#533—941no—
329#533—941no—
330#533—941no—
331#533C2×D4711yescharacteristic
332C2×C4⋊Q8—471no—
333C2×C4⋊Q8—471no—
334C2×#125—941no—
335C2×C22⋊Q8—472no—
336C2×C22⋊Q8—941no—
337C2×C4×Q8—472no—
338C2×C4×Q8—941no—
339C2×#117—941no—
340C22×C42—471no—
341#431—471no—
342#431—472no—
343#431—941no—
344#431—941no—
345#431C2×D4711yescharacteristic
346C2×C4⋊C8—472no—
347C2×C22⋊C8—941no—
348C4×M16—471no—
349C4×M16—472no—
350C4×M16—941no—
351C4×M16—941no—
352C4×M16C2×D4711yescharacteristic
353C2×#97—941no—
354C2×C4×C8—472no—
355C2×C4×C8—941no—
356Q8⋊C8—474no—
357Q8⋊C8—474no—
358Q8⋊C8—474no—
359Q8⋊C8C2×D4714yescomplemented
360C47C2×#148511yescharacteristic, complemented, Sylow
361C22×Q8—472no—
362C22×Q8—941no—
363C23×C4—471no—
364C23×C4—471no—
365C23×C4—471no—
366C2×M16—21no—
367C2×M16—942no—
368C2×M16—948no—
369C2×M16—941no—
370C22×C8—942no—
371C22×C8—942no—
372C4⋊Q8—472no—
373C4⋊Q8—472no—
374C4⋊Q8—471no—
375C4⋊Q8—471no—
376C4⋊Q8—941no—
377C4⋊Q8—941no—
378C4⋊Q8—941no—
379C4⋊Q8—941no—
380C4⋊Q8C4×D4711yescharacteristic
381C4⋊Q8C4×D4711yescharacteristic
382#125—21no—
383#125—942no—
384#125—942no—
385#125—941no—
386#125—941no—
387#125—941no—
388C22⋊Q8—21no—
389C22⋊Q8—472no—
390C22⋊Q8—472no—
391C22⋊Q8—472no—
392C22⋊Q8—942no—
393C22⋊Q8—942no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396C22⋊Q8—941no—
397C22⋊Q8—941no—
398C22⋊Q8—941no—
399C22⋊Q8C4×D4712yes—
400C4×Q8—21no—
401C4×Q8—472no—
402C4×Q8—472no—
403C4×Q8—472no—
404C4×Q8—942no—
405C4×Q8—942no—
406C4×Q8—942no—
407C4×Q8—941no—
408C4×Q8—942no—
409C4×Q8—941no—
410C4×Q8—941no—
411C4×Q8C22×D4712yes—
412#117—21no—
413#117—942no—
414#117—942no—
415#117—941no—
416#117—941no—
417#117—941no—
418C2×C4⋊C4—472no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—942no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4—941no—
424C2×C22⋊C4—942no—
425C2×C42—471no—
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—942no—
437C2×C42C22×D4711yescharacteristic
438C4⋊C8—472no—
439C4⋊C8—942no—
440C4⋊C8C22×D4712yes—
441C22⋊C8—21no—
442C22⋊C8—942no—
443C22⋊C8—941no—
444#97—21no—
445#97—942no—
446#97—941no—
447C4×C8—21no—
448C4×C8—472no—
449C4×C8—942no—
450C4×C8—942no—
451C4×C8—941no—
452C4×C8C22×D4712yes—
453C24—471no—
454C2×Q8—21no—
455C2×Q8—472no—
456C2×Q8—942no—
457C2×Q8—942no—
458C2×Q8—948no—
459C2×Q8—941no—
460C2×Q8—1884no—
461C2×Q8C2×C4×D4712yes—
462C22×C4—471no—
463C22×C4—471no—
464C22×C4—471no—
465C22×C4—471no—
466C22×C4—471no—
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—944no—
478C22×C4—944no—
479C22×C4—944no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4C2×C4×D4711yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485M16—24no—
486M16—948no—
487M16—944no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—948no—
491C2×C8—942no—
492C2×C8—942no—
493C2×C8—1884no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—472no—
500C4⋊C4—942no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—942no—
513C4⋊C4C2×C4×D4712yes—
514C22⋊C4—22no—
515C22⋊C4—942no—
516C22⋊C4—942no—
517C22⋊C4—942no—
518C42—22no—
519C42—471no—
520C42—471no—
521C42—471no—
522C42—471no—
523C42—471no—
524C42—471no—
525C42—471no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—942no—
532C42—942no—
533C42—942no—
534C42C2×C4×D4711yescharacteristic
535C42D4×D4711yescharacteristic
536C42D4×D4711yescharacteristic
537C42C23×D4711yescharacteristic
538C23—471no—
539C23—471no—
540C23—942no—
541C23—942no—
542C23—942no—
543C23C22⋊C4×D4711yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—944no—
547Q8—1884no—
548Q8—1884no—
549Q8—1882no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—471no—
556C2×C4—471no—
557C2×C4—471no—
558C2×C4—474no—
559C2×C4—474no—
560C2×C4—474no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—471no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
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—1884no—
579C2×C4—1884no—
580C2×C4C22⋊C4×D4711yescharacteristic
581C2×C4C22⋊C4×D4711yescharacteristic
582C2×C4C22⋊C4×D4711yescharacteristic
583C2×C4C22×C4×D4711yescharacteristic
584C2×C4C2×D4×D4711yescharacteristic
585C2×C4C2×D4×D4711yescharacteristic
586C8—24no—
587C8—42no—
588C8—944no—
589C8—1882no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—472no—
594C22—472no—
595C22—472no—
596C22—941no—
597C22—941no—
598C22—941no—
599C22—1884no—
600C22C2×C22⋊C4×D4711yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—472no—
607C4—472no—
608C4—472no—
609C4—941no—
610C4—941no—
611C4—941no—
612C4—1882no—
613C4—1882no—
614C4#104×D4712yes—
615C4#131×D4712yes—
616C4#137×D4712yes—
617C2—41no—
618C2—474no—
619C2—1881no—
620C2#408×D4711yescharacteristic
621C2#419×D4711yescharacteristic
622C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1485C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1485D47
hypocenterC47C2×#1485
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
4. #20241810C2semidirect
5. #20241809C2semidirect
6. #20241808C2semidirect
7. #20241807C2semidirect
8. Q8⋊C8×D47C2semidirect
9. C47×#1485C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
313. #1485D47direct (N × H)
320. D47#1485direct (N × H)
359. Q8⋊C8C2×D47semidirect
360. C47C2×#1485semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#431×D472
C4×M16×D472
#202418102
#202418092
#202418082
#202418072
Q8⋊C8×D472
C47×#14852
C2×#148547