Finite Group Databasebeta

← D47×#1894 #26217956

Subgroups — D47×#1894 #26217956

Order 12032.

1966 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×C22⋊Q8×D47C211yesmaximal, characteristic
3C2×#103×D47C212yesmaximal, complemented
4#380×D47C211yesmaximal, characteristic
5#20243822C211yesmaximal, characteristic, complemented
6#20243821C211yesmaximal, characteristic, complemented
7#20243820C212yesmaximal, complemented
8#20243819C211yesmaximal, characteristic, complemented
9#20243818C212yesmaximal, complemented
10#340×D47C212yesmaximal, complemented
11C47×#1894C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C22×#10625329C2211yescharacteristic
15C22×#10625324C2212yes—
16C2×M16×D47—24no—
17C2×M16×D47—28no—
18C22×C8×D47C2212yes—
19C2×#13094004C2211yescharacteristic
20C2×#13094003C2211yescharacteristic
21C2×#13094002—21no—
22C2×#13094001—21no—
23C2×#13094000C2211yescharacteristic
24C22⋊Q8×D47—24no—
25C22⋊Q8×D47C418yescomplemented
26C2×C4⋊C4×D47—21no—
27C2×C4⋊C4×D47C2212yes—
28C2×C4⋊C4×D47C2211yescharacteristic
29C2×C22⋊C4×D47—21no—
30C2×C22⋊C4×D47—21no—
31C2×#13093949C2212yescomplemented
32C2×#13093948C2212yescomplemented
33C2×#13093947C2212yescomplemented
34#103×D47—28no—
35#15688983C2211yescharacteristic
36#15688982—21no—
37#15688981—21no—
38#15688980C2212yes—
39#95×D47—21no—
40#15688886C2212yescomplemented
41#15688885C2212yescomplemented
42#15688885C2212yescomplemented
43C22×M16×C47C2211yescharacteristic
44C2×C22⋊Q8×C47C2211yescharacteristic
45C2×#103×C47C2212yescomplemented
46C47×#380C2211yescharacteristic
47C47×#340C2212yescomplemented
48C24×D47D411yescharacteristic
49C22×Dic94—21no—
50C22×Dic94C2311yescharacteristic
51C2×Q8×D47—22no—
52C2×Q8×D47—24no—
53C2×Q8×D47—24no—
54C2×Q8×D47C2×C414yes—
55C23×Dic47D411yescharacteristic
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—21no—
59C22×C4×D47—21no—
60C22×C4×D47—22no—
61C22×C4×D47C2×C414yes—
62C22×C4×D47D411yescharacteristic
63C22×C4×D47D411yescharacteristic
64C22×C4×D47D414yes—
65C22×C4×D47C2311yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C2×#10625329—22no—
68C2×#10625329—24no—
69C2×#10625324—24no—
70C2×#10625324—24no—
71C2×#10625324—24no—
72M16×D47—232no—
73C22×C47⋊C8C2312yes—
74C2×C8×D47—24no—
75C2×C8×D47—24no—
76C2×C8×D47D418yes—
77#13094004—22no—
78#13094004C2×C414yescomplemented
79#13094003—22no—
80#13094003C2×C414yescomplemented
81#13094002—28no—
82#13094001—28no—
83#13094000—22no—
84#13094000C2×C414yescomplemented
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47C2312yes—
87C2×C4⋊Dic47C2311yescharacteristic
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×Dic47⋊C4—21no—
91C2×Dic47⋊C4—22no—
92C4⋊C4×D47—28no—
93C4⋊C4×D47—22no—
94C4⋊C4×D47—24no—
95C4⋊C4×D47—24no—
96C4⋊C4×D47C2×C414yes—
97C2×C22⋊Dic47—21no—
98C2×C22⋊Dic47—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—22no—
102C22⋊C4×D47—28no—
103C22⋊C4×D47—44no—
104#13093949—24no—
105#13093948—24no—
106#13093947—24no—
107C47⋊#95—21no—
108C47⋊#95—22no—
109C22×Q8×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C2×M16×C47—22no—
112C2×M16×C47—24no—
113C22×C8×C47C2312yes—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47C2×C414yescomplemented
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47C2312yes—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121#103×C47—24no—
122#95×C47—21no—
123C24×C47C2×D411yescharacteristic
124C23×D47—24no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—24no—
128C23×D47C22⋊C414yes—
129C23×D47C2×D411yescharacteristic
130C23×D47C2×D411yescharacteristic
131C2×Q8×C47—21no—
132C2×Q8×C47—22no—
133C2×Q8×C47—22no—
134C2×Q8×C47C22×C412yes—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47C22×C412yes—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2411yescharacteristic
144C22×Dic47—24no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—22no—
148C22×Dic47C22⋊C414yes—
149C22×Dic47C2×D411yescharacteristic
150C22×Dic47C2×D411yescharacteristic
151Q8×D47—216no—
152Q8×D47—44no—
153Q8×D47—44no—
154C2×C4×D47—24no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—24no—
158C2×C4×D47—216no—
159C2×C4×D47—28no—
160C2×C4×D47—28no—
161C2×C4×D47—24no—
162C2×C4×D47—24no—
163C2×C4×D47—44no—
164C2×C4×D47—42no—
165C2×C4×D47—42no—
166C2×C4×D47—44no—
167C2×C4×D47—44no—
168C2×C4×D47—44no—
169C2×C4×D47C22⋊C414yes—
170C2×C4×D47C22⋊C414yes—
171C2×C4×D47C22×C412yes—
172C2×C4×D47C22×C412yes—
173C2×C4×D47C2×D412yes—
174C2×C4×D47C2×D414yes—
175C2×C4×D47C2×D412yes—
176C2×C4×D47#4114yes—
177C2×Dic94—22no—
178C2×Dic94—22no—
179C2×Dic94—21no—
180C2×Dic94—24no—
181C2×Dic94—44no—
182C2×Dic94C22×C412yes—
183M16×C47—28no—
184C2×C8×C47—22no—
185C2×C8×C47—22no—
186C2×C8×C47C2×D414yes—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—22no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47C22×C412yes—
192C22⋊C4×C47—24no—
193C22⋊C4×C47—42no—
194C22⋊Dic47—24no—
195C22⋊Dic47—42no—
196(C2×D47)⋊C4—24no—
197(C2×D47)⋊C4—24no—
198(C2×D47)⋊C4—44no—
199C4⋊Dic47—21no—
200C4⋊Dic47—24no—
201C4⋊Dic47—22no—
202C4⋊Dic47—22no—
203C4⋊Dic47C22×C412yes—
204Dic47⋊C4—24no—
205Dic47⋊C4—24no—
206Dic47⋊C4—24no—
207Dic47⋊C4—44no—
208#10625329—28no—
209C2×C47⋊C8—22no—
210C2×C47⋊C8—22no—
211C2×C47⋊C8C2×D414yes—
212#10625324—216no—
213C8×D47—216no—
214C23×C47—22no—
215C23×C47—21no—
216C23×C47—22no—
217C23×C47—21no—
218C23×C47C2×C22⋊C412yes—
219C23×C47C22×D411yescharacteristic
220C22×D47—22no—
221C22×D47—21no—
222C22×D47—22no—
223C22×D47—21no—
224C22×D47—28no—
225C22×D47—28no—
226C22×D47—28no—
227C22×D47—48no—
228C22×D47—48no—
229C22×D47C2×C22⋊C412yes—
230C22×D47C2×C22⋊C412yes—
231C22×D47#12114yes—
232C22×D47AGL(1,ℤ/8)12yes—
233C22×D47#13712yes—
234C22×D47#13714yes—
235Q8×C47—24no—
236Q8×C47—41no—
237Q8×C47—41no—
238C2×C4×C47—22no—
239C2×C4×C47—24no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—42no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47C2×C22⋊C412yes—
251C2×C4×C47C23×C411yescharacteristic
252C2×C4×C47C22×D412yes—
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47C2×#4112yes—
255C2×Dic47—22no—
256C2×Dic47—28no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—42no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47C2×C22⋊C412yes—
266C2×Dic47C2×C22⋊C412yes—
267C2×Dic47#12114yes—
268C4×D47—28no—
269C4×D47—24no—
270C4×D47—22no—
271C4×D47—22no—
272C4×D47—28no—
273C4×D47—48no—
274C4×D47—48no—
275C4×D47—88no—
276C4×D47C4×D418yes—
277C4×D47#12014yes—
278C4×D47#12314yes—
279Dic94—24no—
280Dic94—41no—
281Dic94—41no—
282Dic94—48no—
283C8×C47—24no—
284C47⋊C8—24no—
285C2×#1894—471nomaximal, Sylow
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—42no—
290C22×C47—42no—
291C22×C47C22×C22⋊C411yescharacteristic
292C22×C47C2×#12112yes—
293C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C47C2×#13712yes—
295C22×C47C2×#13711yescharacteristic
296C2×D47—22no—
297C2×D47—22no—
298C2×D47—22no—
299C2×D47—42no—
300C2×D47—42no—
301C2×D47—416no—
302C2×D47#38614yes—
303C2×D47#41714yes—
304C2×D47#41914yes—
305C2×D47#46818yes—
306C2×D47#47018yes—
307C4×C47—22no—
308C4×C47—42no—
309C4×C47—42no—
310C4×C47—82no—
311C4×C47C2×C4×D412yes—
312C4×C47C2×#12011yescharacteristic
313C4×C47C2×#12311yescharacteristic
314Dic47—22no—
315Dic47—42no—
316Dic47—42no—
317Dic47—82no—
318Dic47#38614yes—
319C23×M16—471no—
320C22×C22⋊Q8—471no—
321C22×#103—472no—
322C2×#380—471no—
323#1894—472no—
324#1894—471no—
325#1894—472no—
326#1894—471no—
327#1894—471no—
328#1894D4711yescharacteristic, direct product factor
329C2×#340—472no—
330C2×C47—42no—
331C2×C47C2×#38611yescharacteristic
332C2×C47C2×#41911yescharacteristic
333C2×C47C2×#41711yescharacteristic
334C2×C47C2×#46812yes—
335C2×C47C2×#47012yes—
336D47—42no—
337D47#189418yesdirect product factor
338C23×Q8—471no—
339C24×C4—471no—
340C22×M16—471no—
341C22×M16—472no—
342C22×M16—948no—
343C22×M16—944no—
344C22×M16C2×D4711yescharacteristic
345C23×C8—472no—
346C2×C22⋊Q8—471no—
347C2×C22⋊Q8—471no—
348C2×C22⋊Q8—478no—
349C2×C22⋊Q8—471no—
350C2×C22⋊Q8—941no—
351C2×C22⋊Q8—941no—
352C2×C22⋊Q8—944no—
353C2×C22⋊Q8C2×D4711yescharacteristic
354C22×C4⋊C4—471no—
355C22×C4⋊C4—472no—
356C22×C4⋊C4—941no—
357C22×C22⋊C4—941no—
358C22×C22⋊C4—941no—
359C2×#103—472no—
360C2×#103—472no—
361C2×#103—472no—
362C2×#103—948no—
363C2×#103C2×D4712yescomplemented
364#380—471no—
365#380—472no—
366#380—941no—
367#380—941no—
368#380C2×D4711yescharacteristic
369C2×#95—941no—
370#340—472no—
371#340—472no—
372#340—472no—
373#340C2×D4712yescomplemented
374C47C2×#189411yescharacteristic, complemented, Sylow
375C25—471no—
376C22×Q8—474no—
377C22×Q8—471no—
378C22×Q8—941no—
379C22×Q8—942no—
380C22×Q8—944no—
381C22×Q8—944no—
382C22×Q8C22×D4711yescharacteristic
383C23×C4—471no—
384C23×C4—471no—
385C23×C4—474no—
386C23×C4—471no—
387C23×C4—474no—
388C23×C4—471no—
389C23×C4—471no—
390C23×C4—944no—
391C23×C4—944no—
392C23×C4—941no—
393C23×C4—941no—
394C23×C4—942no—
395C23×C4C22×D4711yescharacteristic
396C2×M16—22no—
397C2×M16—24no—
398C2×M16—944no—
399C2×M16—944no—
400C2×M16—944no—
401C2×M16—9432no—
402C2×M16—942no—
403C2×M16—944no—
404C22×C8—472no—
405C22×C8—478no—
406C22×C8—944no—
407C22×C8—944no—
408C22×C8C22×D4712yes—
409C22⋊Q8—22no—
410C22⋊Q8—474no—
411C22⋊Q8—474no—
412C22⋊Q8—474no—
413C22⋊Q8—948no—
414C22⋊Q8—948no—
415C22⋊Q8—942no—
416C22⋊Q8—942no—
417C22⋊Q8—942no—
418C22⋊Q8C4×D4714yescomplemented
419C2×C4⋊C4—21no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—474no—
422C2×C4⋊C4—472no—
423C2×C4⋊C4—942no—
424C2×C4⋊C4—948no—
425C2×C4⋊C4—944no—
426C2×C4⋊C4—944no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4—942no—
432C2×C4⋊C4C22×D4712yes—
433C2×C4⋊C4C22×D4711yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—948no—
437C2×C22⋊C4—941no—
438C2×C22⋊C4—941no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4—942no—
441C2×C22⋊C4—941no—
442C2×C22⋊C4—1884no—
443#103—24no—
444#103—944no—
445#103—944no—
446#103—944no—
447#95—21no—
448#95—942no—
449#95—941no—
450C24—471no—
451C24—474no—
452C24—471no—
453C24—942no—
454C24—944no—
455C24—944no—
456C24—942no—
457C24D4×D4711yescharacteristic
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—472no—
462C2×Q8—944no—
463C2×Q8—9416no—
464C2×Q8—941no—
465C2×Q8—942no—
466C2×Q8—942no—
467C2×Q8—1884no—
468C2×Q8—1884no—
469C2×Q8—1884no—
470C2×Q8C2×C4×D4712yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—471no—
477C22×C4—472no—
478C22×C4—474no—
479C22×C4—472no—
480C22×C4—474no—
481C22×C4—474no—
482C22×C4—471no—
483C22×C4—474no—
484C22×C4—474no—
485C22×C4—472no—
486C22×C4—472no—
487C22×C4—948no—
488C22×C4—944no—
489C22×C4—9416no—
490C22×C4—948no—
491C22×C4—944no—
492C22×C4—944no—
493C22×C4—944no—
494C22×C4—944no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—941no—
498C22×C4—941no—
499C22×C4—942no—
500C22×C4—1884no—
501C22×C4—1884no—
502C22×C4—1884no—
503C22×C4—1882no—
504C22×C4—1882no—
505C22×C4—1884no—
506C22×C4C2×C4×D4712yes—
507C22×C4D4×D4711yescharacteristic
508C22×C4D4×D4712yes—
509C22×C4C23×D4711yescharacteristic
510M16—28no—
511M16—9416no—
512M16—948no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—474no—
516C2×C8—9416no—
517C2×C8—942no—
518C2×C8—942no—
519C2×C8D4×D4714yes—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—472no—
525C4⋊C4—944no—
526C4⋊C4—944no—
527C4⋊C4—944no—
528C4⋊C4—944no—
529C4⋊C4—941no—
530C4⋊C4—942no—
531C4⋊C4—942no—
532C4⋊C4—1884no—
533C4⋊C4C2×C4×D4712yes—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—944no—
537C22⋊C4—944no—
538C22⋊C4—944no—
539C22⋊C4—1884no—
540C22⋊C4—1882no—
541C23—22no—
542C23—21no—
543C23—22no—
544C23—21no—
545C23—472no—
546C23—474no—
547C23—472no—
548C23—474no—
549C23—472no—
550C23—472no—
551C23—948no—
552C23—948no—
553C23—948no—
554C23—942no—
555C23—941no—
556C23—942no—
557C23—941no—
558C23—1888no—
559C23—1888no—
560C23C22⋊C4×D4712yes—
561C23C2×D4×D4711yescharacteristic
562Q8—24no—
563Q8—41no—
564Q8—41no—
565Q8—944no—
566Q8—1888no—
567Q8—1881no—
568Q8—1881no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—472no—
582C2×C4—474no—
583C2×C4—478no—
584C2×C4—474no—
585C2×C4—474no—
586C2×C4—472no—
587C2×C4—948no—
588C2×C4—948no—
589C2×C4—948no—
590C2×C4—942no—
591C2×C4—944no—
592C2×C4—942no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—3768no—
597C2×C4—1888no—
598C2×C4—1888no—
599C2×C4—1882no—
600C2×C4—1882no—
601C2×C4—1882no—
602C2×C4—1882no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4C22⋊C4×D4712yes—
606C2×C4C22×C4×D4711yescharacteristic
607C2×C4C2×D4×D4712yes—
608C2×C4C2×D4×D4711yescharacteristic
609C2×C4#41×D4712yes—
610C8—24no—
611C8—944no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—42no—
616C22—42no—
617C22—474no—
618C22—478no—
619C22—478no—
620C22—474no—
621C22—474no—
622C22—942no—
623C22—942no—
624C22—942no—
625C22—18816no—
626C22—1882no—
627C22—1882no—
628C22C2×C22⋊C4×D4711yescharacteristic
629C22#121×D4712yes—
630C22AGL(1,ℤ/8)×D4711yescharacteristic
631C22#137×D4712yes—
632C22#137×D4711yescharacteristic
633C4—22no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—474no—
638C4—942no—
639C4—3762no—
640C4—1882no—
641C4—1882no—
642C4C4×D4×D4712yes—
643C4#120×D4711yescharacteristic
644C4#123×D4711yescharacteristic
645C2—42no—
646C2—478no—
647C2—1882no—
648C2#386×D4711yescharacteristic
649C2#419×D4711yescharacteristic
650C2#417×D4711yescharacteristic
651C2#468×D4712yes—
652C2#470×D4712yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1894C2
socleC23×C47C22×D4
prime radicalC24×D47D4
cosocleC22×C4×C47C24
hypercenter#1894D47
hypocenterC47C2×#1894
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
3. C2×#103×D47C2semidirect
5. #20243822C2semidirect
6. #20243821C2semidirect
7. #20243820C2semidirect
8. #20243819C2semidirect
9. #20243818C2semidirect
10. #340×D47C2semidirect
11. C47×#1894C2semidirect
25. C22⋊Q8×D47C4semidirect
31. C2×#13093949C22semidirect
32. C2×#13093948C22semidirect
33. C2×#13093947C22semidirect
40. #15688886C22semidirect
41. #15688885C22semidirect
42. #15688885C22semidirect
45. C2×#103×C47C22semidirect
47. C47×#340C22semidirect
78. #13094004C2×C4semidirect
80. #13094003C2×C4semidirect
84. #13094000C2×C4semidirect
115. C22⋊Q8×C47C2×C4semidirect
328. #1894D47direct (N × H)
337. D47#1894direct (N × H)
363. C2×#103C2×D47semidirect
373. #340C2×D47semidirect
374. C47C2×#1894semidirect
418. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×C22⋊Q8×D472
C2×#103×D472
#380×D472
#202438222
#202438212
#202438202
#202438192
#202438182
#340×D472
C47×#18942
C2×#189447