Finite Group Databasebeta

← D47×#1583 #26185778

Subgroups — D47×#1583 #26185778

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×Q8×D47C211yesmaximal, characteristic, complemented
2C4×SD16×D47C211yesmaximal, characteristic
3#436×D47C211yesmaximal, characteristic
4#20242234C211yesmaximal, characteristic, complemented
5#20242233C211yesmaximal, characteristic, complemented
6#20242232C211yesmaximal, characteristic, complemented
7#20242231C211yesmaximal, characteristic, complemented
8#20242230C211yesmaximal, characteristic, complemented
9#20242229C211yesmaximal, characteristic, complemented
10#20242228C211yesmaximal, characteristic, complemented
11#334×D47C211yesmaximal, characteristic, complemented
12Q8⋊C8×D47C211yesmaximal, characteristic, complemented
13D4⋊C8×D47C211yesmaximal, characteristic
14#322×D47C211yesmaximal, characteristic, complemented
15C47×#1583C211yesmaximal, characteristic, complemented
16C2×SD16×D47C411yescharacteristic
17C2×M16×D47—21no—
18C4×Q8×D47C2211yescharacteristic
19C4×D4×D47C2211yescharacteristic
20Q8×C47⋊C8C2211yescharacteristic, complemented
21C8×Dic94—21no—
22C8×Dic94C2211yescharacteristic, complemented
23#15689247—21no—
24#15689247C2211yescharacteristic, complemented
25#15689214C411yescharacteristic
26C4×#10625325C2211yescharacteristic
27SD16×Dic47C411yescharacteristic
28C4×#10625336C2211yescharacteristic
29#15689210C411yescharacteristic
30C4×#10625335C2211yescharacteristic
31#15689208C411yescharacteristic
32#15689202C2211yescharacteristic
33#15689201C2211yescharacteristic
34#15689200C2211yescharacteristic
35#15689199—21no—
36#15689198—21no—
37#106×D47C411yescharacteristic
38C4⋊C8×D47—21no—
39C4⋊C8×D47C2211yescharacteristic
40C4⋊C8×D47C2211yescharacteristic
41#103×D47C411yescharacteristic
42#102×D47C411yescharacteristic
43C22⋊C8×D47—21no—
44C4×C8×D47—21no—
45C4×C8×D47C2211yescharacteristic
46C4×C8×D47C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic, complemented
49#15688873C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
53#15688853C2211yescharacteristic, complemented
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688844C2211yescharacteristic, complemented
60C8×Q8×C47C2211yescharacteristic, complemented
61C4×SD16×C47C2211yescharacteristic
62C47×#436C2211yescharacteristic
63C47×#334C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C2×Q8×D47C2×C411yescharacteristic
68C2×D4×D47C2×C411yescharacteristic
69C22×C4×D47—21no—
70C2×#10625325C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625336C2×C411yescharacteristic
73SD16×D47—24no—
74C2×#10625329—21no—
75C2×#10625324—21no—
76C2×#10625324—21no—
77M16×D47—44no—
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81C2×C8×D47C2×C411yescharacteristic
82C2×C8×D47C2×C411yescharacteristic
83C2×C8×D47D411yescharacteristic
84C2×C8×D47D411yescharacteristic
85Q8×Dic47C2×C411yescharacteristic
86C4×Dic94—21no—
87C4×Dic94C2311yescharacteristic
88#13093989—21no—
89#13093989C2×C411yescharacteristic
90C4×D188C2311yescharacteristic
91D4×Dic47C2×C411yescharacteristic
92#13093986C2×C411yescharacteristic
93C4×C22⋊D47—21no—
94(C22⋊D47)⋊C4—21no—
95C4⋊C4×D47—21no—
96C4⋊C4×D47C2×C411yescharacteristic
97C4⋊C4×D47C2×C411yescharacteristic
98C22⋊C4×D47—21no—
99C42×D47—21no—
100C42×D47C2311yescharacteristic
101#13093956C2×C411yescharacteristic
102#13093955C2×C411yescharacteristic
103#13093955C2×C411yescharacteristic
104C4⋊(C47⋊C8)—21no—
105C4⋊(C47⋊C8)C2311yescharacteristic
106C4⋊(C47⋊C8)C2311yescharacteristic
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109Dic47⋊C8—21no—
110Dic47⋊C8—21no—
111#13093949C2×C411yescharacteristic
112#13093948C2×C411yescharacteristic
113#13093947C2×C411yescharacteristic
114#13093946C2×C411yescharacteristic
115#13093945C2×C411yescharacteristic
116#13093944C2×C411yescharacteristic
117C22⋊(C47⋊C8)—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120C4×C47⋊C8—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47C2×C411yescharacteristic
129C8×Dic47D411yescharacteristic
130C8×Dic47D411yescharacteristic
131C2×SD16×C47C2×C411yescharacteristic
132C2×M16×C47—21no—
133C4×Q8×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135#106×C47C2×C411yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139#103×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47—21no—
142C4×C8×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146C23×D47—21no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C2×C22⋊D47—21no—
151C22×Dic47—21no—
152Q8×D47—22no—
153Q8×D47M1614yescomplemented
154D4×D47—22no—
155D4×D47—22no—
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—42no—
163C2×C4×D47—42no—
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C2×D411yescharacteristic
166C2×C4×D47#4111yescharacteristic
167C2×Dic94—21no—
168C2×Dic94C22×C411yescharacteristic
169SD16×C47—22no—
170M16×C47—42no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47C22×C411yescharacteristic
175C2×C8×C47C22×C411yescharacteristic
176C2×C8×C47C2×D411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C4⋊C4×C47—21no—
179C4⋊C4×C47C22×C411yescharacteristic
180C4⋊C4×C47C22×C411yescharacteristic
181C22⋊C4×C47—21no—
182C42×C47—21no—
183C42×C47C2411yescharacteristic
184C22⋊Dic47—21no—
185#10625336—22no—
186#10625335—22no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47C22×C411yescharacteristic
191C4⋊Dic47C22×C411yescharacteristic
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47C22×C411yescharacteristic
200C4×Dic47C2×D411yescharacteristic
201C4×Dic47#4111yescharacteristic
202#10625329—42no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210#10625325—22no—
211#10625324—42no—
212#10625324—42no—
213C8×D47—22no—
214C8×D47—22no—
215C8×D47—22no—
216C8×D47—42no—
217C8×D47—42no—
218C8×D47—42no—
219C8×D47SD1614yescomplemented
220C23×C47—21no—
221C22×D47—21no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47C4×D411yescharacteristic
226Q8×C47—21no—
227Q8×C47C2×M1612yescomplemented
228D4×C47—21no—
229D4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C22⋊D47—42no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—42no—
243C2×Dic47C4×D411yescharacteristic
244C2×Dic47C4×D411yescharacteristic
245C2×Dic47C4×D411yescharacteristic
246D188—21no—
247D188—21no—
248C4×D47—24no—
249C4×D47—22no—
250C4×D47—42no—
251C4×D47—42no—
252C4×D47—41no—
253C4×D47—41no—
254C4×D47—42no—
255C4×D47C2×M1612yes—
256C4×D47#13112yes—
257C4×D47C2×SD1612yes—
258C4×D47#13512yes—
259Dic94—21no—
260Dic94—24no—
261Dic94C2×M1612yescomplemented
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—21no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C8×C47C2×SD1612yescomplemented
269C47⋊C8—21no—
270C47⋊C8—21no—
271C47⋊C8—21no—
272C47⋊C8—41no—
273C47⋊C8—41no—
274C47⋊C8—41no—
275C47⋊C8C2×SD1612yescomplemented
276C2×#1583—471nomaximal, Sylow
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47C2×C4×D411yescharacteristic
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—41no—
284C2×D47—84no—
285C2×D47#43512yes—
286C2×D47C4×SD1612yes—
287C2×D47#44412yes—
288C4×C47—22no—
289C4×C47—21no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47C22×M1611yescharacteristic
293C4×C47C2×#13111yescharacteristic
294C4×C47C22×SD1611yescharacteristic
295C4×C47C2×#13511yescharacteristic
296Dic47—22no—
297Dic47—21no—
298Dic47—41no—
299Dic47—41no—
300Dic47#43512yes—
301Dic47C4×SD1612yes—
302C2×C8×Q8—471no—
303C2×C4×SD16—471no—
304C2×#436—471no—
305#1583—471no—
306#1583—471no—
307#1583—471no—
308#1583—471no—
309#1583—471no—
310#1583—471no—
311#1583—471no—
312#1583D4711yescharacteristic, direct product factor
313C2×#334—471no—
314C2×Q8⋊C8—471no—
315C2×D4⋊C8—471no—
316C2×#322—471no—
317C2×C47—81no—
318C2×C47C2×#43511yescharacteristic
319C2×C47C2×C4×SD1611yescharacteristic
320C2×C47C2×#44411yescharacteristic
321D47—81no—
322D47#158314yesdirect product factor
323C22×SD16—471no—
324C22×M16—941no—
325C2×C4×Q8—471no—
326C2×C4×D4—471no—
327C8×Q8—471no—
328C8×Q8—471no—
329C8×Q8—471no—
330C8×Q8—941no—
331C8×Q8—941no—
332C8×Q8C2×D4711yescharacteristic, complemented
333C4×SD16—471no—
334C4×SD16—471no—
335C4×SD16—471no—
336C4×SD16—471no—
337C4×SD16—471no—
338C4×SD16—471no—
339C4×SD16—471no—
340C4×SD16C2×D4711yescharacteristic
341#436—471no—
342#436—471no—
343#436—471no—
344#436—941no—
345#436—941no—
346#436C2×D4711yescharacteristic
347C2×#106—471no—
348C2×C4⋊C8—471no—
349C2×C4⋊C8—471no—
350C2×C4⋊C8—941no—
351C2×#103—471no—
352C2×#102—471no—
353C2×C22⋊C8—941no—
354C2×C4×C8—471no—
355C2×C4×C8—471no—
356C2×C4×C8—471no—
357C2×C4×C8—941no—
358#334—471no—
359#334—471no—
360#334—471no—
361#334C2×D4711yescharacteristic, complemented
362Q8⋊C8—471no—
363Q8⋊C8—471no—
364Q8⋊C8—471no—
365Q8⋊C8C2×D4711yescharacteristic, complemented
366D4⋊C8—471no—
367D4⋊C8—471no—
368D4⋊C8—471no—
369D4⋊C8C2×D4711yescharacteristic
370#322—471no—
371#322—471no—
372#322—471no—
373#322C2×D4711yescharacteristic, complemented
374C47C2×#158311yescharacteristic, complemented, Sylow
375C22×Q8—471no—
376C22×D4—471no—
377C23×C4—941no—
378C2×SD16—471no—
379C2×SD16—471no—
380C2×SD16—471no—
381C2×SD16—944no—
382C2×SD16C4×D4711yescharacteristic
383C2×M16—21no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—1884no—
388C22×C8—471no—
389C22×C8—471no—
390C22×C8—471no—
391C22×C8—471no—
392C22×C8—941no—
393C22×C8—941no—
394C22×C8—941no—
395C4×Q8—471no—
396C4×Q8—471no—
397C4×Q8—471no—
398C4×Q8—941no—
399C4×Q8—941no—
400C4×Q8C22×D4711yescharacteristic
401C4×D4—471no—
402C4×D4—471no—
403C4×D4—471no—
404C4×D4—941no—
405C4×D4—941no—
406C4×D4C22×D4711yescharacteristic
407C2×C4⋊C4—471no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—941no—
410C2×C22⋊C4—941no—
411C2×C42—471no—
412C2×C42—941no—
413#106—471no—
414#106—471no—
415#106—471no—
416#106C4×D4711yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—471no—
419C4⋊C8—471no—
420C4⋊C8—941no—
421C4⋊C8—941no—
422C4⋊C8—941no—
423C4⋊C8—941no—
424C4⋊C8—941no—
425C4⋊C8C22×D4711yescharacteristic
426C4⋊C8C22×D4711yescharacteristic
427#103—471no—
428#103—471no—
429#103—471no—
430#103C4×D4711yescharacteristic
431#102—471no—
432#102—471no—
433#102—471no—
434#102C4×D4711yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438C22⋊C8—941no—
439C4×C8—21no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—471no—
446C4×C8—471no—
447C4×C8—941no—
448C4×C8—941no—
449C4×C8—941no—
450C4×C8—941no—
451C4×C8C22×D4711yescharacteristic
452C4×C8C22×D4711yescharacteristic
453C4×C8C22×D4711yescharacteristic
454C24—941no—
455C2×Q8—474no—
456C2×Q8—471no—
457C2×Q8—941no—
458C2×Q8—942no—
459C2×Q8C2×C4×D4711yescharacteristic
460C2×D4—471no—
461C2×D4—942no—
462C2×D4—942no—
463C2×D4—941no—
464C2×D4C2×C4×D4711yescharacteristic
465C22×C4—21no—
466C22×C4—471no—
467C22×C4—471no—
468C22×C4—471no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—1882no—
476C22×C4—1882no—
477SD16—22no—
478SD16—942no—
479SD16—942no—
480SD16—942no—
481M16—42no—
482M16—1882no—
483M16—1882no—
484M16—1882no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—471no—
489C2×C8—474no—
490C2×C8—471no—
491C2×C8—471no—
492C2×C8—471no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—942no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C2×C8—1882no—
500C2×C8—1882no—
501C2×C8—1882no—
502C2×C8C2×C4×D4711yescharacteristic
503C2×C8C2×C4×D4711yescharacteristic
504C2×C8D4×D4711yescharacteristic
505C2×C8D4×D4711yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—471no—
508C4⋊C4—471no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4C2×C4×D4711yescharacteristic
515C4⋊C4C2×C4×D4711yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—941no—
518C22⋊C4—941no—
519C22⋊C4—941no—
520C42—21no—
521C42—471no—
522C42—471no—
523C42—471no—
524C42—941no—
525C42—941no—
526C42—941no—
527C42C23×D4711yescharacteristic
528C23—21no—
529C23—471no—
530C23—941no—
531C23—1882no—
532C23—1882no—
533C23—1882no—
534Q8—21no—
535Q8—472no—
536Q8—944no—
537Q8—941no—
538Q8M16×D4712yescomplemented
539D4—21no—
540D4—21no—
541D4—941no—
542D4—941no—
543D4—1882no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—471no—
550C2×C4—471no—
551C2×C4—472no—
552C2×C4—472no—
553C2×C4—472no—
554C2×C4—472no—
555C2×C4—471no—
556C2×C4—942no—
557C2×C4—944no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4C22×C4×D4711yescharacteristic
568C2×C4C2×D4×D4711yescharacteristic
569C2×C4#41×D4711yescharacteristic
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—472no—
577C8—941no—
578C8—941no—
579C8—941no—
580C8—1881no—
581C8—1881no—
582C8—1881no—
583C8SD16×D4712yescomplemented
584C22—41no—
585C22—41no—
586C22—41no—
587C22—472no—
588C22—472no—
589C22—472no—
590C22—3764no—
591C22—1881no—
592C22—1881no—
593C22—1881no—
594C22C4×D4×D4711yescharacteristic
595C4—21no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—472no—
600C4—472no—
601C4—941no—
602C4—942no—
603C4—1881no—
604C4—1881no—
605C4C2×M16×D4711yescharacteristic
606C4#131×D4711yescharacteristic
607C4C2×SD16×D4711yescharacteristic
608C4#135×D4711yescharacteristic
609C2—81no—
610C2—474no—
611C2—3761no—
612C2#435×D4711yescharacteristic
613C2C4×SD16×D4711yescharacteristic
614C2#444×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1583C2
socleC22×C47C2×C4×D4
prime radicalC2×D4×D47C2×C4
cosocleC42×C47C24
hypercenter#1583D47
hypocenterC47C2×#1583
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
1. C8×Q8×D47C2semidirect
4. #20242234C2semidirect
5. #20242233C2semidirect
6. #20242232C2semidirect
7. #20242231C2semidirect
8. #20242230C2semidirect
9. #20242229C2semidirect
10. #20242228C2semidirect
11. #334×D47C2semidirect
12. Q8⋊C8×D47C2semidirect
14. #322×D47C2semidirect
15. C47×#1583C2semidirect
20. Q8×C47⋊C8C22semidirect
22. C8×Dic94C22semidirect
24. #15689247C22semidirect
48. #15688874C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
51. #15688855C22semidirect
52. Q8⋊(C47⋊C8)C22semidirect
53. #15688853C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688844C22semidirect
60. C8×Q8×C47C22semidirect
63. C47×#334C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
153. Q8×D47M16semidirect
219. C8×D47SD16semidirect
227. Q8×C47C2×M16semidirect
261. Dic94C2×M16semidirect
268. C8×C47C2×SD16semidirect
275. C47⋊C8C2×SD16semidirect
312. #1583D47direct (N × H)
322. D47#1583direct (N × H)
332. C8×Q8C2×D47semidirect
361. #334C2×D47semidirect
365. Q8⋊C8C2×D47semidirect
373. #322C2×D47semidirect
374. C47C2×#1583semidirect
538. Q8M16×D47semidirect
583. C8SD16×D47semidirect

Maximal subgroups

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

subgroupindex
C8×Q8×D472
C4×SD16×D472
#436×D472
#202422342
#202422332
#202422322
#202422312
#202422302
#202422292
#202422282
#334×D472
Q8⋊C8×D472
D4⋊C8×D472
#322×D472
C47×#15832
C2×#158347