Finite Group Databasebeta

← D47×#1921 #26218426

Subgroups — D47×#1921 #26218426

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D47C211yesmaximal, characteristic
2#389×D47C211yesmaximal, characteristic
3C4×C4⋊C4×D47C211yesmaximal, characteristic
4#20243983C211yesmaximal, characteristic, complemented
5#20243982C211yesmaximal, characteristic, complemented
6#20243981C211yesmaximal, characteristic, complemented
7#20243980C211yesmaximal, characteristic, complemented
8#20243979C211yesmaximal, characteristic, complemented
9#20243978C211yesmaximal, characteristic, complemented
10#20243977C211yesmaximal, characteristic, complemented
11#340×D47C211yesmaximal, characteristic
12#340×D47C211yesmaximal, characteristic
13#340×D47C211yesmaximal, characteristic
14#336×D47C211yesmaximal, characteristic
15C47×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D47C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4⋊C4×D47—21no—
19C2×C4⋊C4×D47C2211yescharacteristic
20C2×C4⋊C4×D47C2211yescharacteristic
21C2×C4⋊C4×D47C2211yescharacteristic
22C2×C4⋊C4×D47C2211yescharacteristic
23C2×C42×D47—21no—
24C2×C42×D47C2211yescharacteristic
25C2×#13093958C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27C2×#13093957C2211yescharacteristic
28#107×D47C418yescomplemented
29#15689022C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689020—21no—
32#15689019C2211yescharacteristic
33#15689018—21no—
34C4⋊C4×Dic47C2211yescharacteristic
35C4⋊C4×Dic47C2211yescharacteristic
36C4×Dic47⋊C4—21no—
37C4×C4⋊Dic47C2211yescharacteristic
38#15688974—21no—
39#95×D47—21no—
40#95×D47—21no—
41#15688886C2211yescharacteristic
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C47×#389C2211yescharacteristic
55C4×C4⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×C4×D47—21no—
61C22×C4×D47—21no—
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64C22×C4×D47D411yescharacteristic
65C22×C4×D47D411yescharacteristic
66C22×C4×D47C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C2×C8×D47—22no—
70C2×C8×D47—22no—
71C2×C8×D47—22no—
72C2×C8×D47—22no—
73C2×C8×D47—22no—
74C2×C8×D47C2×C414yes—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C4⋊C4×D47—22no—
87C4⋊C4×D47—22no—
88C4⋊C4×D47—22no—
89C4⋊C4×D47—22no—
90C4⋊C4×D47—22no—
91C4⋊C4×D47—44no—
92C4⋊C4×D47C2×C414yes—
93C4⋊C4×D47C2×C414yes—
94C4⋊C4×D47Q814yes—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47D411yescharacteristic
99C2×C4×Dic47D411yescharacteristic
100C2×C4×Dic47C2311yescharacteristic
101C42×D47—22no—
102C42×D47—22no—
103C42×D47—44no—
104#13093958C2×C414yescomplemented
105#13093957C2×C414yescomplemented
106#13093957C2×C414yescomplemented
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122#107×C47C2×C414yescomplemented
123#95×C47—21no—
124#95×C47—21no—
125C23×D47C2×D411yescharacteristic
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47C2×D411yescharacteristic
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—24no—
143C2×C4×D47—24no—
144C2×C4×D47—24no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—42no—
149C2×C4×D47—42no—
150C2×C4×D47—42no—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47—42no—
154C2×C4×D47—42no—
155C2×C4×D47—42no—
156C2×C4×D47—42no—
157C2×C4×D47Q1614yes—
158C2×C4×D47C22×C412yes—
159C2×C4×D47C2×Q812yes—
160C2×C4×D47#4112yes—
161C2×C4×D47#4112yes—
162C2×C4×D47#4112yes—
163C2×C4×D47#4112yes—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C22×C412yes—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47C22×C412yes—
177C4⋊C4×C47C22×C412yes—
178C4⋊C4×C47C2×Q812yes—
179C42×C47—21no—
180C42×C47—21no—
181C42×C47—42no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—42no—
188C4⋊Dic47C22×C412yes—
189C4⋊Dic47C22×C412yes—
190C4⋊Dic47C2×Q812yes—
191Dic47⋊C4—24no—
192Dic47⋊C4—24no—
193Dic47⋊C4—24no—
194Dic47⋊C4—42no—
195Dic47⋊C4—42no—
196Dic47⋊C4—42no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47—22no—
200C4×Dic47—22no—
201C4×Dic47—42no—
202C4×Dic47—42no—
203C4×Dic47—42no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8C22×C412yes—
210C8×D47—28no—
211C8×D47—44no—
212C23×C47C22×D411yescharacteristic
213C22×D47C4×D412yes—
214C22×D47C22⋊Q812yes—
215C22×D47#12312yes—
216C22×D47C2×Q1612yes—
217C22×D47#13512yes—
218C22×D47AGL(1,ℤ/8)12yes—
219C22×D47AGL(1,ℤ/8)12yes—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47C2×Q1612yes—
238C2×C4×C47C23×C411yescharacteristic
239C2×C4×C47C22×Q811yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47C4×D412yes—
262C2×Dic47C22⋊Q812yes—
263C2×Dic47#12312yes—
264C2×Dic47C2×Q1612yes—
265C4×D47—28no—
266C4×D47—48no—
267C4×D47—48no—
268C4×D47—48no—
269C4×D47—44no—
270C4×D47—84no—
271C4×D47#11714yes—
272C4×D47C4×Q814yes—
273C4×D47#12514yes—
274C4×D47#12614yes—
275C8×C47—22no—
276C8×C47—41no—
277C47⋊C8—22no—
278C47⋊C8—41no—
279C2×#1921—471nomaximal, Sylow
280C22×C47C2×C4×D411yescharacteristic
281C22×C47C2×C22⋊Q811yescharacteristic
282C22×C47C2×#12311yescharacteristic
283C22×C47C22×Q1611yescharacteristic
284C22×C47C2×#13511yescharacteristic
285C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
287C2×D47#38714yes—
288C2×D47C4×Q1614yes—
289C2×D47#44214yes—
290C2×D47#47714yes—
291C2×D47#47814yes—
292C2×D47#48214yes—
293C2×D47#48414yes—
294C4×C47—22no—
295C4×C47—42no—
296C4×C47—41no—
297C4×C47—42no—
298C4×C47—42no—
299C4×C47—81no—
300C4×C47C2×#11711yescharacteristic
301C4×C47C2×C4×Q811yescharacteristic
302C4×C47C2×#12511yescharacteristic
303C4×C47C2×#12611yescharacteristic
304Dic47—22no—
305Dic47—42no—
306Dic47—41no—
307Dic47—42no—
308Dic47—42no—
309Dic47—81no—
310Dic47#38714yes—
311C22×#107—471no—
312C2×#389—471no—
313C2×C4×C4⋊C4—471no—
314#1921—471no—
315#1921—471no—
316#1921—471no—
317#1921—471no—
318#1921—471no—
319#1921—471no—
320#1921—471no—
321#1921D4711yescharacteristic, direct product factor
322C2×#340—471no—
323C2×#340—471no—
324C2×#340—471no—
325C2×#336—471no—
326C2×C47C2×#38711yescharacteristic
327C2×C47C2×C4×Q1611yescharacteristic
328C2×C47C2×#44211yescharacteristic
329C2×C47C2×#47811yescharacteristic
330C2×C47C2×#47711yescharacteristic
331C2×C47C2×#48211yescharacteristic
332C2×C47C2×#48411yescharacteristic
333D47#192118yesdirect product factor
334C23×C8—471no—
335C23×C8—471no—
336C22×C4⋊C4—471no—
337C22×C4⋊C4—471no—
338C22×C4⋊C4—471no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4—941no—
341C22×C42—471no—
342C22×C42—941no—
343C2×#107—471no—
344C2×#107—471no—
345C2×#107—471no—
346C2×#107—478no—
347C2×#107C2×D4711yescharacteristic
348#389—471no—
349#389—471no—
350#389—471no—
351#389—941no—
352#389—941no—
353#389C2×D4711yescharacteristic
354C4×C4⋊C4—471no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4—471no—
357C4×C4⋊C4—941no—
358C4×C4⋊C4—941no—
359C4×C4⋊C4C2×D4711yescharacteristic
360C2×#95—941no—
361C2×#95—941no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#340—471no—
369#340—471no—
370#340—471no—
371#340C2×D4711yescharacteristic
372#340C2×D4711yescharacteristic
373#340C2×D4711yescharacteristic
374#336—471no—
375#336—471no—
376#336—471no—
377#336C2×D4711yescharacteristic
378C47C2×#192111yescharacteristic, complemented, Sylow
379C23×C4—471no—
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—941no—
383C23×C4—941no—
384C23×C4—941no—
385C23×C4—941no—
386C22×C8—471no—
387C22×C8—474no—
388C22×C8—471no—
389C22×C8—942no—
390C22×C8—942no—
391C22×C8—942no—
392C22×C8—942no—
393C22×C8—942no—
394C22×C8C22×D4711yescharacteristic
395C22×C8C22×D4711yescharacteristic
396C2×C4⋊C4—21no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—474no—
401C2×C4⋊C4—474no—
402C2×C4⋊C4—474no—
403C2×C4⋊C4—471no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—941no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—941no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—1884no—
417C2×C4⋊C4C22×D4711yescharacteristic
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C4⋊C4C22×D4711yescharacteristic
420C2×C4⋊C4C22×D4711yescharacteristic
421C2×C42—21no—
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—471no—
425C2×C42—942no—
426C2×C42—942no—
427C2×C42—941no—
428C2×C42—941no—
429C2×C42—941no—
430C2×C42—1884no—
431C2×C42C22×D4711yescharacteristic
432#107—474no—
433#107—474no—
434#107—474no—
435#107C4×D4714yescomplemented
436#95—21no—
437#95—21no—
438#95—941no—
439#95—941no—
440#95—941no—
441#95—941no—
442#95—941no—
443#95—941no—
444C24—471no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—471no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—472no—
453C22×C4—472no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—471no—
457C22×C4—474no—
458C22×C4—471no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—944no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—941no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4—1882no—
474C22×C4—1882no—
475C22×C4—1882no—
476C22×C4—1882no—
477C22×C4—1882no—
478C22×C4—1882no—
479C22×C4—1882no—
480C22×C4D4×D4711yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4C23×D4711yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—472no—
489C2×C8—948no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—1884no—
496C2×C8C2×C4×D4712yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—472no—
504C4⋊C4—472no—
505C4⋊C4—472no—
506C4⋊C4—944no—
507C4⋊C4—944no—
508C4⋊C4—944no—
509C4⋊C4—941no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—1882no—
515C4⋊C4—1882no—
516C4⋊C4—1882no—
517C4⋊C4—1882no—
518C4⋊C4C2×C4×D4712yes—
519C4⋊C4C2×C4×D4712yes—
520C4⋊C4Q8×D4712yes—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—942no—
525C42—942no—
526C42—941no—
527C42—941no—
528C42—1882no—
529C42—1882no—
530C42—1882no—
531C23—472no—
532C23—472no—
533C23—472no—
534C23—472no—
535C23—472no—
536C23—472no—
537C23—472no—
538C23C2×D4×D4711yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—472no—
557C2×C4—472no—
558C2×C4—472no—
559C2×C4—474no—
560C2×C4—474no—
561C2×C4—474no—
562C2×C4—474no—
563C2×C4—472no—
564C2×C4—948no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—941no—
573C2×C4—3764no—
574C2×C4—1884no—
575C2×C4—1888no—
576C2×C4—1888no—
577C2×C4—1888no—
578C2×C4—1881no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4Q16×D4712yes—
588C2×C4C22×C4×D4711yescharacteristic
589C2×C4C2×Q8×D4711yescharacteristic
590C2×C4#41×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4#41×D4711yescharacteristic
594C8—22no—
595C8—41no—
596C8—942no—
597C8—1881no—
598C22—474no—
599C22—474no—
600C22—474no—
601C22—474no—
602C22—474no—
603C22—474no—
604C22—474no—
605C22C4×D4×D4711yescharacteristic
606C22C22⋊Q8×D4711yescharacteristic
607C22#123×D4711yescharacteristic
608C22C2×Q16×D4711yescharacteristic
609C22#135×D4711yescharacteristic
610C22AGL(1,ℤ/8)×D4711yescharacteristic
611C22AGL(1,ℤ/8)×D4711yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—474no—
619C4—942no—
620C4—3761no—
621C4—1882no—
622C4—1882no—
623C4—1881no—
624C4—1882no—
625C4#117×D4711yescharacteristic
626C4C4×Q8×D4711yescharacteristic
627C4#125×D4711yescharacteristic
628C4#126×D4711yescharacteristic
629C2—478no—
630C2#387×D4711yescharacteristic
631C2C4×Q16×D4711yescharacteristic
632C2#442×D4711yescharacteristic
633C2#478×D4711yescharacteristic
634C2#477×D4711yescharacteristic
635C2#482×D4711yescharacteristic
636C2#484×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1921C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1921D47
hypocenterC47C2×#1921
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #20243983C2semidirect
5. #20243982C2semidirect
6. #20243981C2semidirect
7. #20243980C2semidirect
8. #20243979C2semidirect
9. #20243978C2semidirect
10. #20243977C2semidirect
15. C47×#1921C2semidirect
28. #107×D47C4semidirect
104. #13093958C2×C4semidirect
105. #13093957C2×C4semidirect
106. #13093957C2×C4semidirect
122. #107×C47C2×C4semidirect
321. #1921D47direct (N × H)
333. D47#1921direct (N × H)
378. C47C2×#1921semidirect
435. #107C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
#389×D472
C4×C4⋊C4×D472
#202439832
#202439822
#202439812
#202439802
#202439792
#202439782
#202439772
#340×D472
#336×D472
C47×#19212
C2×#192147