Finite Group Databasebeta

← D47×#2853 #26422159

Subgroups — D47×#2853 #26422159

Order 12032.

3354 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D47C211yesmaximal, characteristic
2C22×C42×D47C211yesmaximal, characteristic, complemented
3#20251713C212yesmaximal, complemented
4#20251712C214yesmaximal, complemented
5#20251711C211yesmaximal, characteristic, complemented
6#20251710C211yesmaximal, characteristic, complemented
7#20251709C212yesmaximal, complemented
8#20251708C214yesmaximal, complemented
9#20251707C211yesmaximal, characteristic, complemented
10#388×D47C214yesmaximal, complemented
11#387×D47C214yesmaximal, complemented
12#386×D47C212yesmaximal
13#385×D47C212yesmaximal, complemented
14#381×D47C211yesmaximal, characteristic, complemented
15C47×#2853C211yesmaximal, characteristic, complemented
16C22×D4×D47C2211yescharacteristic
17C23×C4×D47C2212yes—
18C23×C4×D47C2211yescharacteristic
19C2×#13094009C2212yes—
20C2×#13094008C2211yescharacteristic
21C2×#13094007C2211yescharacteristic
22C2×#13094006C2212yes—
23C2×#13094005C2211yescharacteristic
24#123×D47—28no—
25C2×C4⋊C4×D47C2214yes—
26C2×C4⋊C4×D47C2212yes—
27C2×C22⋊C4×D47C2212yes—
28C2×C22⋊C4×D47C2211yescharacteristic
29C2×C22⋊C4×D47C2214yes—
30C2×C22⋊C4×D47C2212yes—
31C22×C4×Dic47C2211yescharacteristic, complemented
32C22×C4×Dic47C2212yescomplemented
33C2×C42×D47—28no—
34C2×C42×D47C2214yes—
35C2×C42×D47C2214yescomplemented
36#15689017C2214yescomplemented
37#15689016C2214yescomplemented
38#15689015C2214yescomplemented
39#15689014C2214yescomplemented
40#15689013C2214yescomplemented
41#15689012C2214yescomplemented
42#15689011C2214yescomplemented
43#15689010C2214yescomplemented
44#15689009C2214yescomplemented
45#15689008C2214yescomplemented
46#15689007C2214yescomplemented
47#15689006C2214yescomplemented
48#15689005C2214yescomplemented
49#15689004C2214yescomplemented
50#15689003C2212yes—
51#15689002C2212yes—
52#15689001C2214yes—
53#15689000C2212yes—
54#15688999C2214yes—
55#15688998C2212yescomplemented
56#15688997C2214yescomplemented
57#15688996C2212yescomplemented
58#15688995C2212yescomplemented
59#15688994C2214yescomplemented
60#15688986C2211yescharacteristic, complemented
61#15688985C2214yescomplemented
62#15688984C2212yescomplemented
63#95×D47C2214yes—
64#95×D47C2214yes—
65#95×D47C2214yes—
66C2×#123×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic, complemented
68C47×#388C2214yescomplemented
69C47×#387C2214yescomplemented
70C47×#386C2212yes—
71C47×#385C2212yescomplemented
72C47×#381C2211yescharacteristic, complemented
73C24×D47C2311yescharacteristic
74C24×D47C2311yescharacteristic
75C22×D188C2311yescharacteristic
76C22×C22⋊D47C2311yescharacteristic
77C22×C22⋊D47C2311yescharacteristic
78C2×D4×D47—24no—
79C2×D4×D47—28no—
80C23×Dic47C2312yes—
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—28no—
83C22×C4×D47—28no—
84C22×C4×D47—216no—
85C22×C4×D47D418yes—
86C22×C4×D47C2314yes—
87C22×C4×D47C2311yescharacteristic
88C22×C4×D47C2312yes—
89C22×C4×D47C2314yes—
90C22×C4×D47C2312yes—
91C22×C4×D47C2312yes—
92C22×C4×D47C2314yes—
93#13094009—28no—
94#13094008—24no—
95#13094007—24no—
96#13094006—28no—
97#13094005—24no—
98C2×C4⋊Dic47C2314yes—
99C2×C4⋊Dic47C2312yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2312yes—
103C2×Dic47⋊C4C2312yes—
104C4⋊C4×D47—28no—
105C4⋊C4×D47—216no—
106C2×C22⋊Dic47C2312yes—
107C2×C22⋊Dic47C2311yescharacteristic
108C2×C22⋊Dic47C2314yes—
109C2×C22⋊Dic47C2312yes—
110C2×(C2×D47)⋊C4C2314yes—
111C2×(C2×D47)⋊C4C2312yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2312yes—
115C2×(C2×D47)⋊C4C2312yes—
116C22⋊C4×D47—24no—
117C22⋊C4×D47—28no—
118C22⋊C4×D47—28no—
119C22⋊C4×D47—216no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—28no—
122C2×C4×Dic47C2314yes—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C42×D47—216no—
126C42×D47—216no—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C22×D4×C47C2311yescharacteristic
137C23×C4×C47C2312yes—
138C23×C4×C47C2311yescharacteristic
139#123×C47—24no—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2312yes—
142C2×C22⋊C4×C47C2312yes—
143C2×C22⋊C4×C47C2311yescharacteristic
144C2×C22⋊C4×C47C2314yes—
145C2×C22⋊C4×C47C2312yes—
146C2×C42×C47—24no—
147C2×C42×C47C2314yes—
148#95×C47C2314yes—
149#95×C47C2314yes—
150#95×C47C2314yes—
151C24×C47C2411yescharacteristic
152C24×C47C2411yescharacteristic
153C23×D47—28no—
154C23×D47—22no—
155C23×D47—28no—
156C23×D47—24no—
157C23×D47C2×D414yes—
158C23×D47#4118yes—
159C23×D47C2411yescharacteristic
160C23×D47C2411yescharacteristic
161C23×D47C2411yescharacteristic
162C2×D4×C47—22no—
163C2×D4×C47—24no—
164C22×C4×C47—24no—
165C22×C4×C47—24no—
166C22×C4×C47—28no—
167C22×C4×C47C2×D414yes—
168C22×C4×C47C2412yes—
169C22×C4×C47C2414yes—
170C22×C4×C47C2411yescharacteristic
171C22×C4×C47C2412yes—
172C22×C4×C47C2414yes—
173C2×C22⋊D47—22no—
174C2×C22⋊D47—24no—
175C2×C22⋊D47—22no—
176C2×C22⋊D47—24no—
177C22×Dic47—24no—
178C22×Dic47—24no—
179C22×Dic47—28no—
180C22×Dic47C2×D414yes—
181C22×Dic47C2414yes—
182C22×Dic47C2411yescharacteristic
183C22×Dic47C2412yes—
184C22×Dic47C2412yes—
185C22×Dic47C2414yes—
186D4×D47—416no—
187C2×D188—22no—
188C2×D188—24no—
189C2×C4×D47—264no—
190C2×C4×D47—232no—
191C2×C4×D47—28no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—28no—
195C2×C4×D47—28no—
196C2×C4×D47—28no—
197C2×C4×D47—28no—
198C2×C4×D47—24no—
199C2×C4×D47—22no—
200C2×C4×D47—28no—
201C2×C4×D47—28no—
202C2×C4×D47—28no—
203C2×C4×D47—28no—
204C2×C4×D47—24no—
205C2×C4×D47C2×D418yes—
206C2×C4×D47C2×D418yes—
207C2×C4×D47#41116yes—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—28no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—24no—
212C22⋊C4×C47—24no—
213C22⋊C4×C47—28no—
214C42×C47—28no—
215C22⋊Dic47—22no—
216C22⋊Dic47—24no—
217C22⋊Dic47—24no—
218C22⋊Dic47—28no—
219(C2×D47)⋊C4—24no—
220(C2×D47)⋊C4—28no—
221(C2×D47)⋊C4—24no—
222(C2×D47)⋊C4—28no—
223(C2×D47)⋊C4—24no—
224(C2×D47)⋊C4—28no—
225C4⋊Dic47—24no—
226C4⋊Dic47—28no—
227Dic47⋊C4—24no—
228Dic47⋊C4—28no—
229Dic47⋊C4—24no—
230Dic47⋊C4—28no—
231C4×Dic47—28no—
232C4×Dic47—28no—
233C4×Dic47—28no—
234C23×C47—24no—
235C23×C47—21no—
236C23×C47—24no—
237C23×C47—22no—
238C23×C47C22×D412yes—
239C23×C47C2×#4114yes—
240C23×C47C2511yescharacteristic
241C22×D47—24no—
242C22×D47—216no—
243C22×D47—232no—
244C22×D47—21no—
245C22×D47—24no—
246C22×D47—22no—
247C22×D47—44no—
248C22×D47—48no—
249C22×D47—416no—
250C22×D47#123116yes—
251C22×D47C22×D412yes—
252C22×D47C22×D412yes—
253C22×D47C2×#4114yes—
254C22×D47C2×#4114yes—
255C22×D47C2×#4118yes—
256D4×C47—44no—
257C2×C4×C47—216no—
258C2×C4×C47—28no—
259C2×C4×C47—24no—
260C2×C4×C47—24no—
261C2×C4×C47—24no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—24no—
265C2×C4×C47—24no—
266C2×C4×C47—24no—
267C2×C4×C47—24no—
268C2×C4×C47—22no—
269C2×C4×C47C22×D414yes—
270C2×C4×C47C2×#4118yes—
271C22⋊D47—44no—
272C22⋊D47—44no—
273C2×Dic47—216no—
274C2×Dic47—28no—
275C2×Dic47—24no—
276C2×Dic47—24no—
277C2×Dic47—24no—
278C2×Dic47—21no—
279C2×Dic47—22no—
280C2×Dic47—24no—
281C2×Dic47—24no—
282C2×Dic47—24no—
283C2×Dic47—24no—
284C2×Dic47—22no—
285C2×Dic47C22×D414yes—
286C2×Dic47C2×#4118yes—
287D188—44no—
288C4×D47—232no—
289C4×D47—216no—
290C4×D47—216no—
291C4×D47—232no—
292C4×D47—44no—
293C4×D47—48no—
294C4×D47—416no—
295C2×#2853—471nomaximal, Sylow
296C22×C47—24no—
297C22×C47—28no—
298C22×C47—41no—
299C22×C47—42no—
300C22×C47—44no—
301C22×C47C2×#12314yes—
302C22×C47C23×D411yescharacteristic
303C22×C47C22×#4112yes—
304C22×C47C22×#4114yes—
305C2×D47—24no—
306C2×D47—28no—
307C2×D47—232no—
308C2×D47—41no—
309C2×D47—42no—
310C2×D47—44no—
311C2×D47—88no—
312C2×D47C2×#12314yes—
313C2×D47C2×#12314yes—
314C2×D47#52518yes—
315C2×D47#529116yes—
316C4×C47—24no—
317C4×C47—28no—
318C4×C47—41no—
319C4×C47—42no—
320C4×C47—44no—
321Dic47—24no—
322Dic47—28no—
323Dic47—41no—
324Dic47—42no—
325Dic47—44no—
326C22×#123—471no—
327C23×C42—471no—
328#2853—471no—
329#2853—474no—
330#2853—474no—
331#2853—472no—
332#2853—472no—
333#2853—471no—
334#2853—471no—
335#2853D4711yescharacteristic, direct product factor
336C2×#388—474no—
337C2×#387—474no—
338C2×#386—472no—
339C2×#385—472no—
340C2×#381—471no—
341C2×C47—24no—
342C2×C47—81no—
343C2×C47C22×#12311yescharacteristic
344C2×C47C2×#52512yes—
345C2×C47C2×#52914yes—
346D47—24no—
347D47—81no—
348D47#285318yesdirect product factor
349C23×D4—471no—
350C24×C4—471no—
351C24×C4—472no—
352C2×#123—471no—
353C2×#123—471no—
354C2×#123—472no—
355C2×#123—472no—
356C2×#123—471no—
357C2×#123—948no—
358C2×#123C2×D4711yescharacteristic
359C22×C4⋊C4—472no—
360C22×C4⋊C4—474no—
361C22×C22⋊C4—471no—
362C22×C22⋊C4—472no—
363C22×C22⋊C4—472no—
364C22×C22⋊C4—474no—
365C22×C42—472no—
366C22×C42—471no—
367C22×C42—474no—
368C22×C42—474no—
369C22×C42—948no—
370C22×C42C2×D4711yescharacteristic, complemented
371#388—474no—
372#388—474no—
373#388—474no—
374#388—474no—
375#388—474no—
376#388—474no—
377#388—474no—
378#388C2×D4714yescomplemented
379#387—474no—
380#387—474no—
381#387—474no—
382#387—474no—
383#387—474no—
384#387—474no—
385#387—474no—
386#387C2×D4714yescomplemented
387#386—472no—
388#386—472no—
389#386—474no—
390#386—472no—
391#386—474no—
392#386C2×D4712yes—
393#385—472no—
394#385—474no—
395#385—472no—
396#385—472no—
397#385—474no—
398#385C2×D4712yescomplemented
399#381—471no—
400#381—472no—
401#381—474no—
402#381C2×D4711yescharacteristic, complemented
403C2×#95—474no—
404C2×#95—474no—
405C2×#95—474no—
406C47C2×#285311yescharacteristic, complemented, Sylow
407C25—471no—
408C25—471no—
409C22×D4—471no—
410C22×D4—471no—
411C22×D4—471no—
412C22×D4—944no—
413C22×D4—948no—
414C22×D4C22×D4711yescharacteristic
415C23×C4—471no—
416C23×C4—478no—
417C23×C4—472no—
418C23×C4—474no—
419C23×C4—472no—
420C23×C4—472no—
421C23×C4—472no—
422C23×C4—474no—
423C23×C4—471no—
424C23×C4—474no—
425C23×C4—9416no—
426C23×C4—948no—
427C23×C4—948no—
428C23×C4C22×D4712yes—
429C23×C4C22×D4711yescharacteristic
430#123—24no—
431#123—948no—
432#123—944no—
433#123—948no—
434#123—944no—
435#123—944no—
436C2×C4⋊C4—472no—
437C2×C4⋊C4—472no—
438C2×C4⋊C4—472no—
439C2×C4⋊C4—474no—
440C2×C4⋊C4—474no—
441C2×C4⋊C4—474no—
442C2×C4⋊C4—948no—
443C2×C4⋊C4—9416no—
444C2×C4⋊C4C22×D4712yes—
445C2×C4⋊C4C22×D4714yes—
446C2×C22⋊C4—471no—
447C2×C22⋊C4—472no—
448C2×C22⋊C4—472no—
449C2×C22⋊C4—474no—
450C2×C22⋊C4—472no—
451C2×C22⋊C4—472no—
452C2×C22⋊C4—472no—
453C2×C22⋊C4—474no—
454C2×C22⋊C4—474no—
455C2×C22⋊C4—474no—
456C2×C22⋊C4—948no—
457C2×C22⋊C4—9416no—
458C2×C22⋊C4—944no—
459C2×C22⋊C4—948no—
460C2×C22⋊C4C22×D4711yescharacteristic
461C2×C22⋊C4C22×D4712yes—
462C2×C22⋊C4C22×D4712yes—
463C2×C22⋊C4C22×D4714yes—
464C2×C42—24no—
465C2×C42—474no—
466C2×C42—474no—
467C2×C42—474no—
468C2×C42—9416no—
469C2×C42—9416no—
470C2×C42—948no—
471C2×C42—944no—
472C2×C42C22×D4714yes—
473#95—474no—
474#95—474no—
475#95—474no—
476#95—474no—
477#95—474no—
478#95—474no—
479#95—474no—
480#95—474no—
481#95—474no—
482#95C22×D4714yes—
483#95C22×D4714yes—
484#95C22×D4714yes—
485C24—471no—
486C24—474no—
487C24—478no—
488C24—471no—
489C24—471no—
490C24—948no—
491C24—942no—
492C24—948no—
493C24—944no—
494C24C23×D4711yescharacteristic
495C24C23×D4711yescharacteristic
496C2×D4—22no—
497C2×D4—24no—
498C2×D4—942no—
499C2×D4—944no—
500C2×D4—942no—
501C2×D4—944no—
502C2×D4—942no—
503C2×D4—944no—
504C2×D4—18816no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—28no—
508C22×C4—474no—
509C22×C4—472no—
510C22×C4—474no—
511C22×C4—478no—
512C22×C4—478no—
513C22×C4—4716no—
514C22×C4—474no—
515C22×C4—471no—
516C22×C4—472no—
517C22×C4—948no—
518C22×C4—948no—
519C22×C4—948no—
520C22×C4—9432no—
521C22×C4—948no—
522C22×C4—948no—
523C22×C4—948no—
524C22×C4—9464no—
525C22×C4—944no—
526C22×C4—948no—
527C22×C4—948no—
528C22×C4—942no—
529C22×C4—948no—
530C22×C4—948no—
531C22×C4—944no—
532C22×C4—948no—
533C22×C4—944no—
534C22×C4—944no—
535C22×C4—948no—
536C22×C4D4×D4714yes—
537C22×C4C23×D4714yes—
538C22×C4C23×D4711yescharacteristic
539C22×C4C23×D4712yes—
540C22×C4C23×D4712yes—
541C22×C4C23×D4714yes—
542C4⋊C4—24no—
543C4⋊C4—28no—
544C4⋊C4—948no—
545C4⋊C4—944no—
546C4⋊C4—948no—
547C4⋊C4—944no—
548C4⋊C4—944no—
549C4⋊C4—948no—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—28no—
554C22⋊C4—948no—
555C22⋊C4—944no—
556C22⋊C4—948no—
557C22⋊C4—944no—
558C22⋊C4—948no—
559C22⋊C4—944no—
560C22⋊C4—942no—
561C22⋊C4—944no—
562C22⋊C4—944no—
563C22⋊C4—948no—
564C42—28no—
565C42—948no—
566C42—948no—
567C42—948no—
568C23—24no—
569C23—21no—
570C23—24no—
571C23—22no—
572C23—472no—
573C23—478no—
574C23—474no—
575C23—4716no—
576C23—472no—
577C23—474no—
578C23—9416no—
579C23—9432no—
580C23—944no—
581C23—941no—
582C23—944no—
583C23—942no—
584C23—1884no—
585C23—1888no—
586C23—18816no—
587C23C2×D4×D4712yes—
588C23#41×D4714yes—
589C23C24×D4711yescharacteristic
590D4—44no—
591D4—1884no—
592D4—1884no—
593D4—1884no—
594C2×C4—216no—
595C2×C4—28no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—474no—
607C2×C4—478no—
608C2×C4—9416no—
609C2×C4—9416no—
610C2×C4—9432no—
611C2×C4—9432no—
612C2×C4—9416no—
613C2×C4—948no—
614C2×C4—944no—
615C2×C4—944no—
616C2×C4—944no—
617C2×C4—942no—
618C2×C4—941no—
619C2×C4—944no—
620C2×C4—944no—
621C2×C4—944no—
622C2×C4—944no—
623C2×C4—942no—
624C2×C4—1888no—
625C2×C4—18816no—
626C2×C4—1884no—
627C2×C4C2×D4×D4714yes—
628C2×C4#41×D4718yes—
629C22—24no—
630C22—28no—
631C22—41no—
632C22—42no—
633C22—44no—
634C22—474no—
635C22—478no—
636C22—4716no—
637C22—474no—
638C22—9432no—
639C22—944no—
640C22—948no—
641C22—3768no—
642C22—1881no—
643C22—1882no—
644C22—1884no—
645C22#123×D4714yes—
646C22C22×D4×D4711yescharacteristic
647C22C2×#41×D4712yes—
648C22C2×#41×D4714yes—
649C4—24no—
650C4—28no—
651C4—41no—
652C4—42no—
653C4—44no—
654C4—944no—
655C4—948no—
656C4—1881no—
657C4—1882no—
658C4—1884no—
659C2—24no—
660C2—81no—
661C2—478no—
662C2—944no—
663C2—3761no—
664C2C2×#123×D4711yescharacteristic
665C2#525×D4712yes—
666C2#529×D4714yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2853C2
prime radicalC22×D4×D47C22
hypercenter#2853D47
hypocenterC47C2×#2853
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2853

Complements

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

NH ≅ G/Ntype
2. C22×C42×D47C2semidirect
3. #20251713C2semidirect
4. #20251712C2semidirect
5. #20251711C2semidirect
6. #20251710C2semidirect
7. #20251709C2semidirect
8. #20251708C2semidirect
9. #20251707C2semidirect
10. #388×D47C2semidirect
11. #387×D47C2semidirect
13. #385×D47C2semidirect
14. #381×D47C2semidirect
15. C47×#2853C2semidirect
31. C22×C4×Dic47C22semidirect
32. C22×C4×Dic47C22semidirect
35. C2×C42×D47C22semidirect
36. #15689017C22semidirect
37. #15689016C22semidirect
38. #15689015C22semidirect
39. #15689014C22semidirect
40. #15689013C22semidirect
41. #15689012C22semidirect
42. #15689011C22semidirect
43. #15689010C22semidirect
44. #15689009C22semidirect
45. #15689008C22semidirect
46. #15689007C22semidirect
47. #15689006C22semidirect
48. #15689005C22semidirect
49. #15689004C22semidirect
55. #15688998C22semidirect
56. #15688997C22semidirect
57. #15688996C22semidirect
58. #15688995C22semidirect
59. #15688994C22semidirect
60. #15688986C22semidirect
61. #15688985C22semidirect
62. #15688984C22semidirect
67. C22×C42×C47C22semidirect
68. C47×#388C22semidirect
69. C47×#387C22semidirect
71. C47×#385C22semidirect
72. C47×#381C22semidirect
335. #2853D47direct (N × H)
348. D47#2853direct (N × H)
370. C22×C42C2×D47semidirect
378. #388C2×D47semidirect
386. #387C2×D47semidirect
398. #385C2×D47semidirect
402. #381C2×D47semidirect
406. C47C2×#2853semidirect

Maximal subgroups

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

subgroupindex
C2×#123×D472
C22×C42×D472
#202517132
#202517122
#202517112
#202517102
#202517092
#202517082
#202517072
#388×D472
#387×D472
#386×D472
#385×D472
#381×D472
C47×#28532
C2×#285347