Finite Group Databasebeta

← D47×#2085 #26245242

Subgroups — D47×#2085 #26245242

Order 12032.

998 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
2C2×#106×D47C211yesmaximal, characteristic
3#389×D47C211yesmaximal, characteristic
4#382×D47C211yesmaximal, characteristic
5#20244875C211yesmaximal, characteristic, complemented
6#20244874C211yesmaximal, characteristic, complemented
7#20244873C211yesmaximal, characteristic, complemented
8#20244872C211yesmaximal, characteristic, complemented
9#20244871C211yesmaximal, characteristic, complemented
10#20244870C211yesmaximal, characteristic, complemented
11#20244869C211yesmaximal, characteristic, complemented
12#340×D47C211yesmaximal, characteristic
13#340×D47C211yesmaximal, characteristic
14#336×D47C211yesmaximal, characteristic
15C47×#2085C211yesmaximal, 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×D47C2211yescharacteristic
24C2×#13093958C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27#107×D47—24no—
28C2×#13093956C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31#106×D47—24no—
32#15689022C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689020—21no—
35#15689019C2211yescharacteristic
36#15689018—21no—
37#15688989C2211yescharacteristic
38#15688988C2211yescharacteristic
39#15688988C2211yescharacteristic
40#15688987—21no—
41#15688987—21no—
42#95×D47—21no—
43#95×D47—21no—
44#95×D47—21no—
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×#107×C47C2211yescharacteristic
55C2×#106×C47C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#382C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47—21no—
63C22×C4×D47—21no—
64C22×C4×D47—21no—
65C22×C4×D47D411yescharacteristic
66C22×C4×D47D411yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C2×C8×D47—22no—
71C2×C8×D47—22no—
72C2×C8×D47—22no—
73C2×C8×D47—22no—
74C2×C8×D47Q814yes—
75C2×C8×D47Q814yes—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C4⋊C4×D47—22no—
88C4⋊C4×D47—22no—
89C4⋊C4×D47—22no—
90C4⋊C4×D47—22no—
91C4⋊C4×D47—22no—
92C4⋊C4×D47—22no—
93C4⋊C4×D47—22no—
94C4⋊C4×D47—44no—
95C4⋊C4×D47D414yes—
96C2×C4×Dic47D411yescharacteristic
97C2×C4×Dic47D411yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99C42×D47—22no—
100C42×D47—22no—
101#13093958—22no—
102#13093957—22no—
103#13093957—22no—
104#13093956—22no—
105#13093955—22no—
106#13093955—22no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C47⋊#95—21no—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C22×C8×C47C2311yescharacteristic
117C22×C8×C47C2311yescharacteristic
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#107×C47—22no—
125#106×C47—22no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129C23×D47C2×D411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2411yescharacteristic
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47C2×D411yescharacteristic
142C22×Dic47C2×D411yescharacteristic
143C22×Dic47C2×D411yescharacteristic
144C2×C4×D47—24no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
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×D47—42no—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
160C2×C4×D47—42no—
161C2×C4×D47—42no—
162C2×C4×D47C2×D412yes—
163C2×C4×D47C2×Q812yes—
164C2×C4×D47C2×Q812yes—
165C2×C4×D47#4112yes—
166C2×C4×D47#4112yes—
167C2×C4×D47#4112yes—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47C2×Q812yes—
173C2×C8×C47C2×Q812yes—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—42no—
182C4⋊C4×C47C2×D412yes—
183C42×C47—21no—
184C42×C47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—42no—
193C4⋊Dic47C2×D412yes—
194Dic47⋊C4—24no—
195Dic47⋊C4—42no—
196Dic47⋊C4—42no—
197Dic47⋊C4—42no—
198Dic47⋊C4—42no—
199Dic47⋊C4—42no—
200C4×Dic47—21no—
201C4×Dic47—21no—
202C4×Dic47—22no—
203C4×Dic47—22no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8C2×Q812yes—
209C2×C47⋊C8C2×Q812yes—
210C8×D47—28no—
211C8×D47—28no—
212C23×C47C22×D411yescharacteristic
213C22×D47#12112yes—
214C22×D47#12312yes—
215C22×D47C4⋊Q812yes—
216C22×D47#13512yes—
217C22×D47#13512yes—
218C22×D47AGL(1,ℤ/8)12yes—
219C22×D47#13712yes—
220C2×C4×C47—22no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—41no—
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×C47—41no—
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C22×Q811yescharacteristic
240C2×C4×C47C22×Q811yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×Dic47—22no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—41no—
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×Dic47—41no—
262C2×Dic47#12112yes—
263C2×Dic47#12312yes—
264C2×Dic47C4⋊Q812yes—
265C4×D47—48no—
266C4×D47—44no—
267C4×D47—44no—
268C4×D47—84no—
269C4×D47—84no—
270C4×D47—84no—
271C4×D47C22⋊Q814yes—
272C4×D47C22⋊Q814yes—
273C4×D47#12514yes—
274C4×D47#12514yes—
275C8×C47—22no—
276C8×C47—22no—
277C47⋊C8—22no—
278C47⋊C8—22no—
279C2×#2085—471nomaximal, Sylow
280C22×C47C2×#12111yescharacteristic
281C22×C47C2×#12311yescharacteristic
282C22×C47C2×C4⋊Q811yescharacteristic
283C22×C47C2×#13511yescharacteristic
284C22×C47C2×#13511yescharacteristic
285C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C47C2×#13711yescharacteristic
287C2×D47#39814yes—
288C2×D47#46314yes—
289C2×D47#46414yes—
290C2×D47#48214yes—
291C2×D47#48514yes—
292C2×D47#49914yes—
293C2×D47#50114yes—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—81no—
298C4×C47—81no—
299C4×C47—81no—
300C4×C47C2×C22⋊Q811yescharacteristic
301C4×C47C2×C22⋊Q811yescharacteristic
302C4×C47C2×#12511yescharacteristic
303C4×C47C2×#12511yescharacteristic
304Dic47—41no—
305Dic47—41no—
306Dic47—42no—
307Dic47—81no—
308Dic47—81no—
309Dic47—81no—
310Dic47#39814yes—
311C22×#107—471no—
312C22×#106—471no—
313C2×#389—471no—
314C2×#382—471no—
315#2085—471no—
316#2085—471no—
317#2085—471no—
318#2085—471no—
319#2085—471no—
320#2085—471no—
321#2085—471no—
322#2085D4711yescharacteristic, direct product factor
323C2×#340—471no—
324C2×#340—471no—
325C2×#336—471no—
326C2×C47C2×#39811yescharacteristic
327C2×C47C2×#46311yescharacteristic
328C2×C47C2×#46411yescharacteristic
329C2×C47C2×#48211yescharacteristic
330C2×C47C2×#48511yescharacteristic
331C2×C47C2×#49911yescharacteristic
332C2×C47C2×#50111yescharacteristic
333D47#208518yesdirect 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—
342C2×#107—471no—
343C2×#107—471no—
344C2×#107—471no—
345C2×#107—944no—
346C2×#107C2×D4711yescharacteristic
347C2×#106—471no—
348C2×#106—471no—
349C2×#106—471no—
350C2×#106—944no—
351C2×#106C2×D4711yescharacteristic
352#389—471no—
353#389—471no—
354#389—471no—
355#389—941no—
356#389—941no—
357#389C2×D4711yescharacteristic
358#382—471no—
359#382—471no—
360#382—471no—
361#382—941no—
362#382—941no—
363#382C2×D4711yescharacteristic
364C2×#95—941no—
365C2×#95—941no—
366C2×#95—941no—
367#340—471no—
368#340—471no—
369#340—471no—
370#340—471no—
371#340—471no—
372#340—471no—
373#340C2×D4711yescharacteristic
374#340C2×D4711yescharacteristic
375#336—471no—
376#336—471no—
377#336—471no—
378#336C2×D4711yescharacteristic
379C47C2×#208511yescharacteristic, complemented, Sylow
380C23×C4—471no—
381C23×C4—471no—
382C23×C4—471no—
383C23×C4—941no—
384C23×C4—941no—
385C23×C4—941no—
386C23×C4—941no—
387C22×C8—471no—
388C22×C8—471no—
389C22×C8—474no—
390C22×C8—474no—
391C22×C8—942no—
392C22×C8—942no—
393C22×C8—942no—
394C22×C8—942no—
395C22×C8C22×D4711yescharacteristic
396C22×C8C22×D4711yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—471no—
402C2×C4⋊C4—471no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—942no—
408C2×C4⋊C4—942no—
409C2×C4⋊C4—942no—
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—941no—
417C2×C4⋊C4—1884no—
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C4⋊C4C22×D4711yescharacteristic
420C2×C4⋊C4C22×D4711yescharacteristic
421C2×C4⋊C4C22×D4711yescharacteristic
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—471no—
425C2×C42—942no—
426C2×C42—942no—
427C2×C42C22×D4711yescharacteristic
428#107—22no—
429#107—942no—
430#107—942no—
431#107—942no—
432#106—22no—
433#106—942no—
434#106—942no—
435#106—942no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—941no—
440#95—941no—
441#95—941no—
442#95—941no—
443#95—941no—
444#95—941no—
445#95—941no—
446#95—941no—
447#95—941no—
448C24—471no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—471no—
454C22×C4—472no—
455C22×C4—472no—
456C22×C4—472no—
457C22×C4—472no—
458C22×C4—472no—
459C22×C4—472no—
460C22×C4—471no—
461C22×C4—471no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—944no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—1882no—
474C22×C4—1882no—
475C22×C4—1882no—
476C22×C4—1882no—
477C22×C4—1882no—
478C22×C4—1882no—
479C22×C4—1882no—
480C22×C4—1882no—
481C22×C4—1882no—
482C22×C4—1882no—
483C22×C4—1882no—
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4C23×D4711yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—472no—
492C2×C8—472no—
493C2×C8—948no—
494C2×C8—948no—
495C2×C8—941no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C2×C8Q8×D4712yes—
500C2×C8Q8×D4712yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—472no—
510C4⋊C4—944no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4—1882no—
519C4⋊C4—1882no—
520C4⋊C4—1882no—
521C4⋊C4—1882no—
522C4⋊C4—1882no—
523C4⋊C4—1882no—
524C4⋊C4D4×D4712yes—
525C42—21no—
526C42—21no—
527C42—942no—
528C42—942no—
529C42—941no—
530C42—941no—
531C23—472no—
532C23—472no—
533C23—472no—
534C23—472no—
535C23—472no—
536C23—472no—
537C23—472no—
538C23C2×D4×D4711yescharacteristic
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
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—41no—
557C2×C4—472no—
558C2×C4—472no—
559C2×C4—472no—
560C2×C4—474no—
561C2×C4—474no—
562C2×C4—474no—
563C2×C4—474no—
564C2×C4—942no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—3764no—
572C2×C4—3764no—
573C2×C4—3764no—
574C2×C4—1884no—
575C2×C4—1884no—
576C2×C4—1888no—
577C2×C4—1881no—
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×C4—1881no—
588C2×C4C2×D4×D4711yescharacteristic
589C2×C4C2×Q8×D4711yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4#41×D4711yescharacteristic
594C8—22no—
595C8—22no—
596C8—942no—
597C8—942no—
598C22—474no—
599C22—474no—
600C22—474no—
601C22—474no—
602C22—474no—
603C22—474no—
604C22—474no—
605C22#121×D4711yescharacteristic
606C22#123×D4711yescharacteristic
607C22C4⋊Q8×D4711yescharacteristic
608C22#135×D4711yescharacteristic
609C22#135×D4711yescharacteristic
610C22AGL(1,ℤ/8)×D4711yescharacteristic
611C22#137×D4711yescharacteristic
612C4—41no—
613C4—41no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—474no—
619C4—3761no—
620C4—3761no—
621C4—3761no—
622C4—1881no—
623C4—1881no—
624C4—1882no—
625C4C22⋊Q8×D4711yescharacteristic
626C4C22⋊Q8×D4711yescharacteristic
627C4#125×D4711yescharacteristic
628C4#125×D4711yescharacteristic
629C2—478no—
630C2#398×D4711yescharacteristic
631C2#463×D4711yescharacteristic
632C2#464×D4711yescharacteristic
633C2#482×D4711yescharacteristic
634C2#485×D4711yescharacteristic
635C2#499×D4711yescharacteristic
636C2#501×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2085C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2085D47
hypocenterC47C2×#2085
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2085

Complements

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

NH ≅ G/Ntype
5. #20244875C2semidirect
6. #20244874C2semidirect
7. #20244873C2semidirect
8. #20244872C2semidirect
9. #20244871C2semidirect
10. #20244870C2semidirect
11. #20244869C2semidirect
15. C47×#2085C2semidirect
322. #2085D47direct (N × H)
333. D47#2085direct (N × H)
379. C47C2×#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D472
C2×#106×D472
#389×D472
#382×D472
#202448752
#202448742
#202448732
#202448722
#202448712
#202448702
#202448692
#340×D472
#336×D472
C47×#20852
C2×#208547