Finite Group Databasebeta

← C2×#20244575 #26243740

Subgroups — C2×#20244575 #26243740

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093995C211yesmaximal, characteristic
2C22×#13093955C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
5C2×#15688980C211yesmaximal, characteristic, complemented
6#20244575C218yesmaximal, direct product factor
7C2×#15688886C211yesmaximal, characteristic, complemented
8C22×#102×C47C211yesmaximal, characteristic, complemented
9C23×C22⋊D47—21no—
10C23×C4×D47C2211yescharacteristic
11C23×C47⋊C8C2211yescharacteristic
12C2×#13093995—22no—
13C2×#13093995—24no—
14C2×#13093995—24no—
15C2×#13093995C2214yes—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47—21no—
19C22×(C2×D47)⋊C4—21no—
20C2×#13093955—24no—
21C2×#13093955C2214yescomplemented
22C2×#13093945—24no—
23C2×#13093945C2214yescomplemented
24C2×(C2×D47)⋊C8—24no—
25C2×(C2×D47)⋊C8C2214yescomplemented
26#15688980—22no—
27#15688980C2214yescomplemented
28C2×C47⋊#95—21no—
29#15688886C2214yescomplemented
30C23×D4×C47C2211yescharacteristic
31C23×C8×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C2×#102×C47—24no—
34C2×#102×C47C2214yescomplemented
35C24×D47D411yescharacteristic
36C22×C22⋊D47—28no—
37C22×C22⋊D47—24no—
38C22×C22⋊D47—44no—
39C22×C22⋊D47—44no—
40C23×Dic47—21no—
41C23×Dic47—21no—
42C23×Dic47D411yescharacteristic
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47—22no—
46C22×C4×D47—22no—
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47D412yes—
50C22×C4×D47C2312yes—
51C22×C47⋊C8—22no—
52C22×C47⋊C8—22no—
53C22×C47⋊C8D414yescomplemented
54C22×C47⋊C8C2312yes—
55#13093995—216no—
56#13093995—28no—
57#13093995—28no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47D414yes—
64C2×C4⋊Dic47C2312yes—
65C2×C4⋊Dic47C2312yes—
66C2×C22⋊Dic47—28no—
67C2×C22⋊Dic47—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—44no—
70#13093955—28no—
71#13093945—28no—
72(C2×D47)⋊C8—28no—
73C47⋊#95—24no—
74C25×C47—21no—
75C22×D4×C47—22no—
76C22×D4×C47—21no—
77C22×D4×C47—22no—
78C22×D4×C47—22no—
79C22×D4×C47—22no—
80C22×D4×C47—22no—
81C22×D4×C47D414yes—
82C22×D4×C47C2312yes—
83C23×C4×C47—21no—
84C23×C4×C47C2311yescharacteristic
85C22×C8×C47—22no—
86C22×C8×C47—22no—
87C22×C8×C47—22no—
88C22×C8×C47C2312yes—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47C2312yes—
93#102×C47—28no—
94C24×C47—24no—
95C24×C47—22no—
96C24×C47—42no—
97C24×C47—42no—
98C24×C47—42no—
99C24×C47—42no—
100C24×C47—42no—
101C24×C47—42no—
102C24×C47C2×D411yescharacteristic
103C23×D47—22no—
104C23×D47—22no—
105C23×D47—22no—
106C23×D47—22no—
107C23×D47—22no—
108C23×D47—22no—
109C23×D47SD1614yes—
110C23×D47C2×D412yes—
111C2×D4×C47—24no—
112C2×D4×C47—28no—
113C2×D4×C47—28no—
114C2×D4×C47—22no—
115C2×D4×C47—22no—
116C2×D4×C47—22no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—44no—
120C2×D4×C47—42no—
121C2×D4×C47—42no—
122C2×D4×C47—44no—
123C2×D4×C47C2×D414yes—
124C22×C4×C47—22no—
125C22×C4×C47—42no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×D412yes—
132C22×C4×C47#4112yes—
133C22×C4×C47#4112yes—
134C22×C4×C47#4112yes—
135C22×C4×C47C2411yescharacteristic
136C2×C22⋊D47—216no—
137C2×C22⋊D47—48no—
138C2×C22⋊D47—432no—
139C2×C22⋊D47—48no—
140C22×Dic47—22no—
141C22×Dic47—24no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—42no—
149C22×Dic47—42no—
150C22×Dic47—42no—
151C22×Dic47C2×D412yes—
152C2×C4×D47—24no—
153C2×C4×D47—24no—
154C2×C4×D47—24no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—44no—
162C2×C4×D47—44no—
163C2×C4×D47—44no—
164C2×C4×D47—44no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—44no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—42no—
172C22⋊Dic47—216no—
173(C2×D47)⋊C4—48no—
174C4⋊Dic47—24no—
175C4⋊Dic47—22no—
176C4⋊Dic47—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—42no—
179C4⋊Dic47C2×D414yes—
180C2×C47⋊C8—28no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8C2×D414yescomplemented
184C23×C47—24no—
185C23×C47—42no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47—42no—
190C23×C47—42no—
191C23×C47—48no—
192C23×C47—48no—
193C23×C47—48no—
194C23×C47—84no—
195C23×C47—84no—
196C23×C47—84no—
197C23×C47—84no—
198C23×C47#12012yes—
199C23×C47#12112yes—
200C23×C47#12312yes—
201C23×C47C2×SD1612yes—
202C23×C47#13512yes—
203C23×C47AGL(1,ℤ/8)12yes—
204C23×C47AGL(1,ℤ/8)12yes—
205C23×C47C22×D411yescharacteristic
206C22×D47—22no—
207C22×D47—22no—
208C22×D47—22no—
209C22×D47—22no—
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—28no—
213C22×D47—28no—
214C22×D47—28no—
215C22×D47—44no—
216C22×D47—44no—
217C22×D47—44no—
218C22×D47—44no—
219C22×D47C2×SD1614yes—
220D4×C47—24no—
221D4×C47—24no—
222D4×C47—42no—
223D4×C47—42no—
224D4×C47—48no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—84no—
229C2×C4×C47#12012yes—
230C2×C4×C47#12114yes—
231C2×C4×C47#12114yes—
232C2×C4×C47#12112yes—
233C2×C4×C47#12312yes—
234C2×C4×C47#12314yes—
235C2×C4×C47#12414yes—
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47C2×#4111yescharacteristic
242C22⋊D47—432no—
243C2×Dic47—24no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—44no—
250C2×Dic47—48no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—84no—
255C4×D47—42no—
256C4×D47—42no—
257C4×D47—42no—
258C4×D47—42no—
259C4×D47—48no—
260C8×C47—42no—
261C47⋊C8—24no—
262C2×#2034—471nomaximal, Sylow
263C22×C47—44no—
264C22×C47—44no—
265C22×C47—44no—
266C22×C47—82no—
267C22×C47—82no—
268C22×C47—82no—
269C22×C47—82no—
270C22×C47—816no—
271C22×C47#39414yes—
272C22×C47#44914yes—
273C22×C47#45014yes—
274C22×C47#46514yes—
275C22×C47#46914yes—
276C22×C47#48114yes—
277C22×C47#48214yes—
278C22×C47C2×#12011yescharacteristic
279C22×C47C2×#12111yescharacteristic
280C22×C47C2×#12311yescharacteristic
281C22×C47C22×SD1611yescharacteristic
282C22×C47C2×#13511yescharacteristic
283C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
285C2×D47—24no—
286C2×D47—24no—
287C2×D47—24no—
288C2×D47—42no—
289C2×D47—42no—
290C2×D47—42no—
291C2×D47—42no—
292C2×D47—416no—
293C4×C47—82no—
294C4×C47#39414yes—
295C4×C47C2×#12111yescharacteristic
296C4×C47C2×#12111yescharacteristic
297C4×C47C2×#12311yescharacteristic
298C4×C47C2×#12411yescharacteristic
299Dic47—42no—
300Dic47—44no—
301Dic47—82no—
302C22×#121—471no—
303C22×#106—471no—
304C22×#102—471no—
305C22×#102D4711yescharacteristic, complemented
306C22×C22⋊C8—471no—
307C2×#380—471no—
308#2034—478no—
309C2×#340—471no—
310C2×C47—84no—
311C2×C47#203418yescomplemented
312C2×C47C2×#39411yescharacteristic
313C2×C47C2×#45011yescharacteristic
314C2×C47C2×#44911yescharacteristic
315C2×C47C2×#46511yescharacteristic
316C2×C47C2×#46911yescharacteristic
317C2×C47C2×#48211yescharacteristic
318C2×C47C2×#48111yescharacteristic
319D47—44no—
320C23×D4—941no—
321C23×D4C2×D4711yescharacteristic
322C24×C4—471no—
323C23×C8—471no—
324C23×C8C2×D4711yescharacteristic
325C2×#121—474no—
326C2×#121—944no—
327C2×#121—942no—
328C2×#121—944no—
329C22×C4⋊C4—471no—
330C22×C4⋊C4—471no—
331C22×C4⋊C4C2×D4711yescharacteristic
332C22×C22⋊C4—941no—
333C22×C22⋊C4—941no—
334C2×#106—474no—
335C2×#106—944no—
336C2×#102—24no—
337C2×#102—474no—
338C2×#102—944no—
339C2×#102C2×D4714yescomplemented
340C2×C22⋊C8—474no—
341C2×C22⋊C8—944no—
342#380—474no—
343#380—942no—
344C2×#95—941no—
345#340—474no—
346C47C2×#203411yescharacteristic, complemented, Sylow
347C25—21no—
348C25—471no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—944no—
356C22×D4—948no—
357C22×D4—1884no—
358C22×D4—1884no—
359C22×D4C22⋊D4714yes—
360C22×D4C22×D4712yes—
361C23×C4—21no—
362C23×C4—471no—
363C23×C4—472no—
364C23×C4—472no—
365C23×C4—941no—
366C23×C4—942no—
367C23×C4—942no—
368C23×C4—942no—
369C23×C4—942no—
370C23×C4—942no—
371C23×C4—942no—
372C23×C4—941no—
373C23×C4C22×D4711yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—474no—
378C22×C8—472no—
379C22×C8—942no—
380C22×C8—942no—
381C22×C8C22×D4712yes—
382#121—948no—
383#121—9416no—
384#121—948no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—474no—
389C2×C4⋊C4—472no—
390C2×C4⋊C4—472no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—942no—
393C2×C4⋊C4—942no—
394C2×C4⋊C4—942no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4C22×D4712yes—
397C2×C22⋊C4—944no—
398C2×C22⋊C4—948no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—1884no—
401#106—948no—
402#102—28no—
403#102—948no—
404C22⋊C8—948no—
405#95—944no—
406C24—24no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—474no—
415C24—472no—
416C24—942no—
417C24—942no—
418C24—942no—
419C24—942no—
420C24—942no—
421C24—942no—
422C24D4×D4711yescharacteristic
423C2×D4—24no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—9416no—
436C2×D4—1888no—
437C2×D4—18832no—
438C2×D4—1888no—
439C2×D4C2×C22⋊D4714yes—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—472no—
445C22×C4—942no—
446C22×C4—944no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—944no—
451C22×C4—944no—
452C22×C4—944no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—1882no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4—1882no—
465C22×C4—1884no—
466C22×C4—1884no—
467C22×C4—1884no—
468C22×C4—1884no—
469C22×C4#1062535012yes—
470C22×C4#1062535012yes—
471C22×C4D4×D4711yescharacteristic
472C22×C4D4×D4712yes—
473C22×C4D4×D4712yes—
474C22×C4#1062535212yes—
475C22×C4C2×C22⋊D4712yes—
476C22×C4C23×D4711yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—474no—
482C2×C8—948no—
483C2×C8—942no—
484C2×C8—942no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—474no—
489C4⋊C4—944no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—1882no—
494C22⋊C4—9416no—
495C22⋊C4—1888no—
496C23—24no—
497C23—48no—
498C23—48no—
499C23—48no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—474no—
511C23—948no—
512C23—948no—
513C23—942no—
514C23—942no—
515C23—942no—
516C23—942no—
517C23—942no—
518C23—942no—
519C23—948no—
520C23—1884no—
521C23—1884no—
522C23—1884no—
523C23—1884no—
524C23#1309399212yes—
525C23#1309399712yes—
526C23#1309400612yes—
527C23SD16×D4712yes—
528C23#1309404312yes—
529C23#1309404812yes—
530C23#1309405112yes—
531C23C2×D4×D4711yescharacteristic
532D4—24no—
533D4—24no—
534D4—48no—
535D4—42no—
536D4—42no—
537D4—18832no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—942no—
543C2×C4—944no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—3764no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1888no—
551C2×C4—1884no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1888no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4#1309399212yes—
560C2×C4#1309399614yes—
561C2×C4#1309399712yes—
562C2×C4#1309399714yes—
563C2×C4#1309400612yes—
564C2×C4#1309400714yes—
565C2×C4#1309401014yes—
566C2×C4C2×D4×D4711yescharacteristic
567C2×C4C2×D4×D4711yescharacteristic
568C2×C4C22×C22⋊D4711yescharacteristic
569C2×C4C2×#1062535211yescharacteristic
570C2×C4C2×#1062535011yescharacteristic
571C2×C4C2×#1062535011yescharacteristic
572C8—42no—
573C8—944no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—816no—
581C22—82no—
582C22—944no—
583C22—944no—
584C22—944no—
585C22—1882no—
586C22—1882no—
587C22—1882no—
588C22—18816no—
589C22—1882no—
590C22#1568903814yes—
591C22#1568926514yes—
592C22#1568927214yes—
593C22#1568935114yes—
594C22#1568937514yes—
595C22#1568944014yes—
596C22#1568944514yes—
597C22C2×#1309399211yescharacteristic
598C22C2×#1309399711yescharacteristic
599C22C2×#1309400611yescharacteristic
600C22C2×SD16×D4711yescharacteristic
601C22C2×#1309404311yescharacteristic
602C22C2×#1309404811yescharacteristic
603C22C2×#1309405111yescharacteristic
604C4—82no—
605C4—3762no—
606C4—1882no—
607C4—1884no—
608C4#1568903814yes—
609C4C2×#1309399611yescharacteristic
610C4C2×#1309399711yescharacteristic
611C4C2×#1309400711yescharacteristic
612C4C2×#1309401011yescharacteristic
613C2—84no—
614C2—1884no—
615C2#2024457518yesdirect product factor
616C2C2×#1568903811yescharacteristic
617C2C2×#1568927211yescharacteristic
618C2C2×#1568926511yescharacteristic
619C2C2×#1568935111yescharacteristic
620C2C2×#1568937511yescharacteristic
621C2C2×#1568944511yescharacteristic
622C2C2×#1568944011yescharacteristic
subgroupG/H
centerC24D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC22×#13093995C2
hypercenterC22×#102D47
hypocenterC47C2×#2034
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#13093955C2semidirect
3. C22×#13093945C2semidirect
4. C22×(C2×D47)⋊C8C2semidirect
5. C2×#15688980C2semidirect
6. #20244575C2direct (N × H)
7. C2×#15688886C2semidirect
8. C22×#102×C47C2semidirect
21. C2×#13093955C22semidirect
23. C2×#13093945C22semidirect
25. C2×(C2×D47)⋊C8C22semidirect
27. #15688980C22semidirect
29. #15688886C22semidirect
34. C2×#102×C47C22semidirect
53. C22×C47⋊C8D4semidirect
183. C2×C47⋊C8C2×D4semidirect
305. C22×#102D47semidirect
311. C2×C47#2034semidirect
339. C2×#102C2×D47semidirect
346. C47C2×#2034semidirect
615. C2#20244575direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939952
C22×#130939552
C22×#130939452
C22×(C2×D47)⋊C82
C2×#156889802
#202445752
C2×#156888862
C22×#102×C472
C2×#203447