Finite Group Databasebeta

← C2×#20244579 #26243744

Subgroups — C2×#20244579 #26243744

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×#13093999C211yesmaximal, characteristic
2C22×#13093946C211yesmaximal, characteristic, complemented
3C22×#13093944C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
5C2×#15688980C211yesmaximal, characteristic, complemented
6#20244579C218yesmaximal, direct product factor
7C2×#15688885C211yesmaximal, characteristic, complemented
8C22×#106×C47C211yesmaximal, characteristic, complemented
9C23×D188—21no—
10C23×D188C2211yescharacteristic
11C23×C4×D47C2211yescharacteristic
12C23×C47⋊C8C2211yescharacteristic
13C2×#13093999—24no—
14C2×#13093999—22no—
15C2×#13093999—24no—
16C2×#13093999C2214yes—
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4—21no—
19C22×(C2×D47)⋊C4—21no—
20C2×#13093946—24no—
21C2×#13093946C2214yescomplemented
22C2×#13093944—24no—
23C2×#13093944C2214yescomplemented
24C2×(C2×D47)⋊C8—24no—
25C2×(C2×D47)⋊C8C2214yescomplemented
26#15688980—22no—
27#15688980C2214yescomplemented
28C2×C47⋊#95—21no—
29#15688885C2214yescomplemented
30C23×C8×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C2×#106×C47—24no—
34C2×#106×C47C2214yescomplemented
35C24×D47—21no—
36C24×D47D411yescharacteristic
37C22×D188—22no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188—22no—
41C22×D188—28no—
42C22×D188—24no—
43C22×D188—21no—
44C22×D188—22no—
45C22×D188—44no—
46C22×D188—44no—
47C22×D188D414yes—
48C22×D188C2312yes—
49C23×Dic47—21no—
50C23×Dic47D411yescharacteristic
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47D412yes—
58C22×C4×D47C2312yes—
59C22×C47⋊C8—22no—
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8C2312yes—
63#13093999—216no—
64#13093999—28no—
65#13093999—28no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2312yes—
70C2×(C2×D47)⋊C4—28no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—44no—
74#13093946—28no—
75#13093944—28no—
76(C2×D47)⋊C8—28no—
77C47⋊#95—24no—
78C23×C4×C47—21no—
79C23×C4×C47—21no—
80C23×C4×C47C2311yescharacteristic
81C22×C8×C47—22no—
82C22×C8×C47—22no—
83C22×C8×C47D414yescomplemented
84C22×C8×C47C2312yes—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47D414yes—
91C2×C4⋊C4×C47C2312yes—
92C2×C4⋊C4×C47C2312yes—
93#106×C47—28no—
94C24×C47C2×D411yescharacteristic
95C23×D47—22no—
96C23×D47—22no—
97C23×D47—22no—
98C23×D47—22no—
99C23×D47—22no—
100C23×D47—22no—
101C23×D47—24no—
102C23×D47—22no—
103C23×D47—42no—
104C23×D47—42no—
105C23×D47—42no—
106C23×D47—42no—
107C23×D47—42no—
108C23×D47—42no—
109C23×D47SD1614yes—
110C23×D47C2×D412yes—
111C22×C4×C47—24no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—42no—
115C22×C4×C47—42no—
116C22×C4×C47—42no—
117C22×C4×C47—42no—
118C22×C4×C47—42no—
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×D412yes—
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47#4112yes—
124C22×C4×C47#4112yes—
125C22×C4×C47#4112yes—
126C22×C4×C47C2411yescharacteristic
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—42no—
132C22×Dic47—42no—
133C22×Dic47—42no—
134C22×Dic47C2×D412yes—
135C2×D188—28no—
136C2×D188—28no—
137C2×D188—22no—
138C2×D188—22no—
139C2×D188—22no—
140C2×D188—22no—
141C2×D188—216no—
142C2×D188—24no—
143C2×D188—22no—
144C2×D188—48no—
145C2×D188—432no—
146C2×D188—48no—
147C2×D188—44no—
148C2×D188—42no—
149C2×D188—42no—
150C2×D188—44no—
151C2×D188C2×D414yes—
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—28no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47C2×D414yescomplemented
169C4⋊C4×C47—24no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—42no—
174C4⋊C4×C47C2×D414yes—
175(C2×D47)⋊C4—216no—
176(C2×D47)⋊C4—48no—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179C4⋊Dic47—42no—
180C2×C47⋊C8—22no—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8—44no—
184C23×C47#12012yes—
185C23×C47#12112yes—
186C23×C47#12312yes—
187C23×C47C2×SD1612yes—
188C23×C47#13512yes—
189C23×C47AGL(1,ℤ/8)12yes—
190C23×C47AGL(1,ℤ/8)12yes—
191C23×C47C22×D411yescharacteristic
192C22×D47—22no—
193C22×D47—22no—
194C22×D47—22no—
195C22×D47—22no—
196C22×D47—22no—
197C22×D47—22no—
198C22×D47—28no—
199C22×D47—28no—
200C22×D47—28no—
201C22×D47—24no—
202C22×D47—44no—
203C22×D47—44no—
204C22×D47—44no—
205C22×D47—44no—
206C22×D47—42no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211C22×D47—42no—
212C22×D47—48no—
213C22×D47—48no—
214C22×D47—48no—
215C22×D47—84no—
216C22×D47—84no—
217C22×D47—84no—
218C22×D47—84no—
219C22×D47C2×SD1614yes—
220C2×C4×C47—24no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—48no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—84no—
228C2×C4×C47#12012yes—
229C2×C4×C47#12114yes—
230C2×C4×C47#12114yes—
231C2×C4×C47#12112yes—
232C2×C4×C47#12314yes—
233C2×C4×C47#12312yes—
234C2×C4×C47#12414yes—
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—44no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—84no—
249D188—24no—
250D188—24no—
251D188—432no—
252D188—42no—
253D188—42no—
254D188—48no—
255C4×D47—42no—
256C4×D47—42no—
257C4×D47—42no—
258C4×D47—42no—
259C4×D47—48no—
260C8×C47—24no—
261C47⋊C8—42no—
262C2×#2034—471nomaximal, Sylow
263C22×C47#39414yes—
264C22×C47#44914yes—
265C22×C47#45014yes—
266C22×C47#46514yes—
267C22×C47#46914yes—
268C22×C47#48114yes—
269C22×C47#48214yes—
270C22×C47C2×#12011yescharacteristic
271C22×C47C2×#12111yescharacteristic
272C22×C47C2×#12311yescharacteristic
273C22×C47C22×SD1611yescharacteristic
274C22×C47C2×#13511yescharacteristic
275C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
277C2×D47—24no—
278C2×D47—24no—
279C2×D47—24no—
280C2×D47—42no—
281C2×D47—42no—
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—416no—
285C2×D47—44no—
286C2×D47—44no—
287C2×D47—44no—
288C2×D47—82no—
289C2×D47—82no—
290C2×D47—82no—
291C2×D47—82no—
292C2×D47—816no—
293C4×C47—44no—
294C4×C47—82no—
295C4×C47#39414yes—
296C4×C47C2×#12111yescharacteristic
297C4×C47C2×#12111yescharacteristic
298C4×C47C2×#12311yescharacteristic
299C4×C47C2×#12411yescharacteristic
300Dic47—42no—
301Dic47—82no—
302C22×#121—471no—
303C22×#106D4711yescharacteristic, complemented
304C22×#102—471no—
305C22×#102—471no—
306C22×C22⋊C8—471no—
307C2×#380—471no—
308#2034—478no—
309C2×#340—471no—
310C2×C47#203418yescomplemented
311C2×C47C2×#39411yescharacteristic
312C2×C47C2×#45011yescharacteristic
313C2×C47C2×#44911yescharacteristic
314C2×C47C2×#46511yescharacteristic
315C2×C47C2×#46911yescharacteristic
316C2×C47C2×#48211yescharacteristic
317C2×C47C2×#48111yescharacteristic
318D47—44no—
319D47—84no—
320C23×D4—471no—
321C23×D4—941no—
322C24×C4—471no—
323C23×C8—471no—
324C23×C8C2×D4711yescharacteristic
325C2×#121—474no—
326C2×#121—942no—
327C2×#121—944no—
328C2×#121—944no—
329C22×C4⋊C4—471no—
330C22×C4⋊C4C2×D4711yescharacteristic
331C22×C4⋊C4C2×D4711yescharacteristic
332C22×C22⋊C4—941no—
333C22×C22⋊C4—941no—
334C2×#106—24no—
335C2×#106C2×D4714yescomplemented
336C2×#102—474no—
337C2×#102—474no—
338C2×#102—944no—
339C2×#102—944no—
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—471no—
348C25—941no—
349C22×D4—474no—
350C22×D4—472no—
351C22×D4—944no—
352C22×D4—948no—
353C22×D4—942no—
354C22×D4—942no—
355C22×D4—941no—
356C22×D4—942no—
357C22×D4—942no—
358C22×D4—942no—
359C22×D4—1884no—
360C22×D4—1884no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—471no—
364C23×C4—472no—
365C23×C4—472no—
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—472no—
377C22×C8—942no—
378C22×C8—942no—
379C22×C8—942no—
380C22×C8D18814yescomplemented
381C22×C8C22×D4712yes—
382#121—948no—
383#121—9416no—
384#121—948no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—472no—
391C2×C4⋊C4—942no—
392C2×C4⋊C4—942no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4C22⋊D4714yes—
395C2×C4⋊C4C22×D4712yes—
396C2×C4⋊C4C22×D4712yes—
397C2×C22⋊C4—944no—
398C2×C22⋊C4—948no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—1884no—
401#106—28no—
402#102—948no—
403#102—948no—
404C22⋊C8—948no—
405#95—944no—
406C24—474no—
407C24—472no—
408C24—942no—
409C24—942no—
410C24—942no—
411C24—942no—
412C24—942no—
413C24—942no—
414C24—944no—
415C24—942no—
416C24—1882no—
417C24—1882no—
418C24—1882no—
419C24—1882no—
420C24—1882no—
421C24—1882no—
422C24D4×D4711yescharacteristic
423C2×D4—474no—
424C2×D4—9416no—
425C2×D4—944no—
426C2×D4—948no—
427C2×D4—948no—
428C2×D4—942no—
429C2×D4—942no—
430C2×D4—942no—
431C2×D4—942no—
432C2×D4—942no—
433C2×D4—1888no—
434C2×D4—18832no—
435C2×D4—1888no—
436C2×D4—1884no—
437C2×D4—1882no—
438C2×D4—1882no—
439C2×D4—1884no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—472no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—944no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4—1882no—
465C22×C4—1884no—
466C22×C4—1884no—
467C22×C4—1884no—
468C22×C4—1884no—
469C22×C4C2×D18812yes—
470C22×C4#1062535012yes—
471C22×C4D4×D4711yescharacteristic
472C22×C4D4×D4712yes—
473C22×C4#1062535412yes—
474C22×C4#1062535412yes—
475C22×C4C2×C22⋊D4712yes—
476C22×C4C23×D4711yescharacteristic
477C2×C8—28no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—942no—
481C2×C8—942no—
482C2×C8—942no—
483C2×C8—1884no—
484C2×C8C2×D18814yescomplemented
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—1882no—
493C4⋊C4C2×C22⋊D4714yes—
494C22⋊C4—9416no—
495C22⋊C4—1888no—
496C23—474no—
497C23—948no—
498C23—942no—
499C23—948no—
500C23—942no—
501C23—942no—
502C23—942no—
503C23—942no—
504C23—942no—
505C23—948no—
506C23—944no—
507C23—3764no—
508C23—3764no—
509C23—3764no—
510C23—3764no—
511C23—1888no—
512C23—1888no—
513C23—1888no—
514C23—1882no—
515C23—1882no—
516C23—1882no—
517C23—1882no—
518C23—1882no—
519C23—1882no—
520C23—1884no—
521C23—1884no—
522C23—1884no—
523C23—1884no—
524C23#1309399212yes—
525C23#1309399912yes—
526C23#1309400912yes—
527C23SD16×D4712yes—
528C23#1309404512yes—
529C23#1309405112yes—
530C23#1309405112yes—
531C23C2×D4×D4711yescharacteristic
532D4—944no—
533D4—944no—
534D4—18832no—
535D4—1888no—
536D4—1882no—
537D4—1882no—
538C2×C4—24no—
539C2×C4—48no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—3764no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1884no—
554C2×C4—1888no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4#1309399212yes—
560C2×C4#1309399814yes—
561C2×C4#1309399912yes—
562C2×C4#1309399914yes—
563C2×C4#1309400912yes—
564C2×C4#1309400914yes—
565C2×C4#1309401314yes—
566C2×C4C2×D4×D4711yescharacteristic
567C2×C4C22×C22⋊D4711yescharacteristic
568C2×C4C22×D18811yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C2×C4C2×#1062535411yescharacteristic
571C2×C4C2×#1062535411yescharacteristic
572C8—24no—
573C8—1882no—
574C22—944no—
575C22—944no—
576C22—944no—
577C22—3762no—
578C22—3762no—
579C22—3762no—
580C22—37616no—
581C22—3762no—
582C22—1884no—
583C22—1884no—
584C22—1884no—
585C22—1882no—
586C22—1882no—
587C22—1882no—
588C22—18816no—
589C22—1882no—
590C22#1568904014yes—
591C22#1568926714yes—
592C22#1568927214yes—
593C22#1568935314yes—
594C22#1568937714yes—
595C22#1568944314yes—
596C22#1568944914yes—
597C22C2×#1309399211yescharacteristic
598C22C2×#1309399911yescharacteristic
599C22C2×#1309400911yescharacteristic
600C22C2×SD16×D4711yescharacteristic
601C22C2×#1309404511yescharacteristic
602C22C2×#1309405111yescharacteristic
603C22C2×#1309405111yescharacteristic
604C4—44no—
605C4—82no—
606C4—3762no—
607C4—1882no—
608C4#1568904014yes—
609C4C2×#1309399811yescharacteristic
610C4C2×#1309399911yescharacteristic
611C4C2×#1309400911yescharacteristic
612C4C2×#1309401311yescharacteristic
613C2—3764no—
614C2—1884no—
615C2#2024457918yesdirect product factor
616C2C2×#1568904011yescharacteristic
617C2C2×#1568927211yescharacteristic
618C2C2×#1568926711yescharacteristic
619C2C2×#1568935311yescharacteristic
620C2C2×#1568937711yescharacteristic
621C2C2×#1568944911yescharacteristic
622C2C2×#1568944311yescharacteristic
subgroupG/H
centerC24D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#106×C47C2
socleC24×C47C2×D4
prime radicalC22×#13093999C2
hypercenterC22×#106D47
hypocenterC47C2×#2034
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C22×#13093946C2semidirect
3. C22×#13093944C2semidirect
4. C22×(C2×D47)⋊C8C2semidirect
5. C2×#15688980C2semidirect
6. #20244579C2direct (N × H)
7. C2×#15688885C2semidirect
8. C22×#106×C47C2semidirect
21. C2×#13093946C22semidirect
23. C2×#13093944C22semidirect
25. C2×(C2×D47)⋊C8C22semidirect
27. #15688980C22semidirect
29. #15688885C22semidirect
34. C2×#106×C47C22semidirect
83. C22×C8×C47D4semidirect
168. C2×C8×C47C2×D4semidirect
303. C22×#106D47semidirect
310. C2×C47#2034semidirect
335. C2×#106C2×D47semidirect
346. C47C2×#2034semidirect
380. C22×C8D188semidirect
484. C2×C8C2×D188semidirect
615. C2#20244579direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939992
C22×#130939462
C22×#130939442
C22×(C2×D47)⋊C82
C2×#156889802
#202445792
C2×#156888852
C22×#106×C472
C2×#203447