Finite Group Databasebeta

← C2×#20244611 #26243912

Subgroups — C2×#20244611 #26243912

Order 12032.

1586 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic
2C22×#13093952C211yesmaximal, characteristic, complemented
3C2×#15689125C211yesmaximal, characteristic, complemented
4C2×#15689124C211yesmaximal, characteristic, complemented
5C2×#15688993C211yesmaximal, characteristic, complemented
6#20244611C218yesmaximal, direct product factor
7C2×#15688891C211yesmaximal, characteristic, complemented
8C22×#104×C47C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689701—22no—
12#15689701—22no—
13#15689701—22no—
14#15689701C2214yes—
15C2×#13094003—21no—
16C2×#13094000—21no—
17C2×#13093998—21no—
18C2×#13093996—22no—
19C2×#13093995—21no—
20C22×C4⋊Dic47—22no—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C2×#13093952—24no—
24C2×#13093952C2214yescomplemented
25#15689125—22no—
26#15689125C2214yescomplemented
27#15689124—22no—
28#15689124C2214yescomplemented
29C2×#13093949—21no—
30C2×#13093948—21no—
31C2×#13093946—21no—
32C2×#13093945—21no—
33#15688993—22no—
34#15688993C2214yescomplemented
35#15688891C2214yescomplemented
36C22×#41×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C2×#104×C47—24no—
40C2×#104×C47C2214yescomplemented
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—22no—
44C2×#10625350—22no—
45C2×#10625350—22no—
46C2×#10625350—22no—
47C2×#10625350D412yes—
48C2×#10625350C2312yes—
49C22×Dic94D411yescharacteristic
50C22×D188D411yescharacteristic
51C22×C22⋊D47—21no—
52C22×C22⋊D47—22no—
53C23×Dic47—21no—
54C23×Dic47D412yes—
55C22×C4×D47—21no—
56C2×#10625329—21no—
57C2×#10625329—22no—
58C2×#10625329—22no—
59C2×#10625329C2312yes—
60C22×C47⋊C8—21no—
61#13094003—24no—
62#13094003—24no—
63#13094000—24no—
64#13094000—24no—
65#13093998—24no—
66#13093998—24no—
67#13093996—28no—
68#13093996—28no—
69#13093995—24no—
70#13093995—24no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—28no—
81C2×C4⋊Dic47—48no—
82C2×C4⋊Dic47D412yes—
83C2×C4⋊Dic47C2312yes—
84C2×C4⋊Dic47C2312yes—
85C2×Dic47⋊C4—22no—
86C2×C22⋊Dic47—22no—
87C2×(C2×D47)⋊C4—22no—
88#13093952—28no—
89#13093949—24no—
90#13093948—24no—
91#13093946—24no—
92#13093945—24no—
93C2×#41×C47—21no—
94C2×#41×C47—21no—
95C2×#41×C47—22no—
96C2×#41×C47—22no—
97C2×#41×C47—22no—
98C2×#41×C47—22no—
99C2×#41×C47D412yes—
100C2×#41×C47C2312yes—
101C22×Q8×C47D411yescharacteristic
102C22×D4×C47—21no—
103C22×D4×C47D411yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47—21no—
106C23×C4×C47C2311yescharacteristic
107C2×M16×C47—21no—
108C2×M16×C47—22no—
109C2×M16×C47—22no—
110C2×M16×C47C2312yes—
111C22×C8×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47—22no—
114C2×C42×C47D414yescomplemented
115C2×C42×C47C2312yes—
116#104×C47—28no—
117C24×C47—21no—
118C24×C47C2×D411yescharacteristic
119C23×D47—21no—
120#41×C47—24no—
121#41×C47—24no—
122#41×C47—22no—
123#41×C47—22no—
124#41×C47—22no—
125#41×C47—22no—
126#41×C47—42no—
127#41×C47—42no—
128#41×C47—42no—
129#41×C47—42no—
130C2×Q8×C47—21no—
131C2×Q8×C47—22no—
132C2×Q8×C47—22no—
133C2×Q8×C47C2×D412yes—
134C2×D4×C47—22no—
135C2×D4×C47—22no—
136C2×D4×C47—21no—
137C2×D4×C47—22no—
138C2×D4×C47—22no—
139C2×D4×C47—42no—
140C2×D4×C47—42no—
141C2×D4×C47C2×D412yes—
142C22×C4×C47—24no—
143C22×C4×C47—24no—
144C22×C4×C47—24no—
145C22×C4×C47—22no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D412yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×C4×C47#4112yes—
160C22×C4×C47C2411yescharacteristic
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—28no—
164C2×C22⋊D47—42no—
165C2×C22⋊D47—42no—
166C2×C22⋊D47—84no—
167C22×Dic47—22no—
168C22×Dic47—21no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—44no—
172C22×Dic47—44no—
173C22×Dic47—41no—
174C22×Dic47—41no—
175C22×Dic47C2×D414yes—
176#10625350—24no—
177#10625350—24no—
178#10625350—22no—
179#10625350—22no—
180#10625350—22no—
181#10625350—22no—
182#10625350—42no—
183#10625350—42no—
184#10625350—42no—
185#10625350—42no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—21no—
189C2×D188C2×D412yes—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47—42no—
193C2×C4×D47—42no—
194C2×Dic94—22no—
195C2×Dic94—22no—
196C2×Dic94—21no—
197C2×Dic94C2×D412yes—
198M16×C47—22no—
199M16×C47—22no—
200M16×C47—42no—
201C2×C8×C47—22no—
202C2×C8×C47—42no—
203C42×C47—24no—
204C42×C47—22no—
205C42×C47C2×D414yescomplemented
206C22⋊Dic47—28no—
207(C2×D47)⋊C4—28no—
208C4⋊Dic47—22no—
209C4⋊Dic47—22no—
210C4⋊Dic47—22no—
211C4⋊Dic47—22no—
212C4⋊Dic47—22no—
213C4⋊Dic47—22no—
214C4⋊Dic47—416no—
215C4⋊Dic47—41no—
216C4⋊Dic47—41no—
217Dic47⋊C4—28no—
218#10625329—22no—
219#10625329—22no—
220#10625329—42no—
221C2×C47⋊C8—22no—
222C2×C47⋊C8—42no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47#12011yescharacteristic
230C23×C47#12011yescharacteristic
231C23×C47#12112yes—
232C23×C47#12412yes—
233C23×C47C22×D411yescharacteristic
234C22×D47—22no—
235C22×D47—42no—
236C22×D47—42no—
237C22×D47—42no—
238Q8×C47—22no—
239Q8×C47—22no—
240Q8×C47—42no—
241D4×C47—22no—
242D4×C47—22no—
243D4×C47—42no—
244D4×C47—42no—
245D4×C47—44no—
246D4×C47—42no—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—216no—
250C2×C4×C47—24no—
251C2×C4×C47—22no—
252C2×C4×C47—42no—
253C2×C4×C47—42no—
254C2×C4×C47—42no—
255C2×C4×C47—44no—
256C2×C4×C47#12011yescharacteristic
257C2×C4×C47#12011yescharacteristic
258C2×C4×C47#12112yes—
259C2×C4×C47#12112yes—
260C2×C4×C47#12112yes—
261C2×C4×C47#12112yes—
262C2×C4×C47#12112yes—
263C2×C4×C47#12312yes—
264C2×C4×C47#12312yes—
265C2×C4×C47#12312yes—
266C2×C4×C47#12312yes—
267C2×C4×C47#12412yes—
268C2×C4×C47C22×D411yescharacteristic
269C2×C4×C47C22×D411yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47C2×#4111yescharacteristic
274C22⋊D47—42no—
275C22⋊D47—42no—
276C22⋊D47—44no—
277C22⋊D47—88no—
278C2×Dic47—22no—
279C2×Dic47—24no—
280C2×Dic47—42no—
281C2×Dic47—44no—
282C2×Dic47—44no—
283C2×Dic47—44no—
284C2×Dic47—42no—
285C2×Dic47—82no—
286C2×Dic47—82no—
287C2×Dic47—82no—
288D188—22no—
289D188—22no—
290D188—42no—
291C4×D47—42no—
292C4×D47—42no—
293C4×D47—44no—
294Dic94—22no—
295Dic94—22no—
296Dic94—42no—
297C8×C47—42no—
298C47⋊C8—42no—
299C2×#2039—471nomaximal, Sylow
300C22×C47—21no—
301C22×C47—21no—
302C22×C47—21no—
303C22×C47—21no—
304C22×C47—24no—
305C22×C47—24no—
306C22×C47—42no—
307C22×C47—42no—
308C22×C47—42no—
309C22×C47—84no—
310C22×C47#39412yes—
311C22×C47#39412yes—
312C22×C47#45312yes—
313C22×C47#45612yes—
314C22×C47C2×#12011yescharacteristic
315C22×C47C2×#12111yescharacteristic
316C22×C47C2×#12411yescharacteristic
317C2×D47—42no—
318C2×D47—42no—
319C2×D47—42no—
320C2×D47—84no—
321C4×C47—28no—
322C4×C47—42no—
323C4×C47#39412yes—
324C4×C47#39412yes—
325C4×C47C2×#12111yescharacteristic
326C4×C47C2×#12111yescharacteristic
327C4×C47C2×#12311yescharacteristic
328C4×C47C2×#12311yescharacteristic
329Dic47—42no—
330Dic47—44no—
331Dic47—82no—
332C2×#537—471no—
333C22×#104—471no—
334C22×#104D4711yescharacteristic, complemented
335C2×#417—471no—
336C2×#417—471no—
337C2×#384—471no—
338#2039—478no—
339C2×#343—471no—
340C2×C47—21no—
341C2×C47—21no—
342C2×C47—22no—
343C2×C47—82no—
344C2×C47#203914yescomplemented
345C2×C47C2×#39411yescharacteristic
346C2×C47C2×#45311yescharacteristic
347C2×C47C2×#45611yescharacteristic
348D47—82no—
349C22×#41—471no—
350C22×#41C2×D4711yescharacteristic
351C22×M16—471no—
352C22×M16C2×D4711yescharacteristic
353#537—474no—
354#537—942no—
355#537—942no—
356#537—942no—
357C2×C22⋊Q8—941no—
358C2×C22⋊Q8—941no—
359C2×#121—941no—
360C2×#121—942no—
361C2×#121—941no—
362C22×C4⋊C4—471no—
363C22×C4⋊C4—471no—
364C22×C4⋊C4—942no—
365C22×C42C2×D4711yescharacteristic
366C2×#104—24no—
367C2×#104—474no—
368C2×#104—944no—
369C2×#104C2×D4714yescomplemented
370#417—474no—
371#417—474no—
372#417—942no—
373#417—942no—
374C2×#103—941no—
375C2×#103—941no—
376C2×#102—941no—
377C2×#102—941no—
378#384—474no—
379#384—942no—
380#343—474no—
381C47C2×#203911yescharacteristic, complemented, Sylow
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—472no—
389C2×#41—472no—
390C2×#41—941no—
391C2×#41—941no—
392C2×#41—942no—
393C2×#41—942no—
394C2×#41—942no—
395C2×#41—942no—
396C2×#41D18812yes—
397C2×#41C22×D4712yes—
398C22×Q8—471no—
399C22×Q8D18811yescharacteristic
400C22×D4—21no—
401C22×D4—471no—
402C22×D4—942no—
403C22×D4—941no—
404C22×D4D18811yescharacteristic
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—472no—
408C23×C4—941no—
409C23×C4—941no—
410C23×C4C22×D4711yescharacteristic
411C2×M16—21no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—472no—
415C2×M16—941no—
416C2×M16—942no—
417C2×M16—942no—
418C2×M16C22×D4712yes—
419C22×C8—21no—
420C22×C8—941no—
421C22⋊Q8—944no—
422C22⋊Q8—944no—
423C22⋊Q8—944no—
424C22⋊Q8—944no—
425#121—944no—
426#121—944no—
427#121—948no—
428#121—944no—
429#121—948no—
430#121—944no—
431C2×C4⋊C4—472no—
432C2×C4⋊C4—472no—
433C2×C4⋊C4—472no—
434C2×C4⋊C4—942no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4—941no—
437C2×C4⋊C4—941no—
438C2×C4⋊C4—941no—
439C2×C4⋊C4—941no—
440C2×C4⋊C4—941no—
441C2×C4⋊C4—941no—
442C2×C4⋊C4—941no—
443C2×C4⋊C4—948no—
444C2×C4⋊C4—941no—
445C2×C4⋊C4—1888no—
446C2×C22⋊C4—942no—
447C2×C22⋊C4—942no—
448C2×C42—21no—
449C2×C42—22no—
450C2×C42C22⋊D4714yescomplemented
451C2×C42C22×D4712yes—
452#104—28no—
453#104—948no—
454#103—944no—
455#103—944no—
456#102—944no—
457#102—944no—
458C24—21no—
459C24—941no—
460C24D4×D4711yescharacteristic
461#41—24no—
462#41—24no—
463#41—22no—
464#41—22no—
465#41—22no—
466#41—22no—
467#41—42no—
468#41—42no—
469#41—42no—
470#41—42no—
471#41—944no—
472#41—944no—
473#41—942no—
474#41—942no—
475#41—942no—
476#41—942no—
477#41—1882no—
478#41—1882no—
479#41—1882no—
480#41—1882no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—472no—
485C2×Q8—941no—
486C2×Q8—942no—
487C2×Q8—942no—
488C2×Q8C2×D18812yes—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—472no—
497C2×D4—948no—
498C2×D4—942no—
499C2×D4—942no—
500C2×D4—941no—
501C2×D4—942no—
502C2×D4—942no—
503C2×D4—3764no—
504C2×D4—1882no—
505C2×D4—1882no—
506C2×D4C2×D18812yes—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—474no—
517C22×C4—942no—
518C22×C4—942no—
519C22×C4—941no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—1884no—
524C22×C4—1881no—
525C22×C4—1881no—
526C22×C4—1884no—
527C22×C4—1882no—
528C22×C4—1882no—
529C22×C4C2×D18811yescharacteristic
530C22×C4C2×D18811yescharacteristic
531C22×C4#1062535012yes—
532C22×C4D4×D4711yescharacteristic
533C22×C4D4×D4711yescharacteristic
534C22×C4D4×D4711yescharacteristic
535C22×C4#1062535212yes—
536C22×C4#1062535212yes—
537C22×C4C2×C22⋊D4712yes—
538C22×C4C23×D4711yescharacteristic
539M16—22no—
540M16—22no—
541M16—42no—
542M16—942no—
543M16—942no—
544M16—1882no—
545C2×C8—22no—
546C2×C8—42no—
547C2×C8—942no—
548C2×C8—1882no—
549C4⋊C4—948no—
550C4⋊C4—942no—
551C4⋊C4—942no—
552C4⋊C4—942no—
553C4⋊C4—942no—
554C4⋊C4—942no—
555C4⋊C4—942no—
556C4⋊C4—18816no—
557C4⋊C4—1881no—
558C4⋊C4—1881no—
559C22⋊C4—948no—
560C22⋊C4—948no—
561C42—24no—
562C42—22no—
563C42C2×C22⋊D4714yescomplemented
564C23—22no—
565C23—22no—
566C23—22no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—942no—
571C23—1882no—
572C23—1882no—
573C23—1882no—
574C23#1309399411yescharacteristic
575C23#1309399411yescharacteristic
576C23#1309399612yes—
577C23#1309401012yes—
578C23C2×D4×D4711yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—42no—
582Q8—942no—
583Q8—942no—
584Q8—1882no—
585D4—22no—
586D4—22no—
587D4—44no—
588D4—42no—
589D4—42no—
590D4—42no—
591D4—942no—
592D4—942no—
593D4—3768no—
594D4—1884no—
595D4—1882no—
596D4—1882no—
597D4—1882no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—216no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—42no—
604C2×C4—44no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—944no—
608C2×C4—942no—
609C2×C4—3762no—
610C2×C4—3762no—
611C2×C4—3762no—
612C2×C4—1884no—
613C2×C4—1882no—
614C2×C4—1884no—
615C2×C4—1882no—
616C2×C4—1884no—
617C2×C4—1882no—
618C2×C4—1882no—
619C2×C4—1884no—
620C2×C4#1309399411yescharacteristic
621C2×C4#1309399411yescharacteristic
622C2×C4#1309399512yes—
623C2×C4#1309399512yes—
624C2×C4#1309399612yes—
625C2×C4#1309399812yes—
626C2×C4#1309399812yes—
627C2×C4#1309400612yes—
628C2×C4#1309400612yes—
629C2×C4#1309400812yes—
630C2×C4#1309400812yes—
631C2×C4#1309401012yes—
632C2×C4C2×D4×D4711yescharacteristic
633C2×C4C22×C22⋊D4711yescharacteristic
634C2×C4C22×D18811yescharacteristic
635C2×C4C2×#1062535211yescharacteristic
636C2×C4C2×#1062535211yescharacteristic
637C2×C4C2×#1062535011yescharacteristic
638C8—42no—
639C8—1882no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—24no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—84no—
650C22—3764no—
651C22—1882no—
652C22—1882no—
653C22—1882no—
654C22#1568903912yes—
655C22#1568903912yes—
656C22#1568929212yes—
657C22#1568930712yes—
658C22C2×#1309399411yescharacteristic
659C22C2×#1309399611yescharacteristic
660C22C2×#1309401011yescharacteristic
661C4—28no—
662C4—42no—
663C4—3762no—
664C4—1884no—
665C4—1882no—
666C4#1568903912yes—
667C4#1568903912yes—
668C4C2×#1309399511yescharacteristic
669C4C2×#1309399811yescharacteristic
670C4C2×#1309400611yescharacteristic
671C4C2×#1309400811yescharacteristic
672C2—21no—
673C2—22no—
674C2—21no—
675C2—82no—
676C2—3762no—
677C2#2024461114yesdirect product factor
678C2C2×#1568903911yescharacteristic
679C2C2×#1568929211yescharacteristic
680C2C2×#1568930711yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#104×C47C2
socleC23×C47#120
prime radicalC2×#15689701C2
hypercenterC22×#104D47
hypocenterC47C2×#2039
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#13093952C2semidirect
3. C2×#15689125C2semidirect
4. C2×#15689124C2semidirect
5. C2×#15688993C2semidirect
6. #20244611C2direct (N × H)
7. C2×#15688891C2semidirect
8. C22×#104×C47C2semidirect
24. C2×#13093952C22semidirect
26. #15689125C22semidirect
28. #15689124C22semidirect
34. #15688993C22semidirect
35. #15688891C22semidirect
40. C2×#104×C47C22semidirect
114. C2×C42×C47D4semidirect
205. C42×C47C2×D4semidirect
334. C22×#104D47semidirect
344. C2×C47#2039semidirect
369. C2×#104C2×D47semidirect
381. C47C2×#2039semidirect
450. C2×C42C22⋊D47semidirect
563. C42C2×C22⋊D47semidirect
677. C2#20244611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897012
C22×#130939522
C2×#156891252
C2×#156891242
C2×#156889932
#202446112
C2×#156888912
C22×#104×C472
C2×#203947