Finite Group Databasebeta

← C2×#20244603 #26243869

Subgroups — C2×#20244603 #26243869

Order 12032.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689694C211yesmaximal, characteristic
2C2×#15689163C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic
4C22×#13093942C211yesmaximal, characteristic, complemented
5C2×#15689028C211yesmaximal, characteristic, complemented
6#20244603C218yesmaximal, direct product factor
7C2×#15688884C211yesmaximal, characteristic, complemented
8C2×C47×#417C211yesmaximal, characteristic
9C23×Dic94C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689694—22no—
12#15689694—22no—
13#15689694—22no—
14#15689694C2214yes—
15C2×#13094022—21no—
16C2×#13094011—21no—
17C2×#13094005—22no—
18C2×#13094003—21no—
19C2×#13094003—21no—
20C2×#13093983C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689163—22no—
23#15689163C2214yescomplemented
24C2×#13093957—21no—
25C2×#13093955—21no—
26C2×#13093951—24no—
27C2×#13093951C2214yes—
28C2×#13093942—24no—
29C2×#13093942C2214yescomplemented
30#15689028—22no—
31#15689028C2214yescomplemented
32C2×C47⋊#95—22no—
33#15688884C2214yescomplemented
34C22×#41×C47C2211yescharacteristic
35C22×M16×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C47×#417—22no—
38C47×#417C2214yes—
39C2×#103×C47—21no—
40C2×#102×C47—21no—
41C22×Dic94—22no—
42C22×Dic94—21no—
43C22×Dic94—21no—
44C22×Dic94—21no—
45C22×Dic94—21no—
46C22×Dic94—22no—
47C22×Dic94—22no—
48C22×Dic94—22no—
49C22×Dic94D412yes—
50C22×Dic94C2312yes—
51C23×Dic47—21no—
52C23×Dic47D412yes—
53C2×#10625329—21no—
54C2×#10625329—22no—
55C2×#10625329D414yes—
56C2×#10625329C2312yes—
57C22×C47⋊C8—21no—
58#13094022—24no—
59#13094022—24no—
60#13094011—24no—
61#13094011—24no—
62#13094005—28no—
63#13094005—28no—
64#13094003—24no—
65#13094003—24no—
66#13094003—24no—
67#13094003—24no—
68#13093983—21no—
69#13093983—21no—
70#13093983D412yes—
71#13093983C2312yes—
72C2×C4⋊Dic47D411yescharacteristic
73C2×C4⋊Dic47D411yescharacteristic
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—22no—
78C2×C22⋊Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—22no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47C2312yes—
84#13093957—24no—
85#13093955—24no—
86#13093951—28no—
87#13093942—28no—
88C47⋊#95—28no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—22no—
92C2×#41×C47—22no—
93C2×#41×C47—22no—
94C2×#41×C47—22no—
95C2×#41×C47D412yes—
96C2×#41×C47C2312yes—
97C22×Q8×C47D411yescharacteristic
98C22×D4×C47—21no—
99C22×D4×C47D411yescharacteristic
100C23×C4×C47—21no—
101C23×C4×C47—21no—
102C23×C4×C47C2311yescharacteristic
103C2×M16×C47—21no—
104C2×M16×C47—22no—
105C2×M16×C47—22no—
106C2×M16×C47C2312yes—
107C22×C8×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47C2312yes—
114#103×C47—24no—
115#102×C47—24no—
116C24×C47—21no—
117C24×C47C2×D411yescharacteristic
118#41×C47—24no—
119#41×C47—24no—
120#41×C47—22no—
121#41×C47—22no—
122#41×C47—22no—
123#41×C47—22no—
124#41×C47—42no—
125#41×C47—42no—
126#41×C47—42no—
127#41×C47—42no—
128C2×Q8×C47—21no—
129C2×Q8×C47—22no—
130C2×Q8×C47—22no—
131C2×Q8×C47C2×D412yes—
132C2×D4×C47—22no—
133C2×D4×C47—22no—
134C2×D4×C47—21no—
135C2×D4×C47—22no—
136C2×D4×C47—22no—
137C2×D4×C47—42no—
138C2×D4×C47—42no—
139C2×D4×C47C2×D412yes—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47—44no—
147C22×C4×C47—41no—
148C22×C4×C47—41no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D412yes—
155C22×C4×C47#4112yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×C4×C47C2411yescharacteristic
159C22×Dic47—24no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—24no—
165C22×Dic47—24no—
166C22×Dic47—22no—
167C22×Dic47—42no—
168C22×Dic47—42no—
169C22×Dic47C2×D414yes—
170C2×Dic94—22no—
171C2×Dic94—22no—
172C2×Dic94—24no—
173C2×Dic94—24no—
174C2×Dic94—22no—
175C2×Dic94—22no—
176C2×Dic94—22no—
177C2×Dic94—22no—
178C2×Dic94—22no—
179C2×Dic94—22no—
180C2×Dic94—42no—
181C2×Dic94—42no—
182C2×Dic94—42no—
183C2×Dic94—42no—
184C2×Dic94—42no—
185C2×Dic94—42no—
186C2×Dic94—42no—
187C2×Dic94—42no—
188M16×C47—22no—
189M16×C47—22no—
190M16×C47—42no—
191C2×C8×C47—22no—
192C2×C8×C47—42no—
193C4⋊C4×C47—22no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—41no—
196C4⋊C4×C47—41no—
197C22⋊Dic47—28no—
198C22⋊Dic47—28no—
199C22⋊Dic47—22no—
200C22⋊Dic47—22no—
201C4⋊Dic47—21no—
202C4⋊Dic47—21no—
203C4⋊Dic47C2×D412yes—
204C4⋊Dic47C2×D412yes—
205Dic47⋊C4—28no—
206Dic47⋊C4—28no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47—22no—
210C4×Dic47—22no—
211C4×Dic47—42no—
212#10625329—24no—
213#10625329—22no—
214#10625329C2×D414yes—
215C2×C47⋊C8—24no—
216C2×C47⋊C8—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—42no—
221C23×C47—42no—
222C23×C47—42no—
223C23×C47#12011yescharacteristic
224C23×C47#12011yescharacteristic
225C23×C47#12112yes—
226C23×C47#12312yes—
227C23×C47C22×D411yescharacteristic
228Q8×C47—22no—
229Q8×C47—22no—
230Q8×C47—42no—
231D4×C47—22no—
232D4×C47—22no—
233D4×C47—42no—
234D4×C47—42no—
235D4×C47—44no—
236D4×C47—42no—
237C2×C4×C47—22no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—44no—
242C2×C4×C47—44no—
243C2×C4×C47—42no—
244C2×C4×C47—82no—
245C2×C4×C47—82no—
246C2×C4×C47#12011yescharacteristic
247C2×C4×C47#12011yescharacteristic
248C2×C4×C47#12112yes—
249C2×C4×C47#12112yes—
250C2×C4×C47#12112yes—
251C2×C4×C47#12112yes—
252C2×C4×C47#12112yes—
253C2×C4×C47#12312yes—
254C2×C4×C47#12312yes—
255C2×C4×C47#12312yes—
256C2×C4×C47#12412yes—
257C2×C4×C47#12412yes—
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47C22×D411yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×Dic47—24no—
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—24no—
270C2×Dic47—42no—
271C2×Dic47—48no—
272C2×Dic47—42no—
273C2×Dic47—44no—
274C2×Dic47—44no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277Dic94—42no—
278Dic94—42no—
279Dic94—42no—
280Dic94—42no—
281Dic94—44no—
282Dic94—44no—
283C8×C47—42no—
284C47⋊C8—24no—
285C2×#2038—471nomaximal, Sylow
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—24no—
291C22×C47—24no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47—42no—
295C22×C47—84no—
296C22×C47#39412yes—
297C22×C47#39412yes—
298C22×C47#45412yes—
299C22×C47#45612yes—
300C22×C47C2×#12011yescharacteristic
301C22×C47C2×#12111yescharacteristic
302C22×C47C2×#12311yescharacteristic
303C4×C47—42no—
304C4×C47—82no—
305C4×C47#39412yes—
306C4×C47#39412yes—
307C4×C47C2×#12111yescharacteristic
308C4×C47C2×#12111yescharacteristic
309C4×C47C2×#12311yescharacteristic
310C4×C47C2×#12411yescharacteristic
311Dic47—44no—
312Dic47—44no—
313Dic47—42no—
314Dic47—42no—
315C2×#536—471no—
316C2×#428—471no—
317C22×#104—471no—
318C2×#417D4711yescharacteristic
319C22×#101—471no—
320C2×#391—471no—
321#2038—478no—
322C2×#339—471no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—22no—
326C2×C47—82no—
327C2×C47#203814yescomplemented
328C2×C47C2×#39411yescharacteristic
329C2×C47C2×#45411yescharacteristic
330C2×C47C2×#45611yescharacteristic
331C22×#41C2×D4711yescharacteristic
332C23×Q8—471no—
333C22×M16—471no—
334C22×M16C2×D4711yescharacteristic
335#536—474no—
336#536—942no—
337#536—942no—
338#536—942no—
339C2×C4⋊Q8—941no—
340C2×#124—941no—
341C2×#123—942no—
342C2×C22⋊Q8—941no—
343C2×C22⋊Q8—941no—
344C2×#117—471no—
345C22×C4⋊C4C2×D4711yescharacteristic
346C22×C42—471no—
347#428—474no—
348#428—942no—
349C2×#107—941no—
350C2×#106—941no—
351C2×#104—474no—
352C2×#104—944no—
353#417—22no—
354#417C2×D4714yes—
355C2×#103—21no—
356C2×#102—21no—
357C2×#101—474no—
358C2×#101—944no—
359#391—474no—
360#391—942no—
361C2×#95—942no—
362#339—474no—
363C47C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41C22⋊D4712yes—
371C2×#41C22×D4712yes—
372C22×Q8—472no—
373C22×Q8—472no—
374C22×Q8—942no—
375C22×Q8—942no—
376C22×Q8—941no—
377C22×Q8—941no—
378C22×Q8—942no—
379C22×Q8—942no—
380C22×Q8—941no—
381C22×Q8—941no—
382C22×Q8C22⋊D4711yescharacteristic
383C22×D4—21no—
384C22×D4C22⋊D4711yescharacteristic
385C23×C4—21no—
386C23×C4—21no—
387C23×C4—472no—
388C23×C4—941no—
389C23×C4C22×D4711yescharacteristic
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—22no—
393C2×M16—474no—
394C2×M16—472no—
395C2×M16—942no—
396C2×M16—941no—
397C2×M16C22×D4712yes—
398C22×C8—21no—
399C22×C8—941no—
400C4⋊Q8—944no—
401C4⋊Q8—944no—
402#124—944no—
403#124—944no—
404#123—948no—
405#123—948no—
406C22⋊Q8—944no—
407C22⋊Q8—944no—
408C22⋊Q8—944no—
409C22⋊Q8—944no—
410#117—472no—
411#117—472no—
412#117—941no—
413#117—941no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—471no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—942no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4C22×D4712yes—
424C2×C22⋊C4—942no—
425C2×C22⋊C4—942no—
426C2×C22⋊C4—941no—
427C2×C42—472no—
428C2×C42—941no—
429C2×C42—942no—
430C2×C42—942no—
431C2×C42—941no—
432#107—944no—
433#106—944no—
434#104—948no—
435#103—24no—
436#102—24no—
437#101—948no—
438#95—948no—
439C24—21no—
440C24D4×D4711yescharacteristic
441#41—24no—
442#41—24no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—42no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—942no—
455C2×Q8—942no—
456C2×Q8—944no—
457C2×Q8—944no—
458C2×Q8—942no—
459C2×Q8—942no—
460C2×Q8—942no—
461C2×Q8—942no—
462C2×Q8—942no—
463C2×Q8—942no—
464C2×Q8—1882no—
465C2×Q8—1882no—
466C2×Q8—1882no—
467C2×Q8—1882no—
468C2×Q8—1882no—
469C2×Q8—1882no—
470C2×Q8—1882no—
471C2×Q8—1882no—
472C2×Q8C2×C22⋊D4712yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×C22⋊D4712yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—44no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—474no—
491C22×C4—944no—
492C22×C4—942no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—942no—
496C22×C4—944no—
497C22×C4—944no—
498C22×C4—942no—
499C22×C4—1882no—
500C22×C4—1882no—
501C22×C4#1062535012yes—
502C22×C4#1062535012yes—
503C22×C4D4×D4711yescharacteristic
504C22×C4D4×D4711yescharacteristic
505C22×C4D4×D4711yescharacteristic
506C22×C4D4×D4712yes—
507C22×C4#1062535212yes—
508C22×C4C2×C22⋊D4711yescharacteristic
509C22×C4C2×C22⋊D4711yescharacteristic
510C22×C4C23×D4711yescharacteristic
511M16—22no—
512M16—22no—
513M16—42no—
514M16—474no—
515M16—944no—
516M16—942no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—944no—
520C2×C8—942no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—472no—
526C4⋊C4—472no—
527C4⋊C4—948no—
528C4⋊C4—948no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C22⋊C4—948no—
532C22⋊C4—948no—
533C22⋊C4—942no—
534C22⋊C4—942no—
535C42—942no—
536C42—942no—
537C42—942no—
538C42—942no—
539C42—1882no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#1309399211yescharacteristic
547C23#1309399211yescharacteristic
548C23#1309399712yes—
549C23#1309400612yes—
550C23C2×D4×D4711yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—1884no—
555Q8—1884no—
556Q8—1882no—
557Q8—1882no—
558Q8—1882no—
559Q8—1882no—
560D4—22no—
561D4—22no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566C2×C4—22no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—944no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—944no—
579C2×C4—944no—
580C2×C4—944no—
581C2×C4—1882no—
582C2×C4—1888no—
583C2×C4—1884no—
584C2×C4—1884no—
585C2×C4—1882no—
586C2×C4—1882no—
587C2×C4—1882no—
588C2×C4#1309399211yescharacteristic
589C2×C4#1309399211yescharacteristic
590C2×C4#1309399612yes—
591C2×C4#1309399612yes—
592C2×C4#1309399712yes—
593C2×C4#1309399712yes—
594C2×C4#1309399712yes—
595C2×C4#1309400612yes—
596C2×C4#1309400712yes—
597C2×C4#1309400712yes—
598C2×C4#1309401012yes—
599C2×C4#1309401012yes—
600C2×C4C2×D4×D4711yescharacteristic
601C2×C4C2×D4×D4711yescharacteristic
602C2×C4C22×C22⋊D4711yescharacteristic
603C2×C4C2×#1062535211yescharacteristic
604C2×C4C2×#1062535011yescharacteristic
605C2×C4C2×#1062535011yescharacteristic
606C8—42no—
607C8—944no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1568903812yes—
619C22#1568903812yes—
620C22#1568929412yes—
621C22#1568930412yes—
622C22C2×#1309399211yescharacteristic
623C22C2×#1309399711yescharacteristic
624C22C2×#1309400611yescharacteristic
625C4—42no—
626C4—82no—
627C4—1884no—
628C4—1882no—
629C4—1882no—
630C4—1884no—
631C4#1568903812yes—
632C4#1568903812yes—
633C4C2×#1309399611yescharacteristic
634C4C2×#1309399711yescharacteristic
635C4C2×#1309400711yescharacteristic
636C4C2×#1309401011yescharacteristic
637C2—21no—
638C2—22no—
639C2—21no—
640C2—82no—
641C2#2024460314yesdirect product factor
642C2C2×#1568903811yescharacteristic
643C2C2×#1568929411yescharacteristic
644C2C2×#1568930411yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#417C2
socleC23×C47#120
prime radicalC22×#41×C47C22
hypercenterC2×#417D47
hypocenterC47C2×#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#15689163C2semidirect
4. C22×#13093942C2semidirect
5. C2×#15689028C2semidirect
6. #20244603C2direct (N × H)
7. C2×#15688884C2semidirect
23. #15689163C22semidirect
29. C2×#13093942C22semidirect
31. #15689028C22semidirect
33. #15688884C22semidirect
327. C2×C47#2038semidirect
363. C47C2×#2038semidirect
641. C2#20244603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896942
C2×#156891632
C22×#130939512
C22×#130939422
C2×#156890282
#202446032
C2×#156888842
C2×C47×#4172
C2×#203847