Finite Group Databasebeta

← C2×#20243619 #26217138

Subgroups — C2×#20243619 #26217138

Order 12032.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689606C211yesmaximal, characteristic
2C2×#15689163C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic
4C2×#15688988C211yesmaximal, characteristic, complemented
5#20243619C218yesmaximal, direct product factor
6C2×#15688891C211yesmaximal, characteristic, complemented
7C2×#15688884C211yesmaximal, characteristic, complemented
8C2×C47×#417C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10#15689606—22no—
11#15689606—22no—
12#15689606—22no—
13#15689606C2214yes—
14C2×Q8×Dic47—21no—
15C2×D4×Dic47—22no—
16C2×D4×Dic47—21no—
17C2×#13093983—21no—
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47—21no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689163—22no—
23#15689163C2214yescomplemented
24C2×#13093957—21no—
25C2×#13093955—21no—
26C2×#13093951C418yescomplemented
27C2×#13093951C2214yes—
28#15688988—22no—
29#15688988C2214yescomplemented
30C2×C47⋊#95—22no—
31#15688891C2214yescomplemented
32#15688884C2214yescomplemented
33C22×#41×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C47×#417—22no—
37C47×#417C2214yes—
38C2×#103×C47—21no—
39C2×#102×C47—21no—
40C23×Dic47—21no—
41C23×Dic47—22no—
42C23×Dic47D412yes—
43C2×#10625329—21no—
44C2×#10625329—22no—
45C2×#10625329C2×C414yescomplemented
46C2×#10625329C2312yes—
47C22×C47⋊C8—21no—
48Q8×Dic47—24no—
49Q8×Dic47—24no—
50D4×Dic47—28no—
51D4×Dic47—24no—
52D4×Dic47—24no—
53D4×Dic47—28no—
54#13093983—24no—
55#13093983—21no—
56#13093983—21no—
57#13093983—24no—
58#13093983D412yes—
59#13093983C2312yes—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—24no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—24no—
67C2×C4⋊Dic47D412yes—
68C2×C4⋊Dic47D411yescharacteristic
69C2×C4⋊Dic47D411yescharacteristic
70C2×C4⋊Dic47C2312yes—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—21no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47C2×C414yescomplemented
78C2×C4×Dic47C2312yes—
79#13093957—24no—
80#13093955—24no—
81#13093951C2×C4116yescomplemented
82C47⋊#95—28no—
83C2×#41×C47—21no—
84C2×#41×C47—21no—
85C2×#41×C47—22no—
86C2×#41×C47—22no—
87C2×#41×C47C2×C414yes—
88C2×#41×C47D412yes—
89C2×#41×C47Q814yes—
90C2×#41×C47C2312yes—
91C22×Q8×C47D411yescharacteristic
92C22×D4×C47—21no—
93C22×D4×C47D411yescharacteristic
94C23×C4×C47—21no—
95C23×C4×C47—21no—
96C23×C4×C47C2311yescharacteristic
97C2×M16×C47—21no—
98C2×M16×C47—22no—
99C2×M16×C47—22no—
100C2×M16×C47C2312yes—
101C22×C8×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2312yes—
108#103×C47—24no—
109#102×C47—24no—
110C24×C47—21no—
111C24×C47C2×D411yescharacteristic
112#41×C47—24no—
113#41×C47—24no—
114#41×C47—24no—
115#41×C47—24no—
116#41×C47—24no—
117#41×C47—22no—
118#41×C47—22no—
119#41×C47C4⋊C418yes—
120#41×C47C22×C414yes—
121#41×C47C2×Q814yes—
122C2×Q8×C47—21no—
123C2×Q8×C47—22no—
124C2×Q8×C47C4⋊C414yes—
125C2×Q8×C47C2×D412yes—
126C2×D4×C47—24no—
127C2×D4×C47—22no—
128C2×D4×C47—24no—
129C2×D4×C47—22no—
130C2×D4×C47—21no—
131C2×D4×C47—22no—
132C2×D4×C47C4⋊C414yes—
133C2×D4×C47C2×D412yes—
134C22×C4×C47—21no—
135C22×C4×C47—24no—
136C22×C4×C47—22no—
137C22×C4×C47—24no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—44no—
141C22×C4×C47—41no—
142C22×C4×C47—41no—
143C22×C4×C47C22×C412yes—
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×Q812yes—
150C22×C4×C47#4112yes—
151C22×C4×C47#4112yes—
152C22×C4×C47C2411yescharacteristic
153C22×Dic47—24no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47—21no—
157C22×Dic47—22no—
158C22×Dic47—28no—
159C22×Dic47—22no—
160C22×Dic47—42no—
161C22×Dic47—42no—
162C22×Dic47—44no—
163C22×Dic47—84no—
164C22×Dic47C2×D414yes—
165M16×C47—22no—
166M16×C47—22no—
167M16×C47—42no—
168C2×C8×C47—22no—
169C2×C8×C47—42no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—41no—
173C4⋊C4×C47—41no—
174C22⋊Dic47—28no—
175C22⋊Dic47—22no—
176C22⋊Dic47—22no—
177C4⋊Dic47—28no—
178C4⋊Dic47—22no—
179C4⋊Dic47—21no—
180C4⋊Dic47—22no—
181C4⋊Dic47—21no—
182C4⋊Dic47—22no—
183C4⋊Dic47—22no—
184C4⋊Dic47C2×D412yes—
185C4⋊Dic47C2×D412yes—
186C4×Dic47—28no—
187C4×Dic47—24no—
188C4×Dic47—22no—
189C4×Dic47—22no—
190C4×Dic47—22no—
191C4×Dic47C22×C414yescomplemented
192#10625329—24no—
193#10625329—22no—
194#10625329C22×C414yescomplemented
195C2×C47⋊C8—24no—
196C2×C47⋊C8—22no—
197C23×C47—22no—
198C23×C47—22no—
199C23×C47—22no—
200C23×C47—24no—
201C23×C47—42no—
202C23×C47—42no—
203C23×C47C4×D412yes—
204C23×C47#12011yescharacteristic
205C23×C47#12011yescharacteristic
206C23×C47C22⋊Q812yes—
207C23×C47C22×D411yescharacteristic
208Q8×C47—22no—
209Q8×C47—24no—
210Q8×C47C2×C4⋊C414yes—
211D4×C47—24no—
212D4×C47—24no—
213D4×C47—28no—
214D4×C47—22no—
215D4×C47—24no—
216D4×C47C2×C4⋊C414yes—
217C2×C4×C47—22no—
218C2×C4×C47—24no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—28no—
222C2×C4×C47—44no—
223C2×C4×C47—42no—
224C2×C4×C47—82no—
225C2×C4×C47—82no—
226C2×C4×C47C2×C4⋊C412yes—
227C2×C4×C47C2×C4⋊C412yes—
228C2×C4×C47C4×D412yes—
229C2×C4×C47C4×D412yes—
230C2×C4×C47C4×D412yes—
231C2×C4×C47#12011yescharacteristic
232C2×C4×C47#12011yescharacteristic
233C2×C4×C47C22⋊Q812yes—
234C2×C4×C47C22⋊Q812yes—
235C2×C4×C47C22⋊Q812yes—
236C2×C4×C47#12312yes—
237C2×C4×C47#12312yes—
238C2×C4×C47C23×C411yescharacteristic
239C2×C4×C47C22×D411yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×Q811yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×Dic47—24no—
245C2×Dic47—22no—
246C2×Dic47—24no—
247C2×Dic47—22no—
248C2×Dic47—48no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—44no—
253C2×Dic47—42no—
254C2×Dic47—44no—
255C2×Dic47—82no—
256C2×Dic47—88no—
257C8×C47—42no—
258C47⋊C8—24no—
259C2×#1860—471nomaximal, Sylow
260C22×C47—24no—
261C22×C47—24no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—24no—
267C22×C47—48no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47#38512yes—
271C22×C47#38512yes—
272C22×C47#45412yes—
273C22×C47#45512yes—
274C22×C47C2×C4×D411yescharacteristic
275C22×C47C2×#12011yescharacteristic
276C22×C47C2×C22⋊Q811yescharacteristic
277C4×C47—24no—
278C4×C47—82no—
279C4×C47#38512yes—
280C4×C47#38512yes—
281C4×C47C22×C4⋊C411yescharacteristic
282C4×C47C2×C4×D411yescharacteristic
283C4×C47C2×C22⋊Q811yescharacteristic
284C4×C47C2×#12311yescharacteristic
285Dic47—44no—
286Dic47—44no—
287Dic47—42no—
288Dic47—42no—
289C2×#520—471no—
290C2×#428—471no—
291C22×#104—471no—
292C2×#417D4711yescharacteristic
293C2×#382—471no—
294#1860—478no—
295C2×#343—471no—
296C2×#339—471no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—22no—
300C2×C47—44no—
301C2×C47#186014yescomplemented
302C2×C47C2×#38511yescharacteristic
303C2×C47C2×#45511yescharacteristic
304C2×C47C2×#45411yescharacteristic
305C22×#41C2×D4711yescharacteristic
306C22×M16—471no—
307C22×M16C2×D4711yescharacteristic
308#520—474no—
309#520—942no—
310#520—942no—
311#520—942no—
312C2×C4×Q8—941no—
313C2×C4×D4—942no—
314C2×C4×D4—941no—
315C2×#117—471no—
316C2×#117—941no—
317C22×C4⋊C4—471no—
318C22×C4⋊C4—941no—
319C22×C4⋊C4C2×D4711yescharacteristic
320C22×C42—471no—
321#428—474no—
322#428—942no—
323C2×#107—941no—
324C2×#106—941no—
325C2×#104—478no—
326C2×#104—474no—
327#417—22no—
328#417C2×D4714yes—
329C2×#103—21no—
330C2×#102—21no—
331#382—474no—
332#382—942no—
333C2×#95—942no—
334#343—474no—
335#339—474no—
336C47C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41Dic9414yes—
342C2×#41C4×D4714yes—
343C2×#41C22⋊D4712yes—
344C2×#41C22×D4712yes—
345C22×Q8C22⋊D4711yescharacteristic
346C22×D4—21no—
347C22×D4C22⋊D4711yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—472no—
351C23×C4—942no—
352C23×C4—941no—
353C23×C4C22×D4711yescharacteristic
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—22no—
357C2×M16—474no—
358C2×M16—472no—
359C2×M16—941no—
360C2×M16—942no—
361C2×M16C22×D4712yes—
362C22×C8—21no—
363C22×C8—941no—
364C4×Q8—944no—
365C4×Q8—944no—
366C4×D4—948no—
367C4×D4—948no—
368C4×D4—944no—
369C4×D4—944no—
370#117—472no—
371#117—472no—
372#117—944no—
373#117—944no—
374#117—941no—
375#117—941no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—471no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—472no—
385C2×C4⋊C4—944no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—944no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4C22×D4712yes—
393C2×C22⋊C4—942no—
394C2×C22⋊C4—941no—
395C2×C42—474no—
396C2×C42—472no—
397C2×C42—942no—
398C2×C42—941no—
399C2×C42—942no—
400C2×C42—941no—
401#107—944no—
402#106—944no—
403#104—4716no—
404#103—24no—
405#102—24no—
406#95—948no—
407C24—21no—
408C24D4×D4711yescharacteristic
409#41—24no—
410#41—24no—
411#41—24no—
412#41—24no—
413#41—24no—
414#41—22no—
415#41—22no—
416#41Dic47⋊C418yes—
417#41C2×Dic9414yes—
418#41C2×C4×D4714yes—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8Dic47⋊C414yes—
422C2×Q8C2×C22⋊D4712yes—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4Dic47⋊C414yes—
430C2×D4C2×C22⋊D4712yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—44no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—474no—
441C22×C4—948no—
442C22×C4—942no—
443C22×C4—944no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—3764no—
449C22×C4—1884no—
450C22×C4—1882no—
451C22×C4—1882no—
452C22×C4C2×Dic9412yes—
453C22×C4C2×C4×D4712yes—
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4D4×D4711yescharacteristic
457C22×C4#1062535212yes—
458C22×C4#1062535212yes—
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C23×D4711yescharacteristic
462M16—22no—
463M16—22no—
464M16—42no—
465M16—474no—
466M16—944no—
467M16—942no—
468C2×C8—22no—
469C2×C8—42no—
470C2×C8—944no—
471C2×C8—942no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—472no—
477C4⋊C4—472no—
478C4⋊C4—948no—
479C4⋊C4—941no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C4⋊C4—941no—
483C4⋊C4—942no—
484C4⋊C4—942no—
485C22⋊C4—948no—
486C22⋊C4—942no—
487C22⋊C4—942no—
488C42—474no—
489C42—948no—
490C42—944no—
491C42—942no—
492C42—942no—
493C42—942no—
494C23—22no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23(C22⋊D47)⋊C412yes—
501C23#1309399211yescharacteristic
502C23#1309399211yescharacteristic
503C23#1309400112yes—
504C23C2×D4×D4711yescharacteristic
505Q8—24no—
506Q8—22no—
507Q8C2×Dic47⋊C414yes—
508D4—28no—
509D4—24no—
510D4—24no—
511D4—24no—
512D4—22no—
513D4C2×Dic47⋊C414yes—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—28no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—944no—
527C2×C4—3762no—
528C2×C4—3768no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4—1888no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1884no—
535C2×C4—1884no—
536C2×C4C2×Dic47⋊C412yes—
537C2×C4C2×Dic47⋊C412yes—
538C2×C4(C22⋊D47)⋊C412yes—
539C2×C4(C22⋊D47)⋊C412yes—
540C2×C4(C22⋊D47)⋊C412yes—
541C2×C4#1309399211yescharacteristic
542C2×C4#1309399211yescharacteristic
543C2×C4#1309400112yes—
544C2×C4#1309400112yes—
545C2×C4#1309400112yes—
546C2×C4#1309400512yes—
547C2×C4#1309400512yes—
548C2×C4C22×C4×D4711yescharacteristic
549C2×C4C2×D4×D4711yescharacteristic
550C2×C4C22×C22⋊D4711yescharacteristic
551C2×C4C22×Dic9411yescharacteristic
552C2×C4C2×#1062535211yescharacteristic
553C2×C4C2×#1062535211yescharacteristic
554C8—42no—
555C8—944no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—42no—
565C22—48no—
566C22#1568899512yes—
567C22#1568899512yes—
568C22#1568929412yes—
569C22#1568929912yes—
570C22C2×(C22⋊D47)⋊C411yescharacteristic
571C22C2×#1309399211yescharacteristic
572C22C2×#1309400111yescharacteristic
573C4—24no—
574C4—82no—
575C4—1884no—
576C4—1882no—
577C4—1884no—
578C4—1882no—
579C4#1568899512yes—
580C4#1568899512yes—
581C4C22×Dic47⋊C411yescharacteristic
582C4C2×(C22⋊D47)⋊C411yescharacteristic
583C4C2×#1309400111yescharacteristic
584C4C2×#1309400511yescharacteristic
585C2—21no—
586C2—22no—
587C2—21no—
588C2—44no—
589C2#2024361914yesdirect product factor
590C2C2×#1568899511yescharacteristic
591C2C2×#1568929911yescharacteristic
592C2C2×#1568929411yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#417C2
socleC23×C47#120
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#417D47
hypocenterC47C2×#1860
LCSG ▷ C2×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. C2×#15688988C2semidirect
5. #20243619C2direct (N × H)
6. C2×#15688891C2semidirect
7. C2×#15688884C2semidirect
23. #15689163C22semidirect
26. C2×#13093951C4semidirect
29. #15688988C22semidirect
31. #15688891C22semidirect
32. #15688884C22semidirect
45. C2×#10625329C2×C4semidirect
77. C2×C4×Dic47C2×C4semidirect
81. #13093951C2×C4semidirect
191. C4×Dic47C22×C4semidirect
194. #10625329C22×C4semidirect
301. C2×C47#1860semidirect
336. C47C2×#1860semidirect
589. C2#20243619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896062
C2×#156891632
C22×#130939512
C2×#156889882
#202436192
C2×#156888912
C2×#156888842
C2×C47×#4172
C2×#186047