Finite Group Databasebeta

← C2×#20244586 #26243736

Subgroups — C2×#20244586 #26243736

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094004C211yesmaximal, characteristic
2C22×#13093949C211yesmaximal, characteristic, complemented
3C22×#13093947C211yesmaximal, characteristic, complemented
4C22×(C2×D47)⋊C8C211yesmaximal, characteristic
5C2×#15688980C211yesmaximal, characteristic
6#20244586C218yesmaximal, direct product factor
7C2×#15688885C211yesmaximal, characteristic, complemented
8C22×#106×C47C211yesmaximal, characteristic, complemented
9C23×Dic94C2211yescharacteristic
10C23×C4×D47C2211yescharacteristic
11C23×C47⋊C8C2211yescharacteristic
12C2×#13094004—24no—
13C2×#13094004—22no—
14C2×#13094004—24no—
15C2×#13094004C2214yes—
16C22×C4⋊Dic47—21no—
17C22×C4⋊Dic47C2211yescharacteristic
18C22×(C2×D47)⋊C4—21no—
19C22×(C2×D47)⋊C4—21no—
20C2×#13093949—24no—
21C2×#13093949C2214yescomplemented
22C2×#13093947—24no—
23C2×#13093947C2214yescomplemented
24C2×(C2×D47)⋊C8—24no—
25C2×(C2×D47)⋊C8C2214yes—
26#15688980—22no—
27#15688980C2214yes—
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×D47D411yescharacteristic
36C22×Dic94—22no—
37C22×Dic94—22no—
38C22×Dic94—22no—
39C22×Dic94—22no—
40C22×Dic94—21no—
41C22×Dic94—22no—
42C22×Dic94D414yes—
43C22×Dic94C2312yes—
44C23×Dic47—21no—
45C23×Dic47—21no—
46C23×Dic47D411yescharacteristic
47C22×C4×D47—22no—
48C22×C4×D47—22no—
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47D412yes—
54C22×C4×D47C2312yes—
55C22×C47⋊C8—22no—
56C22×C47⋊C8—22no—
57C22×C47⋊C8—22no—
58C22×C47⋊C8C2312yes—
59#13094004—216no—
60#13094004—28no—
61#13094004—28no—
62C2×C4⋊Dic47—28no—
63C2×C4⋊Dic47—24no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47C2312yes—
68C2×(C2×D47)⋊C4—28no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—44no—
72#13093949—28no—
73#13093947—28no—
74(C2×D47)⋊C8—28no—
75C47⋊#95—24no—
76C23×C4×C47—21no—
77C23×C4×C47—21no—
78C23×C4×C47C2311yescharacteristic
79C22×C8×C47—22no—
80C22×C8×C47—22no—
81C22×C8×C47D414yes—
82C22×C8×C47C2312yes—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47D414yes—
89C2×C4⋊C4×C47C2312yes—
90C2×C4⋊C4×C47C2312yes—
91#106×C47—28no—
92C24×C47C2×D411yescharacteristic
93C23×D47—22no—
94C23×D47—22no—
95C23×D47—22no—
96C23×D47—22no—
97C23×D47—22no—
98C23×D47—22no—
99C23×D47SD1614yes—
100C23×D47C2×D412yes—
101C22×C4×C47—24no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—42no—
105C22×C4×C47—42no—
106C22×C4×C47—42no—
107C22×C4×C47—42no—
108C22×C4×C47—42no—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D412yes—
111C22×C4×C47C2×D412yes—
112C22×C4×C47C2×D412yes—
113C22×C4×C47#4112yes—
114C22×C4×C47#4112yes—
115C22×C4×C47#4112yes—
116C22×C4×C47C2411yescharacteristic
117C22×Dic47—24no—
118C22×Dic47—22no—
119C22×Dic47—22no—
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—22no—
123C22×Dic47—42no—
124C22×Dic47—42no—
125C22×Dic47—42no—
126C22×Dic47—42no—
127C22×Dic47—42no—
128C22×Dic47C2×D412yes—
129C2×C4×D47—24no—
130C2×C4×D47—24no—
131C2×C4×D47—24no—
132C2×C4×D47—22no—
133C2×C4×D47—22no—
134C2×C4×D47—22no—
135C2×C4×D47—22no—
136C2×C4×D47—22no—
137C2×C4×D47—22no—
138C2×C4×D47—44no—
139C2×C4×D47—44no—
140C2×C4×D47—44no—
141C2×C4×D47—44no—
142C2×Dic94—28no—
143C2×Dic94—28no—
144C2×Dic94—22no—
145C2×Dic94—22no—
146C2×Dic94—22no—
147C2×Dic94—22no—
148C2×Dic94—24no—
149C2×Dic94—22no—
150C2×Dic94—44no—
151C2×Dic94—42no—
152C2×Dic94—42no—
153C2×Dic94—44no—
154C2×Dic94C2×D414yes—
155C2×C8×C47—28no—
156C2×C8×C47—22no—
157C2×C8×C47—22no—
158C2×C8×C47C2×D414yes—
159C4⋊C4×C47—24no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47C2×D414yes—
165(C2×D47)⋊C4—216no—
166(C2×D47)⋊C4—48no—
167C4⋊Dic47—216no—
168C4⋊Dic47—22no—
169C4⋊Dic47—22no—
170C4⋊Dic47—42no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—44no—
175C23×C47#12012yes—
176C23×C47#12112yes—
177C23×C47#12312yes—
178C23×C47C2×SD1612yes—
179C23×C47#13512yes—
180C23×C47#13712yes—
181C23×C47#13712yes—
182C23×C47C22×D411yescharacteristic
183C22×D47—22no—
184C22×D47—22no—
185C22×D47—22no—
186C22×D47—22no—
187C22×D47—22no—
188C22×D47—22no—
189C22×D47—28no—
190C22×D47—28no—
191C22×D47—28no—
192C22×D47—44no—
193C22×D47—44no—
194C22×D47—44no—
195C22×D47—44no—
196C22×D47C2×SD1614yes—
197C2×C4×C47—24no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—48no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—84no—
205C2×C4×C47#12012yes—
206C2×C4×C47#12114yes—
207C2×C4×C47#12114yes—
208C2×C4×C47#12112yes—
209C2×C4×C47#12314yes—
210C2×C4×C47#12312yes—
211C2×C4×C47#12414yes—
212C2×C4×C47C22×D411yescharacteristic
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C47C2×#4111yescharacteristic
216C2×C4×C47C2×#4111yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×Dic47—22no—
219C2×Dic47—24no—
220C2×Dic47—22no—
221C2×Dic47—22no—
222C2×Dic47—42no—
223C2×Dic47—42no—
224C2×Dic47—48no—
225C2×Dic47—44no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47—42no—
229C2×Dic47—84no—
230C4×D47—42no—
231C4×D47—42no—
232C4×D47—42no—
233C4×D47—42no—
234C4×D47—48no—
235Dic94—24no—
236Dic94—24no—
237Dic94—42no—
238Dic94—42no—
239Dic94—48no—
240C8×C47—24no—
241C47⋊C8—42no—
242C2×#2035—471nomaximal, Sylow
243C22×C47#39414yes—
244C22×C47#44814yes—
245C22×C47#45214yes—
246C22×C47#46514yes—
247C22×C47#47014yes—
248C22×C47#48314yes—
249C22×C47#48514yes—
250C22×C47C2×#12011yescharacteristic
251C22×C47C2×#12111yescharacteristic
252C22×C47C2×#12311yescharacteristic
253C22×C47C22×SD1611yescharacteristic
254C22×C47C2×#13511yescharacteristic
255C22×C47C2×#13711yescharacteristic
256C22×C47C2×#13711yescharacteristic
257C2×D47—24no—
258C2×D47—24no—
259C2×D47—24no—
260C2×D47—42no—
261C2×D47—42no—
262C2×D47—42no—
263C2×D47—42no—
264C2×D47—416no—
265C4×C47—44no—
266C4×C47—82no—
267C4×C47#39414yes—
268C4×C47C2×#12111yescharacteristic
269C4×C47C2×#12111yescharacteristic
270C4×C47C2×#12311yescharacteristic
271C4×C47C2×#12411yescharacteristic
272Dic47—44no—
273Dic47—42no—
274Dic47—82no—
275C22×C22⋊Q8—471no—
276C22×#106D4711yescharacteristic, complemented
277C22×#103—471no—
278C22×#103—471no—
279C22×C22⋊C8—471no—
280C2×#380—471no—
281#2035—478no—
282C2×#340—471no—
283C2×C47#203518yescomplemented
284C2×C47C2×#39411yescharacteristic
285C2×C47C2×#44811yescharacteristic
286C2×C47C2×#45211yescharacteristic
287C2×C47C2×#46511yescharacteristic
288C2×C47C2×#47011yescharacteristic
289C2×C47C2×#48311yescharacteristic
290C2×C47C2×#48511yescharacteristic
291D47—44no—
292C23×Q8—471no—
293C24×C4—471no—
294C23×C8—471no—
295C23×C8C2×D4711yescharacteristic
296C2×C22⋊Q8—474no—
297C2×C22⋊Q8—942no—
298C2×C22⋊Q8—944no—
299C2×C22⋊Q8—944no—
300C22×C4⋊C4—471no—
301C22×C4⋊C4—941no—
302C22×C4⋊C4C2×D4711yescharacteristic
303C22×C4⋊C4C2×D4711yescharacteristic
304C22×C22⋊C4—941no—
305C22×C22⋊C4—941no—
306C2×#106—24no—
307C2×#106C2×D4714yescomplemented
308C2×#103—474no—
309C2×#103—474no—
310C2×#103—944no—
311C2×#103—944no—
312C2×C22⋊C8—474no—
313C2×C22⋊C8—944no—
314#380—474no—
315#380—942no—
316C2×#95—941no—
317#340—474no—
318C47C2×#203511yescharacteristic, complemented, Sylow
319C25—471no—
320C22×Q8—474no—
321C22×Q8—472no—
322C22×Q8—941no—
323C22×Q8—942no—
324C22×Q8—942no—
325C22×Q8—942no—
326C22×Q8—942no—
327C22×Q8—942no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—471no—
331C23×C4—472no—
332C23×C4—472no—
333C23×C4—941no—
334C23×C4—942no—
335C23×C4—942no—
336C23×C4—942no—
337C23×C4—942no—
338C23×C4—942no—
339C23×C4—942no—
340C23×C4—941no—
341C23×C4C22×D4711yescharacteristic
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—472no—
345C22×C8—942no—
346C22×C8—942no—
347C22×C8—942no—
348C22×C8D18814yes—
349C22×C8C22×D4712yes—
350C22⋊Q8—948no—
351C22⋊Q8—9416no—
352C22⋊Q8—948no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—472no—
359C2×C4⋊C4—944no—
360C2×C4⋊C4—948no—
361C2×C4⋊C4—942no—
362C2×C4⋊C4—942no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4C22⋊D4714yes—
365C2×C4⋊C4C22×D4712yes—
366C2×C4⋊C4C22×D4712yes—
367C2×C22⋊C4—944no—
368C2×C22⋊C4—948no—
369C2×C22⋊C4—944no—
370C2×C22⋊C4—1884no—
371#106—28no—
372#103—948no—
373#103—948no—
374C22⋊C8—948no—
375#95—944no—
376C24—474no—
377C24—472no—
378C24—942no—
379C24—942no—
380C24—942no—
381C24—942no—
382C24—942no—
383C24—942no—
384C24D4×D4711yescharacteristic
385C2×Q8—474no—
386C2×Q8—944no—
387C2×Q8—942no—
388C2×Q8—948no—
389C2×Q8—948no—
390C2×Q8—942no—
391C2×Q8—942no—
392C2×Q8—942no—
393C2×Q8—942no—
394C2×Q8—1884no—
395C2×Q8—1882no—
396C2×Q8—1882no—
397C2×Q8—1884no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—472no—
407C22×C4—944no—
408C22×C4—942no—
409C22×C4—942no—
410C22×C4—942no—
411C22×C4—942no—
412C22×C4—944no—
413C22×C4—944no—
414C22×C4—944no—
415C22×C4—942no—
416C22×C4—942no—
417C22×C4—942no—
418C22×C4—942no—
419C22×C4—942no—
420C22×C4—942no—
421C22×C4—942no—
422C22×C4—1882no—
423C22×C4—1882no—
424C22×C4—1882no—
425C22×C4—1882no—
426C22×C4—1882no—
427C22×C4—1884no—
428C22×C4—1884no—
429C22×C4—1884no—
430C22×C4—1884no—
431C22×C4C2×D18812yes—
432C22×C4#1062535012yes—
433C22×C4D4×D4711yescharacteristic
434C22×C4D4×D4712yes—
435C22×C4#1062535412yes—
436C22×C4#1062535412yes—
437C22×C4C2×C22⋊D4712yes—
438C22×C4C23×D4711yescharacteristic
439C2×C8—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—942no—
443C2×C8—942no—
444C2×C8—942no—
445C2×C8—1884no—
446C2×C8C2×D18814yes—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—9416no—
453C4⋊C4—942no—
454C4⋊C4—942no—
455C4⋊C4—1882no—
456C4⋊C4C2×C22⋊D4714yes—
457C22⋊C4—9416no—
458C22⋊C4—1888no—
459C23—474no—
460C23—948no—
461C23—942no—
462C23—948no—
463C23—942no—
464C23—942no—
465C23—942no—
466C23—942no—
467C23—942no—
468C23—948no—
469C23—1884no—
470C23—1884no—
471C23—1884no—
472C23—1884no—
473C23#1309399212yes—
474C23#1309399912yes—
475C23#1309400912yes—
476C23SD16×D4712yes—
477C23#1309404512yes—
478C23#1309405312yes—
479C23#1309405312yes—
480C23C2×D4×D4711yescharacteristic
481Q8—944no—
482Q8—944no—
483Q8—1888no—
484Q8—1882no—
485Q8—1882no—
486C2×C4—24no—
487C2×C4—48no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4—944no—
495C2×C4—942no—
496C2×C4—942no—
497C2×C4—942no—
498C2×C4—3764no—
499C2×C4—1882no—
500C2×C4—1882no—
501C2×C4—1882no—
502C2×C4—1884no—
503C2×C4—1888no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4—1888no—
507C2×C4—1882no—
508C2×C4—1882no—
509C2×C4—1882no—
510C2×C4—1882no—
511C2×C4#1309399212yes—
512C2×C4#1309399814yes—
513C2×C4#1309399912yes—
514C2×C4#1309399914yes—
515C2×C4#1309400912yes—
516C2×C4#1309400914yes—
517C2×C4#1309401314yes—
518C2×C4C2×D4×D4711yescharacteristic
519C2×C4C22×C22⋊D4711yescharacteristic
520C2×C4C22×D18811yescharacteristic
521C2×C4C2×#1062535011yescharacteristic
522C2×C4C2×#1062535411yescharacteristic
523C2×C4C2×#1062535411yescharacteristic
524C8—24no—
525C8—1882no—
526C22—944no—
527C22—944no—
528C22—944no—
529C22—1882no—
530C22—1882no—
531C22—1882no—
532C22—18816no—
533C22—1882no—
534C22#1568904014yes—
535C22#1568926014yes—
536C22#1568928214yes—
537C22#1568935314yes—
538C22#1568938214yes—
539C22#1568945514yes—
540C22#1568946714yes—
541C22C2×#1309399211yescharacteristic
542C22C2×#1309399911yescharacteristic
543C22C2×#1309400911yescharacteristic
544C22C2×SD16×D4711yescharacteristic
545C22C2×#1309404511yescharacteristic
546C22C2×#1309405311yescharacteristic
547C22C2×#1309405311yescharacteristic
548C4—44no—
549C4—82no—
550C4—3762no—
551C4—1882no—
552C4—1884no—
553C4#1568904014yes—
554C4C2×#1309399811yescharacteristic
555C4C2×#1309399911yescharacteristic
556C4C2×#1309400911yescharacteristic
557C4C2×#1309401311yescharacteristic
558C2—1884no—
559C2#2024458618yesdirect product factor
560C2C2×#1568904011yescharacteristic
561C2C2×#1568926011yescharacteristic
562C2C2×#1568928211yescharacteristic
563C2C2×#1568935311yescharacteristic
564C2C2×#1568938211yescharacteristic
565C2C2×#1568945511yescharacteristic
566C2C2×#1568946711yescharacteristic
subgroupG/H
centerC24D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#106×C47C2
socleC24×C47C2×D4
prime radicalC24×D47D4
hypercenterC22×#106D47
hypocenterC47C2×#2035
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×#13093949C2semidirect
3. C22×#13093947C2semidirect
6. #20244586C2direct (N × H)
7. C2×#15688885C2semidirect
8. C22×#106×C47C2semidirect
21. C2×#13093949C22semidirect
23. C2×#13093947C22semidirect
29. #15688885C22semidirect
34. C2×#106×C47C22semidirect
276. C22×#106D47semidirect
283. C2×C47#2035semidirect
307. C2×#106C2×D47semidirect
318. C47C2×#2035semidirect
559. C2#20244586direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940042
C22×#130939492
C22×#130939472
C22×(C2×D47)⋊C82
C2×#156889802
#202445862
C2×#156888852
C22×#106×C472
C2×#203547