Finite Group Databasebeta

← C2×#20254561 #27088313

Subgroups — C2×#20254561 #27088313

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689659C211yesmaximal, characteristic
2C22×#13094015C211yesmaximal, characteristic, complemented
3#20254561C2116yesmaximal, direct product factor
4C2×#15689524C212yesmaximal, complemented
5C2×#15689479C212yesmaximal, complemented
6C2×#15689441C211yesmaximal, characteristic
7C2×#15689451C211yesmaximal, characteristic, complemented
8C2×#15689437C211yesmaximal, characteristic
9C2×#15689432C212yesmaximal, complemented
10C2×#15689426C212yesmaximal, complemented
11C2×#15689173C211yesmaximal, characteristic, complemented
12C2×C47×#484C211yesmaximal, characteristic, complemented
13#15689659—24no—
14#15689659C2218yes—
15C2×#13094019—21no—
16C2×#13094015—21no—
17C2×#13094015—21no—
18C2×#13094015—24no—
19C2×#13094015C2212yes—
20C2×#13094015C2212yes—
21C2×#13094015C2211yescharacteristic
22C2×#13094015C2218yescomplemented
23C2×#13094013C2211yescharacteristic
24C2×#13094008—21no—
25C2×#13093998C2211yescharacteristic
26C2×Q8×Dic47C2211yescharacteristic
27C2×#13093986C2211yescharacteristic
28C2×(C22⋊D47)⋊C4—21no—
29C2×#13093982—21no—
30C22×C4⋊Dic47—21no—
31C22×C4⋊Dic47C2211yescharacteristic
32C22×Dic47⋊C4—21no—
33C22×C4×Dic47C2211yescharacteristic
34#15689524C22116yescomplemented
35#15689479C22116yescomplemented
36#15689451C2218yescomplemented
37#15689441C2218yes—
38#15689437C2218yes—
39#15689432C22116yescomplemented
40#15689426C22116yescomplemented
41#15689173C2218yescomplemented
42C2×#13093958C2212yes—
43C2×#13093955C2212yes—
44C2×#13093955C2212yes—
45C2×Dic47⋊C8C2212yes—
46C2×#13093948C2212yes—
47C2×#13093946C2212yes—
48C2×#13093944C2212yes—
49C2×C22⋊(C47⋊C8)C2211yescharacteristic
50C2×C8×Dic47C2212yes—
51C2×C22⋊Q8×C47C2211yescharacteristic
52C22×C4⋊C4×C47C2211yescharacteristic
53C47×#484C2218yescomplemented
54C2×#107×C47C2212yes—
55C2×#103×C47C2212yes—
56C2×C22⋊C8×C47C2211yescharacteristic
57C22×D188C2311yescharacteristic
58C22×C22⋊D47—21no—
59C23×Dic47—21no—
60C23×Dic47D411yescharacteristic
61C23×Dic47D411yescharacteristic
62C22×C4×D47—21no—
63C22×C47⋊C8C2312yes—
64#13094019—28no—
65#13094015—24no—
66#13094015—24no—
67#13094015—28no—
68#13094015—28no—
69#13094015—22no—
70#13094015C2318yes—
71#13094015C2314yes—
72#13094015C2318yes—
73#13094013—22no—
74#13094013C2314yes—
75#13094008—28no—
76#13093998—22no—
77#13093998C2314yes—
78Q8×Dic47—22no—
79Q8×Dic47C2314yes—
80#13093986—22no—
81#13093986C2314yes—
82(C22⋊D47)⋊C4—28no—
83#13093982—28no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—22no—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—28no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47C2312yes—
92C2×C4⋊Dic47C2314yes—
93C2×C4⋊Dic47C2311yescharacteristic
94C2×Dic47⋊C4—22no—
95C2×Dic47⋊C4—22no—
96C2×Dic47⋊C4—28no—
97C2×Dic47⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×(C2×D47)⋊C4—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47D411yescharacteristic
104C2×C4×Dic47D411yescharacteristic
105C2×C4×Dic47D414yes—
106C2×C4×Dic47C2311yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108C2×C4×Dic47C2314yes—
109#13093958C2318yes—
110#13093955C2318yes—
111#13093955C2318yes—
112Dic47⋊C8C2318yes—
113#13093948C2318yes—
114#13093946C2318yes—
115#13093944C2318yes—
116C22⋊(C47⋊C8)C2314yes—
117C8×Dic47C2318yes—
118C22×Q8×C47C2311yescharacteristic
119C23×C4×C47—21no—
120C23×C4×C47C2311yescharacteristic
121C22×C8×C47C2312yes—
122C22⋊Q8×C47—22no—
123C22⋊Q8×C47C2314yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47C2314yes—
128C2×C4⋊C4×C47C2312yes—
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47—21no—
131#107×C47C2318yes—
132#103×C47C2318yes—
133C22⋊C8×C47C2314yes—
134C24×C47C2×D411yescharacteristic
135C23×D47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—24no—
138C2×Q8×C47C2412yes—
139C22×C4×C47—24no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—24no—
143C22×C4×C47—22no—
144C22×C4×C47—44no—
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D412yes—
147C22×C4×C47C2412yes—
148C22×C4×C47C2411yescharacteristic
149C2×C22⋊D47—24no—
150C2×C22⋊D47—44no—
151C22×Dic47—24no—
152C22×Dic47—21no—
153C22×Dic47—24no—
154C22×Dic47—22no—
155C22×Dic47—42no—
156C22×Dic47—44no—
157C22×Dic47C2×D411yescharacteristic
158C22×Dic47C2×D411yescharacteristic
159C22×Dic47C2×D411yescharacteristic
160C22×Dic47C2×D411yescharacteristic
161C22×Dic47C2×D414yes—
162C22×Dic47C2×D414yes—
163C2×D188—24no—
164C2×D188—21no—
165C2×D188C2412yes—
166C2×C4×D47—24no—
167C2×C4×D47—44no—
168C2×C8×C47—24no—
169C2×C8×C47C2414yes—
170C4⋊C4×C47—24no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—24no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47C2414yes—
175C4⋊C4×C47C2412yes—
176C22⋊C4×C47—24no—
177(C2×D47)⋊C4—24no—
178(C2×D47)⋊C4—24no—
179(C2×D47)⋊C4—24no—
180(C2×D47)⋊C4—24no—
181C4⋊Dic47—24no—
182C4⋊Dic47—22no—
183C4⋊Dic47—21no—
184C4⋊Dic47—28no—
185C4⋊Dic47—28no—
186C4⋊Dic47—24no—
187C4⋊Dic47—24no—
188C4⋊Dic47C2414yes—
189C4⋊Dic47C2412yes—
190Dic47⋊C4—28no—
191Dic47⋊C4—28no—
192Dic47⋊C4—24no—
193C4×Dic47—24no—
194C4×Dic47C2×D414yes—
195C4×Dic47C2×D412yes—
196C4×Dic47C2×D412yes—
197C4×Dic47C2×D414yes—
198C4×Dic47C2412yes—
199C4×Dic47C2412yes—
200C2×C47⋊C8—24no—
201C2×C47⋊C8C2414yes—
202C23×C47—22no—
203C23×C47—22no—
204C23×C47#13514yes—
205C23×C47C22×D412yes—
206C23×C47C22×D411yescharacteristic
207C22×D47—22no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211Q8×C47—24no—
212Q8×C47—42no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—48no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—44no—
223C2×C4×C47C22×D412yes—
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C472−1+414yes—
226C2×C4×C47C2511yescharacteristic
227C22⋊D47—48no—
228C2×Dic47—28no—
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—22no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—24no—
235C2×Dic47—44no—
236C2×Dic47—48no—
237C2×Dic47—44no—
238C2×Dic47—42no—
239C2×Dic47C22×D412yes—
240C2×Dic47C22×D412yes—
241C2×Dic47C22×D412yes—
242C2×Dic47C22×D412yes—
243D188—24no—
244D188—42no—
245C4×D47—48no—
246C8×C47—24no—
247C47⋊C8—24no—
248C2×#3232—471nomaximal, Sylow
249C22×C47—22no—
250C22×C47—28no—
251C22×C47—22no—
252C22×C47#53612yes—
253C22×C47C2×#13514yes—
254C22×C47C2×#13512yes—
255C22×C47#57512yes—
256C22×C47C23×D411yescharacteristic
257C2×D47—42no—
258C2×D47—42no—
259C2×D47—42no—
260C2×D47—84no—
261C4×C47—22no—
262C4×C47—42no—
263C4×C47—42no—
264C4×C47—44no—
265C4×C47#53612yes—
266C4×C47C2×2−1+412yes—
267Dic47—22no—
268Dic47—22no—
269Dic47—22no—
270Dic47—22no—
271Dic47—44no—
272Dic47—42no—
273C2×#529—471no—
274C22×#125—471no—
275#3232—4716no—
276C2×#499—472no—
277C2×#488—472no—
278C2×#484D4711yescharacteristic, complemented
279C2×#481—471no—
280C2×#483—471no—
281C2×#480—471no—
282C2×#479—472no—
283C2×#478—472no—
284C2×#431—471no—
285C2×C47—24no—
286C2×C47#323214yescomplemented
287C2×C47C2×#53611yescharacteristic
288C2×C47C22×#13511yescharacteristic
289C2×C47C2×#57511yescharacteristic
290D47—82no—
291#529—478no—
292#529—944no—
293C2×#126—941no—
294C2×#125—472no—
295C2×#125—472no—
296C2×#125—471no—
297C2×#125—478no—
298C2×#125—941no—
299C2×#125—941no—
300C2×#125—944no—
301C2×#124—471no—
302C2×#123—941no—
303C2×C22⋊Q8C2×D4711yescharacteristic
304C2×#121—471no—
305C2×C4×Q8—471no—
306C2×C4×D4—471no—
307C2×C4×D4—941no—
308C2×#117—941no—
309C22×C4⋊C4—471no—
310C22×C4⋊C4—941no—
311C22×C4⋊C4—941no—
312C22×C4⋊C4C2×D4711yescharacteristic
313C22×C42—471no—
314#499—4716no—
315#488—4716no—
316#484C2×D4718yescomplemented
317#483—478no—
318#481—478no—
319#480—478no—
320#479—4716no—
321#478—4716no—
322#431—478no—
323C2×#107—472no—
324C2×#107C2×D4712yes—
325C2×#106—472no—
326C2×#106—472no—
327C2×C4⋊C8—472no—
328C2×#103—472no—
329C2×#103C2×D4712yes—
330C2×#102—472no—
331C2×#102—472no—
332C2×C22⋊C8—471no—
333C2×C22⋊C8C2×D4711yescharacteristic
334C2×C4×C8—472no—
335C47C2×#323211yescharacteristic, complemented, Sylow
336C22×Q8C22×D4711yescharacteristic
337C22×D4—471no—
338C22×D4—941no—
339C23×C4—21no—
340C23×C4—471no—
341C23×C4—471no—
342C23×C4—941no—
343C23×C4—941no—
344C23×C4C22×D4711yescharacteristic
345C22×C8—472no—
346C22×C8C22×D4712yes—
347#126—948no—
348#125—478no—
349#125—478no—
350#125—474no—
351#125—948no—
352#125—944no—
353#125—944no—
354#125—948no—
355#125—942no—
356#124—474no—
357#124—942no—
358#123—948no—
359C22⋊Q8—22no—
360C22⋊Q8C22×D4714yes—
361#121—474no—
362#121—942no—
363C4×Q8—474no—
364C4×Q8—942no—
365C4×D4—474no—
366C4×D4—942no—
367C4×D4—948no—
368#117—948no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—472no—
373C2×C4⋊C4—474no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—948no—
376C2×C4⋊C4—942no—
377C2×C4⋊C4—942no—
378C2×C4⋊C4—948no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4—941no—
383C2×C4⋊C4—941no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4C22×D4712yes—
387C2×C4⋊C4C22×D4714yes—
388C2×C4⋊C4C22×D4711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—941no—
391C2×C22⋊C4—941no—
392C2×C22⋊C4—941no—
393C2×C22⋊C4—941no—
394C2×C42—471no—
395C2×C42—471no—
396C2×C42—474no—
397C2×C42—471no—
398C2×C42—471no—
399C2×C42—474no—
400C2×C42—941no—
401#107—478no—
402#107C22×D4718yes—
403#106—478no—
404#106—478no—
405C4⋊C8—478no—
406#103—478no—
407#103C22×D4718yes—
408#102—478no—
409#102—478no—
410C22⋊C8—474no—
411C22⋊C8C22×D4714yes—
412C4×C8—478no—
413C24—941no—
414C24D4×D4711yescharacteristic
415C2×Q8—21no—
416C2×Q8—24no—
417C2×Q8C23×D4712yes—
418C2×D4—472no—
419C2×D4—944no—
420C2×D4—941no—
421C2×D4—944no—
422C2×D4—1884no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—44no—
429C22×C4—474no—
430C22×C4—471no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—471no—
434C22×C4—474no—
435C22×C4—944no—
436C22×C4—944no—
437C22×C4—944no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—1884no—
441C22×C4—1882no—
442C22×C4—1884no—
443C22×C4D4×D4712yes—
444C22×C4D4×D4711yescharacteristic
445C22×C4C23×D4712yes—
446C22×C4C23×D4711yescharacteristic
447C2×C8—24no—
448C2×C8—474no—
449C2×C8—944no—
450C2×C8C23×D4714yes—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—474no—
456C4⋊C4—472no—
457C4⋊C4—948no—
458C4⋊C4—948no—
459C4⋊C4—944no—
460C4⋊C4—948no—
461C4⋊C4—948no—
462C4⋊C4—944no—
463C4⋊C4—944no—
464C4⋊C4—944no—
465C4⋊C4—942no—
466C4⋊C4—941no—
467C4⋊C4C23×D4714yes—
468C4⋊C4C23×D4712yes—
469C22⋊C4—24no—
470C22⋊C4—944no—
471C22⋊C4—944no—
472C22⋊C4—944no—
473C22⋊C4—944no—
474C42—474no—
475C42—472no—
476C42—472no—
477C42—474no—
478C42—472no—
479C42—472no—
480C42—944no—
481C23—22no—
482C23—22no—
483C23—942no—
484C23—1882no—
485C23—1882no—
486C23—1882no—
487C23#1309404714yes—
488C23C2×D4×D4712yes—
489C23C2×D4×D4711yescharacteristic
490Q8—24no—
491Q8—42no—
492D4—944no—
493D4—1888no—
494D4—1882no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—472no—
506C2×C4—472no—
507C2×C4—472no—
508C2×C4—472no—
509C2×C4—948no—
510C2×C4—942no—
511C2×C4—942no—
512C2×C4—942no—
513C2×C4—942no—
514C2×C4—942no—
515C2×C4—944no—
516C2×C4—1888no—
517C2×C4—1884no—
518C2×C4—1888no—
519C2×C4—1884no—
520C2×C4—1882no—
521C2×C4C2×D4×D4712yes—
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4#1309407114yes—
524C2×C4C24×D4711yescharacteristic
525C8—24no—
526C8—944no—
527C22—22no—
528C22—28no—
529C22—22no—
530C22—3764no—
531C22—1882no—
532C22—1882no—
533C22—1882no—
534C22#1568969512yes—
535C22C2×#1309404714yes—
536C22C2×#1309404712yes—
537C22#1568991912yes—
538C22C22×D4×D4711yescharacteristic
539C4—22no—
540C4—44no—
541C4—42no—
542C4—42no—
543C4—942no—
544C4—942no—
545C4—942no—
546C4—942no—
547C4—1884no—
548C4—1882no—
549C4#1568969512yes—
550C4C2×#1309407112yes—
551C2—24no—
552C2—3762no—
553C2#2025456114yesdirect product factor
554C2C2×#1568969511yescharacteristic
555C2C22×#1309404711yescharacteristic
556C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#484C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#484D47
hypocenterC47C2×#3232
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×#13094015C2semidirect
3. #20254561C2direct (N × H)
4. C2×#15689524C2semidirect
5. C2×#15689479C2semidirect
7. C2×#15689451C2semidirect
9. C2×#15689432C2semidirect
10. C2×#15689426C2semidirect
11. C2×#15689173C2semidirect
12. C2×C47×#484C2semidirect
22. C2×#13094015C22semidirect
34. #15689524C22semidirect
35. #15689479C22semidirect
36. #15689451C22semidirect
39. #15689432C22semidirect
40. #15689426C22semidirect
41. #15689173C22semidirect
53. C47×#484C22semidirect
278. C2×#484D47semidirect
286. C2×C47#3232semidirect
316. #484C2×D47semidirect
335. C47C2×#3232semidirect
553. C2#20254561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896592
C22×#130940152
#202545612
C2×#156895242
C2×#156894792
C2×#156894412
C2×#156894512
C2×#156894372
C2×#156894322
C2×#156894262
C2×#156891732
C2×C47×#4842
C2×#323247