Finite Group Databasebeta

← C2×#20254631 #27088442

Subgroups — C2×#20254631 #27088442

Order 12032.

1790 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×#15689678C211yesmaximal, characteristic, complemented
2C2×#15689658C211yesmaximal, characteristic
3#20254631C2116yesmaximal, direct product factor
4C2×#15689533C211yesmaximal, characteristic, complemented
5C2×#15689485C211yesmaximal, characteristic, complemented
6C2×#15689483C211yesmaximal, characteristic, complemented
7C2×#15689467C212yesmaximal, complemented
8C2×#15689450C212yesmaximal
9C2×#15689429C212yesmaximal, complemented
10C2×#15689422C212yesmaximal, complemented
11C2×#15689178C211yesmaximal, characteristic, complemented
12C2×C47×#501C211yesmaximal, characteristic, complemented
13#15689678—24no—
14#15689678C2218yescomplemented
15C2×#13094024C2211yescharacteristic
16#15689658—24no—
17#15689658C2218yes—
18C2×#13094019—21no—
19C2×#13094015C2212yes—
20C2×#13094012C2211yescharacteristic
21C2×#13094009—21no—
22C2×#13094004—21no—
23C2×#13094004C2211yescharacteristic
24C2×#13094000—21no—
25C2×#13093999C2211yescharacteristic
26C2×Q8×Dic47—21no—
27C2×#13093989—21no—
28C2×#13093989C2211yescharacteristic
29C2×#13093986—21no—
30C2×#13093986C2211yescharacteristic
31C2×#13093982—21no—
32C2×#13093982C2212yes—
33C2×C42×D47C2211yescharacteristic
34#15689533C2218yescomplemented
35#15689485C2218yescomplemented
36#15689483C2218yescomplemented
37#15689467C22116yescomplemented
38#15689450C22116yes—
39#15689429C22116yescomplemented
40#15689422C22116yescomplemented
41#15689178C2218yescomplemented
42C2×#13093957C2212yes—
43C2×#13093955C2212yes—
44C2×Dic47⋊C8C2212yes—
45C2×#13093949C2212yes—
46C2×#13093947C2212yes—
47C2×#13093946C2212yes—
48C2×#13093944C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×#13093935C2211yescharacteristic
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×#125×C47C2211yescharacteristic
53C47×#501C2218yescomplemented
54C2×#107×C47C2212yes—
55C2×#106×C47C2212yes—
56C2×#97×C47C2211yescharacteristic
57C22×Dic94—21no—
58C22×Dic94C2311yescharacteristic
59C22×D188—21no—
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C4×D47D411yescharacteristic
63C22×C4×D47D411yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C22×C47⋊C8C2312yes—
66#13094024—22no—
67#13094024C2314yes—
68#13094019—28no—
69#13094015—24no—
70#13094015C2318yes—
71#13094012—22no—
72#13094012C2314yes—
73#13094009—28no—
74#13094004—28no—
75#13094004—22no—
76#13094004C2314yes—
77#13094000—28no—
78#13093999—22no—
79#13093999C2314yes—
80Q8×Dic47—28no—
81#13093989—28no—
82#13093989—22no—
83#13093989C2314yes—
84#13093986—28no—
85#13093986—22no—
86#13093986C2314yes—
87#13093982—24no—
88#13093982—28no—
89#13093982C2318yes—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—22no—
93C2×C4⋊Dic47C2312yes—
94C2×Dic47⋊C4—22no—
95C2×Dic47⋊C4—21no—
96C2×(C2×D47)⋊C4—22no—
97C2×(C2×D47)⋊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×Dic47—22no—
104C2×C4×Dic47D411yescharacteristic
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47C2311yescharacteristic
107C42×D47D414yes—
108C42×D47C2314yes—
109#13093957C2318yes—
110#13093955C2318yes—
111Dic47⋊C8C2318yes—
112#13093949C2318yes—
113#13093947C2318yes—
114#13093946C2318yes—
115#13093944C2318yes—
116(C2×D47)⋊C8C2318yes—
117#13093935C2314yes—
118C22×Q8×C47—21no—
119C22×C8×C47C2312yes—
120C4⋊Q8×C47—22no—
121C4⋊Q8×C47C2314yes—
122#125×C47—22no—
123#125×C47C2314yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2312yes—
130C2×C42×C47C2311yescharacteristic
131#107×C47C2318yes—
132#106×C47C2318yes—
133#97×C47C2314yes—
134C23×D47—21no—
135C23×D47C2×D411yescharacteristic
136C2×Q8×C47—24no—
137C2×Q8×C47—44no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—22no—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2411yescharacteristic
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47C2×D411yescharacteristic
147C22×Dic47C2×D411yescharacteristic
148C22×Dic47C2×D411yescharacteristic
149C2×D188—24no—
150C2×D188—24no—
151C2×D188—21no—
152C2×D188—44no—
153C2×D188C2412yes—
154C2×C4×D47—24no—
155C2×C4×D47—24no—
156C2×C4×D47—42no—
157C2×C4×D47—42no—
158C2×C4×D47—44no—
159C2×C4×D47C2×D412yes—
160C2×C4×D47C2×D414yes—
161C2×C4×D47C2×D414yes—
162C2×C4×D47C2412yes—
163C2×Dic94—24no—
164C2×Dic94—21no—
165C2×Dic94—24no—
166C2×Dic94—44no—
167C2×Dic94C2412yes—
168C2×C8×C47—24no—
169C2×C8×C47C2414yes—
170C4⋊C4×C47—24no—
171C4⋊C4×C47—24no—
172C4⋊C4×C47—24no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47C2412yes—
177C4⋊C4×C47C2414yes—
178C4⋊C4×C47C2412yes—
179C42×C47C2×D412yes—
180C42×C47C2412yes—
181(C2×D47)⋊C4—28no—
182(C2×D47)⋊C4—24no—
183(C2×D47)⋊C4—24no—
184(C2×D47)⋊C4—24no—
185(C2×D47)⋊C4—24no—
186(C2×D47)⋊C4—24no—
187C4⋊Dic47—24no—
188C4⋊Dic47—22no—
189C4⋊Dic47—24no—
190C4⋊Dic47—28no—
191C4⋊Dic47C2414yes—
192Dic47⋊C4—28no—
193Dic47⋊C4—24no—
194C4×Dic47—24no—
195C4×Dic47—28no—
196C4×Dic47C2×D412yes—
197C4×Dic47C2×D414yes—
198C4×Dic47C2×D414yes—
199C4×Dic47C2412yes—
200C2×C47⋊C8—24no—
201C2×C47⋊C8C2414yes—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—42no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47C22×D412yes—
211Q8×C47—48no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—44no—
220C2×C4×C47C22×D412yes—
221C2×C4×C47C22×D412yes—
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C472−1+414yes—
224C2×C4×C47C2511yescharacteristic
225C2×Dic47—22no—
226C2×Dic47—22no—
227C2×Dic47—22no—
228C2×Dic47—24no—
229C2×Dic47—22no—
230C2×Dic47—42no—
231C2×Dic47—44no—
232C2×Dic47C22×D412yes—
233C2×Dic47C22×D412yes—
234C2×Dic47C22×D412yes—
235D188—24no—
236D188—48no—
237D188—42no—
238C4×D47—24no—
239C4×D47—24no—
240C4×D47—44no—
241C4×D47—44no—
242C4×D47—48no—
243Dic94—24no—
244Dic94—48no—
245Dic94—42no—
246C8×C47—24no—
247C47⋊C8—24no—
248C2×#3240—471nomaximal, Sylow
249C22×C47#53612yes—
250C22×C47#57512yes—
251C22×C47#57512yes—
252C22×C47C23×D411yescharacteristic
253C2×D47—22no—
254C2×D47—22no—
255C2×D47—22no—
256C2×D47—44no—
257C2×D47—42no—
258C2×D47—42no—
259C2×D47—42no—
260C2×D47—84no—
261C4×C47—22no—
262C4×C47—22no—
263C4×C47—42no—
264C4×C47—42no—
265C4×C47—44no—
266C4×C47#53612yes—
267C4×C47C2×2−1+412yes—
268Dic47—22no—
269Dic47—22no—
270Dic47—22no—
271Dic47—42no—
272Dic47—44no—
273C2×#533—471no—
274C2×#529—471no—
275#3240—4716no—
276C2×#501—471no—
277C2×#501D4711yescharacteristic, complemented
278C2×#489—471no—
279C2×#489—471no—
280C2×#485—472no—
281C2×#482—472no—
282C2×#479—472no—
283C2×#478—472no—
284C2×#432—471no—
285C2×C47#324014yescomplemented
286C2×C47C2×#53611yescharacteristic
287C2×C47C2×#57511yescharacteristic
288C2×C47C2×#57511yescharacteristic
289D47—42no—
290D47—82no—
291#533—478no—
292#533—944no—
293C2×C4⋊Q8—471no—
294C2×C4⋊Q8C2×D4711yescharacteristic
295#529—478no—
296#529—944no—
297C2×#126—941no—
298C2×#125—472no—
299C2×#125C2×D4711yescharacteristic
300C2×#124—471no—
301C2×#123—941no—
302C2×C22⋊Q8—471no—
303C2×C22⋊Q8—941no—
304C2×C22⋊Q8—941no—
305C2×#121—471no—
306C2×C4×Q8—471no—
307C2×C4×Q8—941no—
308C2×C4×Q8—941no—
309C2×C4×D4—471no—
310C2×C4×D4—941no—
311C2×#117—472no—
312C2×#117—941no—
313C22×C42—471no—
314#501—478no—
315#501C2×D4718yescomplemented
316#489—478no—
317#489—478no—
318#485—4716no—
319#482—4716no—
320#479—4716no—
321#478—4716no—
322#432—478no—
323C2×#107—472no—
324C2×#107C2×D4712yes—
325C2×#106—472no—
326C2×#106C2×D4712yes—
327C2×C4⋊C8—472no—
328C2×#103—472no—
329C2×#103—472no—
330C2×#102—472no—
331C2×#102—472no—
332C2×C22⋊C8—472no—
333C2×#97—471no—
334C2×#97C2×D4711yescharacteristic
335C47C2×#324011yescharacteristic, complemented, Sylow
336C22×Q8—21no—
337C22×Q8—471no—
338C22×Q8—941no—
339C22×D4—471no—
340C22×D4—941no—
341C23×C4—471no—
342C23×C4—471no—
343C23×C4—471no—
344C23×C4—941no—
345C22×C8—472no—
346C22×C8C22×D4712yes—
347C4⋊Q8—22no—
348C4⋊Q8—474no—
349C4⋊Q8—942no—
350C4⋊Q8C22×D4714yes—
351#126—948no—
352#125—22no—
353#125—478no—
354#125—944no—
355#125C22×D4714yes—
356#124—474no—
357#124—942no—
358#123—948no—
359C22⋊Q8—474no—
360C22⋊Q8—942no—
361C22⋊Q8—948no—
362C22⋊Q8—948no—
363#121—474no—
364#121—942no—
365C4×Q8—474no—
366C4×Q8—942no—
367C4×Q8—948no—
368C4×Q8—948no—
369C4×D4—474no—
370C4×D4—942no—
371C4×D4—948no—
372#117—478no—
373#117—948no—
374#117—944no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—472no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4—942no—
382C2×C4⋊C4—942no—
383C2×C4⋊C4—941no—
384C2×C4⋊C4C22×D4712yes—
385C2×C4⋊C4C22×D4711yescharacteristic
386C2×C4⋊C4C22×D4711yescharacteristic
387C2×C22⋊C4—941no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—942no—
390C2×C22⋊C4—941no—
391C2×C22⋊C4—941no—
392C2×C22⋊C4—941no—
393C2×C42—471no—
394C2×C42—471no—
395C2×C42—471no—
396C2×C42—474no—
397C2×C42—474no—
398C2×C42—942no—
399C2×C42—941no—
400C2×C42C22×D4711yescharacteristic
401#107—478no—
402#107C22×D4718yes—
403#106—478no—
404#106C22×D4718yes—
405C4⋊C8—478no—
406#103—478no—
407#103—478no—
408#102—478no—
409#102—478no—
410C22⋊C8—478no—
411#97—474no—
412#97C22×D4714yes—
413C24—471no—
414C24—941no—
415C2×Q8—24no—
416C2×Q8—44no—
417C2×Q8—472no—
418C2×Q8—941no—
419C2×Q8—944no—
420C2×Q8—944no—
421C2×Q8—1884no—
422C2×D4—472no—
423C2×D4—944no—
424C2×D4—941no—
425C2×D4—944no—
426C2×D4—1884no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—471no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—474no—
436C22×C4—474no—
437C22×C4—944no—
438C22×C4—944no—
439C22×C4—941no—
440C22×C4—942no—
441C22×C4—1882no—
442C22×C4—1882no—
443C22×C4—1884no—
444C22×C4D4×D4711yescharacteristic
445C22×C4D4×D4711yescharacteristic
446C22×C4C23×D4711yescharacteristic
447C2×C8—24no—
448C2×C8—474no—
449C2×C8—944no—
450C2×C8C23×D4714yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—474no—
458C4⋊C4—944no—
459C4⋊C4—948no—
460C4⋊C4—944no—
461C4⋊C4—948no—
462C4⋊C4—942no—
463C4⋊C4—944no—
464C4⋊C4C23×D4714yes—
465C4⋊C4C23×D4712yes—
466C4⋊C4C23×D4712yes—
467C22⋊C4—944no—
468C22⋊C4—944no—
469C22⋊C4—948no—
470C22⋊C4—944no—
471C22⋊C4—944no—
472C22⋊C4—944no—
473C42—474no—
474C42—472no—
475C42—474no—
476C42—472no—
477C42—948no—
478C42—944no—
479C42D4×D4712yes—
480C42C23×D4712yes—
481C23—472no—
482C23—942no—
483C23—942no—
484C23—942no—
485C23—942no—
486C23—1882no—
487C23—1882no—
488C23—1882no—
489C23C2×D4×D4711yescharacteristic
490Q8—48no—
491Q8—944no—
492Q8—1888no—
493Q8—1882no—
494D4—944no—
495D4—1888no—
496D4—1882no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—472no—
506C2×C4—472no—
507C2×C4—472no—
508C2×C4—942no—
509C2×C4—942no—
510C2×C4—942no—
511C2×C4—944no—
512C2×C4—944no—
513C2×C4—942no—
514C2×C4—944no—
515C2×C4—1884no—
516C2×C4—1884no—
517C2×C4—1888no—
518C2×C4—1884no—
519C2×C4—1882no—
520C2×C4C2×D4×D4712yes—
521C2×C4C2×D4×D4712yes—
522C2×C4C2×D4×D4711yescharacteristic
523C2×C4#1309407214yes—
524C2×C4C24×D4711yescharacteristic
525C8—24no—
526C8—944no—
527C22—942no—
528C22—942no—
529C22—942no—
530C22—3764no—
531C22—1882no—
532C22—1882no—
533C22—1882no—
534C22—1884no—
535C22#1568969812yes—
536C22#1568991912yes—
537C22#1568992212yes—
538C22C22×D4×D4711yescharacteristic
539C4—22no—
540C4—22no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—942no—
545C4—942no—
546C4—942no—
547C4—1884no—
548C4—1882no—
549C4#1568969812yes—
550C4C2×#1309407212yes—
551C2—3762no—
552C2—1882no—
553C2#2025463114yesdirect product factor
554C2C2×#1568969811yescharacteristic
555C2C2×#1568991911yescharacteristic
556C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
prime radicalC2×#13093999C22
hypercenterC2×#501D47
hypocenterC47C2×#3240
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#15689678C2semidirect
3. #20254631C2direct (N × H)
4. C2×#15689533C2semidirect
5. C2×#15689485C2semidirect
6. C2×#15689483C2semidirect
7. C2×#15689467C2semidirect
9. C2×#15689429C2semidirect
10. C2×#15689422C2semidirect
11. C2×#15689178C2semidirect
12. C2×C47×#501C2semidirect
14. #15689678C22semidirect
34. #15689533C22semidirect
35. #15689485C22semidirect
36. #15689483C22semidirect
37. #15689467C22semidirect
39. #15689429C22semidirect
40. #15689422C22semidirect
41. #15689178C22semidirect
53. C47×#501C22semidirect
277. C2×#501D47semidirect
285. C2×C47#3240semidirect
315. #501C2×D47semidirect
335. C47C2×#3240semidirect
553. C2#20254631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896782
C2×#156896582
#202546312
C2×#156895332
C2×#156894852
C2×#156894832
C2×#156894672
C2×#156894502
C2×#156894292
C2×#156894222
C2×#156891782
C2×C47×#5012
C2×#324047