Finite Group Databasebeta

← C2×#20241962 #26183596

Subgroups — C2×#20241962 #26183596

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689654C211yesmaximal, characteristic
2C2×#15689173C211yesmaximal, characteristic, complemented
3C2×#15688990C211yesmaximal, characteristic, complemented
4#20241962C218yesmaximal, direct product factor
5C2×#15688861C211yesmaximal, characteristic, complemented
6C2×#15688859C211yesmaximal, characteristic, complemented
7C2×#15688857C211yesmaximal, characteristic
8C2×C47×#327C211yesmaximal, characteristic
9#15689654—22no—
10#15689654—22no—
11#15689654C414yescomplemented
12#15689654C2214yes—
13C2×#13094017—21no—
14C2×#13094015C411yescharacteristic, complemented
15C2×#13094011C411yescharacteristic, complemented
16C2×#13094005—21no—
17C2×#13094003C2211yescharacteristic
18C2×#13093989C411yescharacteristic, complemented
19C2×D4×Dic47—21no—
20C2×D4×Dic47C411yescharacteristic, complemented
21C2×#13093980—21no—
22C22×C4×Dic47C2211yescharacteristic
23#15689173—22no—
24#15689173C2214yescomplemented
25C2×Dic47⋊C8—21no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C8×Dic47—21no—
28#15688990—22no—
29#15688990C2214yescomplemented
30C2×C47⋊#95—21no—
31C2×C47⋊#95—21no—
32C2×C47⋊#95C2211yescharacteristic
33#15688861C2214yescomplemented
34#15688859C2214yescomplemented
35#15688857C2214yes—
36C2×#121×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C47×#327C2214yes—
40C22×Dic94C2×C411yescharacteristic
41C23×Dic47—21no—
42C23×Dic47—21no—
43C23×Dic47D411yescharacteristic
44C23×Dic47D411yescharacteristic
45C22×C47⋊C8—21no—
46#13094017—24no—
47#13094017—24no—
48#13094015—22no—
49#13094015C2×C414yescomplemented
50#13094011—22no—
51#13094011C2×C414yescomplemented
52#13094005—24no—
53#13094005—24no—
54#13094003—21no—
55#13094003—21no—
56#13094003C2×C412yes—
57#13094003C2312yes—
58#13093989—22no—
59#13093989C2×C414yescomplemented
60D4×Dic47—24no—
61D4×Dic47—24no—
62D4×Dic47—22no—
63D4×Dic47C2×C414yescomplemented
64#13093980—24no—
65#13093980—24no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47C2×C411yescharacteristic
68C2×Dic47⋊C4—21no—
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47C2×C411yescharacteristic
77C2×C4×Dic47C2×C411yescharacteristic
78C2×C4×Dic47C2×C412yes—
79C2×C4×Dic47D412yes—
80C2×C4×Dic47D411yescharacteristic
81C2×C4×Dic47D411yescharacteristic
82C2×C4×Dic47D412yes—
83C2×C4×Dic47C2312yes—
84Dic47⋊C8—24no—
85C22⋊(C47⋊C8)—21no—
86C22⋊(C47⋊C8)C2312yes—
87C8×Dic47—24no—
88C47⋊#95—21no—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95C2312yes—
92C22×D4×C47—21no—
93C22×D4×C47C2×C411yescharacteristic
94C23×C4×C47—21no—
95C23×C4×C47C2311yescharacteristic
96C22×C8×C47—21no—
97#121×C47—21no—
98#121×C47—21no—
99#121×C47C2×C412yes—
100#121×C47C2312yes—
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C22⋊C4×C47—21no—
103C22⋊C8×C47—21no—
104C22⋊C8×C47C2312yes—
105#95×C47—21no—
106#95×C47C2312yes—
107C24×C47—21no—
108C24×C47C2×D411yescharacteristic
109C2×D4×C47—22no—
110C2×D4×C47—22no—
111C2×D4×C47—21no—
112C2×D4×C47—42no—
113C2×D4×C47—42no—
114C2×D4×C47—42no—
115C2×D4×C47C22×C412yes—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—42no—
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2411yescharacteristic
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—24no—
133C22×Dic47—22no—
134C22×Dic47—42no—
135C22×Dic47—44no—
136C22×Dic47—42no—
137C22×Dic47—42no—
138C22×Dic47—42no—
139C22×Dic47C22⋊C411yescharacteristic
140C22×Dic47C22⋊C411yescharacteristic
141C22×Dic47C22⋊C411yescharacteristic
142C22×Dic47C22⋊C411yescharacteristic
143C22×Dic47C22⋊C412yes—
144C22×Dic47C22⋊C412yes—
145C22×Dic47C2×D412yes—
146C22×Dic47C2×D412yes—
147C2×Dic94—21no—
148C2×Dic94—42no—
149C2×Dic94C22×C412yes—
150C2×C8×C47—22no—
151C2×C8×C47—42no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47C22×C412yes—
154C22⋊C4×C47—22no—
155C22⋊C4×C47—22no—
156C22⋊Dic47—22no—
157C22⋊Dic47—22no—
158C22⋊Dic47—24no—
159C22⋊Dic47—24no—
160C22⋊Dic47—24no—
161C4⋊Dic47—21no—
162C4⋊Dic47—24no—
163C4⋊Dic47C22×C412yes—
164Dic47⋊C4—22no—
165Dic47⋊C4—22no—
166Dic47⋊C4—24no—
167Dic47⋊C4—24no—
168C4×Dic47—24no—
169C4×Dic47C22⋊C412yes—
170C4×Dic47C22⋊C412yes—
171C4×Dic47C22⋊C412yes—
172C4×Dic47C22⋊C412yes—
173C4×Dic47C22×C412yes—
174C4×Dic47C22×C412yes—
175C4×Dic47C2×D412yes—
176C4×Dic47C2×D412yes—
177C2×C47⋊C8—22no—
178C2×C47⋊C8—42no—
179C23×C47—22no—
180C23×C47—22no—
181C23×C47—22no—
182C23×C47—42no—
183C23×C47—42no—
184C23×C47—42no—
185C23×C47C2×C22⋊C411yescharacteristic
186C23×C47C2×C22⋊C411yescharacteristic
187C23×C47#13512yes—
188C23×C47#13512yes—
189C23×C47C22×D411yescharacteristic
190D4×C47—42no—
191D4×C47—42no—
192D4×C47—42no—
193D4×C47—42no—
194D4×C47—44no—
195C2×C4×C47—22no—
196C2×C4×C47—22no—
197C2×C4×C47—22no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—84no—
207C2×C4×C47C2×C22⋊C411yescharacteristic
208C2×C4×C47C2×C22⋊C411yescharacteristic
209C2×C4×C47C23×C411yescharacteristic
210C2×C4×C47C22×D411yescharacteristic
211C2×Dic47—22no—
212C2×Dic47—22no—
213C2×Dic47—24no—
214C2×Dic47—22no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—22no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—42no—
221C2×Dic47—42no—
222C2×Dic47—48no—
223C2×Dic47—42no—
224C2×Dic47—42no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47—84no—
229C2×Dic47C2×C22⋊C412yes—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C412yes—
232C2×Dic47C2×C22⋊C412yes—
233Dic94—42no—
234Dic94—42no—
235C8×C47—42no—
236C47⋊C8—42no—
237C2×#1521—471nomaximal, Sylow
238C22×C47—21no—
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—24no—
243C22×C47—24no—
244C22×C47—42no—
245C22×C47—42no—
246C22×C47—42no—
247C22×C47—84no—
248C22×C47#41012yes—
249C22×C47#41612yes—
250C22×C47#41612yes—
251C22×C47#42112yes—
252C22×C47C22×C22⋊C411yescharacteristic
253C22×C47C2×#13511yescharacteristic
254C22×C47C2×#13511yescharacteristic
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—42no—
260C4×C47—82no—
261Dic47—22no—
262Dic47—22no—
263Dic47—22no—
264Dic47—22no—
265Dic47—42no—
266Dic47—42no—
267Dic47—82no—
268C2×#529—471no—
269C2×#431—471no—
270C2×#383—471no—
271#1521—478no—
272C2×#328—471no—
273C2×#328—471no—
274C2×#327—471no—
275C2×#327D4711yescharacteristic
276C2×C47—21no—
277C2×C47—21no—
278C2×C47—22no—
279C2×C47—82no—
280C2×C47#152114yescomplemented
281C2×C47C2×#41011yescharacteristic
282C2×C47C2×#41611yescharacteristic
283C2×C47C2×#42111yescharacteristic
284#529—474no—
285#529—474no—
286#529—942no—
287#529—942no—
288C2×#126—941no—
289C2×#125—471no—
290C2×#124—471no—
291C2×#123—941no—
292C2×C22⋊Q8—471no—
293C2×#121C2×D4711yescharacteristic
294C2×C4×Q8—471no—
295C2×C4×D4—471no—
296C2×C4×D4—941no—
297C2×#117—941no—
298C22×C42—471no—
299#431—474no—
300#431—942no—
301C2×C4⋊C8—941no—
302C2×C22⋊C8—471no—
303C2×C22⋊C8C2×D4711yescharacteristic
304C2×C4×C8—941no—
305#383—474no—
306#383—942no—
307C2×#95—471no—
308C2×#95—941no—
309C2×#95—941no—
310C2×#95C2×D4711yescharacteristic
311#328—474no—
312#328—474no—
313#327—474no—
314#327C2×D4714yes—
315C47C2×#152111yescharacteristic, complemented, Sylow
316C22×Q8—471no—
317C22×D4—21no—
318C22×D4C4×D4711yescharacteristic
319C23×C4—21no—
320C23×C4—471no—
321C23×C4—471no—
322C23×C4—941no—
323C23×C4—941no—
324C23×C4C22×D4711yescharacteristic
325C22×C8—21no—
326C22×C8—941no—
327#126—944no—
328#126—944no—
329#125—474no—
330#125—942no—
331#124—474no—
332#124—942no—
333#123—944no—
334#123—944no—
335C22⋊Q8—472no—
336C22⋊Q8—472no—
337C22⋊Q8—941no—
338C22⋊Q8—941no—
339#121—21no—
340#121—21no—
341#121C4×D4712yes—
342#121C22×D4712yes—
343C4×Q8—474no—
344C4×Q8—942no—
345C4×D4—474no—
346C4×D4—942no—
347C4×D4—944no—
348C4×D4—944no—
349#117—944no—
350#117—944no—
351C2×C4⋊C4—471no—
352C2×C4⋊C4—941no—
353C2×C4⋊C4—941no—
354C2×C4⋊C4—941no—
355C2×C4⋊C4—941no—
356C2×C4⋊C4C4×D4711yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—941no—
359C2×C22⋊C4—941no—
360C2×C22⋊C4—941no—
361C2×C22⋊C4—941no—
362C2×C42—471no—
363C2×C42—471no—
364C2×C42—472no—
365C2×C42—471no—
366C2×C42—471no—
367C2×C42—472no—
368C2×C42—472no—
369C2×C42—472no—
370C2×C42—941no—
371C4⋊C8—944no—
372C22⋊C8—21no—
373C22⋊C8—472no—
374C22⋊C8—941no—
375C22⋊C8C22×D4712yes—
376C4×C8—944no—
377#95—21no—
378#95—472no—
379#95—944no—
380#95—944no—
381#95—941no—
382#95C22×D4712yes—
383C24—21no—
384C24D4×D4711yescharacteristic
385C2×Q8—472no—
386C2×Q8—941no—
387C2×Q8—1882no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4C2×C4×D4712yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—472no—
402C22×C4—471no—
403C22×C4—471no—
404C22×C4—471no—
405C22×C4—471no—
406C22×C4—472no—
407C22×C4—472no—
408C22×C4—472no—
409C22×C4—944no—
410C22×C4—942no—
411C22×C4—942no—
412C22×C4—941no—
413C22×C4—941no—
414C22×C4—942no—
415C22×C4—1882no—
416C22×C4—1884no—
417C22×C4—1882no—
418C22×C4—1882no—
419C22×C4—1882no—
420C22×C4C2×C4×D4711yescharacteristic
421C22×C4C2×C4×D4711yescharacteristic
422C22×C4D4×D4711yescharacteristic
423C22×C4D4×D4711yescharacteristic
424C22×C4D4×D4711yescharacteristic
425C22×C4C23×D4711yescharacteristic
426C2×C8—22no—
427C2×C8—42no—
428C2×C8—942no—
429C2×C8—1882no—
430C4⋊C4—21no—
431C4⋊C4—472no—
432C4⋊C4—944no—
433C4⋊C4—944no—
434C4⋊C4—944no—
435C4⋊C4—942no—
436C4⋊C4—941no—
437C4⋊C4—942no—
438C4⋊C4C2×C4×D4712yes—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—944no—
442C22⋊C4—944no—
443C22⋊C4—944no—
444C22⋊C4—942no—
445C22⋊C4—942no—
446C42—472no—
447C42—472no—
448C42—472no—
449C42—472no—
450C42—472no—
451C42—472no—
452C42—472no—
453C42—472no—
454C42—944no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23C22⋊C4×D4711yescharacteristic
462C23C22⋊C4×D4711yescharacteristic
463C23#1309404312yes—
464C23#1309404512yes—
465C23C2×D4×D4711yescharacteristic
466Q8—1882no—
467Q8—1882no—
468D4—42no—
469D4—42no—
470D4—44no—
471D4—42no—
472D4—42no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—84no—
485C2×C4—472no—
486C2×C4—472no—
487C2×C4—472no—
488C2×C4—472no—
489C2×C4—944no—
490C2×C4—942no—
491C2×C4—942no—
492C2×C4—942no—
493C2×C4—942no—
494C2×C4—942no—
495C2×C4—942no—
496C2×C4—942no—
497C2×C4—942no—
498C2×C4—3764no—
499C2×C4—1882no—
500C2×C4—1882no—
501C2×C4—1888no—
502C2×C4—1882no—
503C2×C4—1882no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4—1882no—
507C2×C4C22⋊C4×D4711yescharacteristic
508C2×C4C22⋊C4×D4711yescharacteristic
509C2×C4C22×C4×D4711yescharacteristic
510C2×C4C2×D4×D4711yescharacteristic
511C8—42no—
512C8—1882no—
513C22—21no—
514C22—21no—
515C22—24no—
516C22—24no—
517C22—21no—
518C22—21no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—84no—
523C22#1568909512yes—
524C22#1568911612yes—
525C22#1568911612yes—
526C22#1568913812yes—
527C22C2×C22⋊C4×D4711yescharacteristic
528C22C2×#1309404311yescharacteristic
529C22C2×#1309404511yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—82no—
536C4—942no—
537C4—942no—
538C4—942no—
539C4—942no—
540C4—3762no—
541C4—1882no—
542C4—1882no—
543C2—21no—
544C2—21no—
545C2—22no—
546C2—82no—
547C2#2024196214yesdirect product factor
548C2C2×#1568909511yescharacteristic
549C2C2×#1568911611yescharacteristic
550C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#327C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#121×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#327D47
hypocenterC47C2×#1521
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#15689173C2semidirect
3. C2×#15688990C2semidirect
4. #20241962C2direct (N × H)
5. C2×#15688861C2semidirect
6. C2×#15688859C2semidirect
11. #15689654C4semidirect
14. C2×#13094015C4semidirect
15. C2×#13094011C4semidirect
18. C2×#13093989C4semidirect
20. C2×D4×Dic47C4semidirect
24. #15689173C22semidirect
29. #15688990C22semidirect
33. #15688861C22semidirect
34. #15688859C22semidirect
49. #13094015C2×C4semidirect
51. #13094011C2×C4semidirect
59. #13093989C2×C4semidirect
63. D4×Dic47C2×C4semidirect
280. C2×C47#1521semidirect
315. C47C2×#1521semidirect
547. C2#20241962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896542
C2×#156891732
C2×#156889902
#202419622
C2×#156888612
C2×#156888592
C2×#156888572
C2×C47×#3272
C2×#152147