Finite Group Databasebeta

← C2×#20241964 #26183598

Subgroups — C2×#20241964 #26183598

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×#15689659C211yesmaximal, characteristic
2C2×#15689173C211yesmaximal, characteristic, complemented
3C2×#15688990C211yesmaximal, characteristic, complemented
4#20241964C218yesmaximal, direct product factor
5C2×#15688860C211yesmaximal, characteristic, complemented
6C2×#15688858C211yesmaximal, characteristic
7C2×#15688856C211yesmaximal, characteristic
8C2×C47×#328C211yesmaximal, characteristic, complemented
9#15689659—22no—
10#15689659—22no—
11#15689659C414yescomplemented
12#15689659C2214yes—
13C2×#13094019—21no—
14C2×#13094015C411yescharacteristic, complemented
15C2×#13094013C411yescharacteristic, complemented
16C2×#13094008—21no—
17C2×#13093998C2211yescharacteristic
18C2×Q8×Dic47C411yescharacteristic, complemented
19C2×#13093986C411yescharacteristic, complemented
20C2×(C22⋊D47)⋊C4—21no—
21C2×#13093982—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#15688860C2214yescomplemented
34#15688858C2214yes—
35#15688856C2214yes—
36C2×C22⋊Q8×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C47×#328C2214yescomplemented
40C22×D188C2×C411yescharacteristic
41C22×C22⋊D47—21no—
42C23×Dic47—21no—
43C23×Dic47D411yescharacteristic
44C23×Dic47D411yescharacteristic
45C22×C4×D47—21no—
46C22×C47⋊C8—21no—
47#13094019—24no—
48#13094019—24no—
49#13094015—22no—
50#13094015C2×C414yescomplemented
51#13094013—22no—
52#13094013C2×C414yescomplemented
53#13094008—24no—
54#13094008—24no—
55#13093998—21no—
56#13093998—21no—
57#13093998C2×C412yes—
58#13093998C2312yes—
59Q8×Dic47—22no—
60Q8×Dic47C2×C414yescomplemented
61#13093986—22no—
62#13093986C2×C414yescomplemented
63(C22⋊D47)⋊C4—24no—
64(C22⋊D47)⋊C4—24no—
65#13093982—24no—
66#13093982—24no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×(C2×D47)⋊C4—21no—
72C2×(C2×D47)⋊C4—21no—
73C2×(C2×D47)⋊C4—21no—
74C2×(C2×D47)⋊C4—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×Q8×C47C2×C411yescharacteristic
93C23×C4×C47—21no—
94C23×C4×C47C2311yescharacteristic
95C22×C8×C47—21no—
96C22⋊Q8×C47—21no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47C2×C412yes—
99C22⋊Q8×C47C2312yes—
100C2×C4⋊C4×C47—21no—
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×C47C2×D411yescharacteristic
108C23×D47—21no—
109C2×Q8×C47—21no—
110C2×Q8×C47—42no—
111C2×Q8×C47C22×C412yes—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—42no—
116C22×C4×C47—42no—
117C22×C4×C47—42no—
118C22×C4×C47—42no—
119C22×C4×C47C22×C411yescharacteristic
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2411yescharacteristic
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—42no—
128C2×C22⋊D47—42no—
129C22×Dic47—22no—
130C22×Dic47—22no—
131C22×Dic47—21no—
132C22×Dic47—22no—
133C22×Dic47—42no—
134C22×Dic47—42no—
135C22×Dic47—42no—
136C22×Dic47—42no—
137C22×Dic47C22⋊C411yescharacteristic
138C22×Dic47C22⋊C411yescharacteristic
139C22×Dic47C22⋊C411yescharacteristic
140C22×Dic47C22⋊C411yescharacteristic
141C22×Dic47C22⋊C412yes—
142C22×Dic47C22⋊C412yes—
143C22×Dic47C2×D412yes—
144C22×Dic47C2×D412yes—
145C2×D188—21no—
146C2×D188—42no—
147C2×D188C22×C412yes—
148C2×C4×D47—24no—
149C2×C4×D47—44no—
150C2×C8×C47—22no—
151C2×C8×C47—42no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47C22×C412yes—
156C22⋊C4×C47—22no—
157C22⋊C4×C47—22no—
158(C2×D47)⋊C4—22no—
159(C2×D47)⋊C4—22no—
160(C2×D47)⋊C4—24no—
161(C2×D47)⋊C4—24no—
162(C2×D47)⋊C4—24no—
163C4⋊Dic47—21no—
164C4⋊Dic47—24no—
165C4⋊Dic47—24no—
166C4⋊Dic47C22×C412yes—
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×C47C2×C22⋊C411yescharacteristic
182C23×C47C2×C22⋊C411yescharacteristic
183C23×C47#13512yes—
184C23×C47#13512yes—
185C23×C47C22×D411yescharacteristic
186C22×D47—22no—
187C22×D47—42no—
188C22×D47—42no—
189C22×D47—42no—
190Q8×C47—42no—
191Q8×C47—42no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—84no—
206C2×C4×C47C2×C22⋊C411yescharacteristic
207C2×C4×C47C2×C22⋊C411yescharacteristic
208C2×C4×C47C23×C411yescharacteristic
209C2×C4×C47C22×D411yescharacteristic
210C22⋊D47—42no—
211C22⋊D47—42no—
212C22⋊D47—44no—
213C2×Dic47—22no—
214C2×Dic47—22no—
215C2×Dic47—24no—
216C2×Dic47—22no—
217C2×Dic47—22no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—22no—
221C2×Dic47—42no—
222C2×Dic47—42no—
223C2×Dic47—42no—
224C2×Dic47—42no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—84no—
228C2×Dic47C2×C22⋊C412yes—
229C2×Dic47C2×C22⋊C412yes—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C412yes—
232D188—42no—
233D188—42no—
234C4×D47—48no—
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#41012yes—
245C22×C47#41612yes—
246C22×C47#41612yes—
247C22×C47#42112yes—
248C22×C47C22×C22⋊C411yescharacteristic
249C22×C47C2×#13511yescharacteristic
250C22×C47C2×#13511yescharacteristic
251C2×D47—42no—
252C2×D47—42no—
253C2×D47—42no—
254C2×D47—84no—
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—42no—
260C4×C47—42no—
261C4×C47—82no—
262Dic47—22no—
263Dic47—22no—
264Dic47—22no—
265Dic47—22no—
266Dic47—42no—
267Dic47—82no—
268C2×#529—471no—
269C2×#431—471no—
270C2×#383—471no—
271#1521—478no—
272C2×#328—471no—
273C2×#328D4711yescharacteristic, complemented
274C2×#327—471no—
275C2×#327—471no—
276C2×C47—21no—
277C2×C47—21no—
278C2×C47—22no—
279C2×C47#152114yescomplemented
280C2×C47C2×#41011yescharacteristic
281C2×C47C2×#41611yescharacteristic
282C2×C47C2×#42111yescharacteristic
283D47—82no—
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⋊Q8C2×D4711yescharacteristic
293C2×#121—471no—
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#328C2×D4714yescomplemented
313#327—474no—
314#327—474no—
315C47C2×#152111yescharacteristic, complemented, Sylow
316C22×Q8C4×D4711yescharacteristic
317C22×D4—471no—
318C22×D4—941no—
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—21no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D4712yes—
338C22⋊Q8C22×D4712yes—
339#121—472no—
340#121—472no—
341#121—941no—
342#121—941no—
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—21no—
352C2×C4⋊C4—471no—
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—941no—
384C24D4×D4711yescharacteristic
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8C2×C4×D4712yes—
388C2×D4—472no—
389C2×D4—942no—
390C2×D4—942no—
391C2×D4—941no—
392C2×D4—1882no—
393C2×D4—1882no—
394C2×D4—1882no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—472no—
403C22×C4—471no—
404C22×C4—471no—
405C22×C4—471no—
406C22×C4—471no—
407C22×C4—472no—
408C22×C4—472no—
409C22×C4—472no—
410C22×C4—944no—
411C22×C4—942no—
412C22×C4—942no—
413C22×C4—941no—
414C22×C4—942no—
415C22×C4—1884no—
416C22×C4—1882no—
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—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—472no—
434C4⋊C4—944no—
435C4⋊C4—944no—
436C4⋊C4—944no—
437C4⋊C4—941no—
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—942no—
458C23—1882no—
459C23—1882no—
460C23—1882no—
461C23C22⋊C4×D4711yescharacteristic
462C23C22⋊C4×D4711yescharacteristic
463C23#1309404512yes—
464C23#1309404712yes—
465C23C2×D4×D4711yescharacteristic
466Q8—42no—
467Q8—42no—
468D4—1882no—
469D4—1882no—
470D4—1884no—
471D4—1882no—
472D4—1882no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—84no—
487C2×C4—472no—
488C2×C4—472no—
489C2×C4—472no—
490C2×C4—472no—
491C2×C4—944no—
492C2×C4—942no—
493C2×C4—942no—
494C2×C4—942no—
495C2×C4—942no—
496C2×C4—942no—
497C2×C4—942no—
498C2×C4—942no—
499C2×C4—3764no—
500C2×C4—1888no—
501C2×C4—1882no—
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—3764no—
520C22—1882no—
521C22—1882no—
522C22—1882no—
523C22#1568909512yes—
524C22#1568911812yes—
525C22#1568911812yes—
526C22#1568913812yes—
527C22C2×C22⋊C4×D4711yescharacteristic
528C22C2×#1309404511yescharacteristic
529C22C2×#1309404711yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—42no—
535C4—42no—
536C4—82no—
537C4—942no—
538C4—942no—
539C4—942no—
540C4—942no—
541C4—3762no—
542C4—1882no—
543C2—21no—
544C2—21no—
545C2—22no—
546C2—3762no—
547C2#2024196414yesdirect product factor
548C2C2×#1568909511yescharacteristic
549C2C2×#1568911811yescharacteristic
550C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#328C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC2×#328D47
hypocenterC47C2×#1521
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×#15689173C2semidirect
3. C2×#15688990C2semidirect
4. #20241964C2direct (N × H)
5. C2×#15688860C2semidirect
8. C2×C47×#328C2semidirect
11. #15689659C4semidirect
14. C2×#13094015C4semidirect
15. C2×#13094013C4semidirect
18. C2×Q8×Dic47C4semidirect
19. C2×#13093986C4semidirect
24. #15689173C22semidirect
29. #15688990C22semidirect
33. #15688860C22semidirect
39. C47×#328C22semidirect
50. #13094015C2×C4semidirect
52. #13094013C2×C4semidirect
60. Q8×Dic47C2×C4semidirect
62. #13093986C2×C4semidirect
273. C2×#328D47semidirect
279. C2×C47#1521semidirect
312. #328C2×D47semidirect
315. C47C2×#1521semidirect
547. C2#20241964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896592
C2×#156891732
C2×#156889902
#202419642
C2×#156888602
C2×#156888582
C2×#156888562
C2×C47×#3282
C2×#152147