Finite Group Databasebeta

← C2×#20241873 #26183365

Subgroups — C2×#20241873 #26183365

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689659C211yesmaximal, characteristic
2C2×#15689173C211yesmaximal, characteristic, complemented
3C2×#15688968C211yesmaximal, characteristic, complemented
4#20241873C218yesmaximal, 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×Dic47—21no—
23C22×C4×Dic47C2211yescharacteristic
24#15689173—22no—
25#15689173C2214yescomplemented
26C2×Dic47⋊C8—21no—
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×C8×Dic47—21no—
29#15688968—22no—
30#15688968C2214yescomplemented
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—28no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47C2×C411yescharacteristic
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47C2×C412yes—
81C2×C4×Dic47D412yes—
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47D412yes—
85C2×C4×Dic47C2312yes—
86Dic47⋊C8—24no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)C2312yes—
89C8×Dic47—24no—
90C47⋊#95—21no—
91C47⋊#95—24no—
92C47⋊#95C2312yes—
93C22×Q8×C47C2×C411yescharacteristic
94C23×C4×C47—21no—
95C23×C4×C47C2311yescharacteristic
96C22×C8×C47—21no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47—21no—
99C22⋊Q8×C47C2×C412yes—
100C22⋊Q8×C47C2312yes—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47—21no—
104C22⋊C8×C47—21no—
105C22⋊C8×C47C2312yes—
106#95×C47—21no—
107#95×C47C2312yes—
108C24×C47C2×D411yescharacteristic
109C23×D47—21no—
110C2×Q8×C47—21no—
111C2×Q8×C47—42no—
112C2×Q8×C47C22×C412yes—
113C22×C4×C47—24no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—22no—
117C22×C4×C47—42no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47C22×C411yescharacteristic
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—42no—
129C2×C22⋊D47—42no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—24no—
133C22×Dic47—24no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—42no—
137C22×Dic47—42no—
138C22×Dic47C22⋊C411yescharacteristic
139C22×Dic47C22⋊C411yescharacteristic
140C22×Dic47C22⋊C411yescharacteristic
141C22×Dic47C22⋊C412yes—
142C22×Dic47C22⋊C412yes—
143C22×Dic47C22⋊C411yescharacteristic
144C22×Dic47C2×D412yes—
145C22×Dic47C2×D412yes—
146C2×D188—21no—
147C2×D188—42no—
148C2×D188C22×C412yes—
149C2×C4×D47—24no—
150C2×C4×D47—44no—
151C2×C8×C47—22no—
152C2×C8×C47—42no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47C22×C412yes—
157C22⋊C4×C47—22no—
158C22⋊C4×C47—22no—
159(C2×D47)⋊C4—22no—
160(C2×D47)⋊C4—22no—
161(C2×D47)⋊C4—24no—
162(C2×D47)⋊C4—24no—
163(C2×D47)⋊C4—24no—
164C4⋊Dic47—21no—
165C4⋊Dic47—24no—
166C4⋊Dic47—24no—
167C4⋊Dic47C22×C412yes—
168Dic47⋊C4—24no—
169C4×Dic47—216no—
170C4×Dic47—24no—
171C4×Dic47C22⋊C412yes—
172C4×Dic47C22⋊C412yes—
173C4×Dic47C22⋊C412yes—
174C4×Dic47C22⋊C412yes—
175C4×Dic47C22×C412yes—
176C4×Dic47C22×C412yes—
177C4×Dic47C2×D412yes—
178C4×Dic47C2×D412yes—
179C2×C47⋊C8—22no—
180C2×C47⋊C8—42no—
181C23×C47—22no—
182C23×C47—22no—
183C23×C47C2×C22⋊C411yescharacteristic
184C23×C47C2×C22⋊C411yescharacteristic
185C23×C47#13512yes—
186C23×C47#13512yes—
187C23×C47C22×D411yescharacteristic
188C22×D47—22no—
189C22×D47—42no—
190C22×D47—42no—
191C22×D47—42no—
192Q8×C47—42no—
193Q8×C47—42no—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—48no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47C2×C22⋊C411yescharacteristic
209C2×C4×C47C2×C22⋊C411yescharacteristic
210C2×C4×C47C23×C411yescharacteristic
211C2×C4×C47C22×D411yescharacteristic
212C22⋊D47—42no—
213C22⋊D47—42no—
214C22⋊D47—44no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—22no—
221C2×Dic47—24no—
222C2×Dic47—24no—
223C2×Dic47—24no—
224C2×Dic47—22no—
225C2×Dic47—42no—
226C2×Dic47—48no—
227C2×Dic47—42no—
228C2×Dic47—42no—
229C2×Dic47#10414yes—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C412yes—
232C2×Dic47C2×C22⋊C412yes—
233C2×Dic47C2×C22⋊C412yes—
234D188—42no—
235D188—42no—
236C4×D47—48no—
237C8×C47—42no—
238C47⋊C8—42no—
239C2×#1500—471nomaximal, Sylow
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—21no—
243C22×C47—21no—
244C22×C47—24no—
245C22×C47—24no—
246C22×C47#41012yes—
247C22×C47#41612yes—
248C22×C47#41612yes—
249C22×C47C2×#10412yes—
250C22×C47C22×C22⋊C411yescharacteristic
251C22×C47C2×#13511yescharacteristic
252C22×C47C2×#13511yescharacteristic
253C2×D47—42no—
254C2×D47—42no—
255C2×D47—42no—
256C2×D47—84no—
257C4×C47—21no—
258C4×C47—21no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—44no—
262C4×C47—42no—
263C4×C47—42no—
264Dic47—22no—
265Dic47—22no—
266Dic47—22no—
267Dic47—44no—
268Dic47—42no—
269Dic47C2×#10414yes—
270C2×#529—471no—
271C2×#431—471no—
272C2×#376—471no—
273#1500—478no—
274C2×#328—471no—
275C2×#328D4711yescharacteristic, complemented
276C2×#327—471no—
277C2×#327—471no—
278C2×C47—21no—
279C2×C47—21no—
280C2×C47—22no—
281C2×C47#150014yescomplemented
282C2×C47C2×#41011yescharacteristic
283C2×C47C2×#41611yescharacteristic
284C2×C47C22×#10411yescharacteristic
285D47—82no—
286#529—474no—
287#529—474no—
288#529—942no—
289#529—942no—
290C2×#126—941no—
291C2×#125—471no—
292C2×#124—471no—
293C2×#123—941no—
294C2×C22⋊Q8C2×D4711yescharacteristic
295C2×#121—471no—
296C2×C4×Q8—471no—
297C2×C4×D4—471no—
298C2×C4×D4—941no—
299C2×#117—941no—
300C22×C42—471no—
301C22×C42—941no—
302#431—474no—
303#431—942no—
304C2×C4⋊C8—941no—
305C2×C22⋊C8—471no—
306C2×C22⋊C8C2×D4711yescharacteristic
307C2×C4×C8—941no—
308#376—474no—
309#376—942no—
310C2×#95—471no—
311C2×#95—941no—
312C2×#95C2×D4711yescharacteristic
313#328—474no—
314#328C2×D4714yescomplemented
315#327—474no—
316#327—474no—
317C47C2×#150011yescharacteristic, complemented, Sylow
318C22×Q8C4×D4711yescharacteristic
319C22×D4—471no—
320C22×D4—941no—
321C23×C4—21no—
322C23×C4—471no—
323C23×C4—471no—
324C23×C4—941no—
325C23×C4—941no—
326C23×C4C22×D4711yescharacteristic
327C22×C8—21no—
328C22×C8—941no—
329#126—944no—
330#126—944no—
331#125—474no—
332#125—942no—
333#124—474no—
334#124—942no—
335#123—944no—
336#123—944no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339C22⋊Q8C4×D4712yes—
340C22⋊Q8C22×D4712yes—
341#121—472no—
342#121—472no—
343#121—941no—
344#121—941no—
345C4×Q8—474no—
346C4×Q8—942no—
347C4×D4—474no—
348C4×D4—942no—
349C4×D4—944no—
350C4×D4—944no—
351#117—944no—
352#117—944no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—471no—
355C2×C4⋊C4—941no—
356C2×C4⋊C4—941no—
357C2×C4⋊C4—941no—
358C2×C4⋊C4C4×D4711yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—941no—
361C2×C22⋊C4—941no—
362C2×C22⋊C4—941no—
363C2×C22⋊C4—941no—
364C2×C42—471no—
365C2×C42—471no—
366C2×C42—472no—
367C2×C42—471no—
368C2×C42—471no—
369C2×C42—472no—
370C2×C42—472no—
371C2×C42—472no—
372C2×C42—941no—
373C2×C42—944no—
374C2×C42—948no—
375C4⋊C8—944no—
376C22⋊C8—21no—
377C22⋊C8—472no—
378C22⋊C8—941no—
379C22⋊C8C22×D4712yes—
380C4×C8—944no—
381#95—21no—
382#95—472no—
383#95—944no—
384#95—941no—
385#95C22×D4712yes—
386C24—941no—
387C24D4×D4711yescharacteristic
388C2×Q8—21no—
389C2×Q8—42no—
390C2×Q8C2×C4×D4712yes—
391C2×D4—472no—
392C2×D4—942no—
393C2×D4—942no—
394C2×D4—941no—
395C2×D4—1882no—
396C2×D4—1882no—
397C2×D4—1882no—
398C22×C4—24no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—471no—
406C22×C4—472no—
407C22×C4—472no—
408C22×C4—471no—
409C22×C4—471no—
410C22×C4—471no—
411C22×C4—472no—
412C22×C4—472no—
413C22×C4—944no—
414C22×C4—944no—
415C22×C4—942no—
416C22×C4—942no—
417C22×C4—944no—
418C22×C4—941no—
419C22×C4—942no—
420C22×C4—1884no—
421C22×C4—1882no—
422C22×C4—1882no—
423C22×C4C2×C4×D4711yescharacteristic
424C22×C4C2×C4×D4711yescharacteristic
425C22×C4D4×D4711yescharacteristic
426C22×C4D4×D4711yescharacteristic
427C22×C4D4×D4711yescharacteristic
428C22×C4C23×D4711yescharacteristic
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—942no—
432C2×C8—1882no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—472no—
437C4⋊C4—944no—
438C4⋊C4—944no—
439C4⋊C4—944no—
440C4⋊C4—941no—
441C4⋊C4C2×C4×D4712yes—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—944no—
445C22⋊C4—944no—
446C22⋊C4—944no—
447C22⋊C4—942no—
448C22⋊C4—942no—
449C42—472no—
450C42—472no—
451C42—472no—
452C42—472no—
453C42—472no—
454C42—472no—
455C42—472no—
456C42—472no—
457C42—944no—
458C42—9416no—
459C23—22no—
460C23—22no—
461C23—942no—
462C23—1882no—
463C23—1882no—
464C23—1882no—
465C23C22⋊C4×D4711yescharacteristic
466C23C22⋊C4×D4711yescharacteristic
467C23#1309404512yes—
468C23#1309404712yes—
469C23C2×D4×D4711yescharacteristic
470Q8—42no—
471Q8—42no—
472D4—1882no—
473D4—1882no—
474D4—1884no—
475D4—1882no—
476D4—1882no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—48no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—472no—
492C2×C4—474no—
493C2×C4—472no—
494C2×C4—472no—
495C2×C4—472no—
496C2×C4—944no—
497C2×C4—944no—
498C2×C4—944no—
499C2×C4—942no—
500C2×C4—942no—
501C2×C4—942no—
502C2×C4—942no—
503C2×C4—942no—
504C2×C4—944no—
505C2×C4—942no—
506C2×C4—1888no—
507C2×C4—1882no—
508C2×C4—1888no—
509C2×C4—1882no—
510C2×C4—1882no—
511C2×C4C22⋊C4×D4711yescharacteristic
512C2×C4C22⋊C4×D4711yescharacteristic
513C2×C4C22×C4×D4711yescharacteristic
514C2×C4C2×D4×D4711yescharacteristic
515C8—42no—
516C8—1882no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—24no—
522C22—24no—
523C22—3764no—
524C22—1882no—
525C22—1882no—
526C22—1882no—
527C22#1568909512yes—
528C22#1568911812yes—
529C22#1568911812yes—
530C22#104×D4712yes—
531C22C2×C22⋊C4×D4711yescharacteristic
532C22C2×#1309404511yescharacteristic
533C22C2×#1309404711yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—44no—
539C4—42no—
540C4—42no—
541C4—474no—
542C4—942no—
543C4—942no—
544C4—942no—
545C4—1884no—
546C4—1882no—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—3762no—
551C2#2024187314yesdirect product factor
552C2C2×#1568909511yescharacteristic
553C2C2×#1568911811yescharacteristic
554C2C2×#104×D4711yescharacteristic
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×#1500
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×#15688968C2semidirect
4. #20241873C2direct (N × H)
5. C2×#15688860C2semidirect
8. C2×C47×#328C2semidirect
11. #15689659C4semidirect
14. C2×#13094015C4semidirect
15. C2×#13094013C4semidirect
18. C2×Q8×Dic47C4semidirect
19. C2×#13093986C4semidirect
25. #15689173C22semidirect
30. #15688968C22semidirect
33. #15688860C22semidirect
39. C47×#328C22semidirect
50. #13094015C2×C4semidirect
52. #13094013C2×C4semidirect
60. Q8×Dic47C2×C4semidirect
62. #13093986C2×C4semidirect
275. C2×#328D47semidirect
281. C2×C47#1500semidirect
314. #328C2×D47semidirect
317. C47C2×#1500semidirect
551. C2#20241873direct (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×#156889682
#202418732
C2×#156888602
C2×#156888582
C2×#156888562
C2×C47×#3282
C2×#150047