Finite Group Databasebeta

← C2×#20241910 #26183402

Subgroups — C2×#20241910 #26183402

Order 12032.

1206 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689654C211yesmaximal, characteristic
2C2×#15689177C211yesmaximal, characteristic, complemented
3C2×#15688974C211yesmaximal, characteristic, complemented
4#20241910C218yesmaximal, 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×Dic47⋊C4—21no—
23C22×C4×Dic47—21no—
24C22×C4×Dic47C2211yescharacteristic
25#15689177—22no—
26#15689177C2214yescomplemented
27C2×Dic47⋊C8—21no—
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×#13093934—21no—
30#15688974—22no—
31#15688974C2214yescomplemented
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—28no—
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—24no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—24no—
79C2×C4×Dic47—44no—
80C2×C4×Dic47C2×C411yescharacteristic
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47C2×C412yes—
83C2×C4×Dic47D412yes—
84C2×C4×Dic47D411yescharacteristic
85C2×C4×Dic47D411yescharacteristic
86C2×C4×Dic47D412yes—
87C2×C4×Dic47C2312yes—
88Dic47⋊C8—24no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)C2312yes—
91#13093934—24no—
92C47⋊#95—21no—
93C47⋊#95C2312yes—
94C22×D4×C47—21no—
95C22×D4×C47C2×C411yescharacteristic
96C23×C4×C47—21no—
97C23×C4×C47C2311yescharacteristic
98C22×C8×C47—21no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47C2×C412yes—
102#121×C47C2312yes—
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47—21no—
105C22⋊C8×C47—21no—
106C22⋊C8×C47C2312yes—
107#95×C47—21no—
108#95×C47C2312yes—
109C24×C47—21no—
110C24×C47C2×D411yescharacteristic
111C2×D4×C47—22no—
112C2×D4×C47—22no—
113C2×D4×C47—21no—
114C2×D4×C47—42no—
115C2×D4×C47—42no—
116C2×D4×C47—42no—
117C2×D4×C47C22×C412yes—
118C22×C4×C47—24no—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47—42no—
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2411yescharacteristic
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—24no—
133C22×Dic47—24no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—24no—
138C22×Dic47—42no—
139C22×Dic47—42no—
140C22×Dic47—44no—
141C22×Dic47C22⋊C411yescharacteristic
142C22×Dic47C22⋊C411yescharacteristic
143C22×Dic47C22⋊C411yescharacteristic
144C22×Dic47C22⋊C412yes—
145C22×Dic47C22⋊C412yes—
146C22×Dic47C22⋊C411yescharacteristic
147C22×Dic47C2×D412yes—
148C22×Dic47C2×D412yes—
149C2×Dic94—21no—
150C2×Dic94—42no—
151C2×Dic94C22×C412yes—
152C2×C8×C47—22no—
153C2×C8×C47—42no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47C22×C412yes—
156C22⋊C4×C47—22no—
157C22⋊C4×C47—22no—
158C22⋊Dic47—22no—
159C22⋊Dic47—22no—
160C22⋊Dic47—24no—
161C22⋊Dic47—24no—
162C22⋊Dic47—24no—
163C4⋊Dic47—21no—
164C4⋊Dic47—24no—
165C4⋊Dic47C22×C412yes—
166Dic47⋊C4—216no—
167Dic47⋊C4—22no—
168Dic47⋊C4—22no—
169Dic47⋊C4—24no—
170Dic47⋊C4—24no—
171C4×Dic47—24no—
172C4×Dic47—48no—
173C4×Dic47C22⋊C412yes—
174C4×Dic47C22⋊C412yes—
175C4×Dic47C22⋊C412yes—
176C4×Dic47C22⋊C412yes—
177C4×Dic47C22×C412yes—
178C4×Dic47C22×C412yes—
179C4×Dic47C2×D412yes—
180C4×Dic47C2×D412yes—
181C2×C47⋊C8—22no—
182C2×C47⋊C8—42no—
183C23×C47—22no—
184C23×C47—22no—
185C23×C47—22no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47C2×C22⋊C411yescharacteristic
190C23×C47C2×C22⋊C411yescharacteristic
191C23×C47AGL(1,ℤ/8)12yes—
192C23×C47#13712yes—
193C23×C47C22×D411yescharacteristic
194D4×C47—42no—
195D4×C47—42no—
196D4×C47—42no—
197D4×C47—42no—
198D4×C47—44no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—24no—
202C2×C4×C47—22no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—42no—
208C2×C4×C47—48no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47C2×C22⋊C411yescharacteristic
212C2×C4×C47C2×C22⋊C411yescharacteristic
213C2×C4×C47C23×C411yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
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—22no—
226C2×Dic47—42no—
227C2×Dic47—48no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—42no—
231C2×Dic47—48no—
232C2×Dic47#10414yes—
233C2×Dic47C2×C22⋊C412yes—
234C2×Dic47C2×C22⋊C412yes—
235C2×Dic47C2×C22⋊C412yes—
236C2×Dic47C2×C22⋊C412yes—
237Dic94—42no—
238Dic94—42no—
239C8×C47—42no—
240C47⋊C8—42no—
241C2×#1509—471nomaximal, Sylow
242C22×C47—21no—
243C22×C47—21no—
244C22×C47—21no—
245C22×C47—21no—
246C22×C47—24no—
247C22×C47—24no—
248C22×C47—42no—
249C22×C47—42no—
250C22×C47—42no—
251C22×C47—84no—
252C22×C47#41012yes—
253C22×C47#41712yes—
254C22×C47#41712yes—
255C22×C47C2×#10412yes—
256C22×C47C22×C22⋊C411yescharacteristic
257C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C47C2×#13711yescharacteristic
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—44no—
264C4×C47—42no—
265Dic47—22no—
266Dic47—22no—
267Dic47—22no—
268Dic47—44no—
269Dic47—42no—
270Dic47—42no—
271Dic47C2×#10414yes—
272C2×#529—471no—
273C2×#432—471no—
274C2×C4×C4⋊C4—471no—
275#1509—478no—
276C2×#328—471no—
277C2×#328—471no—
278C2×#327—471no—
279C2×#327D4711yescharacteristic
280C2×C47—21no—
281C2×C47—21no—
282C2×C47—22no—
283C2×C47—82no—
284C2×C47#150914yescomplemented
285C2×C47C2×#41011yescharacteristic
286C2×C47C2×#41711yescharacteristic
287C2×C47C22×#10411yescharacteristic
288#529—474no—
289#529—474no—
290#529—942no—
291#529—942no—
292C2×#126—941no—
293C2×#125—471no—
294C2×#124—471no—
295C2×#123—941no—
296C2×C22⋊Q8—471no—
297C2×#121C2×D4711yescharacteristic
298C2×C4×Q8—471no—
299C2×C4×D4—471no—
300C2×C4×D4—941no—
301C2×#117—941no—
302C22×C4⋊C4—941no—
303C22×C42—471no—
304C22×C42—941no—
305#432—474no—
306#432—942no—
307C2×C4⋊C8—941no—
308C2×C22⋊C8—471no—
309C2×C22⋊C8C2×D4711yescharacteristic
310C2×#97—941no—
311C4×C4⋊C4—474no—
312C4×C4⋊C4—942no—
313C2×#95—471no—
314C2×#95C2×D4711yescharacteristic
315#328—474no—
316#328—474no—
317#327—474no—
318#327C2×D4714yes—
319C47C2×#150911yescharacteristic, complemented, Sylow
320C22×Q8—471no—
321C22×D4—21no—
322C22×D4C4×D4711yescharacteristic
323C23×C4—21no—
324C23×C4—471no—
325C23×C4—471no—
326C23×C4—941no—
327C23×C4—941no—
328C23×C4C22×D4711yescharacteristic
329C22×C8—21no—
330C22×C8—941no—
331#126—944no—
332#126—944no—
333#125—474no—
334#125—942no—
335#124—474no—
336#124—942no—
337#123—944no—
338#123—944no—
339C22⋊Q8—472no—
340C22⋊Q8—472no—
341C22⋊Q8—941no—
342C22⋊Q8—941no—
343#121—21no—
344#121—21no—
345#121C4×D4712yes—
346#121C22×D4712yes—
347C4×Q8—474no—
348C4×Q8—942no—
349C4×D4—474no—
350C4×D4—942no—
351C4×D4—944no—
352C4×D4—944no—
353#117—944no—
354#117—944no—
355C2×C4⋊C4—471no—
356C2×C4⋊C4—944no—
357C2×C4⋊C4—941no—
358C2×C4⋊C4—941no—
359C2×C4⋊C4—941no—
360C2×C4⋊C4—948no—
361C2×C4⋊C4—941no—
362C2×C4⋊C4C4×D4711yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—941no—
365C2×C22⋊C4—941no—
366C2×C22⋊C4—941no—
367C2×C22⋊C4—941no—
368C2×C42—471no—
369C2×C42—471no—
370C2×C42—472no—
371C2×C42—471no—
372C2×C42—471no—
373C2×C42—472no—
374C2×C42—472no—
375C2×C42—472no—
376C2×C42—941no—
377C2×C42—944no—
378C2×C42—1884no—
379C4⋊C8—944no—
380C22⋊C8—21no—
381C22⋊C8—472no—
382C22⋊C8—941no—
383C22⋊C8C22×D4712yes—
384#97—944no—
385#95—21no—
386#95—472no—
387#95—941no—
388#95C22×D4712yes—
389C24—21no—
390C24D4×D4711yescharacteristic
391C2×Q8—472no—
392C2×Q8—941no—
393C2×Q8—1882no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4C2×C4×D4712yes—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—471no—
408C22×C4—472no—
409C22×C4—472no—
410C22×C4—471no—
411C22×C4—471no—
412C22×C4—471no—
413C22×C4—472no—
414C22×C4—472no—
415C22×C4—944no—
416C22×C4—944no—
417C22×C4—942no—
418C22×C4—942no—
419C22×C4—944no—
420C22×C4—941no—
421C22×C4—941no—
422C22×C4—942no—
423C22×C4—1884no—
424C22×C4—1882no—
425C22×C4—1882no—
426C22×C4C2×C4×D4711yescharacteristic
427C22×C4C2×C4×D4711yescharacteristic
428C22×C4D4×D4711yescharacteristic
429C22×C4D4×D4711yescharacteristic
430C22×C4D4×D4711yescharacteristic
431C22×C4C23×D4711yescharacteristic
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—942no—
435C2×C8—1882no—
436C4⋊C4—21no—
437C4⋊C4—472no—
438C4⋊C4—944no—
439C4⋊C4—944no—
440C4⋊C4—944no—
441C4⋊C4—9416no—
442C4⋊C4—942no—
443C4⋊C4—941no—
444C4⋊C4—942no—
445C4⋊C4C2×C4×D4712yes—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—944no—
449C22⋊C4—944no—
450C22⋊C4—944no—
451C22⋊C4—942no—
452C22⋊C4—942no—
453C42—472no—
454C42—472no—
455C42—472no—
456C42—472no—
457C42—472no—
458C42—472no—
459C42—472no—
460C42—472no—
461C42—944no—
462C42—1888no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23C22⋊C4×D4711yescharacteristic
470C23C22⋊C4×D4711yescharacteristic
471C23#1309404812yes—
472C23#1309405312yes—
473C23C2×D4×D4711yescharacteristic
474Q8—1882no—
475Q8—1882no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—42no—
480D4—42no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—48no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—472no—
494C2×C4—474no—
495C2×C4—472no—
496C2×C4—472no—
497C2×C4—472no—
498C2×C4—944no—
499C2×C4—944no—
500C2×C4—944no—
501C2×C4—942no—
502C2×C4—942no—
503C2×C4—942no—
504C2×C4—942no—
505C2×C4—942no—
506C2×C4—944no—
507C2×C4—942no—
508C2×C4—942no—
509C2×C4—1888no—
510C2×C4—1882no—
511C2×C4—1888no—
512C2×C4—1882no—
513C2×C4—1882no—
514C2×C4—1882no—
515C2×C4C22⋊C4×D4711yescharacteristic
516C2×C4C22⋊C4×D4711yescharacteristic
517C2×C4C22×C4×D4711yescharacteristic
518C2×C4C2×D4×D4711yescharacteristic
519C8—42no—
520C8—1882no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—24no—
526C22—24no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22#1568909512yes—
532C22#1568912112yes—
533C22#1568912112yes—
534C22#104×D4712yes—
535C22C2×C22⋊C4×D4711yescharacteristic
536C22C2×#1309404811yescharacteristic
537C22C2×#1309405311yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—42no—
544C4—474no—
545C4—942no—
546C4—942no—
547C4—942no—
548C4—1884no—
549C4—1882no—
550C4—1882no—
551C2—21no—
552C2—22no—
553C2—21no—
554C2—82no—
555C2#2024191014yesdirect product factor
556C2C2×#1568909511yescharacteristic
557C2C2×#1568912111yescharacteristic
558C2C2×#104×D4711yescharacteristic
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×#1509
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×#15689177C2semidirect
3. C2×#15688974C2semidirect
4. #20241910C2direct (N × H)
5. C2×#15688861C2semidirect
6. C2×#15688859C2semidirect
11. #15689654C4semidirect
14. C2×#13094015C4semidirect
15. C2×#13094011C4semidirect
18. C2×#13093989C4semidirect
20. C2×D4×Dic47C4semidirect
26. #15689177C22semidirect
31. #15688974C22semidirect
33. #15688861C22semidirect
34. #15688859C22semidirect
49. #13094015C2×C4semidirect
51. #13094011C2×C4semidirect
59. #13093989C2×C4semidirect
63. D4×Dic47C2×C4semidirect
284. C2×C47#1509semidirect
319. C47C2×#1509semidirect
555. C2#20241910direct (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×#156891772
C2×#156889742
#202419102
C2×#156888612
C2×#156888592
C2×#156888572
C2×C47×#3272
C2×#150947