Finite Group Databasebeta

← C2×#20241992 #26184188

Subgroups — C2×#20241992 #26184188

Order 12032.

1070 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689652C211yesmaximal, characteristic
2C2×#15689178C211yesmaximal, characteristic, complemented
3C2×#15689075C211yesmaximal, characteristic, complemented
4#20241992C218yesmaximal, direct product factor
5C2×#15688864C211yesmaximal, characteristic, complemented
6C2×#15688864C211yesmaximal, characteristic, complemented
7C2×#15688863C211yesmaximal, characteristic, complemented
8C2×C47×#329C211yesmaximal, characteristic, complemented
9C22×#10625324—21no—
10#15689652—22no—
11#15689652—22no—
12#15689652C414yes—
13#15689652C2214yes—
14C2×#13094017—21no—
15C2×#13094016C2211yescharacteristic
16C2×#13094006—21no—
17C2×#13094000C411yescharacteristic
18C2×#13093995C411yescharacteristic
19C2×Q8×Dic47C411yescharacteristic
20C2×D4×Dic47C411yescharacteristic
21C2×(C22⋊D47)⋊C4—21no—
22C2×#13093980—21no—
23C2×C42×D47C2211yescharacteristic
24#15689178—22no—
25#15689178C2214yescomplemented
26C2×Dic47⋊C8—21no—
27C2×(C2×D47)⋊C8—21no—
28#15689075—22no—
29#15689075C2214yescomplemented
30C2×#13093935C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C8×Dic47—21no—
33#15688864C2214yescomplemented
34#15688864C2214yescomplemented
35#15688863C2214yescomplemented
36C2×#124×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C47×#329C2214yescomplemented
40C22×C22⋊D47—21no—
41C23×Dic47—21no—
42C22×C4×D47C2×C411yescharacteristic
43C22×C4×D47D411yescharacteristic
44C22×C4×D47D411yescharacteristic
45C2×#10625324—28no—
46C2×#10625324—24no—
47C22×C47⋊C8—21no—
48C22×C47⋊C8—21no—
49#13094017—24no—
50#13094017—24no—
51#13094016—21no—
52#13094016—21no—
53#13094016C2×C412yes—
54#13094016C2312yes—
55#13094006—24no—
56#13094006—24no—
57#13094000—22no—
58#13094000C2×C414yes—
59#13093995—22no—
60#13093995C2×C414yes—
61Q8×Dic47—22no—
62Q8×Dic47C2×C414yes—
63D4×Dic47—22no—
64D4×Dic47C2×C414yes—
65(C22⋊D47)⋊C4—24no—
66(C22⋊D47)⋊C4—24no—
67#13093980—24no—
68#13093980—24no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47C2×C411yescharacteristic
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47D411yescharacteristic
81C2×C4×Dic47D411yescharacteristic
82C42×D47C2×C412yes—
83C42×D47D412yes—
84C42×D47D412yes—
85C42×D47C2312yes—
86Dic47⋊C8—24no—
87(C2×D47)⋊C8—24no—
88#13093935—21no—
89#13093935—21no—
90#13093935C2312yes—
91#13093935C2312yes—
92C8×Dic47—24no—
93C22×Q8×C47C2×C411yescharacteristic
94C22×D4×C47C2×C411yescharacteristic
95C22×C8×C47—21no—
96C22×C8×C47—21no—
97#124×C47—21no—
98#124×C47—21no—
99#124×C47C2×C412yes—
100#124×C47C2312yes—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C42×C47C2311yescharacteristic
104#97×C47—21no—
105#97×C47—21no—
106#97×C47C2312yes—
107#97×C47C2312yes—
108C24×C47—21no—
109C23×D47C22⋊C411yescharacteristic
110C2×Q8×C47—21no—
111C2×Q8×C47—42no—
112C2×Q8×C47C22×C412yes—
113C2×D4×C47—21no—
114C2×D4×C47—42no—
115C2×D4×C47C22×C412yes—
116C22×C4×C47—21no—
117C22×C4×C47C22×C411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C2×C22⋊D47—24no—
121C2×C22⋊D47—44no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—24no—
125C22×Dic47—44no—
126C22×Dic47C22⋊C411yescharacteristic
127C22×Dic47C22⋊C411yescharacteristic
128C22×Dic47C22⋊C411yescharacteristic
129C2×C4×D47—24no—
130C2×C4×D47—42no—
131C2×C4×D47—42no—
132C2×C4×D47C22⋊C412yes—
133C2×C4×D47C22⋊C412yes—
134C2×C4×D47C22⋊C412yes—
135C2×C4×D47C22×C412yes—
136C2×C4×D47C2×D412yes—
137C2×C4×D47C2×D412yes—
138C2×C8×C47—24no—
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—42no—
142C22⋊C4×C47—22no—
143C22⋊C4×C47—22no—
144C22⋊C4×C47—22no—
145C22⋊C4×C47—22no—
146C42×C47C22×C411yescharacteristic
147C42×C47C2×D411yescharacteristic
148C42×C47C2×D411yescharacteristic
149C42×C47C2411yescharacteristic
150C22⋊Dic47—24no—
151C22⋊Dic47—24no—
152(C2×D47)⋊C4—24no—
153C4⋊Dic47—21no—
154C4⋊Dic47—21no—
155C4⋊Dic47—24no—
156C4⋊Dic47C22×C412yes—
157C4⋊Dic47C22×C412yes—
158Dic47⋊C4—22no—
159Dic47⋊C4—22no—
160Dic47⋊C4—22no—
161Dic47⋊C4—22no—
162Dic47⋊C4—24no—
163C4×Dic47—24no—
164C4×Dic47C22⋊C412yes—
165C4×Dic47C22⋊C412yes—
166C4×Dic47C22⋊C412yes—
167C4×Dic47C22×C412yes—
168C4×Dic47C2×D412yes—
169C4×Dic47C2×D412yes—
170C2×C47⋊C8—24no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—42no—
174#10625324—216no—
175C23×C47—22no—
176C23×C47—42no—
177C23×C47—42no—
178C23×C47—42no—
179C23×C47C2×C22⋊C411yescharacteristic
180C22×D47—22no—
181C22×D47—22no—
182C22×D47—22no—
183C22×D47C2×C22⋊C412yes—
184Q8×C47—42no—
185Q8×C47—42no—
186D4×C47—42no—
187D4×C47—42no—
188C2×C4×C47—22no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—22no—
192C2×C4×C47—42no—
193C2×C4×C47C2×C22⋊C411yescharacteristic
194C2×C4×C47C2×C22⋊C411yescharacteristic
195C2×C4×C47C2×C22⋊C411yescharacteristic
196C2×C4×C47C23×C411yescharacteristic
197C2×C4×C47C22×D411yescharacteristic
198C2×C4×C47C22×D411yescharacteristic
199C22⋊D47—48no—
200C2×Dic47—22no—
201C2×Dic47—22no—
202C2×Dic47—22no—
203C2×Dic47—22no—
204C2×Dic47—42no—
205C2×Dic47—42no—
206C2×Dic47—48no—
207C2×Dic47#10414yes—
208C2×Dic47C2×C22⋊C412yes—
209C2×Dic47C2×C22⋊C412yes—
210C2×Dic47C2×C22⋊C412yes—
211C4×D47—24no—
212C4×D47—24no—
213C4×D47—42no—
214C4×D47—42no—
215C4×D47—42no—
216C4×D47—42no—
217C8×C47—24no—
218C8×C47—42no—
219C47⋊C8—24no—
220C47⋊C8—42no—
221C2×#1529—471nomaximal, Sylow
222C22×C47—42no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—84no—
226C22×C47#41312yes—
227C22×C47C2×#10412yes—
228C22×C47#42112yes—
229C22×C47C22×C22⋊C411yescharacteristic
230C2×D47—22no—
231C2×D47—22no—
232C2×D47—22no—
233C2×D47—44no—
234C4×C47—21no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—42no—
241Dic47—22no—
242Dic47—22no—
243Dic47—42no—
244Dic47—42no—
245Dic47C2×#10414yes—
246C2×#529—471no—
247C2×#432—471no—
248C2×C4×M16—471no—
249#1529—478no—
250C2×#330—471no—
251C2×#330—471no—
252C2×#329—471no—
253C2×#329D4711yescharacteristic, complemented
254C2×C47—82no—
255C2×C47#152914yescomplemented
256C2×C47C2×#41311yescharacteristic
257C2×C47C22×#10411yescharacteristic
258C2×C47C2×#42111yescharacteristic
259D47—42no—
260C22×M16—941no—
261#529—474no—
262#529—474no—
263#529—942no—
264#529—942no—
265C2×#126—941no—
266C2×#125—471no—
267C2×#124C2×D4711yescharacteristic
268C2×#123—941no—
269C2×C22⋊Q8—471no—
270C2×#121—471no—
271C2×C4×Q8—471no—
272C2×C4×D4—471no—
273C2×C4×D4—941no—
274C2×#117—941no—
275C22×C42—471no—
276#432—474no—
277#432—942no—
278C2×C4⋊C8—941no—
279C2×C22⋊C8—941no—
280C4×M16—474no—
281C4×M16—942no—
282C2×#97—471no—
283C2×#97—471no—
284C2×#97C2×D4711yescharacteristic
285C2×#97C2×D4711yescharacteristic
286C2×C4×C8—941no—
287#330—474no—
288#330—474no—
289#329—474no—
290#329C2×D4714yescomplemented
291C47C2×#152911yescharacteristic, complemented, Sylow
292C22×Q8C4×D4711yescharacteristic
293C22×D4—941no—
294C22×D4C4×D4711yescharacteristic
295C23×C4—471no—
296C23×C4—471no—
297C23×C4—471no—
298C23×C4—941no—
299C2×M16—944no—
300C2×M16—948no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—941no—
304C22×C8—941no—
305#126—944no—
306#126—944no—
307#125—472no—
308#125—472no—
309#125—941no—
310#125—941no—
311#124—21no—
312#124—21no—
313#124C4×D4712yes—
314#124C22×D4712yes—
315#123—944no—
316#123—944no—
317C22⋊Q8—474no—
318C22⋊Q8—942no—
319#121—474no—
320#121—942no—
321C4×Q8—474no—
322C4×Q8—942no—
323C4×D4—474no—
324C4×D4—942no—
325C4×D4—944no—
326C4×D4—944no—
327#117—944no—
328#117—944no—
329C2×C4⋊C4—471no—
330C2×C4⋊C4—471no—
331C2×C4⋊C4—941no—
332C2×C4⋊C4—941no—
333C2×C4⋊C4—941no—
334C2×C4⋊C4—941no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—941no—
338C2×C22⋊C4—941no—
339C2×C22⋊C4—941no—
340C2×C42—471no—
341C2×C42—471no—
342C2×C42—471no—
343C2×C42—472no—
344C2×C42—472no—
345C2×C42—472no—
346C2×C42—472no—
347C2×C42—941no—
348C2×C42C22×D4711yescharacteristic
349C4⋊C8—944no—
350C22⋊C8—944no—
351#97—21no—
352#97—21no—
353#97—472no—
354#97—472no—
355#97—941no—
356#97—941no—
357#97C22×D4712yes—
358#97C22×D4712yes—
359C4×C8—944no—
360C24—21no—
361C24—471no—
362C2×Q8—21no—
363C2×Q8—42no—
364C2×Q8C2×C4×D4712yes—
365C2×D4—21no—
366C2×D4—42no—
367C2×D4—944no—
368C2×D4—1884no—
369C2×D4C2×C4×D4712yes—
370C22×C4—21no—
371C22×C4—471no—
372C22×C4—471no—
373C22×C4—471no—
374C22×C4—472no—
375C22×C4—472no—
376C22×C4—472no—
377C22×C4—472no—
378C22×C4—472no—
379C22×C4—472no—
380C22×C4—944no—
381C22×C4—944no—
382C22×C4—941no—
383C22×C4—941no—
384C22×C4—1882no—
385C22×C4—1882no—
386C22×C4—1884no—
387C22×C4C2×C4×D4711yescharacteristic
388C22×C4D4×D4711yescharacteristic
389C22×C4D4×D4711yescharacteristic
390M16—9416no—
391C2×C8—24no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—42no—
395C2×C8—944no—
396C2×C8—942no—
397C2×C8—942no—
398C2×C8—1882no—
399C4⋊C4—472no—
400C4⋊C4—472no—
401C4⋊C4—944no—
402C4⋊C4—944no—
403C4⋊C4—942no—
404C4⋊C4—942no—
405C4⋊C4—941no—
406C4⋊C4—941no—
407C4⋊C4—942no—
408C4⋊C4—942no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—944no—
414C22⋊C4—944no—
415C22⋊C4—944no—
416C42—472no—
417C42—472no—
418C42—472no—
419C42—472no—
420C42—472no—
421C42—472no—
422C42—944no—
423C42C2×C4×D4711yescharacteristic
424C42D4×D4711yescharacteristic
425C42D4×D4711yescharacteristic
426C42C23×D4711yescharacteristic
427C23—22no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—472no—
432C23—942no—
433C23—942no—
434C23—942no—
435C23C22⋊C4×D4711yescharacteristic
436Q8—42no—
437Q8—42no—
438D4—42no—
439D4—42no—
440D4—1888no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—42no—
446C2×C4—472no—
447C2×C4—474no—
448C2×C4—472no—
449C2×C4—472no—
450C2×C4—944no—
451C2×C4—944no—
452C2×C4—942no—
453C2×C4—942no—
454C2×C4—942no—
455C2×C4—942no—
456C2×C4—1882no—
457C2×C4—1882no—
458C2×C4—1882no—
459C2×C4—1882no—
460C2×C4—1888no—
461C2×C4—1882no—
462C2×C4—1882no—
463C2×C4C22⋊C4×D4711yescharacteristic
464C2×C4C22⋊C4×D4711yescharacteristic
465C2×C4C22⋊C4×D4711yescharacteristic
466C2×C4C22×C4×D4711yescharacteristic
467C2×C4C2×D4×D4711yescharacteristic
468C2×C4C2×D4×D4711yescharacteristic
469C8—24no—
470C8—42no—
471C8—944no—
472C8—1882no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—84no—
477C22—942no—
478C22—942no—
479C22—942no—
480C22—1884no—
481C22#1568910412yes—
482C22#104×D4712yes—
483C22#1568913812yes—
484C22C2×C22⋊C4×D4711yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—474no—
493C4—942no—
494C4—942no—
495C4—1882no—
496C4—1882no—
497C2—82no—
498C2—1882no—
499C2#2024199214yesdirect product factor
500C2C2×#1568910411yescharacteristic
501C2C2×#104×D4711yescharacteristic
502C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#329C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093995C4
cosocleC42×C47C24
hypercenterC2×#329D47
hypocenterC47C2×#1529
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. C2×#15689178C2semidirect
3. C2×#15689075C2semidirect
4. #20241992C2direct (N × H)
5. C2×#15688864C2semidirect
6. C2×#15688864C2semidirect
7. C2×#15688863C2semidirect
8. C2×C47×#329C2semidirect
25. #15689178C22semidirect
29. #15689075C22semidirect
33. #15688864C22semidirect
34. #15688864C22semidirect
35. #15688863C22semidirect
39. C47×#329C22semidirect
253. C2×#329D47semidirect
255. C2×C47#1529semidirect
290. #329C2×D47semidirect
291. C47C2×#1529semidirect
499. C2#20241992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896522
C2×#156891782
C2×#156890752
#202419922
C2×#156888642
C2×#156888632
C2×C47×#3292
C2×#152947