Finite Group Databasebeta

← C2×#20241994 #26184190

Subgroups — C2×#20241994 #26184190

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×#15689658C211yesmaximal, characteristic
2C2×#15689178C211yesmaximal, characteristic, complemented
3C2×#15689075C211yesmaximal, characteristic, complemented
4#20241994C218yesmaximal, direct product factor
5C2×#15688865C211yesmaximal, characteristic, complemented
6C2×#15688862C211yesmaximal, characteristic, complemented
7C2×#15688862C211yesmaximal, characteristic, complemented
8C2×C47×#330C211yesmaximal, characteristic, complemented
9C22×#10625324—21no—
10#15689658—22no—
11#15689658—22no—
12#15689658C414yes—
13#15689658C2214yes—
14C2×#13094019—21no—
15C2×#13094012C2211yescharacteristic
16C2×#13094009—21no—
17C2×#13094004C411yescharacteristic
18C2×#13093999C411yescharacteristic
19C2×#13093989C411yescharacteristic
20C2×#13093986—21no—
21C2×#13093986C411yescharacteristic
22C2×#13093982—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#15688865C2214yescomplemented
34#15688862C2214yescomplemented
35#15688862C2214yescomplemented
36C2×#125×C47C2211yescharacteristic
37C2×#97×C47C2211yescharacteristic
38C2×#97×C47C2211yescharacteristic
39C47×#330C2214yescomplemented
40C22×Dic94C2×C411yescharacteristic
41C22×D188—21no—
42C22×D188C2×C411yescharacteristic
43C22×C4×D47—21no—
44C22×C4×D47C2×C411yescharacteristic
45C22×C4×D47D411yescharacteristic
46C22×C4×D47D411yescharacteristic
47C2×#10625324—28no—
48C2×#10625324—24no—
49C22×C47⋊C8—21no—
50C22×C47⋊C8—21no—
51#13094019—24no—
52#13094019—24no—
53#13094012—21no—
54#13094012—21no—
55#13094012C2×C412yes—
56#13094012C2312yes—
57#13094009—24no—
58#13094009—24no—
59#13094004—22no—
60#13094004C2×C414yes—
61#13093999—22no—
62#13093999C2×C414yes—
63#13093989—22no—
64#13093989C2×C414yes—
65#13093986—24no—
66#13093986—24no—
67#13093986—22no—
68#13093986C2×C414yes—
69#13093982—24no—
70#13093982—24no—
71C2×C4⋊Dic47—21no—
72C2×Dic47⋊C4—21no—
73C2×(C2×D47)⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—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×C8×C47—21no—
94C22×C8×C47—21no—
95#125×C47—21no—
96#125×C47—21no—
97#125×C47C2×C412yes—
98#125×C47C2312yes—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#97×C47—21no—
105#97×C47—21no—
106#97×C47C2312yes—
107#97×C47C2312yes—
108C23×D47—21no—
109C23×D47C22⋊C411yescharacteristic
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×Dic47—21no—
116C22×Dic47C22⋊C411yescharacteristic
117C22×Dic47C22⋊C411yescharacteristic
118C22×Dic47C22⋊C411yescharacteristic
119C2×D188—24no—
120C2×D188—21no—
121C2×D188—42no—
122C2×D188—44no—
123C2×D188C22×C412yes—
124C2×C4×D47—24no—
125C2×C4×D47—24no—
126C2×C4×D47—42no—
127C2×C4×D47—42no—
128C2×C4×D47—44no—
129C2×C4×D47C22⋊C412yes—
130C2×C4×D47C22⋊C412yes—
131C2×C4×D47C22⋊C412yes—
132C2×C4×D47C22×C412yes—
133C2×C4×D47C2×D412yes—
134C2×C4×D47C2×D412yes—
135C2×Dic94—21no—
136C2×Dic94—42no—
137C2×Dic94C22×C412yes—
138C2×C8×C47—24no—
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—42no—
142C4⋊C4×C47—22no—
143C4⋊C4×C47—22no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—22no—
147C4⋊C4×C47—22no—
148C4⋊C4×C47C22×C412yes—
149C4⋊C4×C47C22×C412yes—
150C42×C47C22×C411yescharacteristic
151C42×C47C2×D411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C42×C47C2411yescharacteristic
154(C2×D47)⋊C4—24no—
155(C2×D47)⋊C4—22no—
156(C2×D47)⋊C4—22no—
157(C2×D47)⋊C4—22no—
158(C2×D47)⋊C4—22no—
159(C2×D47)⋊C4—24no—
160(C2×D47)⋊C4—24no—
161C4⋊Dic47—24no—
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×C47C2×C22⋊C411yescharacteristic
176C22×D47—22no—
177C22×D47—22no—
178C22×D47—22no—
179C22×D47—22no—
180C22×D47—42no—
181C22×D47—42no—
182C22×D47—42no—
183C22×D47C2×C22⋊C412yes—
184C2×C4×C47—22no—
185C2×C4×C47—22no—
186C2×C4×C47—22no—
187C2×C4×C47—22no—
188C2×C4×C47—22no—
189C2×C4×C47—42no—
190C2×C4×C47—42no—
191C2×C4×C47C2×C22⋊C411yescharacteristic
192C2×C4×C47C2×C22⋊C411yescharacteristic
193C2×C4×C47C2×C22⋊C411yescharacteristic
194C2×C4×C47C23×C411yescharacteristic
195C2×C4×C47C22×D411yescharacteristic
196C2×C4×C47C22×D411yescharacteristic
197C2×Dic47—22no—
198C2×Dic47—22no—
199C2×Dic47—22no—
200C2×Dic47—42no—
201C2×Dic47#10414yes—
202C2×Dic47C2×C22⋊C412yes—
203C2×Dic47C2×C22⋊C412yes—
204C2×Dic47C2×C22⋊C412yes—
205D188—42no—
206D188—42no—
207D188—48no—
208C4×D47—24no—
209C4×D47—24no—
210C4×D47—42no—
211C4×D47—42no—
212C4×D47—42no—
213C4×D47—42no—
214C4×D47—48no—
215Dic94—42no—
216Dic94—42no—
217C8×C47—24no—
218C8×C47—42no—
219C47⋊C8—24no—
220C47⋊C8—42no—
221C2×#1529—471nomaximal, Sylow
222C22×C47#41312yes—
223C22×C47C2×#10412yes—
224C22×C47#42112yes—
225C22×C47C22×C22⋊C411yescharacteristic
226C2×D47—22no—
227C2×D47—22no—
228C2×D47—22no—
229C2×D47—44no—
230C2×D47—42no—
231C2×D47—42no—
232C2×D47—42no—
233C2×D47—84no—
234C4×C47—21no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—42no—
241C4×C47—42no—
242Dic47—22no—
243Dic47—22no—
244Dic47—42no—
245Dic47C2×#10414yes—
246C2×#529—471no—
247C2×#432—471no—
248C2×C4×M16—471no—
249#1529—478no—
250C2×#330—471no—
251C2×#330D4711yescharacteristic, complemented
252C2×#329—471no—
253C2×#329—471no—
254C2×C47#152914yescomplemented
255C2×C47C2×#41311yescharacteristic
256C2×C47C22×#10411yescharacteristic
257C2×C47C2×#42111yescharacteristic
258D47—42no—
259D47—82no—
260C22×M16—941no—
261#529—474no—
262#529—474no—
263#529—942no—
264#529—942no—
265C2×#126—941no—
266C2×#125C2×D4711yescharacteristic
267C2×#124—471no—
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#330C2×D4714yescomplemented
289#329—474no—
290#329—474no—
291C47C2×#152911yescharacteristic, complemented, Sylow
292C22×Q8—471no—
293C22×D4—471no—
294C22×D4—941no—
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—21no—
308#125—21no—
309#125C4×D4712yes—
310#125C22×D4712yes—
311#124—472no—
312#124—472no—
313#124—941no—
314#124—941no—
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—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—941no—
332C2×C4⋊C4—941no—
333C2×C4⋊C4C4×D4711yescharacteristic
334C2×C4⋊C4C4×D4711yescharacteristic
335C2×C22⋊C4—941no—
336C2×C22⋊C4—941no—
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—471no—
361C24—941no—
362C2×Q8—472no—
363C2×Q8—941no—
364C2×Q8—1882no—
365C2×D4—472no—
366C2×D4—944no—
367C2×D4—941no—
368C2×D4—1882no—
369C2×D4—1884no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—471no—
373C22×C4—471no—
374C22×C4—471no—
375C22×C4—472no—
376C22×C4—472no—
377C22×C4—472no—
378C22×C4—472no—
379C22×C4—472no—
380C22×C4—472no—
381C22×C4—944no—
382C22×C4—944no—
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—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—944no—
406C4⋊C4—944no—
407C4⋊C4C2×C4×D4712yes—
408C4⋊C4C2×C4×D4712yes—
409C22⋊C4—944no—
410C22⋊C4—944no—
411C22⋊C4—944no—
412C22⋊C4—942no—
413C22⋊C4—942no—
414C22⋊C4—942no—
415C22⋊C4—942no—
416C42—472no—
417C42—472no—
418C42—472no—
419C42—472no—
420C42—472no—
421C42—472no—
422C42—944no—
423C42C2×C4×D4711yescharacteristic
424C42D4×D4711yescharacteristic
425C42D4×D4711yescharacteristic
426C42C23×D4711yescharacteristic
427C23—472no—
428C23—942no—
429C23—942no—
430C23—942no—
431C23—942no—
432C23—1882no—
433C23—1882no—
434C23—1882no—
435C23C22⋊C4×D4711yescharacteristic
436Q8—1882no—
437Q8—1882no—
438D4—1882no—
439D4—1882no—
440D4—1888no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—472no—
449C2×C4—474no—
450C2×C4—472no—
451C2×C4—472no—
452C2×C4—944no—
453C2×C4—944no—
454C2×C4—942no—
455C2×C4—942no—
456C2×C4—942no—
457C2×C4—1882no—
458C2×C4—1882no—
459C2×C4—1882no—
460C2×C4—1882no—
461C2×C4—1888no—
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—942no—
474C22—942no—
475C22—942no—
476C22—3764no—
477C22—1882no—
478C22—1882no—
479C22—1882no—
480C22—1884no—
481C22#1568910612yes—
482C22#104×D4712yes—
483C22#1568913812yes—
484C22C2×C22⋊C4×D4711yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—474no—
494C4—942no—
495C4—942no—
496C4—1882no—
497C2—3762no—
498C2—1882no—
499C2#2024199414yesdirect product factor
500C2C2×#1568910611yescharacteristic
501C2C2×#104×D4711yescharacteristic
502C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×#330C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093999C4
cosocleC42×C47C24
hypercenterC2×#330D47
hypocenterC47C2×#1529
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
2. C2×#15689178C2semidirect
3. C2×#15689075C2semidirect
4. #20241994C2direct (N × H)
5. C2×#15688865C2semidirect
6. C2×#15688862C2semidirect
7. C2×#15688862C2semidirect
8. C2×C47×#330C2semidirect
25. #15689178C22semidirect
29. #15689075C22semidirect
33. #15688865C22semidirect
34. #15688862C22semidirect
35. #15688862C22semidirect
39. C47×#330C22semidirect
251. C2×#330D47semidirect
254. C2×C47#1529semidirect
288. #330C2×D47semidirect
291. C47C2×#1529semidirect
499. C2#20241994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896582
C2×#156891782
C2×#156890752
#202419942
C2×#156888652
C2×#156888622
C2×C47×#3302
C2×#152947