Finite Group Databasebeta

← C2×#20241975 #26184161

Subgroups — C2×#20241975 #26184161

Order 12032.

1166 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic
2C2×#15689075C211yesmaximal, characteristic, complemented
3C2×#97×D47C211yesmaximal, characteristic, complemented
4#20241975C218yesmaximal, direct product factor
5C2×#15688865C211yesmaximal, characteristic, complemented
6C2×#15688862C211yesmaximal, characteristic, complemented
7C2×#15688862C211yesmaximal, characteristic, complemented
8C2×C47×#330C211yesmaximal, characteristic, complemented
9C22×#10625324—21no—
10C22×C8×D47—21no—
11#15689658—22no—
12#15689658—22no—
13#15689658C414yes—
14#15689658C2214yes—
15C2×#13094019—21no—
16C2×#13094012C2211yescharacteristic
17C2×#13094009—21no—
18C2×#13094004C411yescharacteristic
19C2×#13093999C411yescharacteristic
20C2×#13093989C411yescharacteristic
21C2×#13093986—21no—
22C2×#13093986C411yescharacteristic
23C2×#13093982—21no—
24C2×C42×D47C2211yescharacteristic
25#15689075—22no—
26#15689075C2214yescomplemented
27C2×#13093935C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093934—21no—
30#97×D47—22no—
31#97×D47C2214yescomplemented
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—
51C2×C8×D47—28no—
52C2×C8×D47—24no—
53#13094019—24no—
54#13094019—24no—
55#13094012—21no—
56#13094012—21no—
57#13094012C2×C412yes—
58#13094012C2312yes—
59#13094009—24no—
60#13094009—24no—
61#13094004—22no—
62#13094004C2×C414yes—
63#13093999—22no—
64#13093999C2×C414yes—
65#13093989—22no—
66#13093989C2×C414yes—
67#13093986—24no—
68#13093986—24no—
69#13093986—22no—
70#13093986C2×C414yes—
71#13093982—24no—
72#13093982—24no—
73C2×C4⋊Dic47—21no—
74C2×Dic47⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×C4×Dic47—21no—
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C42×D47C2×C412yes—
85C42×D47D412yes—
86C42×D47D412yes—
87C42×D47C2312yes—
88#13093935—21no—
89#13093935—21no—
90#13093935C2312yes—
91#13093935C2312yes—
92#13093934—24no—
93C8×Dic47—24no—
94C22×C8×C47—21no—
95C22×C8×C47—21no—
96#125×C47—21no—
97#125×C47—21no—
98#125×C47C2×C412yes—
99#125×C47C2312yes—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C42×C47C2311yescharacteristic
105#97×C47—21no—
106#97×C47—21no—
107#97×C47C2312yes—
108#97×C47C2312yes—
109C23×D47—21no—
110C23×D47C22⋊C411yescharacteristic
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×Dic47—21no—
117C22×Dic47C22⋊C411yescharacteristic
118C22×Dic47C22⋊C411yescharacteristic
119C22×Dic47C22⋊C411yescharacteristic
120C2×D188—24no—
121C2×D188—21no—
122C2×D188—42no—
123C2×D188—44no—
124C2×D188C22×C412yes—
125C2×C4×D47—24no—
126C2×C4×D47—24no—
127C2×C4×D47—24no—
128C2×C4×D47—42no—
129C2×C4×D47—44no—
130C2×C4×D47C22⋊C412yes—
131C2×C4×D47C22⋊C412yes—
132C2×C4×D47C22⋊C412yes—
133C2×C4×D47C22×C412yes—
134C2×C4×D47C2×D412yes—
135C2×C4×D47C2×D412yes—
136C2×Dic94—21no—
137C2×Dic94—42no—
138C2×Dic94C22×C412yes—
139C2×C8×C47—24no—
140C2×C8×C47—24no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C4⋊C4×C47—22no—
144C4⋊C4×C47—22no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—22no—
148C4⋊C4×C47—22no—
149C4⋊C4×C47C22×C412yes—
150C4⋊C4×C47C22×C412yes—
151C42×C47C22×C411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C42×C47C2×D411yescharacteristic
154C42×C47C2411yescharacteristic
155(C2×D47)⋊C4—24no—
156(C2×D47)⋊C4—22no—
157(C2×D47)⋊C4—22no—
158(C2×D47)⋊C4—22no—
159(C2×D47)⋊C4—22no—
160(C2×D47)⋊C4—24no—
161(C2×D47)⋊C4—24no—
162C4⋊Dic47—24no—
163Dic47⋊C4—24no—
164C4×Dic47—24no—
165C4×Dic47C22⋊C412yes—
166C4×Dic47C22⋊C412yes—
167C4×Dic47C22⋊C412yes—
168C4×Dic47C22×C412yes—
169C4×Dic47C2×D412yes—
170C4×Dic47C2×D412yes—
171C2×C47⋊C8—24no—
172C2×C47⋊C8—24no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175#10625324—216no—
176C8×D47—216no—
177C23×C47C2×C22⋊C411yescharacteristic
178C22×D47—22no—
179C22×D47—22no—
180C22×D47—22no—
181C22×D47—42no—
182C22×D47—42no—
183C22×D47—42no—
184C22×D47#10414yes—
185C22×D47C2×C22⋊C412yes—
186C2×C4×C47—22no—
187C2×C4×C47—22no—
188C2×C4×C47—22no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—42no—
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
199C2×Dic47—22no—
200C2×Dic47—22no—
201C2×Dic47—22no—
202C2×Dic47—42no—
203C2×Dic47#10414yes—
204C2×Dic47C2×C22⋊C412yes—
205C2×Dic47C2×C22⋊C412yes—
206C2×Dic47C2×C22⋊C412yes—
207D188—42no—
208D188—42no—
209D188—48no—
210C4×D47—24no—
211C4×D47—24no—
212C4×D47—24no—
213C4×D47—24no—
214C4×D47—42no—
215C4×D47—42no—
216C4×D47—48no—
217Dic94—42no—
218Dic94—42no—
219C8×C47—24no—
220C8×C47—24no—
221C47⋊C8—24no—
222C47⋊C8—24no—
223C2×#1524—471nomaximal, Sylow
224C22×C47#41312yes—
225C22×C47C2×#10412yes—
226C22×C47C2×#10412yes—
227C22×C47C22×C22⋊C411yescharacteristic
228C2×D47—22no—
229C2×D47—22no—
230C2×D47—28no—
231C2×D47—42no—
232C2×D47—42no—
233C2×D47—42no—
234C2×D47—84no—
235C2×D47C2×#10414yes—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—21no—
240C4×C47—21no—
241C4×C47—21no—
242C4×C47—42no—
243C4×C47—42no—
244Dic47—22no—
245Dic47—22no—
246Dic47—42no—
247Dic47C2×#10414yes—
248C2×#529—471no—
249C2×C4×M16—471no—
250C22×#97—471no—
251#1524—478no—
252C2×#330—471no—
253C2×#330D4711yescharacteristic, complemented
254C2×#329—471no—
255C2×#329—471no—
256C2×C47#152414yescomplemented
257C2×C47C2×#41311yescharacteristic
258C2×C47C22×#10411yescharacteristic
259C2×C47C22×#10411yescharacteristic
260D47—24no—
261D47—82no—
262C22×M16—941no—
263C23×C8—941no—
264#529—474no—
265#529—474no—
266#529—942no—
267#529—942no—
268C2×#126—941no—
269C2×#125C2×D4711yescharacteristic
270C2×#124—471no—
271C2×#123—941no—
272C2×C22⋊Q8—471no—
273C2×#121—471no—
274C2×C4×Q8—471no—
275C2×C4×D4—471no—
276C2×C4×D4—941no—
277C2×#117—941no—
278C22×C42—471no—
279C4×M16—474no—
280C4×M16—942no—
281C2×#97—471no—
282C2×#97—471no—
283C2×#97—474no—
284C2×#97—942no—
285C2×#97—941no—
286C2×#97C2×D4711yescharacteristic
287C2×#97C2×D4711yescharacteristic
288C2×C4×C8—941no—
289#330—474no—
290#330C2×D4714yescomplemented
291#329—474no—
292#329—474no—
293C47C2×#152411yescharacteristic, complemented, Sylow
294C22×Q8—471no—
295C22×D4—471no—
296C22×D4—941no—
297C23×C4—471no—
298C23×C4—471no—
299C23×C4—471no—
300C23×C4—941no—
301C2×M16—944no—
302C2×M16—948no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—944no—
306C22×C8—948no—
307C22×C8—941no—
308C22×C8—941no—
309#126—944no—
310#126—944no—
311#125—21no—
312#125—21no—
313#125C4×D4712yes—
314#125C22×D4712yes—
315#124—472no—
316#124—472no—
317#124—941no—
318#124—941no—
319#123—944no—
320#123—944no—
321C22⋊Q8—474no—
322C22⋊Q8—942no—
323#121—474no—
324#121—942no—
325C4×Q8—474no—
326C4×Q8—942no—
327C4×D4—474no—
328C4×D4—942no—
329C4×D4—944no—
330C4×D4—944no—
331#117—944no—
332#117—944no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—941no—
336C2×C4⋊C4—941no—
337C2×C4⋊C4C4×D4711yescharacteristic
338C2×C4⋊C4C4×D4711yescharacteristic
339C2×C22⋊C4—941no—
340C2×C22⋊C4—941no—
341C2×C22⋊C4—941no—
342C2×C22⋊C4—941no—
343C2×C22⋊C4—941no—
344C2×C42—471no—
345C2×C42—471no—
346C2×C42—471no—
347C2×C42—472no—
348C2×C42—472no—
349C2×C42—472no—
350C2×C42—472no—
351C2×C42—941no—
352C2×C42C22×D4711yescharacteristic
353#97—21no—
354#97—21no—
355#97—472no—
356#97—472no—
357#97—944no—
358#97—941no—
359#97—941no—
360#97C22×D4712yes—
361#97C22×D4712yes—
362C4×C8—944no—
363C24—471no—
364C24—941no—
365C2×Q8—472no—
366C2×Q8—941no—
367C2×Q8—1882no—
368C2×D4—472no—
369C2×D4—944no—
370C2×D4—941no—
371C2×D4—1882no—
372C2×D4—1884no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—471no—
376C22×C4—471no—
377C22×C4—471no—
378C22×C4—472no—
379C22×C4—472no—
380C22×C4—472no—
381C22×C4—472no—
382C22×C4—472no—
383C22×C4—472no—
384C22×C4—944no—
385C22×C4—944no—
386C22×C4—944no—
387C22×C4—941no—
388C22×C4—1882no—
389C22×C4—1884no—
390C22×C4C2×C4×D4711yescharacteristic
391C22×C4D4×D4711yescharacteristic
392C22×C4D4×D4711yescharacteristic
393M16—9416no—
394C2×C8—24no—
395C2×C8—24no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—9416no—
399C2×C8—944no—
400C2×C8—944no—
401C2×C8—942no—
402C2×C8—942no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—944no—
410C4⋊C4—944no—
411C4⋊C4C2×C4×D4712yes—
412C4⋊C4C2×C4×D4712yes—
413C22⋊C4—944no—
414C22⋊C4—944no—
415C22⋊C4—944no—
416C22⋊C4—942no—
417C22⋊C4—942no—
418C22⋊C4—942no—
419C22⋊C4—942no—
420C42—472no—
421C42—472no—
422C42—472no—
423C42—472no—
424C42—472no—
425C42—472no—
426C42—944no—
427C42C2×C4×D4711yescharacteristic
428C42D4×D4711yescharacteristic
429C42D4×D4711yescharacteristic
430C42C23×D4711yescharacteristic
431C23—472no—
432C23—474no—
433C23—942no—
434C23—942no—
435C23—942no—
436C23—1882no—
437C23—1882no—
438C23—1882no—
439C23C22⋊C4×D4711yescharacteristic
440Q8—1882no—
441Q8—1882no—
442D4—1882no—
443D4—1882no—
444D4—1888no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—472no—
453C2×C4—474no—
454C2×C4—472no—
455C2×C4—472no—
456C2×C4—944no—
457C2×C4—944no—
458C2×C4—944no—
459C2×C4—944no—
460C2×C4—942no—
461C2×C4—942no—
462C2×C4—942no—
463C2×C4—1882no—
464C2×C4—1882no—
465C2×C4—1888no—
466C2×C4—1882no—
467C2×C4C22⋊C4×D4711yescharacteristic
468C2×C4C22⋊C4×D4711yescharacteristic
469C2×C4C22⋊C4×D4711yescharacteristic
470C2×C4C22×C4×D4711yescharacteristic
471C2×C4C2×D4×D4711yescharacteristic
472C2×C4C2×D4×D4711yescharacteristic
473C8—24no—
474C8—24no—
475C8—944no—
476C8—944no—
477C22—474no—
478C22—942no—
479C22—948no—
480C22—942no—
481C22—3764no—
482C22—1882no—
483C22—1882no—
484C22—1882no—
485C22#1568910612yes—
486C22#104×D4712yes—
487C22#104×D4712yes—
488C22C2×C22⋊C4×D4711yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—42no—
496C4—42no—
497C4—474no—
498C4—942no—
499C4—942no—
500C4—1882no—
501C2—944no—
502C2—3762no—
503C2#2024197514yesdirect product factor
504C2C2×#1568910611yescharacteristic
505C2C2×#104×D4711yescharacteristic
506C2C2×#104×D4711yescharacteristic
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×#1524
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×#15689075C2semidirect
3. C2×#97×D47C2semidirect
4. #20241975C2direct (N × H)
5. C2×#15688865C2semidirect
6. C2×#15688862C2semidirect
7. C2×#15688862C2semidirect
8. C2×C47×#330C2semidirect
26. #15689075C22semidirect
31. #97×D47C22semidirect
33. #15688865C22semidirect
34. #15688862C22semidirect
35. #15688862C22semidirect
39. C47×#330C22semidirect
253. C2×#330D47semidirect
256. C2×C47#1524semidirect
290. #330C2×D47semidirect
293. C47C2×#1524semidirect
503. C2#20241975direct (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×#156890752
C2×#97×D472
#202419752
C2×#156888652
C2×#156888622
C2×C47×#3302
C2×#152447