Finite Group Databasebeta

← C2×#20256011 #27095025

Subgroups — C2×#20256011 #27095025

Order 12032.

1930 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689839C211yesmaximal, characteristic
2C2×#15689833C211yesmaximal, characteristic, complemented
3#20256011C2116yesmaximal, direct product factor
4C2×#15689526C211yesmaximal, characteristic, complemented
5C2×#15689462C212yesmaximal, complemented
6C2×#15689438C212yesmaximal, complemented
7C2×#15689414C211yesmaximal, characteristic, complemented
8C2×#15689372C212yesmaximal, complemented
9C2×C4×#10625336C211yesmaximal, characteristic, complemented
10C2×#15689200C211yesmaximal, characteristic, complemented
11C2×#15689164C212yesmaximal, complemented
12C2×C47×#477C211yesmaximal, characteristic, complemented
13C22×#10625336C2211yescharacteristic
14C22×#10625324C2212yes—
15#15689839—24no—
16#15689839C2218yes—
17#15689833—24no—
18#15689833C2218yescomplemented
19C2×#13094024C2211yescharacteristic
20C2×#13094016—21no—
21C2×#13094013—22no—
22C2×#13094002—22no—
23C2×#13094000C2212yes—
24C2×#13093999—21no—
25C2×#13093999C2212yes—
26C2×C4×D188—21no—
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×#13093982—21no—
30C2×#13093982C2212yes—
31C2×C4⋊C4×D47C2212yes—
32#15689526C2218yescomplemented
33#15689462C22116yescomplemented
34#15689438C22116yescomplemented
35#15689414C2218yescomplemented
36#15689372C22116yescomplemented
37C4×#10625336C2218yescomplemented
38#15689200C2218yescomplemented
39#15689164C22116yescomplemented
40C2×#13093957C2212yes—
41C2×#13093957C2212yes—
42C2×#13093956C2212yes—
43C2×#13093955C2211yescharacteristic
44C2×#13093948C2211yescharacteristic
45C2×#13093946C2212yes—
46C2×#13093944C2211yescharacteristic
47C2×(C2×D47)⋊C8C2212yes—
48C2×C4×C47⋊C8C2211yescharacteristic
49C2×C4⋊Q8×C47C2211yescharacteristic
50C2×C4×Q8×C47C2211yescharacteristic
51C47×#477C2218yescomplemented
52C2×#107×C47C2212yes—
53C2×C4⋊C8×C47C2211yescharacteristic
54C2×#103×C47C2212yes—
55C22×Dic94—21no—
56C22×D188—22no—
57C22×D188D411yescharacteristic
58C22×D188C2311yescharacteristic
59C22×C4×D47—21no—
60C22×C4×D47—22no—
61C22×C4×D47C2312yes—
62C2×#10625336—24no—
63C2×#10625336C2314yes—
64C2×#10625324—28no—
65C2×#10625324C2318yes—
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094024—22no—
69#13094024C2314yes—
70#13094016—28no—
71#13094013—216no—
72#13094002—216no—
73#13094000—24no—
74#13094000C2318yes—
75#13093999—28no—
76#13093999—24no—
77#13093999C2318yes—
78C4×D188—28no—
79C4×D188—22no—
80C4×D188D414yes—
81C4×D188C2314yes—
82C4×D188C2314yes—
83#13093982—24no—
84#13093982—28no—
85#13093982C2318yes—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47D411yescharacteristic
88C2×C4⋊Dic47C2312yes—
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—22no—
91C2×Dic47⋊C4—22no—
92C4⋊C4×D47—24no—
93C4⋊C4×D47C2318yes—
94C2×(C2×D47)⋊C4—22no—
95C2×(C2×D47)⋊C4—22no—
96C2×(C2×D47)⋊C4—21no—
97C2×(C2×D47)⋊C4—22no—
98C2×(C2×D47)⋊C4D412yes—
99C2×C4×Dic47—22no—
100#13093957C2318yes—
101#13093957C2318yes—
102#13093956C2318yes—
103#13093955C2314yes—
104#13093948C2314yes—
105#13093946C2318yes—
106#13093944C2314yes—
107(C2×D47)⋊C8C2318yes—
108C4×C47⋊C8C2314yes—
109C22×Q8×C47—21no—
110C22×Q8×C47C2311yescharacteristic
111C22×C8×C47C2312yes—
112C4⋊Q8×C47—22no—
113C4⋊Q8×C47C2314yes—
114C4×Q8×C47—22no—
115C4×Q8×C47C2314yes—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2312yes—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122#107×C47C2318yes—
123C4⋊C8×C47C2314yes—
124#103×C47C2318yes—
125C23×D47—21no—
126C23×D47C2×D412yes—
127C2×Q8×C47—21no—
128C2×Q8×C47—24no—
129C2×Q8×C47—22no—
130C2×Q8×C47—22no—
131C2×Q8×C47—82no—
132C2×Q8×C47C2412yes—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—22no—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×Dic47—21no—
140C22×Dic47—22no—
141C22×Dic47C2×D412yes—
142C2×D188—24no—
143C2×D188—22no—
144C2×D188—22no—
145C2×D188—21no—
146C2×D188—28no—
147C2×D188—84no—
148C2×D188C2×D414yes—
149C2×D188C2412yes—
150C2×C4×D47—24no—
151C2×C4×D47—24no—
152C2×C4×D47—24no—
153C2×C4×D47—28no—
154C2×C4×D47—44no—
155C2×C4×D47—84no—
156C2×C4×D47C2×D414yes—
157C2×C4×D47C2414yes—
158C2×Dic94—24no—
159C2×Dic94—82no—
160C2×C8×C47—24no—
161C2×C8×C47C2414yes—
162C4⋊C4×C47—24no—
163C4⋊C4×C47—24no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47C2414yes—
167C4⋊C4×C47C2412yes—
168C42×C47—24no—
169C42×C47C2×D412yes—
170C42×C47C2412yes—
171#10625336—28no—
172(C2×D47)⋊C4—28no—
173(C2×D47)⋊C4—28no—
174(C2×D47)⋊C4—24no—
175(C2×D47)⋊C4—28no—
176(C2×D47)⋊C4C2×D418yes—
177C4⋊Dic47—22no—
178C4⋊Dic47—24no—
179C4⋊Dic47—21no—
180C4⋊Dic47C2×D414yes—
181C4⋊Dic47C2414yes—
182C4⋊Dic47C2412yes—
183Dic47⋊C4—28no—
184Dic47⋊C4—28no—
185C4×Dic47—28no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8#4114yes—
188C2×C47⋊C8C2412yes—
189C2×C47⋊C8C2412yes—
190#10625324—216no—
191C23×C47C22×D411yescharacteristic
192C22×D47—24no—
193C22×D47—24no—
194C22×D47—24no—
195C22×D47—22no—
196C22×D47—42no—
197C22×D47—42no—
198C22×D47—42no—
199C22×D47C22×D414yes—
200Q8×C47—22no—
201Q8×C47—22no—
202Q8×C47—42no—
203Q8×C47—84no—
204C2×C4×C47—22no—
205C2×C4×C47—24no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—44no—
211C2×C4×C47#13714yes—
212C2×C4×C47C22×D412yes—
213C2×C4×C47C22×D411yescharacteristic
214C2×C4×C47C22×D412yes—
215C2×C4×C47C2×#4112yes—
216C2×C4×C472−1+412yes—
217C2×C4×C47C2511yescharacteristic
218C2×Dic47—24no—
219C2×Dic47—22no—
220C2×Dic47—24no—
221C2×Dic47—42no—
222C2×Dic47—44no—
223C2×Dic47C22×D414yes—
224D188—28no—
225D188—22no—
226D188—22no—
227D188—42no—
228D188—88no—
229C4×D47—28no—
230C4×D47—24no—
231C4×D47—24no—
232C4×D47—48no—
233C4×D47—88no—
234Dic94—84no—
235C8×C47—24no—
236C47⋊C8—22no—
237C47⋊C8C2×#4114yes—
238C2×#3357—471nomaximal, Sylow
239C22×C47#54712yes—
240C22×C47C2×#13712yes—
241C22×C47#57612yes—
242C22×C47C23×D411yescharacteristic
243C2×D47—24no—
244C2×D47—24no—
245C2×D47—24no—
246C2×D47—48no—
247C2×D47—42no—
248C2×D47—42no—
249C2×D47—42no—
250C2×D47—84no—
251C4×C47—22no—
252C4×C47—42no—
253C4×C47—42no—
254C4×C47—44no—
255C4×C47#54712yes—
256C4×C47C2×#13714yes—
257C4×C47C22×#4111yescharacteristic
258C4×C47C2×2−1+411yescharacteristic
259Dic47—24no—
260Dic47—42no—
261Dic47—44no—
262C2×#555—471no—
263C2×#554—471no—
264#3357—4716no—
265C2×#500—471no—
266C2×#485—472no—
267C2×#480—472no—
268C2×#477D4711yescharacteristic, complemented
269C2×#476—471no—
270C2×#468—472no—
271C2×C4×SD16—471no—
272C2×#436—471no—
273C2×#428—472no—
274C2×C47#335714yescomplemented
275C2×C47C2×#54711yescharacteristic
276C2×C47C22×#13711yescharacteristic
277C2×C47C2×#57611yescharacteristic
278D47—44no—
279D47—82no—
280C22×SD16—471no—
281C22×M16—472no—
282#555—478no—
283#555—944no—
284#554—478no—
285#554—944no—
286C2×C4⋊Q8—471no—
287C2×C4⋊Q8C2×D4711yescharacteristic
288C2×#125—941no—
289C2×#124—942no—
290C2×C22⋊Q8—472no—
291C2×C22⋊Q8—942no—
292C2×#121—472no—
293C2×#121—941no—
294C2×C4×Q8C2×D4711yescharacteristic
295C2×C4×D4—471no—
296C2×C4×D4—471no—
297C2×C4×D4—941no—
298C2×#117—472no—
299C2×#117—941no—
300C22×C4⋊C4—472no—
301#500—478no—
302#485—4716no—
303#480—4716no—
304#477C2×D4718yescomplemented
305#476—478no—
306#468—4716no—
307C4×SD16—478no—
308#436—478no—
309#428—4716no—
310C2×#107—472no—
311C2×#107—472no—
312C2×#107C2×D4712yes—
313C2×#106—472no—
314C2×#106—471no—
315C2×C4⋊C8C2×D4711yescharacteristic
316C2×#103—471no—
317C2×#103C2×D4712yes—
318C2×#102—472no—
319C2×#102—471no—
320C2×C22⋊C8—472no—
321C2×C4×C8—471no—
322C47C2×#335711yescharacteristic, complemented, Sylow
323C22×Q8—21no—
324C22×Q8—941no—
325C22×Q8C22×D4711yescharacteristic
326C22×D4—471no—
327C22×D4—471no—
328C22×D4—942no—
329C23×C4—472no—
330C23×C4—942no—
331C23×C4—941no—
332C2×SD16—474no—
333C2×SD16—944no—
334C2×M16—478no—
335C2×M16—948no—
336C22×C8—471no—
337C22×C8—471no—
338C22×C8C22×D4712yes—
339C4⋊Q8—22no—
340C4⋊Q8—474no—
341C4⋊Q8—942no—
342C4⋊Q8C22×D4714yes—
343#125—948no—
344#124—9416no—
345C22⋊Q8—478no—
346C22⋊Q8—9416no—
347C22⋊Q8—944no—
348#121—478no—
349#121—944no—
350#121—948no—
351C4×Q8—22no—
352C4×Q8C22×D4714yes—
353C4×D4—474no—
354C4×D4—474no—
355C4×D4—474no—
356C4×D4—948no—
357C4×D4—942no—
358#117—478no—
359#117—948no—
360#117—944no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—471no—
364C2×C4⋊C4—472no—
365C2×C4⋊C4—471no—
366C2×C4⋊C4—478no—
367C2×C4⋊C4—944no—
368C2×C4⋊C4—942no—
369C2×C4⋊C4—942no—
370C2×C4⋊C4—941no—
371C2×C4⋊C4C22×D4711yescharacteristic
372C2×C4⋊C4C22×D4712yes—
373C2×C22⋊C4—472no—
374C2×C22⋊C4—942no—
375C2×C22⋊C4—942no—
376C2×C22⋊C4—942no—
377C2×C22⋊C4—941no—
378C2×C42—21no—
379C2×C42—942no—
380C2×C42C22×D4711yescharacteristic
381#107—478no—
382#107—478no—
383#107C22×D4718yes—
384#106—478no—
385#106—474no—
386C4⋊C8C22×D4714yes—
387#103—474no—
388#103C22×D4718yes—
389#102—478no—
390#102—474no—
391C22⋊C8—478no—
392C4×C8—474no—
393C24—472no—
394C24—941no—
395C2×Q8—21no—
396C2×Q8—24no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—82no—
400C2×Q8—944no—
401C2×Q8—3762no—
402C2×Q8C23×D4712yes—
403C2×D4—474no—
404C2×D4—472no—
405C2×D4—948no—
406C2×D4—944no—
407C2×D4—941no—
408C2×D4—942no—
409C2×D4—942no—
410C2×D4—3764no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—472no—
415C22×C4—474no—
416C22×C4—474no—
417C22×C4—948no—
418C22×C4—944no—
419C22×C4—944no—
420C22×C4—941no—
421C22×C4—942no—
422C22×C4—944no—
423C22×C4—3764no—
424C22×C4—1884no—
425C22×C4D4×D4711yescharacteristic
426C22×C4D4×D4711yescharacteristic
427C22×C4C23×D4711yescharacteristic
428SD16—948no—
429M16—9416no—
430C2×C8—24no—
431C2×C8—474no—
432C2×C8—472no—
433C2×C8—472no—
434C2×C8—942no—
435C2×C8C23×D4714yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—474no—
441C4⋊C4—474no—
442C4⋊C4—472no—
443C4⋊C4—948no—
444C4⋊C4—948no—
445C4⋊C4—942no—
446C4⋊C4—941no—
447C4⋊C4—944no—
448C4⋊C4C23×D4712yes—
449C4⋊C4C23×D4714yes—
450C22⋊C4—478no—
451C22⋊C4—948no—
452C22⋊C4—948no—
453C22⋊C4—948no—
454C22⋊C4—944no—
455C42—24no—
456C42—948no—
457C42D4×D4712yes—
458C42C23×D4712yes—
459C23—474no—
460C23—944no—
461C23—944no—
462C23—944no—
463C23—942no—
464C23—1882no—
465C23—1882no—
466C23—1882no—
467C23C2×D4×D4711yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—84no—
472Q8—3764no—
473D4—948no—
474D4—942no—
475D4—942no—
476D4—3768no—
477D4—1882no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—474no—
486C2×C4—944no—
487C2×C4—948no—
488C2×C4—944no—
489C2×C4—944no—
490C2×C4—942no—
491C2×C4—944no—
492C2×C4—3768no—
493C2×C4—1882no—
494C2×C4—1884no—
495C2×C4—1888no—
496C2×C4#1309405614yes—
497C2×C4C2×D4×D4712yes—
498C2×C4C2×D4×D4711yescharacteristic
499C2×C4C2×D4×D4712yes—
500C2×C4#41×D4712yes—
501C2×C4#1309407212yes—
502C2×C4C24×D4711yescharacteristic
503C8—24no—
504C8—474no—
505C8—942no—
506C22—944no—
507C22—944no—
508C22—944no—
509C22—3764no—
510C22—1882no—
511C22—1882no—
512C22—1882no—
513C22—1888no—
514C22#1568977512yes—
515C22C2×#1309405612yes—
516C22#1568992712yes—
517C22C22×D4×D4711yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—44no—
522C4—944no—
523C4—1882no—
524C4—1884no—
525C4#1568977512yes—
526C4C2×#1309405614yes—
527C4C2×#41×D4711yescharacteristic
528C4C2×#1309407211yescharacteristic
529C2—3762no—
530C2—1884no—
531C2#2025601114yesdirect product factor
532C2C2×#1568977511yescharacteristic
533C2C22×#1309405611yescharacteristic
534C2C2×#1568992711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#477C2
socleC23×C47C22×D4
prime radicalC2×#15689839C2
hypercenterC2×#477D47
hypocenterC47C2×#3357
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
2. C2×#15689833C2semidirect
3. #20256011C2direct (N × H)
4. C2×#15689526C2semidirect
5. C2×#15689462C2semidirect
6. C2×#15689438C2semidirect
7. C2×#15689414C2semidirect
8. C2×#15689372C2semidirect
9. C2×C4×#10625336C2semidirect
10. C2×#15689200C2semidirect
11. C2×#15689164C2semidirect
12. C2×C47×#477C2semidirect
18. #15689833C22semidirect
32. #15689526C22semidirect
33. #15689462C22semidirect
34. #15689438C22semidirect
35. #15689414C22semidirect
36. #15689372C22semidirect
37. C4×#10625336C22semidirect
38. #15689200C22semidirect
39. #15689164C22semidirect
51. C47×#477C22semidirect
268. C2×#477D47semidirect
274. C2×C47#3357semidirect
304. #477C2×D47semidirect
322. C47C2×#3357semidirect
531. C2#20256011direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898392
C2×#156898332
#202560112
C2×#156895262
C2×#156894622
C2×#156894382
C2×#156894142
C2×#156893722
C2×C4×#106253362
C2×#156892002
C2×#156891642
C2×C47×#4772
C2×#335747