Finite Group Databasebeta

← C2×#20256073 #27095890

Subgroups — C2×#20256073 #27095890

Order 12032.

1830 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689846C211yesmaximal, characteristic
2#20256073C2116yesmaximal, direct product factor
3C2×#15689480C212yesmaximal
4C2×#15689475C211yesmaximal, characteristic, complemented
5C2×#15689427C212yesmaximal, complemented
6C2×#15689400C211yesmaximal, characteristic
7C2×#15689345C212yesmaximal
8C2×#15689333C211yesmaximal, characteristic, complemented
9C2×Q8×C47⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#10625337C212yesmaximal, complemented
11C2×C4×#10625336C211yesmaximal, characteristic
12C2×C47×#557C211yesmaximal, characteristic, complemented
13C22×#10625337C2212yes—
14C22×#10625336C2211yescharacteristic
15#15689846—24no—
16#15689846C2218yes—
17C2×#13094024C2211yescharacteristic
18C2×#13094019—22no—
19C2×#13094012C2212yes—
20C2×#13094000—21no—
21C2×C4×Dic94C2212yes—
22C2×C4×D188C2211yescharacteristic
23C2×#13093982—21no—
24#15689480C22116yes—
25#15689475C2218yescomplemented
26#15689427C22116yescomplemented
27#15689400C2218yes—
28#15689345C22116yes—
29#15689333C2218yescomplemented
30Q8×C47⋊C8C2218yescomplemented
31C4×#10625337C22116yescomplemented
32C4×#10625336C2218yes—
33C2×#13093957C2212yes—
34C2×#13093955C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×C4⋊(C47⋊C8)C2212yes—
37C2×#13093948C2211yescharacteristic
38C2×#13093947C2212yes—
39C2×#13093947C2212yes—
40C2×#13093947C2212yes—
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2212yes—
43C2×C4×C47⋊C8C2211yescharacteristic
44C2×C4×C47⋊C8C2212yes—
45C47×#557—24no—
46C47×#557C2218yescomplemented
47C2×C4⋊Q8×C47—21no—
48C2×C4⋊Q8×C47C2211yescharacteristic
49C2×#125×C47—22no—
50C2×#125×C47C2212yes—
51C2×C4×Q8×C47—21no—
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2212yes—
54C2×C4×Q8×C47C2211yescharacteristic
55C22×Dic94C2312yes—
56C22×D188C2311yescharacteristic
57C22×C4×D47—21no—
58C2×#10625337—28no—
59C2×#10625337C2318yes—
60C2×#10625336—24no—
61C2×#10625336C2314yes—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2312yes—
64C22×C47⋊C8C2311yescharacteristic
65#13094024—22no—
66#13094024C2314yes—
67#13094019—216no—
68#13094012—24no—
69#13094012C2318yes—
70#13094000—28no—
71C4×Dic94—24no—
72C4×Dic94C2318yes—
73C4×D188—22no—
74C4×D188C2314yes—
75#13093982—28no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47C2311yescharacteristic
79C2×Dic47⋊C4—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×(C2×D47)⋊C4—21no—
82C2×(C2×D47)⋊C4—22no—
83C2×C4×Dic47—22no—
84#13093957C2318yes—
85#13093955C2314yes—
86C4⋊(C47⋊C8)C2314yes—
87C4⋊(C47⋊C8)C2318yes—
88#13093948C2314yes—
89#13093947C2318yes—
90#13093947C2318yes—
91#13093947C2318yes—
92#13093944C2314yes—
93#13093944C2318yes—
94C4×C47⋊C8C2318yes—
95C4×C47⋊C8C2314yes—
96C22×Q8×C47—21no—
97C22×Q8×C47D411yescharacteristic
98C22×Q8×C47C2311yescharacteristic
99C4⋊Q8×C47—28no—
100C4⋊Q8×C47—22no—
101C4⋊Q8×C47C2314yes—
102#125×C47—216no—
103#125×C47—24no—
104#125×C47C2318yes—
105C4×Q8×C47—28no—
106C4×Q8×C47—24no—
107C4×Q8×C47—22no—
108C4×Q8×C47D414yes—
109C4×Q8×C47C2318yes—
110C4×Q8×C47C2314yes—
111C4×Q8×C47C2314yes—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—22no—
117C2×C4⋊C4×C47D411yescharacteristic
118C2×C4⋊C4×C47D412yes—
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2312yes—
121C2×C42×C47—22no—
122C2×C42×C47—21no—
123C2×C42×C47C2312yes—
124C2×C42×C47C2311yescharacteristic
125C23×D47—21no—
126C2×Q8×C47—24no—
127C2×Q8×C47—21no—
128C2×Q8×C47—24no—
129C2×Q8×C47—22no—
130C2×Q8×C47—44no—
131C2×Q8×C47C2×D414yes—
132C2×Q8×C47#4114yes—
133C2×Q8×C47C2412yes—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×Dic47—21no—
143C22×Dic47—22no—
144C2×D188—22no—
145C2×D188—22no—
146C2×D188—21no—
147C2×D188C2412yes—
148C2×C4×D47—24no—
149C2×C4×D47—44no—
150C2×Dic94—24no—
151C2×Dic94—24no—
152C2×Dic94—22no—
153C2×Dic94C2414yes—
154C4⋊C4×C47—28no—
155C4⋊C4×C47—24no—
156C4⋊C4×C47—28no—
157C4⋊C4×C47—24no—
158C4⋊C4×C47—28no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47C2×D414yes—
162C4⋊C4×C47C2×D418yes—
163C4⋊C4×C47C2412yes—
164C4⋊C4×C47C2414yes—
165C42×C47—28no—
166C42×C47—24no—
167C42×C47C2×D414yes—
168C42×C47C2×D412yes—
169C42×C47C2414yes—
170C42×C47C2412yes—
171#10625337—216no—
172#10625336—28no—
173(C2×D47)⋊C4—28no—
174(C2×D47)⋊C4—24no—
175(C2×D47)⋊C4—28no—
176C4⋊Dic47—24no—
177C4⋊Dic47—24no—
178C4⋊Dic47—21no—
179C4⋊Dic47C2412yes—
180Dic47⋊C4—28no—
181C4×Dic47—28no—
182C2×C47⋊C8—22no—
183C2×C47⋊C8—24no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8C2412yes—
186C2×C47⋊C8C2414yes—
187C2×C47⋊C8C2412yes—
188C23×C47C22×D411yescharacteristic
189C22×D47—22no—
190C22×D47—42no—
191C22×D47—42no—
192C22×D47—42no—
193Q8×C47—24no—
194Q8×C47—28no—
195Q8×C47—22no—
196Q8×C47—48no—
197Q8×C47C2×#4114yes—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—24no—
205C2×C4×C47—44no—
206C2×C4×C47—42no—
207C2×C4×C47#13514yes—
208C2×C4×C47C22×D414yes—
209C2×C4×C47C22×D414yes—
210C2×C4×C47C22×D412yes—
211C2×C4×C47C22×D411yescharacteristic
212C2×C4×C47C22×D412yes—
213C2×C4×C47C2×#4112yes—
214C2×C4×C472−1+412yes—
215C2×C4×C47C2511yescharacteristic
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—44no—
219C2×Dic47—42no—
220D188—22no—
221D188—22no—
222D188—42no—
223C4×D47—48no—
224Dic94—24no—
225Dic94—24no—
226Dic94—44no—
227C47⋊C8—22no—
228C47⋊C8—24no—
229C47⋊C8—22no—
230C2×#3364—471nomaximal, Sylow
231C22×C47#54812yes—
232C22×C47C2×#13512yes—
233C22×C47#57812yes—
234C22×C47C23×D411yescharacteristic
235C2×D47—42no—
236C2×D47—42no—
237C2×D47—42no—
238C2×D47—84no—
239C4×C47—24no—
240C4×C47—24no—
241C4×C47—24no—
242C4×C47—22no—
243C4×C47—44no—
244C4×C47—42no—
245C4×C47#54812yes—
246C4×C47C2×#13514yes—
247C4×C47C22×#4111yescharacteristic
248C4×C47C2×2−1+411yescharacteristic
249Dic47—44no—
250Dic47—42no—
251C2×#557D4711yescharacteristic, complemented
252C2×#556—471no—
253#3364—4716no—
254C2×#488—472no—
255C2×#487—471no—
256C2×#479—472no—
257C2×#474—471no—
258C2×#464—472no—
259C2×#462—471no—
260C2×C8×Q8—471no—
261C2×C4×Q16—472no—
262C2×C4×SD16—471no—
263C2×C47#336414yescomplemented
264C2×C47C2×#54811yescharacteristic
265C2×C47C22×#13511yescharacteristic
266C2×C47C2×#57811yescharacteristic
267D47—82no—
268C22×Q16—472no—
269C22×SD16—471no—
270#557—24no—
271#557C2×D4718yescomplemented
272#556—478no—
273#556—944no—
274C2×C4⋊Q8—21no—
275C2×C4⋊Q8—471no—
276C2×C4⋊Q8C2×D4711yescharacteristic
277C2×#126—942no—
278C2×#125—22no—
279C2×#125C2×D4712yes—
280C2×#124—472no—
281C2×C22⋊Q8—941no—
282C2×C4×Q8—21no—
283C2×C4×Q8—472no—
284C2×C4×Q8C2×D4711yescharacteristic
285C2×C4×Q8C2×D4712yes—
286C2×C4×Q8C2×D4711yescharacteristic
287C2×C4×D4—471no—
288C2×#117—941no—
289#488—4716no—
290#487—478no—
291#479—4716no—
292#474—478no—
293#464—4716no—
294#462—478no—
295C8×Q8—478no—
296C4×Q16—4716no—
297C4×SD16—478no—
298C2×#107—472no—
299C2×#106—471no—
300C2×C4⋊C8—472no—
301C2×C4⋊C8—471no—
302C2×#103—471no—
303C2×#103—472no—
304C2×#103—472no—
305C2×#103—472no—
306C2×#102—471no—
307C2×#102—472no—
308C2×C4×C8—471no—
309C2×C4×C8—472no—
310C47C2×#336411yescharacteristic, complemented, Sylow
311C22×Q8—21no—
312C22×Q8—472no—
313C22×Q8C22⋊D4711yescharacteristic
314C22×Q8C22×D4711yescharacteristic
315C22×D4—471no—
316C23×C4—941no—
317C2×Q16—478no—
318C2×Q16—948no—
319C2×SD16—474no—
320C2×SD16—944no—
321C22×C8—471no—
322C22×C8—472no—
323C22×C8—471no—
324C4⋊Q8—28no—
325C4⋊Q8—22no—
326C4⋊Q8—474no—
327C4⋊Q8—942no—
328C4⋊Q8C22×D4714yes—
329#126—9416no—
330#125—216no—
331#125—24no—
332#125C22×D4718yes—
333#124—478no—
334#124—944no—
335C22⋊Q8—948no—
336C4×Q8—28no—
337C4×Q8—24no—
338C4×Q8—22no—
339C4×Q8—478no—
340C4×Q8—944no—
341C4×Q8C22⋊D4714yes—
342C4×Q8C22×D4714yes—
343C4×Q8C22×D4718yes—
344C4×Q8C22×D4714yes—
345C4×D4—474no—
346C4×D4—942no—
347#117—948no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—471no—
354C2×C4⋊C4—941no—
355C2×C4⋊C4—942no—
356C2×C4⋊C4—941no—
357C2×C4⋊C4C22⋊D4711yescharacteristic
358C2×C4⋊C4C22⋊D4712yes—
359C2×C4⋊C4C22×D4711yescharacteristic
360C2×C4⋊C4C22×D4712yes—
361C2×C22⋊C4—942no—
362C2×C22⋊C4—941no—
363C2×C22⋊C4—942no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42—942no—
367C2×C42C22×D4711yescharacteristic
368C2×C42C22×D4712yes—
369#107—478no—
370#106—474no—
371C4⋊C8—474no—
372C4⋊C8—478no—
373#103—474no—
374#103—478no—
375#103—478no—
376#103—478no—
377#102—474no—
378#102—478no—
379C4×C8—474no—
380C4×C8—478no—
381C24—941no—
382C2×Q8—24no—
383C2×Q8—21no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—44no—
387C2×Q8—474no—
388C2×Q8—942no—
389C2×Q8—944no—
390C2×Q8—944no—
391C2×Q8#1062535414yes—
392C2×Q8C2×C22⋊D4714yes—
393C2×Q8C23×D4712yes—
394C2×D4—472no—
395C2×D4—941no—
396C2×D4—942no—
397C2×D4—942no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—941no—
402C22×C4—942no—
403C22×C4—944no—
404C22×C4—1884no—
405C22×C4C2×C22⋊D4712yes—
406C22×C4C2×C22⋊D4711yescharacteristic
407C22×C4C2×C22⋊D4712yes—
408C22×C4C2×C22⋊D4711yescharacteristic
409C22×C4C23×D4711yescharacteristic
410Q16—9416no—
411SD16—948no—
412C2×C8—472no—
413C2×C8—474no—
414C2×C8—472no—
415C2×C8—942no—
416C2×C8—944no—
417C2×C8—942no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—28no—
421C4⋊C4—24no—
422C4⋊C4—28no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—472no—
426C4⋊C4—948no—
427C4⋊C4—941no—
428C4⋊C4—944no—
429C4⋊C4—944no—
430C4⋊C4C2×C22⋊D4714yes—
431C4⋊C4C2×C22⋊D4718yes—
432C4⋊C4C23×D4712yes—
433C4⋊C4C23×D4714yes—
434C22⋊C4—948no—
435C22⋊C4—944no—
436C22⋊C4—948no—
437C42—28no—
438C42—24no—
439C42—948no—
440C42C2×C22⋊D4712yes—
441C42C2×C22⋊D4714yes—
442C42C23×D4712yes—
443C42C23×D4714yes—
444C23—942no—
445C23—1882no—
446C23—1882no—
447C23—1882no—
448C23C22×C22⋊D4711yescharacteristic
449Q8—24no—
450Q8—28no—
451Q8—22no—
452Q8—48no—
453Q8—944no—
454Q8—944no—
455Q8—1884no—
456Q8C2×#1062535414yes—
457D4—942no—
458D4—942no—
459D4—1882no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—942no—
470C2×C4—944no—
471C2×C4—1884no—
472C2×C4—1882no—
473C2×C4—1888no—
474C2×C4#1309404414yes—
475C2×C4C22×C22⋊D4714yes—
476C2×C4C22×C22⋊D4712yes—
477C2×C4C22×C22⋊D4714yes—
478C2×C4C22×C22⋊D4711yescharacteristic
479C2×C4C22×C22⋊D4712yes—
480C2×C4C2×#1062535412yes—
481C2×C4#1309407212yes—
482C2×C4C24×D4711yescharacteristic
483C8—942no—
484C8—944no—
485C8—942no—
486C22—3764no—
487C22—1882no—
488C22—1882no—
489C22—1882no—
490C22#1568978412yes—
491C22C2×#1309404412yes—
492C22#1568993812yes—
493C22C23×C22⋊D4711yescharacteristic
494C4—24no—
495C4—24no—
496C4—24no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—1882no—
501C4—1884no—
502C4#1568978412yes—
503C4C2×#1309404414yes—
504C4C22×#1062535411yescharacteristic
505C4C2×#1309407211yescharacteristic
506C2—3762no—
507C2#2025607314yesdirect product factor
508C2C2×#1568978411yescharacteristic
509C2C22×#1309404411yescharacteristic
510C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#557C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC2×#557D47
hypocenterC47C2×#3364
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #20256073C2direct (N × H)
4. C2×#15689475C2semidirect
5. C2×#15689427C2semidirect
8. C2×#15689333C2semidirect
9. C2×Q8×C47⋊C8C2semidirect
10. C2×C4×#10625337C2semidirect
12. C2×C47×#557C2semidirect
25. #15689475C22semidirect
26. #15689427C22semidirect
29. #15689333C22semidirect
30. Q8×C47⋊C8C22semidirect
31. C4×#10625337C22semidirect
46. C47×#557C22semidirect
251. C2×#557D47semidirect
263. C2×C47#3364semidirect
271. #557C2×D47semidirect
310. C47C2×#3364semidirect
507. C2#20256073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
#202560732
C2×#156894802
C2×#156894752
C2×#156894272
C2×#156894002
C2×#156893452
C2×#156893332
C2×Q8×C47⋊C82
C2×C4×#106253372
C2×C4×#106253362
C2×C47×#5572
C2×#336447