Finite Group Databasebeta

← C2×#20255800 #27094761

Subgroups — C2×#20255800 #27094761

Order 12032.

1918 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689847C211yesmaximal, characteristic, complemented
2C2×#15689839C211yesmaximal, characteristic
3#20255800C2116yesmaximal, direct product factor
4C2×#15689467C212yesmaximal, complemented
5C2×#15689449C212yesmaximal, complemented
6C2×#15689415C211yesmaximal, characteristic, complemented
7C2×#15689400C211yesmaximal, characteristic, complemented
8C2×#15689353C212yesmaximal, complemented
9C2×C4×#10625325C211yesmaximal, characteristic, complemented
10C2×C8×D188C211yesmaximal, characteristic, complemented
11C2×#15689158C212yesmaximal, complemented
12C2×C47×#498C211yesmaximal, characteristic, complemented
13C22×#10625325C2211yescharacteristic
14C22×C8×D47C2212yes—
15#15689847—24no—
16#15689847C2218yescomplemented
17#15689839—24no—
18#15689839C2218yes—
19C2×#13094019—22no—
20C2×#13094013—21no—
21C2×#13094013—22no—
22C2×#13094004C2212yes—
23C2×#13093999—21no—
24C2×#13093999C2212yes—
25C2×Q8×Dic47—21no—
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×#13093982—21no—
30C2×#13093982C2212yes—
31C2×#13093982C2212yes—
32#15689467C22116yescomplemented
33#15689449C22116yescomplemented
34#15689415C2218yescomplemented
35#15689400C2218yescomplemented
36#15689353C22116yescomplemented
37C4×#10625325C2218yescomplemented
38C8×D188C2218yescomplemented
39#15689158C22116yescomplemented
40C2×#13093957C2212yes—
41C2×#13093957C2212yes—
42C2×#13093956C2211yescharacteristic
43C2×C4⋊(C47⋊C8)C2211yescharacteristic
44C2×#13093949C2211yescharacteristic
45C2×#13093947C2212yes—
46C2×#13093946C2211yescharacteristic
47C2×#13093944C2212yes—
48C2×(C2×D47)⋊C8C2212yes—
49C2×C4⋊Q8×C47C2211yescharacteristic
50C2×C4⋊Q8×C47C2211yescharacteristic
51C47×#498C2218yescomplemented
52C2×#106×C47C2212yes—
53C2×#106×C47C2212yes—
54C2×C4×C8×C47C2211yescharacteristic
55C22×Dic94C2311yescharacteristic
56C22×D188—22no—
57C22×D188D411yescharacteristic
58C22×D188C2311yescharacteristic
59C22×C4×D47—21no—
60C22×C4×D47C2312yes—
61C2×#10625325—24no—
62C2×#10625325C2314yes—
63C22×C47⋊C8C2312yes—
64C2×C8×D47—28no—
65C2×C8×D47C2318yes—
66#13094019—216no—
67#13094013—28no—
68#13094013—216no—
69#13094004—24no—
70#13094004C2318yes—
71#13093999—28no—
72#13093999—24no—
73#13093999C2318yes—
74Q8×Dic47—28no—
75C4×Dic94—22no—
76C4×Dic94C2314yes—
77C4×D188—22no—
78C4×D188D414yes—
79C4×D188C2314yes—
80C4×D188C2314yes—
81#13093982—24no—
82#13093982—24no—
83#13093982—28no—
84#13093982C2318yes—
85#13093982C2318yes—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47D411yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×(C2×D47)⋊C4—22no—
92C2×(C2×D47)⋊C4—22no—
93C2×(C2×D47)⋊C4—22no—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—22no—
96C2×(C2×D47)⋊C4D412yes—
97C2×C4×Dic47—21no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—22no—
100#13093957C2318yes—
101#13093957C2318yes—
102#13093956C2314yes—
103C4⋊(C47⋊C8)C2314yes—
104#13093949C2314yes—
105#13093947C2318yes—
106#13093946C2314yes—
107#13093944C2318yes—
108(C2×D47)⋊C8C2318yes—
109C22×Q8×C47—21no—
110C22×Q8×C47—21no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C4⋊Q8×C47—22no—
114C4⋊Q8×C47—22no—
115C4⋊Q8×C47C2314yes—
116C4⋊Q8×C47C2314yes—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47C2312yes—
120C2×C4⋊C4×C47C2312yes—
121C2×C42×C47C2311yescharacteristic
122#106×C47C2318yes—
123#106×C47C2318yes—
124C4×C8×C47C2314yes—
125C23×D47—21no—
126C23×D47C2×D412yes—
127C2×Q8×C47—24no—
128C2×Q8×C47—24no—
129C2×Q8×C47—44no—
130C2×Q8×C47—82no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2411yescharacteristic
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47C2×D412yes—
140C2×D188—24no—
141C2×D188—22no—
142C2×D188—22no—
143C2×D188—21no—
144C2×D188—28no—
145C2×D188—84no—
146C2×D188C2×D414yes—
147C2×D188C2412yes—
148C2×C4×D47—24no—
149C2×C4×D47—24no—
150C2×C4×D47—24no—
151C2×C4×D47—44no—
152C2×C4×D47C2×D414yes—
153C2×C4×D47C2414yes—
154C2×Dic94—22no—
155C2×Dic94—22no—
156C2×Dic94—21no—
157C2×Dic94C2412yes—
158C2×C8×C47—22no—
159C2×C8×C47#4114yes—
160C2×C8×C47C2412yes—
161C2×C8×C47C2412yes—
162C4⋊C4×C47—24no—
163C4⋊C4×C47—24no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47C2414yes—
167C4⋊C4×C47C2414yes—
168C42×C47C2×D412yes—
169C42×C47C2412yes—
170(C2×D47)⋊C4—28no—
171(C2×D47)⋊C4—28no—
172(C2×D47)⋊C4—28no—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—28no—
175(C2×D47)⋊C4C2×D418yes—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—28no—
179C4⋊Dic47C2×D414yes—
180C4⋊Dic47C2412yes—
181C4⋊Dic47C2412yes—
182Dic47⋊C4—24no—
183C4×Dic47—24no—
184C4×Dic47—28no—
185C4×Dic47—28no—
186C2×C47⋊C8—24no—
187C2×C47⋊C8C2414yes—
188#10625325—28no—
189C8×D47—216no—
190C23×C47C22×D411yescharacteristic
191C22×D47—24no—
192C22×D47—24no—
193C22×D47—24no—
194C22×D47—22no—
195C22×D47—42no—
196C22×D47—42no—
197C22×D47—42no—
198C22×D47C22×D414yes—
199Q8×C47—48no—
200Q8×C47—84no—
201C2×C4×C47—22no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—44no—
205C2×C4×C47—44no—
206C2×C4×C47#13514yes—
207C2×C4×C47C22×D412yes—
208C2×C4×C47C22×D411yescharacteristic
209C2×C4×C47C22×D412yes—
210C2×C4×C47C2×#4112yes—
211C2×C4×C472−1+412yes—
212C2×C4×C47C2511yescharacteristic
213C2×Dic47—24no—
214C2×Dic47—22no—
215C2×Dic47—22no—
216C2×Dic47—22no—
217C2×Dic47—42no—
218C2×Dic47—42no—
219C2×Dic47—42no—
220C2×Dic47C22×D414yes—
221D188—28no—
222D188—22no—
223D188—22no—
224D188—42no—
225D188—88no—
226C4×D47—28no—
227C4×D47—24no—
228C4×D47—24no—
229C4×D47—48no—
230Dic94—22no—
231Dic94—22no—
232Dic94—42no—
233C8×C47—22no—
234C8×C47C2×#4114yes—
235C47⋊C8—24no—
236C2×#3340—471nomaximal, Sylow
237C22×C47#54712yes—
238C22×C47C2×#13512yes—
239C22×C47#57712yes—
240C22×C47C23×D411yescharacteristic
241C2×D47—24no—
242C2×D47—24no—
243C2×D47—24no—
244C2×D47—48no—
245C2×D47—42no—
246C2×D47—42no—
247C2×D47—42no—
248C2×D47—84no—
249C4×C47—22no—
250C4×C47—44no—
251C4×C47—44no—
252C4×C47#54712yes—
253C4×C47C2×#13514yes—
254C4×C47C22×#4111yescharacteristic
255C4×C47C2×2−1+411yescharacteristic
256Dic47—24no—
257Dic47—42no—
258Dic47—42no—
259Dic47—42no—
260C2×#556—471no—
261C2×#555—471no—
262#3340—4716no—
263C2×#498D4711yescharacteristic, complemented
264C2×#485—472no—
265C2×#482—472no—
266C2×#477—471no—
267C2×#474—471no—
268C2×#465—472no—
269C2×C4×SD16—471no—
270C2×C8×D4—471no—
271C2×#427—472no—
272C2×C47#334014yescomplemented
273C2×C47C2×#54711yescharacteristic
274C2×C47C22×#13511yescharacteristic
275C2×C47C2×#57711yescharacteristic
276D47—44no—
277D47—82no—
278C22×SD16—471no—
279C23×C8—472no—
280#556—478no—
281#556—944no—
282#555—478no—
283#555—944no—
284C2×C4⋊Q8C2×D4711yescharacteristic
285C2×C4⋊Q8C2×D4711yescharacteristic
286C2×#126—942no—
287C2×#124—942no—
288C2×#124—941no—
289C2×C22⋊Q8—472no—
290C2×#121—472no—
291C2×#121—941no—
292C2×C4×Q8—471no—
293C2×C4×Q8—941no—
294C2×C4×D4—471no—
295C2×C4×D4—471no—
296C2×#117—472no—
297C2×#117—472no—
298C2×#117—941no—
299#498C2×D4718yescomplemented
300#485—4716no—
301#482—4716no—
302#477—478no—
303#474—478no—
304#465—4716no—
305C4×SD16—478no—
306C8×D4—478no—
307#427—4716no—
308C2×#107—472no—
309C2×#107—472no—
310C2×#106—471no—
311C2×#106C2×D4712yes—
312C2×#106C2×D4712yes—
313C2×C4⋊C8—471no—
314C2×#103—471no—
315C2×#103—472no—
316C2×#102—471no—
317C2×#102—472no—
318C2×C22⋊C8—472no—
319C2×C4×C8C2×D4711yescharacteristic
320C47C2×#334011yescharacteristic, complemented, Sylow
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—471no—
324C22×D4—471no—
325C22×D4—471no—
326C22×D4—942no—
327C23×C4—472no—
328C23×C4—941no—
329C2×SD16—474no—
330C2×SD16—944no—
331C22×C8—472no—
332C22×C8—478no—
333C22×C8—948no—
334C22×C8C22×D4711yescharacteristic
335C22×C8C22×D4711yescharacteristic
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8C22×D4714yes—
339C4⋊Q8C22×D4714yes—
340#126—9416no—
341#124—9416no—
342#124—948no—
343C22⋊Q8—478no—
344C22⋊Q8—944no—
345#121—478no—
346#121—944no—
347#121—948no—
348C4×Q8—474no—
349C4×Q8—948no—
350C4×Q8—942no—
351C4×D4—474no—
352C4×D4—474no—
353C4×D4—474no—
354C4×D4—942no—
355#117—478no—
356#117—478no—
357#117—948no—
358#117—944no—
359#117—944no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—471no—
364C2×C4⋊C4—471no—
365C2×C4⋊C4—942no—
366C2×C4⋊C4—941no—
367C2×C4⋊C4C22×D4712yes—
368C2×C4⋊C4C22×D4712yes—
369C2×C22⋊C4—472no—
370C2×C22⋊C4—942no—
371C2×C22⋊C4—942no—
372C2×C22⋊C4—942no—
373C2×C22⋊C4—942no—
374C2×C22⋊C4—941no—
375C2×C42—942no—
376C2×C42—942no—
377C2×C42—941no—
378C2×C42C22×D4711yescharacteristic
379#107—478no—
380#107—478no—
381#106—474no—
382#106C22×D4718yes—
383#106C22×D4718yes—
384C4⋊C8—474no—
385#103—474no—
386#103—478no—
387#102—474no—
388#102—478no—
389C22⋊C8—478no—
390C4×C8C22×D4714yes—
391C24—472no—
392C24—941no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—44no—
396C2×Q8—82no—
397C2×Q8—472no—
398C2×Q8—941no—
399C2×Q8—942no—
400C2×Q8—942no—
401C2×D4—474no—
402C2×D4—472no—
403C2×D4—948no—
404C2×D4—944no—
405C2×D4—941no—
406C2×D4—942no—
407C2×D4—942no—
408C2×D4—3764no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—472no—
412C22×C4—474no—
413C22×C4—474no—
414C22×C4—944no—
415C22×C4—944no—
416C22×C4—941no—
417C22×C4—941no—
418C22×C4—941no—
419C22×C4—944no—
420C22×C4—1884no—
421C22×C4D4×D4711yescharacteristic
422C22×C4D4×D4711yescharacteristic
423C22×C4C23×D4711yescharacteristic
424SD16—948no—
425C2×C8—22no—
426C2×C8—474no—
427C2×C8—944no—
428C2×C8—9416no—
429C2×C8#1062535414yes—
430C2×C8C23×D4712yes—
431C2×C8C23×D4712yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—474no—
437C4⋊C4—472no—
438C4⋊C4—472no—
439C4⋊C4—948no—
440C4⋊C4—944no—
441C4⋊C4—941no—
442C4⋊C4—941no—
443C4⋊C4C23×D4714yes—
444C4⋊C4C23×D4714yes—
445C22⋊C4—478no—
446C22⋊C4—948no—
447C22⋊C4—948no—
448C22⋊C4—948no—
449C22⋊C4—948no—
450C22⋊C4—944no—
451C42—948no—
452C42—948no—
453C42—944no—
454C42D4×D4712yes—
455C42C23×D4712yes—
456C23—474no—
457C23—944no—
458C23—944no—
459C23—944no—
460C23—942no—
461C23—1882no—
462C23—1882no—
463C23—1882no—
464C23C2×D4×D4711yescharacteristic
465Q8—48no—
466Q8—84no—
467Q8—942no—
468Q8—942no—
469Q8—1882no—
470D4—948no—
471D4—942no—
472D4—942no—
473D4—3768no—
474D4—1882no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—474no—
481C2×C4—944no—
482C2×C4—948no—
483C2×C4—944no—
484C2×C4—944no—
485C2×C4—942no—
486C2×C4—942no—
487C2×C4—942no—
488C2×C4—1882no—
489C2×C4—1882no—
490C2×C4—1882no—
491C2×C4—1888no—
492C2×C4#1309404514yes—
493C2×C4C2×D4×D4712yes—
494C2×C4C2×D4×D4711yescharacteristic
495C2×C4C2×D4×D4712yes—
496C2×C4C2×#1062535412yes—
497C2×C4#1309407212yes—
498C2×C4C24×D4711yescharacteristic
499C8—22no—
500C8—944no—
501C8C2×#1062535414yes—
502C22—944no—
503C22—944no—
504C22—944no—
505C22—3764no—
506C22—1882no—
507C22—1882no—
508C22—1882no—
509C22—1888no—
510C22#1568977612yes—
511C22C2×#1309404512yes—
512C22#1568992912yes—
513C22C22×D4×D4711yescharacteristic
514C4—22no—
515C4—44no—
516C4—44no—
517C4—944no—
518C4—1882no—
519C4—1882no—
520C4—1882no—
521C4#1568977612yes—
522C4C2×#1309404514yes—
523C4C22×#1062535411yescharacteristic
524C4C2×#1309407211yescharacteristic
525C2—3762no—
526C2—1884no—
527C2#2025580014yesdirect product factor
528C2C2×#1568977611yescharacteristic
529C2C22×#1309404511yescharacteristic
530C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#498C2
socleC23×C47C22×D4
prime radicalC2×#15689839C2
hypercenterC2×#498D47
hypocenterC47C2×#3340
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#15689847C2semidirect
3. #20255800C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689449C2semidirect
6. C2×#15689415C2semidirect
7. C2×#15689400C2semidirect
8. C2×#15689353C2semidirect
9. C2×C4×#10625325C2semidirect
10. C2×C8×D188C2semidirect
11. C2×#15689158C2semidirect
12. C2×C47×#498C2semidirect
16. #15689847C22semidirect
32. #15689467C22semidirect
33. #15689449C22semidirect
34. #15689415C22semidirect
35. #15689400C22semidirect
36. #15689353C22semidirect
37. C4×#10625325C22semidirect
38. C8×D188C22semidirect
39. #15689158C22semidirect
51. C47×#498C22semidirect
263. C2×#498D47semidirect
272. C2×C47#3340semidirect
299. #498C2×D47semidirect
320. C47C2×#3340semidirect
527. C2#20255800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898472
C2×#156898392
#202558002
C2×#156894672
C2×#156894492
C2×#156894152
C2×#156894002
C2×#156893532
C2×C4×#106253252
C2×C8×D1882
C2×#156891582
C2×C47×#4982
C2×#334047