Finite Group Databasebeta

← C2×#20253560 #27084427

Subgroups — C2×#20253560 #27084427

Order 12032.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689659C211yesmaximal, characteristic
2C22×Q8×Dic47C211yesmaximal, characteristic, complemented
3#20253560C2116yesmaximal, direct product factor
4C2×#15689456C211yesmaximal, characteristic, complemented
5C2×#15689442C211yesmaximal, characteristic
6C2×#15689428C212yesmaximal, complemented
7C2×#15689347C212yesmaximal, complemented
8C2×#15689262C211yesmaximal, characteristic
9C2×#15689230C212yesmaximal, complemented
10C2×#15689226C212yesmaximal, complemented
11C2×#15689177C211yesmaximal, characteristic, complemented
12C2×C47×#451C211yesmaximal, characteristic, complemented
13C22×#10625336C2212yes—
14#15689659—24no—
15#15689659C2218yes—
16C2×#13094019—21no—
17C2×#13094015C2211yescharacteristic
18C2×#13094013C2211yescharacteristic
19C2×#13094008—21no—
20C2×#13093998C2211yescharacteristic
21C2×Q8×Dic47—21no—
22C2×Q8×Dic47—21no—
23C2×Q8×Dic47—24no—
24C2×Q8×Dic47C2212yes—
25C2×Q8×Dic47C2211yescharacteristic
26C2×Q8×Dic47C2212yes—
27C2×Q8×Dic47C2218yescomplemented
28C2×#13093986C2211yescharacteristic
29C2×(C22⋊D47)⋊C4—21no—
30C2×#13093982—21no—
31C22×C4⋊Dic47—21no—
32C22×C4⋊Dic47C2211yescharacteristic
33C22×C4×Dic47—21no—
34C22×C4×Dic47C2211yescharacteristic
35#15689456C2218yescomplemented
36#15689442C2218yes—
37#15689428C22116yescomplemented
38#15689347C22116yescomplemented
39#15689262C2218yes—
40#15689230C22116yescomplemented
41#15689226C22116yescomplemented
42#15689177C2218yescomplemented
43C2×#13093957C2212yes—
44C2×#13093956C2212yes—
45C2×Dic47⋊C8C2212yes—
46C2×#13093948C2212yes—
47C2×#13093948C2212yes—
48C2×#13093946C2212yes—
49C2×C22⋊(C47⋊C8)C2211yescharacteristic
50C2×#13093934C2212yes—
51C23×Q8×C47C2211yescharacteristic
52C22×Q16×C47C2212yes—
53C2×C22⋊Q8×C47C2211yescharacteristic
54C47×#451C2218yescomplemented
55C2×#103×C47C2212yes—
56C2×C22⋊C8×C47C2211yescharacteristic
57C22×D188C2311yescharacteristic
58C22×C22⋊D47—21no—
59C23×Dic47—21no—
60C23×Dic47D411yescharacteristic
61C23×Dic47D411yescharacteristic
62C22×C4×D47—21no—
63C2×#10625336—28no—
64C2×#10625336C2318yes—
65C22×C47⋊C8C2312yes—
66#13094019—28no—
67#13094015—22no—
68#13094015C2314yes—
69#13094013—22no—
70#13094013C2314yes—
71#13094008—28no—
72#13093998—22no—
73#13093998C2314yes—
74Q8×Dic47—24no—
75Q8×Dic47—24no—
76Q8×Dic47—28no—
77Q8×Dic47—28no—
78Q8×Dic47—22no—
79Q8×Dic47C2318yes—
80Q8×Dic47C2314yes—
81Q8×Dic47C2318yes—
82#13093986—22no—
83#13093986C2314yes—
84(C22⋊D47)⋊C4—28no—
85#13093982—28no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—22no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—28no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2312yes—
94C2×C4⋊Dic47C2314yes—
95C2×C4⋊Dic47C2311yescharacteristic
96C2×Dic47⋊C4—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×(C2×D47)⋊C4—21no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—28no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C2×C4×Dic47D414yes—
108C2×C4×Dic47C2311yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C2×C4×Dic47C2314yes—
111#13093957C2318yes—
112#13093956C2318yes—
113Dic47⋊C8C2318yes—
114#13093948C2318yes—
115#13093948C2318yes—
116#13093946C2318yes—
117C22⋊(C47⋊C8)C2314yes—
118#13093934C2318yes—
119C22×Q8×C47—28no—
120C22×Q8×C47—21no—
121C22×Q8×C47—22no—
122C22×Q8×C47C2314yes—
123C22×Q8×C47C2311yescharacteristic
124C22×Q8×C47C2312yes—
125C23×C4×C47—21no—
126C23×C4×C47C2311yescharacteristic
127C2×Q16×C47—28no—
128C2×Q16×C47C2318yes—
129C22×C8×C47C2312yes—
130C22⋊Q8×C47—22no—
131C22⋊Q8×C47C2314yes—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47—21no—
135#103×C47C2318yes—
136C22⋊C8×C47C2314yes—
137C24×C47C2×D411yescharacteristic
138C23×D47—21no—
139C2×Q8×C47—216no—
140C2×Q8×C47—28no—
141C2×Q8×C47—216no—
142C2×Q8×C47—24no—
143C2×Q8×C47—22no—
144C2×Q8×C47—21no—
145C2×Q8×C47—24no—
146C2×Q8×C47—24no—
147C2×Q8×C47#4118yes—
148C2×Q8×C47C2412yes—
149C2×Q8×C47C2414yes—
150C22×C4×C47—28no—
151C22×C4×C47—24no—
152C22×C4×C47—22no—
153C22×C4×C47—24no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2412yes—
159C22×C4×C47C2411yescharacteristic
160C2×C22⋊D47—24no—
161C2×C22⋊D47—44no—
162C22×Dic47—24no—
163C22×Dic47—24no—
164C22×Dic47—22no—
165C22×Dic47—21no—
166C22×Dic47—42no—
167C22×Dic47—44no—
168C22×Dic47C2×D411yescharacteristic
169C22×Dic47C2×D411yescharacteristic
170C22×Dic47C2×D414yes—
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173C22×Dic47C2×D414yes—
174C2×D188—24no—
175C2×D188—21no—
176C2×D188C2412yes—
177C2×C4×D47—24no—
178C2×C4×D47—44no—
179Q16×C47—216no—
180C2×C8×C47—24no—
181C2×C8×C47C2414yes—
182C4⋊C4×C47—24no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47C2412yes—
185C22⋊C4×C47—24no—
186#10625336—216no—
187(C2×D47)⋊C4—24no—
188(C2×D47)⋊C4—24no—
189(C2×D47)⋊C4—24no—
190(C2×D47)⋊C4—24no—
191C4⋊Dic47—24no—
192C4⋊Dic47—22no—
193C4⋊Dic47—21no—
194C4⋊Dic47—28no—
195C4⋊Dic47—28no—
196C4⋊Dic47—24no—
197C4⋊Dic47—24no—
198C4⋊Dic47C2414yes—
199C4⋊Dic47C2412yes—
200Dic47⋊C4—24no—
201C4×Dic47—28no—
202C4×Dic47—28no—
203C4×Dic47—24no—
204C4×Dic47C2×D414yes—
205C4×Dic47C2×D412yes—
206C4×Dic47C2×D412yes—
207C4×Dic47C2×D414yes—
208C4×Dic47C2412yes—
209C4×Dic47C2412yes—
210C2×C47⋊C8—24no—
211C2×C47⋊C8C2414yes—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47#13714yes—
215C23×C47C22×D412yes—
216C23×C47C22×D411yescharacteristic
217C22×D47—22no—
218C22×D47—42no—
219C22×D47—42no—
220C22×D47—42no—
221Q8×C47—216no—
222Q8×C47—28no—
223Q8×C47—24no—
224Q8×C47—24no—
225Q8×C47—42no—
226Q8×C47C2×#4118yes—
227C2×C4×C47—216no—
228C2×C4×C47—28no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—24no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47C22×D412yes—
238C2×C4×C47C22×D411yescharacteristic
239C2×C4×C47C2×#4114yes—
240C2×C4×C47C2511yescharacteristic
241C22⋊D47—48no—
242C2×Dic47—28no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—22no—
249C2×Dic47—44no—
250C2×Dic47—48no—
251C2×Dic47—42no—
252C2×Dic47—44no—
253C2×Dic47C22×D412yes—
254C2×Dic47C22×D412yes—
255C2×Dic47C22×D412yes—
256C2×Dic47C22×D412yes—
257D188—24no—
258D188—42no—
259C4×D47—48no—
260C8×C47—24no—
261C47⋊C8—24no—
262C2×#3117—471nomaximal, Sylow
263C22×C47—28no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47#52512yes—
267C22×C47C2×#13714yes—
268C22×C47C2×#13712yes—
269C22×C47#57512yes—
270C22×C47C23×D411yescharacteristic
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—84no—
275C4×C47—28no—
276C4×C47—22no—
277C4×C47—42no—
278C4×C47—42no—
279C4×C47#52512yes—
280C4×C47C22×#4112yes—
281Dic47—22no—
282Dic47—22no—
283Dic47—22no—
284Dic47—22no—
285Dic47—42no—
286Dic47—44no—
287C2×#529—471no—
288C22×C4×Q8—471no—
289#3117—4716no—
290C2×#484—471no—
291C2×#481—471no—
292C2×#479—472no—
293C2×#464—472no—
294C2×#451D4711yescharacteristic, complemented
295C2×#448—471no—
296C2×#441—472no—
297C2×#440—472no—
298C2×#432—471no—
299C2×C47—24no—
300C2×C47#311714yescomplemented
301C2×C47C2×#52511yescharacteristic
302C2×C47C22×#13711yescharacteristic
303C2×C47C2×#57511yescharacteristic
304D47—82no—
305C23×Q8C2×D4711yescharacteristic
306C22×Q16C2×D4712yes—
307C22×SD16—472no—
308#529—478no—
309#529—944no—
310C2×#126—941no—
311C2×#125—471no—
312C2×#124—471no—
313C2×#123—941no—
314C2×C22⋊Q8C2×D4711yescharacteristic
315C2×#121—471no—
316C2×C4×Q8—472no—
317C2×C4×Q8—478no—
318C2×C4×Q8—472no—
319C2×C4×Q8—471no—
320C2×C4×Q8—941no—
321C2×C4×Q8—941no—
322C2×C4×Q8—944no—
323C2×C4×D4—471no—
324C2×C4×D4—941no—
325C2×#117—941no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4—941no—
328C22×C42—471no—
329C22×C42—941no—
330#484—478no—
331#481—478no—
332#479—4716no—
333#464—4716no—
334#451C2×D4718yescomplemented
335#448—478no—
336#441—4716no—
337#440—4716no—
338#432—478no—
339C2×#107—472no—
340C2×#106—472no—
341C2×C4⋊C8—472no—
342C2×#103—472no—
343C2×#103—472no—
344C2×#103C2×D4712yes—
345C2×#102—472no—
346C2×C22⋊C8—471no—
347C2×C22⋊C8C2×D4711yescharacteristic
348C2×#97—472no—
349C47C2×#311711yescharacteristic, complemented, Sylow
350C22×Q8—28no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8C22×D4714yes—
354C22×Q8C22×D4711yescharacteristic
355C22×Q8C22×D4712yes—
356C22×D4—471no—
357C22×D4—941no—
358C23×C4—21no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—941no—
362C23×C4—941no—
363C23×C4C22×D4711yescharacteristic
364C2×Q16—28no—
365C2×Q16C22×D4718yes—
366C2×SD16—478no—
367C2×SD16—948no—
368C22×C8—472no—
369C22×C8C22×D4712yes—
370#126—948no—
371#125—474no—
372#125—942no—
373#124—474no—
374#124—942no—
375#123—948no—
376C22⋊Q8—22no—
377C22⋊Q8C22×D4714yes—
378#121—474no—
379#121—942no—
380C4×Q8—478no—
381C4×Q8—478no—
382C4×Q8—474no—
383C4×Q8—948no—
384C4×Q8—944no—
385C4×Q8—944no—
386C4×Q8—948no—
387C4×Q8—942no—
388C4×D4—474no—
389C4×D4—942no—
390C4×D4—948no—
391#117—948no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—474no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—948no—
397C2×C4⋊C4—942no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4C22×D4711yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—941no—
407C2×C22⋊C4—941no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C42—471no—
411C2×C42—471no—
412C2×C42—474no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—474no—
416C2×C42—941no—
417C2×C42—948no—
418C2×C42—942no—
419C2×C42—942no—
420#107—478no—
421#106—478no—
422C4⋊C8—478no—
423#103—478no—
424#103—478no—
425#103C22×D4718yes—
426#102—478no—
427C22⋊C8—474no—
428C22⋊C8C22×D4714yes—
429#97—478no—
430C24—941no—
431C24D4×D4711yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8#1062535218yes—
441C2×Q8C23×D4712yes—
442C2×Q8C23×D4714yes—
443C2×D4—472no—
444C2×D4—944no—
445C2×D4—941no—
446C2×D4—944no—
447C2×D4—1884no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—474no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—474no—
460C22×C4—944no—
461C22×C4—944no—
462C22×C4—944no—
463C22×C4—942no—
464C22×C4—941no—
465C22×C4—1884no—
466C22×C4—1882no—
467C22×C4—1884no—
468C22×C4D4×D4712yes—
469C22×C4D4×D4711yescharacteristic
470C22×C4C23×D4712yes—
471C22×C4C23×D4711yescharacteristic
472Q16—216no—
473SD16—9416no—
474C2×C8—24no—
475C2×C8—474no—
476C2×C8—944no—
477C2×C8C23×D4714yes—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—474no—
481C4⋊C4—472no—
482C4⋊C4—944no—
483C4⋊C4—948no—
484C4⋊C4—948no—
485C4⋊C4—944no—
486C4⋊C4—944no—
487C4⋊C4—944no—
488C4⋊C4—942no—
489C4⋊C4—941no—
490C4⋊C4C23×D4712yes—
491C22⋊C4—24no—
492C22⋊C4—944no—
493C22⋊C4—944no—
494C22⋊C4—944no—
495C22⋊C4—944no—
496C42—474no—
497C42—472no—
498C42—472no—
499C42—474no—
500C42—472no—
501C42—472no—
502C42—948no—
503C42—948no—
504C42—944no—
505C23—22no—
506C23—22no—
507C23—942no—
508C23—1882no—
509C23—1882no—
510C23—1882no—
511C23#1309405614yes—
512C23C2×D4×D4712yes—
513C23C2×D4×D4711yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8C2×#1062535218yes—
520D4—944no—
521D4—1888no—
522D4—1882no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—472no—
534C2×C4—472no—
535C2×C4—472no—
536C2×C4—472no—
537C2×C4—948no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—944no—
543C2×C4—942no—
544C2×C4—1888no—
545C2×C4—1884no—
546C2×C4—1888no—
547C2×C4—1882no—
548C2×C4—1884no—
549C2×C4C2×D4×D4712yes—
550C2×C4C2×D4×D4711yescharacteristic
551C2×C4C2×#1062535214yes—
552C2×C4C24×D4711yescharacteristic
553C8—24no—
554C8—944no—
555C22—22no—
556C22—22no—
557C22—28no—
558C22—3764no—
559C22—1882no—
560C22—1882no—
561C22—1882no—
562C22#1568962912yes—
563C22C2×#1309405614yes—
564C22C2×#1309405612yes—
565C22#1568992212yes—
566C22C22×D4×D4711yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—942no—
572C4—942no—
573C4—942no—
574C4—942no—
575C4—1882no—
576C4—1884no—
577C4#1568962912yes—
578C4C22×#1062535212yes—
579C2—24no—
580C2—3762no—
581C2#2025356014yesdirect product factor
582C2C2×#1568962911yescharacteristic
583C2C22×#1309405611yescharacteristic
584C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#451D47
hypocenterC47C2×#3117
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic47C2semidirect
3. #20253560C2direct (N × H)
4. C2×#15689456C2semidirect
6. C2×#15689428C2semidirect
7. C2×#15689347C2semidirect
9. C2×#15689230C2semidirect
10. C2×#15689226C2semidirect
11. C2×#15689177C2semidirect
12. C2×C47×#451C2semidirect
27. C2×Q8×Dic47C22semidirect
35. #15689456C22semidirect
37. #15689428C22semidirect
38. #15689347C22semidirect
40. #15689230C22semidirect
41. #15689226C22semidirect
42. #15689177C22semidirect
54. C47×#451C22semidirect
294. C2×#451D47semidirect
300. C2×C47#3117semidirect
334. #451C2×D47semidirect
349. C47C2×#3117semidirect
581. C2#20253560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896592
C22×Q8×Dic472
#202535602
C2×#156894562
C2×#156894422
C2×#156894282
C2×#156893472
C2×#156892622
C2×#156892302
C2×#156892262
C2×#156891772
C2×C47×#4512
C2×#311747