Finite Group Databasebeta

← D47×#1460 #26182078

Subgroups — D47×#1460 #26182078

Order 12032.

1714 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2#431×D47C212yesmaximal, complemented
3#20241709C211yesmaximal, characteristic, complemented
4#20241708C212yesmaximal, complemented
5#20241707C214yesmaximal, complemented
6#323×D47C214yesmaximal, complemented
7C47×#1460C211yesmaximal, characteristic, complemented
8C22×D4×D47C411yescharacteristic
9C23×C4×D47C412yes—
10C2×C4×D188C2211yescharacteristic
11C2×D4×Dic47C411yescharacteristic
12C2×#13093986C411yescharacteristic
13C2×C4×C22⋊D47C412yes—
14C2×(C22⋊D47)⋊C4C2212yes—
15C4×D4×D47—22no—
16C4×D4×D47—22no—
17C4×D4×D47—22no—
18C4×D4×D47—22no—
19C2×C4⋊C4×D47C411yescharacteristic
20C2×C22⋊C4×D47C2212yes—
21C2×C42×D47C2211yescharacteristic
22#15689176C2212yescomplemented
23#15689175—22no—
24#15689174—22no—
25#15689173C2214yescomplemented
26C4⋊C8×D47—22no—
27C22⋊C8×D47C2214yes—
28C4×C8×D47—22no—
29#15688847C2214yescomplemented
30#15688846C2218yescomplemented
31C2×C4×D4×C47C2211yescharacteristic
32C47×#431C2212yescomplemented
33C47×#323C2214yescomplemented
34C24×D47C2×C412yes—
35C22×D188C2×C411yescharacteristic
36C22×C22⋊D47C2×C412yes—
37C2×D4×D47—22no—
38C2×D4×D47—22no—
39C2×D4×D47—24no—
40C2×D4×D47C818yescomplemented
41C23×Dic47C2×C412yes—
42C22×C4×D47—22no—
43C22×C4×D47—22no—
44C22×C4×D47—22no—
45C22×C4×D47—22no—
46C22×C4×D47—48no—
47C22×C4×D47C2×C411yescharacteristic
48C22×C4×D47C2×C412yes—
49C22×C4×D47C2×C412yes—
50C22×C4×D47C2×C412yes—
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47C2311yescharacteristic
53C2×C8×D47—24no—
54C4×D188—22no—
55C4×D188—22no—
56D4×Dic47—22no—
57D4×Dic47—22no—
58#13093986—22no—
59#13093986—22no—
60C4×C22⋊D47—24no—
61C4×C22⋊D47—24no—
62(C22⋊D47)⋊C4—24no—
63(C22⋊D47)⋊C4—24no—
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×Dic47⋊C4C2×C412yes—
66C4⋊C4×D47—22no—
67C4⋊C4×D47—22no—
68C2×C22⋊Dic47C2×C412yes—
69C2×(C2×D47)⋊C4C2×C412yes—
70C2×(C2×D47)⋊C4C2312yes—
71C22⋊C4×D47—24no—
72C22⋊C4×D47—24no—
73C2×C4×Dic47C2×C411yescharacteristic
74C2×C4×Dic47C2×C411yescharacteristic
75C2×C4×Dic47C2311yescharacteristic
76C42×D47D412yes—
77C42×D47D412yes—
78C42×D47D412yes—
79C42×D47D412yes—
80C4⋊(C47⋊C8)—22no—
81Dic47⋊C8—24no—
82C22⋊(C47⋊C8)C2314yes—
83(C2×D47)⋊C8—24no—
84C4×C47⋊C8—22no—
85C8×Dic47—24no—
86C22×D4×C47C2×C411yescharacteristic
87C23×C4×C47C2×C412yes—
88C4×D4×C47—22no—
89C4×D4×C47—22no—
90C2×C4⋊C4×C47C2×C411yescharacteristic
91C2×C22⋊C4×C47C2312yes—
92C2×C42×C47C2311yescharacteristic
93C4⋊C8×C47—22no—
94C22⋊C8×C47C2314yes—
95C4×C8×C47—22no—
96C24×C47C22×C412yes—
97C23×D47—22no—
98C23×D47—22no—
99C23×D47—24no—
100C23×D47—44no—
101C23×D47—44no—
102C23×D47C2×C818yes—
103C23×D47C22×C411yescharacteristic
104C23×D47C22×C412yes—
105C2×D4×C47—22no—
106C2×D4×C47—22no—
107C2×D4×C47C2×C814yescomplemented
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—44no—
111C22×C4×C47C22×C411yescharacteristic
112C22×C4×C47C22×C412yes—
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C2411yescharacteristic
115C2×C22⋊D47—24no—
116C2×C22⋊D47—24no—
117C2×C22⋊D47C2×C818yescomplemented
118C22×Dic47—22no—
119C22×Dic47—22no—
120C22×Dic47—44no—
121C22×Dic47C22×C411yescharacteristic
122C22×Dic47C22×C412yes—
123C22×Dic47C22×C411yescharacteristic
124C22×Dic47C22×C411yescharacteristic
125D4×D47—216no—
126D4×D47—216no—
127C2×D188—22no—
128C2×D188—22no—
129C2×D188C2×C814yescomplemented
130C2×C4×D47—24no—
131C2×C4×D47—22no—
132C2×C4×D47—22no—
133C2×C4×D47—22no—
134C2×C4×D47—22no—
135C2×C4×D47—22no—
136C2×C4×D47—22no—
137C2×C4×D47—42no—
138C2×C4×D47—48no—
139C2×C4×D47—48no—
140C2×C4×D47—48no—
141C2×C4×D47—48no—
142C2×C4×D47—44no—
143C2×C4×D47—44no—
144C2×C4×D47—44no—
145C2×C4×D47C22⋊C411yescharacteristic
146C2×C4×D47C22⋊C411yescharacteristic
147C2×C4×D47C22⋊C411yescharacteristic
148C2×C4×D47C22⋊C412yes—
149C2×C4×D47C22⋊C412yes—
150C2×C4×D47C22⋊C411yescharacteristic
151C2×C4×D47C2×C814yes—
152C2×C4×D47M1614yes—
153C2×C4×D47C2×D412yes—
154C2×C4×D47C2×D412yes—
155C2×C8×C47—24no—
156C4⋊C4×C47—22no—
157C22⋊C4×C47—24no—
158C42×C47C2×D412yes—
159C42×C47C2×D412yes—
160C22⋊Dic47—24no—
161(C2×D47)⋊C4—24no—
162(C2×D47)⋊C4—24no—
163C4⋊Dic47—22no—
164Dic47⋊C4—24no—
165C4×Dic47C22⋊C412yes—
166C4×Dic47C22⋊C412yes—
167C4×Dic47C22⋊C412yes—
168C4×Dic47C22⋊C412yes—
169C4×Dic47C2×D412yes—
170C4×Dic47C2×D412yes—
171C2×C47⋊C8—24no—
172C8×D47—48no—
173C23×C47—22no—
174C23×C47—22no—
175C23×C47—42no—
176C23×C47—42no—
177C23×C47C22×C814yes—
178C23×C47C23×C411yescharacteristic
179C22×D47—22no—
180C22×D47—22no—
181C22×D47—22no—
182C22×D47—22no—
183C22×D47—28no—
184C22×D47—28no—
185C22×D47—44no—
186C22×D47—44no—
187C22×D47—416no—
188C22×D47—416no—
189C22×D47—44no—
190C22×D47—44no—
191C22×D47—42no—
192C22×D47—42no—
193C22×D47C2×C22⋊C411yescharacteristic
194C22×D47C2×C22⋊C411yescharacteristic
195C22×D47C22×C812yes—
196C22×D47C22×C814yes—
197C22×D47C2×M1612yes—
198D4×C47—28no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—41no—
202C2×C4×C47—44no—
203C2×C4×C47—44no—
204C2×C4×C47—42no—
205C2×C4×C47C2×C22⋊C411yescharacteristic
206C2×C4×C47C2×C22⋊C412yes—
207C2×C4×C47C2×C22⋊C411yescharacteristic
208C2×C4×C47C22×C812yes—
209C2×C4×C47C2×M1612yes—
210C2×C4×C47C22×D412yes—
211C22⋊D47—216no—
212C2×Dic47—22no—
213C2×Dic47—22no—
214C2×Dic47—41no—
215C2×Dic47—44no—
216C2×Dic47—44no—
217C2×Dic47—42no—
218C2×Dic47C2×C22⋊C412yes—
219C2×Dic47C2×C22⋊C411yescharacteristic
220C2×Dic47C2×C22⋊C412yes—
221C2×Dic47C2×C22⋊C411yescharacteristic
222C2×Dic47C22×C812yes—
223C2×Dic47C2×M1612yes—
224D188—28no—
225C4×D47—24no—
226C4×D47—22no—
227C4×D47—22no—
228C4×D47—22no—
229C4×D47—42no—
230C4×D47—44no—
231C4×D47—44no—
232C4×D47—44no—
233C4×D47—44no—
234C4×D47—44no—
235C4×D47—44no—
236C4×D47C22⋊C818yes—
237C4×D47C22⋊C818yes—
238C4×D47#10014yes—
239C8×C47—44no—
240C47⋊C8—44no—
241C2×#1460—471nomaximal, Sylow
242C22×C47—21no—
243C22×C47—21no—
244C22×C47—24no—
245C22×C47—44no—
246C22×C47—44no—
247C22×C47—42no—
248C22×C47—42no—
249C22×C47C22×C22⋊C411yescharacteristic
250C22×C47C23×C811yescharacteristic
251C22×C47C22×M1611yescharacteristic
252C2×D47—21no—
253C2×D47—21no—
254C2×D47—24no—
255C2×D47—24no—
256C2×D47—24no—
257C2×D47—416no—
258C2×D47—44no—
259C2×D47—42no—
260C2×D47—42no—
261C2×D47—416no—
262C2×D47—44no—
263C2×D47C2×C22⋊C812yes—
264C2×D47C2×C22⋊C812yes—
265C2×D47#41012yes—
266C2×D47C2×#10012yes—
267C4×C47—22no—
268C4×C47—21no—
269C4×C47—42no—
270C4×C47C2×C22⋊C814yes—
271C4×C47C2×#10012yes—
272Dic47—22no—
273Dic47—21no—
274Dic47—42no—
275Dic47C2×C22⋊C814yes—
276Dic47C2×#10012yes—
277C22×C4×D4—471no—
278C2×#431—472no—
279#1460—472no—
280#1460—474no—
281#1460—471no—
282#1460D4711yescharacteristic, direct product factor
283C2×#323—474no—
284C2×C47—21no—
285C2×C47—21no—
286C2×C47—44no—
287C2×C47C22×C22⋊C811yescharacteristic
288C2×C47C2×#41011yescharacteristic
289C2×C47C22×#10011yescharacteristic
290D47—22no—
291D47—44no—
292D47#146014yesdirect product factor
293C23×D4—471no—
294C24×C4—472no—
295C2×C4×D4—471no—
296C2×C4×D4—472no—
297C2×C4×D4—471no—
298C2×C4×D4—472no—
299C2×C4×D4—471no—
300C2×C4×D4—942no—
301C2×C4×D4—942no—
302C2×C4×D4—942no—
303C2×C4×D4—942no—
304C2×C4×D4C2×D4711yescharacteristic
305C22×C4⋊C4—471no—
306C22×C22⋊C4—472no—
307C22×C42—471no—
308#431—472no—
309#431—474no—
310#431—942no—
311#431—942no—
312#431C2×D4712yescomplemented
313C2×C4⋊C8—942no—
314C2×C22⋊C8—474no—
315C2×C4×C8—942no—
316#323—474no—
317#323—478no—
318#323C2×D4714yescomplemented
319C47C2×#146011yescharacteristic, complemented, Sylow
320C25—472no—
321C22×D4—472no—
322C22×D4—478no—
323C22×D4—471no—
324C22×D4—942no—
325C22×D4—942no—
326C22×D4—944no—
327C22×D4C4×D4711yescharacteristic
328C23×C4—471no—
329C23×C4—471no—
330C23×C4—471no—
331C23×C4—472no—
332C23×C4—472no—
333C23×C4—472no—
334C23×C4—472no—
335C23×C4—942no—
336C23×C4—942no—
337C23×C4—942no—
338C23×C4—942no—
339C23×C4—1888no—
340C23×C4C4×D4712yes—
341C22×C8—944no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—944no—
345C4×D4—944no—
346C4×D4—942no—
347C4×D4—942no—
348C4×D4—944no—
349C4×D4—944no—
350C4×D4—942no—
351C4×D4—942no—
352C4×D4—942no—
353C4×D4—942no—
354C2×C4⋊C4—472no—
355C2×C4⋊C4—471no—
356C2×C4⋊C4—942no—
357C2×C4⋊C4—942no—
358C2×C4⋊C4C4×D4711yescharacteristic
359C2×C22⋊C4—472no—
360C2×C22⋊C4—472no—
361C2×C22⋊C4—472no—
362C2×C22⋊C4—944no—
363C2×C22⋊C4—944no—
364C2×C22⋊C4C22×D4712yes—
365C2×C42—471no—
366C2×C42—471no—
367C2×C42—471no—
368C2×C42—472no—
369C2×C42—472no—
370C2×C42—472no—
371C2×C42—472no—
372C2×C42C22×D4711yescharacteristic
373C4⋊C8—22no—
374C4⋊C8—944no—
375C4⋊C8—942no—
376C22⋊C8—474no—
377C22⋊C8—944no—
378C22⋊C8C22×D4714yes—
379C4×C8—22no—
380C4×C8—944no—
381C4×C8—942no—
382C24—471no—
383C24—478no—
384C24—472no—
385C24—942no—
386C24—942no—
387C24—944no—
388C24—1884no—
389C24—1884no—
390C24C2×C4×D4712yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—478no—
394C2×D4—474no—
395C2×D4—9416no—
396C2×D4—9416no—
397C2×D4—944no—
398C2×D4—944no—
399C2×D4—942no—
400C2×D4—942no—
401C2×D4C8×D4714yescomplemented
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—44no—
405C22×C4—471no—
406C22×C4—472no—
407C22×C4—472no—
408C22×C4—471no—
409C22×C4—474no—
410C22×C4—474no—
411C22×C4—471no—
412C22×C4—471no—
413C22×C4—471no—
414C22×C4—471no—
415C22×C4—471no—
416C22×C4—472no—
417C22×C4—472no—
418C22×C4—472no—
419C22×C4—944no—
420C22×C4—942no—
421C22×C4—942no—
422C22×C4—942no—
423C22×C4—942no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—942no—
427C22×C4—942no—
428C22×C4—1884no—
429C22×C4—1888no—
430C22×C4—1882no—
431C22×C4—1888no—
432C22×C4—1888no—
433C22×C4—1888no—
434C22×C4—1884no—
435C22×C4—1884no—
436C22×C4—1884no—
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4C2×C4×D4712yes—
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4C23×D4711yescharacteristic
441C2×C8—24no—
442C2×C8—944no—
443C2×C8—1888no—
444C4⋊C4—22no—
445C4⋊C4—944no—
446C4⋊C4—942no—
447C22⋊C4—24no—
448C22⋊C4—944no—
449C22⋊C4—944no—
450C22⋊C4—944no—
451C42—472no—
452C42—472no—
453C42—472no—
454C42—472no—
455C42—472no—
456C42—472no—
457C42D4×D4712yes—
458C42D4×D4712yes—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—471no—
464C23—471no—
465C23—472no—
466C23—472no—
467C23—474no—
468C23—942no—
469C23—942no—
470C23—948no—
471C23—948no—
472C23—942no—
473C23—942no—
474C23—1882no—
475C23—1882no—
476C23—1884no—
477C23—1884no—
478C23—18816no—
479C23—1884no—
480C23—18816no—
481C23—1884no—
482C23C2×C8×D4714yes—
483C23C22×C4×D4711yescharacteristic
484D4—28no—
485D4—9416no—
486D4—948no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—472no—
494C2×C4—471no—
495C2×C4—472no—
496C2×C4—472no—
497C2×C4—478no—
498C2×C4—478no—
499C2×C4—474no—
500C2×C4—472no—
501C2×C4—471no—
502C2×C4—942no—
503C2×C4—944no—
504C2×C4—942no—
505C2×C4—942no—
506C2×C4—942no—
507C2×C4—942no—
508C2×C4—1882no—
509C2×C4—1884no—
510C2×C4—1884no—
511C2×C4—1884no—
512C2×C4—1884no—
513C2×C4—1884no—
514C2×C4—1884no—
515C2×C4—1881no—
516C2×C4—1884no—
517C2×C4—1884no—
518C2×C4—1882no—
519C2×C4C22⋊C4×D4711yescharacteristic
520C2×C4C22⋊C4×D4712yes—
521C2×C4C22⋊C4×D4711yescharacteristic
522C2×C4C2×C8×D4712yes—
523C2×C4M16×D4712yes—
524C2×C4C2×D4×D4712yes—
525C8—44no—
526C8—1884no—
527C22—21no—
528C22—21no—
529C22—24no—
530C22—44no—
531C22—44no—
532C22—42no—
533C22—42no—
534C22—472no—
535C22—472no—
536C22—472no—
537C22—472no—
538C22—944no—
539C22—944no—
540C22—941no—
541C22—941no—
542C22—944no—
543C22—1884no—
544C22—1884no—
545C22—18816no—
546C22—18816no—
547C22—1882no—
548C22—1882no—
549C22C2×C22⋊C4×D4711yescharacteristic
550C22C22×C8×D4711yescharacteristic
551C22C2×M16×D4711yescharacteristic
552C4—22no—
553C4—21no—
554C4—42no—
555C4—474no—
556C4—472no—
557C4—942no—
558C4—941no—
559C4—1882no—
560C4C22⋊C8×D4714yes—
561C4#100×D4712yes—
562C2—21no—
563C2—21no—
564C2—44no—
565C2—474no—
566C2—942no—
567C2—1884no—
568C2C2×C22⋊C8×D4711yescharacteristic
569C2#410×D4711yescharacteristic
570C2C2×#100×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC47×#1460C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×D47C4
cosocleC22×C4×C47C24
hypercenter#1460D47
hypocenterC47C2×#1460
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #431×D47C2semidirect
3. #20241709C2semidirect
4. #20241708C2semidirect
5. #20241707C2semidirect
6. #323×D47C2semidirect
7. C47×#1460C2semidirect
22. #15689176C22semidirect
25. #15689173C22semidirect
29. #15688847C22semidirect
30. #15688846C22semidirect
32. C47×#431C22semidirect
33. C47×#323C22semidirect
40. C2×D4×D47C8semidirect
107. C2×D4×C47C2×C8semidirect
117. C2×C22⋊D47C2×C8semidirect
129. C2×D188C2×C8semidirect
282. #1460D47direct (N × H)
292. D47#1460direct (N × H)
312. #431C2×D47semidirect
318. #323C2×D47semidirect
319. C47C2×#1460semidirect
401. C2×D4C8×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
#431×D472
#202417092
#202417082
#202417072
#323×D472
C47×#14602
C2×#146047