Finite Group Databasebeta

← D47×#1763 #26214039

Subgroups — D47×#1763 #26214039

Order 12032.

1686 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2C2×#103×D47C212yesmaximal
3C2×#97×D47C211yesmaximal, characteristic
4C4×C4⋊C4×D47C211yesmaximal, characteristic
5#20243221C211yesmaximal, characteristic, complemented
6#20243220C212yesmaximal, complemented
7#20243219C211yesmaximal, characteristic, complemented
8#20243218C211yesmaximal, characteristic, complemented
9#20243217C212yesmaximal, complemented
10#340×D47C212yesmaximal
11C47×#1763C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C22×C8×D47C2212yes—
14C2×Q8×Dic47C2211yescharacteristic
15C2×C4×Dic94—21no—
16C2×C4×Dic94C2211yescharacteristic
17C2×#13093989—21no—
18C2×#13093989C2211yescharacteristic
19C4×Q8×D47—24no—
20C4×Q8×D47C418yescomplemented
21C2×C4⋊C4×D47—21no—
22C2×C4⋊C4×D47C2211yescharacteristic
23C2×C4⋊C4×D47C2212yes—
24C2×C42×D47—21no—
25C2×C42×D47—21no—
26C2×C42×D47C2211yescharacteristic
27C2×#13093949C2212yes—
28C2×#13093948C2212yes—
29C2×#13093947C2212yes—
30#103×D47C4116yescomplemented
31C2×#13093935C2211yescharacteristic
32C2×#13093934C2212yes—
33#97×D47—24no—
34C4⋊C4×Dic47C2212yes—
35C4×Dic47⋊C4—21no—
36C4×C4⋊Dic47C2211yescharacteristic
37#15688974—21no—
38#95×D47—21no—
39#15688886C2212yes—
40#15688885C2212yes—
41#15688885C2212yes—
42C2×C4×Q8×C47C2211yescharacteristic
43C2×#103×C47C2212yes—
44C2×#97×C47C2211yescharacteristic
45C4×C4⋊C4×C47C2211yescharacteristic
46C47×#340C2212yes—
47C22×Dic94—21no—
48C22×Dic94C2311yescharacteristic
49C2×Q8×D47—22no—
50C2×Q8×D47—24no—
51C2×Q8×D47C2×C414yes—
52C2×Q8×D47C2×C418yes—
53C22×C4×D47—21no—
54C22×C4×D47—22no—
55C22×C4×D47—21no—
56C22×C4×D47D411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47C2311yescharacteristic
59C22×C47⋊C8C2312yes—
60C2×C8×D47—24no—
61C2×C8×D47—24no—
62C2×C8×D47C2×C418yes—
63Q8×Dic47—22no—
64Q8×Dic47C2×C414yescomplemented
65C4×Dic94—22no—
66C4×Dic94—28no—
67C4×Dic94C2×C414yescomplemented
68#13093989—28no—
69#13093989—22no—
70#13093989C2×C414yescomplemented
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47C2312yes—
73C2×C4⋊Dic47C2311yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—21no—
77C2×Dic47⋊C4—21no—
78C4⋊C4×D47—28no—
79C4⋊C4×D47—22no—
80C4⋊C4×D47—24no—
81C4⋊C4×D47C2×C414yes—
82C4⋊C4×D47C2×C418yes—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47D411yescharacteristic
89C2×C4×Dic47D411yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47—28no—
92C42×D47—44no—
93C42×D47C2×C414yes—
94C42×D47D414yes—
95#13093949C2×C418yescomplemented
96#13093948C2×C418yescomplemented
97#13093947C2×C418yescomplemented
98#13093935—22no—
99#13093934—24no—
100C47⋊#95—21no—
101C47⋊#95—22no—
102C22×Q8×C47C2311yescharacteristic
103C22×C8×C47C2312yes—
104C4×Q8×C47—22no—
105C4×Q8×C47C2×C414yescomplemented
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47C2312yes—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C42×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47C2311yescharacteristic
112#103×C47C2×C418yescomplemented
113#97×C47—22no—
114#95×C47—21no—
115C23×D47C2×D411yescharacteristic
116C2×Q8×C47—21no—
117C2×Q8×C47—22no—
118C2×Q8×C47C22×C414yes—
119C2×Q8×C47C22×C412yes—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C22×Dic47—21no—
127C22×Dic47—22no—
128C22×Dic47—21no—
129C22×Dic47C2×D411yescharacteristic
130C22×Dic47C2×D411yescharacteristic
131C22×Dic47C2×D411yescharacteristic
132Q8×D47—28no—
133Q8×D47—216no—
134Q8×D47C42116yescomplemented
135C2×C4×D47—24no—
136C2×C4×D47—28no—
137C2×C4×D47—22no—
138C2×C4×D47—22no—
139C2×C4×D47—24no—
140C2×C4×D47—24no—
141C2×C4×D47—28no—
142C2×C4×D47—44no—
143C2×C4×D47—42no—
144C2×C4×D47—42no—
145C2×C4×D47—44no—
146C2×C4×D47C22⋊C414yes—
147C2×C4×D47C22⋊C414yes—
148C2×C4×D47C22×C412yes—
149C2×C4×D47C22×C414yes—
150C2×C4×D47C2×D412yes—
151C2×C4×D47#4114yes—
152C2×Dic94—21no—
153C2×Dic94—22no—
154C2×Dic94—24no—
155C2×Dic94—28no—
156C2×Dic94C22×C414yes—
157C2×Dic94C22×C412yes—
158C2×C8×C47—22no—
159C2×C8×C47—22no—
160C2×C8×C47C22×C414yes—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47C22×C414yes—
165C4⋊C4×C47C22×C412yes—
166C42×C47—24no—
167C42×C47—42no—
168C42×C47C22×C412yes—
169C42×C47C2×D412yes—
170C4⋊Dic47—21no—
171C4⋊Dic47—22no—
172C4⋊Dic47—24no—
173C4⋊Dic47C22×C414yes—
174C4⋊Dic47C22×C412yes—
175Dic47⋊C4—24no—
176Dic47⋊C4—24no—
177Dic47⋊C4—24no—
178Dic47⋊C4—28no—
179C4×Dic47—24no—
180C4×Dic47—24no—
181C4×Dic47—24no—
182C4×Dic47—44no—
183C4×Dic47—42no—
184C4×Dic47C22⋊C414yes—
185C4×Dic47C22⋊C414yes—
186C4×Dic47C22×C412yes—
187C4×Dic47C2×D412yes—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8C22×C414yes—
191C8×D47—216no—
192C23×C47C22×D411yescharacteristic
193C22×D47C2×C22⋊C412yes—
194C22×D47C4×D414yes—
195C22×D47AGL(1,ℤ/8)12yes—
196C22×D47#13712yes—
197C22×D47#13714yes—
198Q8×C47—22no—
199Q8×C47—24no—
200Q8×C47C2×C4214yescomplemented
201C2×C4×C47—22no—
202C2×C4×C47—24no—
203C2×C4×C47—21no—
204C2×C4×C47—22no—
205C2×C4×C47—21no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—42no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—42no—
212C2×C4×C47C2×C22⋊C412yes—
213C2×C4×C47C2×C22⋊C412yes—
214C2×C4×C47C23×C411yescharacteristic
215C2×C4×C47C23×C412yes—
216C2×C4×C47C22×D411yescharacteristic
217C2×C4×C47C2×#4112yes—
218C2×Dic47—22no—
219C2×Dic47—24no—
220C2×Dic47—21no—
221C2×Dic47—22no—
222C2×Dic47—21no—
223C2×Dic47—22no—
224C2×Dic47—24no—
225C2×Dic47—42no—
226C2×Dic47—41no—
227C2×Dic47—41no—
228C2×Dic47—42no—
229C2×Dic47C2×C22⋊C412yes—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C412yes—
232C2×Dic47C4×D414yes—
233C4×D47—216no—
234C4×D47—28no—
235C4×D47—28no—
236C4×D47—48no—
237C4×D47—416no—
238C4×D47C2×C4214yes—
239C4×D47#11714yes—
240C4×D47C4×D418yes—
241Dic94—22no—
242Dic94—24no—
243Dic94—216no—
244Dic94C2×C4214yescomplemented
245C8×C47—24no—
246C47⋊C8—24no—
247C2×#1763—471nomaximal, Sylow
248C22×C47C22×C22⋊C411yescharacteristic
249C22×C47C2×C4×D412yes—
250C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C47C2×#13712yes—
252C22×C47C2×#13711yescharacteristic
253C2×D47C4×C22⋊C414yes—
254C2×D47#41714yes—
255C2×D47#41914yes—
256C2×D47#44018yes—
257C2×D47#44118yes—
258C4×C47—22no—
259C4×C47—22no—
260C4×C47—24no—
261C4×C47—42no—
262C4×C47—44no—
263C4×C47C22×C4211yescharacteristic
264C4×C47C2×#11711yescharacteristic
265C4×C47C2×C4×D412yes—
266Dic47—22no—
267Dic47—22no—
268Dic47—24no—
269Dic47—42no—
270Dic47—44no—
271Dic47C4×C22⋊C414yes—
272C22×C4×Q8—471no—
273C22×#103—472no—
274C22×#97—471no—
275C2×C4×C4⋊C4—471no—
276#1763—472no—
277#1763—471no—
278#1763—471no—
279#1763—472no—
280#1763—471no—
281#1763D4711yescharacteristic, direct product factor
282C2×#340—472no—
283C2×C47C2×C4×C22⋊C411yescharacteristic
284C2×C47C2×#41911yescharacteristic
285C2×C47C2×#41711yescharacteristic
286C2×C47C2×#44012yes—
287C2×C47C2×#44112yes—
288D47#176318yesdirect product factor
289C23×Q8—471no—
290C23×C8—472no—
291C2×C4×Q8—471no—
292C2×C4×Q8—478no—
293C2×C4×Q8—471no—
294C2×C4×Q8—471no—
295C2×C4×Q8—941no—
296C2×C4×Q8—941no—
297C2×C4×Q8—944no—
298C2×C4×Q8C2×D4711yescharacteristic
299C22×C4⋊C4—472no—
300C22×C4⋊C4—471no—
301C22×C4⋊C4—941no—
302C22×C42—471no—
303C22×C42—941no—
304C22×C42—941no—
305C2×#103—472no—
306C2×#103—472no—
307C2×#103—472no—
308C2×#103—4716no—
309C2×#103C2×D4712yes—
310C2×#97—472no—
311C2×#97—471no—
312C2×#97—944no—
313C2×#97C2×D4711yescharacteristic
314C4×C4⋊C4—472no—
315C4×C4⋊C4—471no—
316C4×C4⋊C4—941no—
317C4×C4⋊C4—941no—
318C4×C4⋊C4C2×D4711yescharacteristic
319C2×#95—941no—
320#340—472no—
321#340—472no—
322#340—472no—
323#340C2×D4712yes—
324C47C2×#176311yescharacteristic, complemented, Sylow
325C22×Q8—474no—
326C22×Q8—478no—
327C22×Q8—471no—
328C22×Q8—941no—
329C22×Q8—942no—
330C22×Q8—944no—
331C22×Q8C22×D4711yescharacteristic
332C23×C4—471no—
333C23×C4—471no—
334C23×C4—471no—
335C23×C4—941no—
336C23×C4—941no—
337C23×C4—942no—
338C22×C8—472no—
339C22×C8—478no—
340C22×C8—944no—
341C22×C8—944no—
342C22×C8C22×D4712yes—
343C4×Q8—22no—
344C4×Q8—474no—
345C4×Q8—474no—
346C4×Q8—474no—
347C4×Q8—948no—
348C4×Q8—948no—
349C4×Q8—942no—
350C4×Q8—942no—
351C4×Q8—942no—
352C4×Q8C4×D4714yescomplemented
353C2×C4⋊C4—21no—
354C2×C4⋊C4—471no—
355C2×C4⋊C4—472no—
356C2×C4⋊C4—474no—
357C2×C4⋊C4—478no—
358C2×C4⋊C4—942no—
359C2×C4⋊C4—944no—
360C2×C4⋊C4—948no—
361C2×C4⋊C4—941no—
362C2×C4⋊C4—942no—
363C2×C4⋊C4—941no—
364C2×C4⋊C4—941no—
365C2×C4⋊C4—941no—
366C2×C4⋊C4C22×D4711yescharacteristic
367C2×C4⋊C4C22×D4712yes—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—471no—
371C2×C42—471no—
372C2×C42—471no—
373C2×C42—474no—
374C2×C42—474no—
375C2×C42—948no—
376C2×C42—941no—
377C2×C42—941no—
378C2×C42—941no—
379C2×C42—942no—
380C2×C42—941no—
381C2×C42—1884no—
382C2×C42C22×D4711yescharacteristic
383#103—478no—
384#103—478no—
385#103—478no—
386#103C4×D4718yescomplemented
387#97—22no—
388#97—944no—
389#97—942no—
390#95—21no—
391#95—942no—
392#95—941no—
393C24—471no—
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—4716no—
397C2×Q8—474no—
398C2×Q8—472no—
399C2×Q8—944no—
400C2×Q8—948no—
401C2×Q8—948no—
402C2×Q8—9416no—
403C2×Q8—941no—
404C2×Q8—942no—
405C2×Q8C2×C4×D4714yes—
406C2×Q8C2×C4×D4712yes—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—471no—
411C22×C4—472no—
412C22×C4—474no—
413C22×C4—472no—
414C22×C4—474no—
415C22×C4—471no—
416C22×C4—471no—
417C22×C4—474no—
418C22×C4—474no—
419C22×C4—944no—
420C22×C4—942no—
421C22×C4—942no—
422C22×C4—944no—
423C22×C4—948no—
424C22×C4—944no—
425C22×C4—948no—
426C22×C4—941no—
427C22×C4—942no—
428C22×C4—941no—
429C22×C4—1884no—
430C22×C4—1882no—
431C22×C4—1882no—
432C22×C4—1884no—
433C22×C4D4×D4711yescharacteristic
434C22×C4D4×D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—474no—
439C2×C8—9416no—
440C2×C8—942no—
441C2×C8—942no—
442C2×C8C2×C4×D4714yes—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—474no—
447C4⋊C4—472no—
448C4⋊C4—948no—
449C4⋊C4—944no—
450C4⋊C4—944no—
451C4⋊C4—944no—
452C4⋊C4—944no—
453C4⋊C4—941no—
454C4⋊C4—942no—
455C4⋊C4C2×C4×D4714yes—
456C4⋊C4C2×C4×D4712yes—
457C42—24no—
458C42—42no—
459C42—474no—
460C42—474no—
461C42—472no—
462C42—472no—
463C42—944no—
464C42—944no—
465C42—944no—
466C42—1882no—
467C42—1884no—
468C42C2×C4×D4712yes—
469C42D4×D4712yes—
470C23—472no—
471C23—474no—
472C23—472no—
473C23—474no—
474C23—472no—
475C23C2×D4×D4711yescharacteristic
476Q8—22no—
477Q8—24no—
478Q8—474no—
479Q8—9416no—
480Q8—942no—
481Q8—944no—
482Q8C42×D4714yescomplemented
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—472no—
495C2×C4—474no—
496C2×C4—474no—
497C2×C4—474no—
498C2×C4—478no—
499C2×C4—472no—
500C2×C4—472no—
501C2×C4—948no—
502C2×C4—948no—
503C2×C4—9416no—
504C2×C4—942no—
505C2×C4—944no—
506C2×C4—941no—
507C2×C4—942no—
508C2×C4—941no—
509C2×C4—942no—
510C2×C4—944no—
511C2×C4—18816no—
512C2×C4—1888no—
513C2×C4—1882no—
514C2×C4—1881no—
515C2×C4—1882no—
516C2×C4—1881no—
517C2×C4C22⋊C4×D4712yes—
518C2×C4C22⋊C4×D4712yes—
519C2×C4C22×C4×D4711yescharacteristic
520C2×C4C22×C4×D4712yes—
521C2×C4C2×D4×D4711yescharacteristic
522C2×C4#41×D4712yes—
523C8—24no—
524C8—944no—
525C22—478no—
526C22—478no—
527C22—474no—
528C22—474no—
529C22—474no—
530C22C2×C22⋊C4×D4711yescharacteristic
531C22C4×D4×D4712yes—
532C22AGL(1,ℤ/8)×D4711yescharacteristic
533C22#137×D4712yes—
534C22#137×D4711yescharacteristic
535C4—24no—
536C4—22no—
537C4—22no—
538C4—44no—
539C4—42no—
540C4—474no—
541C4—944no—
542C4—942no—
543C4—942no—
544C4—1884no—
545C4—1882no—
546C4C2×C42×D4711yescharacteristic
547C4#117×D4711yescharacteristic
548C4C4×D4×D4712yes—
549C2—478no—
550C2C4×C22⋊C4×D4711yescharacteristic
551C2#419×D4711yescharacteristic
552C2#417×D4711yescharacteristic
553C2#440×D4712yes—
554C2#441×D4712yes—
subgroupG/H
centerC23C2×D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1763C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1763D47
hypocenterC47C2×#1763
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
5. #20243221C2semidirect
6. #20243220C2semidirect
7. #20243219C2semidirect
8. #20243218C2semidirect
9. #20243217C2semidirect
11. C47×#1763C2semidirect
20. C4×Q8×D47C4semidirect
30. #103×D47C4semidirect
64. Q8×Dic47C2×C4semidirect
67. C4×Dic94C2×C4semidirect
70. #13093989C2×C4semidirect
95. #13093949C2×C4semidirect
96. #13093948C2×C4semidirect
97. #13093947C2×C4semidirect
105. C4×Q8×C47C2×C4semidirect
112. #103×C47C2×C4semidirect
134. Q8×D47C42semidirect
200. Q8×C47C2×C42semidirect
244. Dic94C2×C42semidirect
281. #1763D47direct (N × H)
288. D47#1763direct (N × H)
324. C47C2×#1763semidirect
352. C4×Q8C4×D47semidirect
386. #103C4×D47semidirect
482. Q8C42×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
C2×#103×D472
C2×#97×D472
C4×C4⋊C4×D472
#202432212
#202432202
#202432192
#202432182
#202432172
#340×D472
C47×#17632
C2×#176347