Finite Group Databasebeta

← D47×#2058 #26244301

Subgroups — D47×#2058 #26244301

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D47C211yesmaximal, characteristic
2C2×#106×D47C212yesmaximal
3#389×D47C211yesmaximal, characteristic
4#20244722C211yesmaximal, characteristic, complemented
5#20244721C211yesmaximal, characteristic, complemented
6#20244720C212yesmaximal, complemented
7#20244719C212yesmaximal, complemented
8#20244718C211yesmaximal, characteristic, complemented
9#340×D47C212yesmaximal
10#336×D47C211yesmaximal, characteristic
11C47×#2058C211yesmaximal, characteristic, complemented
12C22×Q8×D47—21no—
13C22×C8×D47C2212yes—
14C2×#13094024C2211yescharacteristic
15C2×#13094023—21no—
16C2×#13094023C2212yes—
17C2×#13094022—21no—
18C4⋊Q8×D47—28no—
19C2×C4⋊C4×D47—21no—
20C2×C4⋊C4×D47—21no—
21C2×C4⋊C4×D47C2211yescharacteristic
22C2×C4⋊C4×D47C2212yes—
23C2×C4⋊C4×D47C2211yescharacteristic
24C2×C42×D47C2211yescharacteristic
25C2×#13093956C2212yes—
26C2×#13093955C2212yes—
27C2×#13093955C2212yes—
28#106×D47—28no—
29#15689022C2211yescharacteristic
30#15689021C2211yescharacteristic
31#15689020—21no—
32#15689019C2211yescharacteristic
33#15689018—21no—
34#95×D47—21no—
35#15688886C2212yes—
36#15688885C2212yes—
37#15688885C2212yes—
38#15688878C2211yescharacteristic
39#15688877C2212yes—
40C2×C4⋊Q8×C47C2211yescharacteristic
41C2×#106×C47C2212yes—
42C47×#389C2211yescharacteristic
43C47×#340C2212yes—
44C47×#336C2211yescharacteristic
45C22×Dic94—21no—
46C22×Dic94—22no—
47C2×Q8×D47—28no—
48C2×Q8×D47—44no—
49C2×Q8×D47—44no—
50C22×C4×D47—21no—
51C22×C4×D47—22no—
52C22×C4×D47—21no—
53C22×C4×D47D411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47C2311yescharacteristic
56C22×C47⋊C8C2312yes—
57C2×C8×D47—24no—
58C2×C8×D47—24no—
59C2×C8×D47Q818yescomplemented
60#13094024—24no—
61#13094023—28no—
62#13094023—24no—
63#13094023—24no—
64#13094022—28no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2312yes—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
76C4⋊C4×D47—28no—
77C4⋊C4×D47—24no—
78C4⋊C4×D47—22no—
79C4⋊C4×D47—24no—
80C4⋊C4×D47—44no—
81C4⋊C4×D47D418yes—
82C4⋊C4×D47Q814yescomplemented
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47D411yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86C42×D47—24no—
87#13093956—24no—
88#13093955—24no—
89#13093955—24no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C22×Q8×C47—21no—
94C22×C8×C47C2312yes—
95C4⋊Q8×C47—24no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2312yes—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102#106×C47—24no—
103#95×C47—21no—
104C23×D47C2×D411yescharacteristic
105C2×Q8×C47—24no—
106C2×Q8×C47—42no—
107C2×Q8×C47—42no—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2411yescharacteristic
114C22×Dic47—21no—
115C22×Dic47—22no—
116C22×Dic47—21no—
117C22×Dic47C2×D411yescharacteristic
118C22×Dic47C2×D411yescharacteristic
119C22×Dic47C2×D411yescharacteristic
120Q8×D47—432no—
121C2×C4×D47—22no—
122C2×C4×D47—22no—
123C2×C4×D47—22no—
124C2×C4×D47—22no—
125C2×C4×D47—28no—
126C2×C4×D47—24no—
127C2×C4×D47—42no—
128C2×C4×D47—44no—
129C2×C4×D47—42no—
130C2×C4×D47—44no—
131C2×C4×D47—42no—
132C2×C4×D47—42no—
133C2×C4×D47—42no—
134C2×C4×D47SD1614yes—
135C2×C4×D47SD1614yes—
136C2×C4×D47C2×D414yes—
137C2×C4×D47C2×Q814yes—
138C2×C4×D47C2×Q812yes—
139C2×C4×D47#4112yes—
140C2×Dic94—24no—
141C2×Dic94—28no—
142C2×Dic94—44no—
143C2×Dic94—42no—
144C2×Dic94—42no—
145C2×Dic94—44no—
146C2×C8×C47—22no—
147C2×C8×C47—22no—
148C2×C8×C47C2×Q814yescomplemented
149C4⋊C4×C47—24no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47C2×D414yes—
155C4⋊C4×C47C2×Q812yescomplemented
156C42×C47—22no—
157C4⋊Dic47—24no—
158C4⋊Dic47—22no—
159C4⋊Dic47—21no—
160C4⋊Dic47—22no—
161C4⋊Dic47—42no—
162C4⋊Dic47C2×D414yes—
163C4⋊Dic47C2×Q812yescomplemented
164Dic47⋊C4—28no—
165Dic47⋊C4—28no—
166Dic47⋊C4—24no—
167Dic47⋊C4—42no—
168Dic47⋊C4—42no—
169Dic47⋊C4—42no—
170C4×Dic47—22no—
171C4×Dic47—22no—
172C4×Dic47—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8C2×Q814yescomplemented
176C8×D47—216no—
177C23×C47C22×D411yescharacteristic
178C22×D47#12012yes—
179C22×D47C22⋊Q812yes—
180C22×D47C4⋊Q812yes—
181C22×D47C2×SD1612yes—
182C22×D47C2×SD1612yes—
183C22×D47AGL(1,ℤ/8)12yes—
184C22×D47#13712yes—
185Q8×C47—48no—
186C2×C4×C47—21no—
187C2×C4×C47—21no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—41no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—41no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47C2×SD1612yes—
200C2×C4×C47C2×SD1612yes—
201C2×C4×C47C22×D412yes—
202C2×C4×C47C22×Q812yes—
203C2×C4×C47C22×Q811yescharacteristic
204C2×C4×C47C2×#4111yescharacteristic
205C2×Dic47—21no—
206C2×Dic47—21no—
207C2×Dic47—21no—
208C2×Dic47—21no—
209C2×Dic47—24no—
210C2×Dic47—22no—
211C2×Dic47—41no—
212C2×Dic47—42no—
213C2×Dic47—42no—
214C2×Dic47—41no—
215C2×Dic47—41no—
216C2×Dic47—41no—
217C2×Dic47—41no—
218C2×Dic47#12012yes—
219C2×Dic47C22⋊Q812yes—
220C2×Dic47C4⋊Q812yes—
221C2×Dic47C2×SD1612yes—
222C2×Dic47C2×SD1612yes—
223C4×D47—28no—
224C4×D47—28no—
225C4×D47—416no—
226C4×D47—48no—
227C4×D47—84no—
228C4×D47C22⋊Q818yes—
229C4×D47C4⋊Q818yes—
230Dic94—416no—
231Dic94—48no—
232C8×C47—24no—
233C47⋊C8—24no—
234C2×#2058—471nomaximal, Sylow
235C22×C47C2×#12011yescharacteristic
236C22×C47C2×C22⋊Q811yescharacteristic
237C22×C47C2×C4⋊Q811yescharacteristic
238C22×C47C22×SD1611yescharacteristic
239C22×C47C22×SD1611yescharacteristic
240C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C47C2×#13711yescharacteristic
242C2×D47#39514yes—
243C2×D47#44814yes—
244C2×D47#45014yes—
245C2×D47#47514yes—
246C2×D47#47614yes—
247C2×D47#49814yes—
248C2×D47#50114yes—
249C4×C47—22no—
250C4×C47—22no—
251C4×C47—44no—
252C4×C47—42no—
253C4×C47—81no—
254C4×C47C2×C22⋊Q812yes—
255C4×C47C2×C4⋊Q812yes—
256Dic47—22no—
257Dic47—22no—
258Dic47—44no—
259Dic47—42no—
260Dic47—81no—
261Dic47#39514yes—
262C22×C4⋊Q8—471no—
263C22×#106—472no—
264C2×#389—471no—
265#2058—472no—
266#2058—471no—
267#2058—472no—
268#2058—471no—
269#2058—471no—
270#2058D4711yescharacteristic, direct product factor
271C2×#340—472no—
272C2×#336—471no—
273C2×C47C2×#39511yescharacteristic
274C2×C47C2×#45011yescharacteristic
275C2×C47C2×#44811yescharacteristic
276C2×C47C2×#47611yescharacteristic
277C2×C47C2×#47511yescharacteristic
278C2×C47C2×#49811yescharacteristic
279C2×C47C2×#50111yescharacteristic
280D47#205818yesdirect product factor
281C23×Q8—941no—
282C23×C8—472no—
283C2×C4⋊Q8—472no—
284C2×C4⋊Q8—471no—
285C2×C4⋊Q8—941no—
286C2×C4⋊Q8—941no—
287C2×C4⋊Q8—948no—
288C2×C4⋊Q8C2×D4711yescharacteristic
289C22×C4⋊C4—472no—
290C22×C4⋊C4—471no—
291C22×C4⋊C4—471no—
292C22×C4⋊C4—941no—
293C22×C4⋊C4—941no—
294C22×C42—471no—
295C2×#106—472no—
296C2×#106—472no—
297C2×#106—472no—
298C2×#106—948no—
299C2×#106C2×D4712yes—
300#389—471no—
301#389—471no—
302#389—471no—
303#389—941no—
304#389—941no—
305#389C2×D4711yescharacteristic
306C2×#95—941no—
307#340—472no—
308#340—472no—
309#340—472no—
310#340C2×D4712yes—
311#336—472no—
312#336—471no—
313#336C2×D4711yescharacteristic
314C47C2×#205811yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8—942no—
317C22×Q8—948no—
318C22×Q8—941no—
319C22×Q8—1884no—
320C22×Q8—1884no—
321C23×C4—471no—
322C23×C4—471no—
323C23×C4—471no—
324C23×C4—942no—
325C23×C4—941no—
326C23×C4—941no—
327C22×C8—472no—
328C22×C8—478no—
329C22×C8—944no—
330C22×C8—944no—
331C22×C8C22×D4712yes—
332C4⋊Q8—24no—
333C4⋊Q8—944no—
334C4⋊Q8—944no—
335C4⋊Q8—948no—
336C4⋊Q8—948no—
337C4⋊Q8—944no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—472no—
341C2×C4⋊C4—471no—
342C2×C4⋊C4—478no—
343C2×C4⋊C4—474no—
344C2×C4⋊C4—471no—
345C2×C4⋊C4—944no—
346C2×C4⋊C4—942no—
347C2×C4⋊C4—948no—
348C2×C4⋊C4—944no—
349C2×C4⋊C4—942no—
350C2×C4⋊C4—941no—
351C2×C4⋊C4—942no—
352C2×C4⋊C4—941no—
353C2×C4⋊C4—941no—
354C2×C4⋊C4—941no—
355C2×C4⋊C4—941no—
356C2×C4⋊C4—941no—
357C2×C4⋊C4—1884no—
358C2×C4⋊C4C22×D4711yescharacteristic
359C2×C4⋊C4C22×D4712yes—
360C2×C4⋊C4C22×D4711yescharacteristic
361C2×C42—471no—
362C2×C42—471no—
363C2×C42—471no—
364C2×C42—944no—
365C2×C42C22×D4711yescharacteristic
366#106—24no—
367#106—944no—
368#106—944no—
369#106—944no—
370#95—21no—
371#95—941no—
372#95—941no—
373#95—941no—
374C24—471no—
375C2×Q8—24no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—944no—
379C2×Q8—948no—
380C2×Q8—1882no—
381C2×Q8—1884no—
382C2×Q8—1884no—
383C2×Q8—18832no—
384C2×Q8—1882no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—471no—
389C22×C4—474no—
390C22×C4—472no—
391C22×C4—474no—
392C22×C4—472no—
393C22×C4—471no—
394C22×C4—471no—
395C22×C4—474no—
396C22×C4—474no—
397C22×C4—942no—
398C22×C4—942no—
399C22×C4—942no—
400C22×C4—942no—
401C22×C4—948no—
402C22×C4—944no—
403C22×C4—941no—
404C22×C4—942no—
405C22×C4—941no—
406C22×C4—1882no—
407C22×C4—1882no—
408C22×C4—1882no—
409C22×C4—1882no—
410C22×C4—1882no—
411C22×C4—1884no—
412C22×C4—1884no—
413C22×C4D4×D4711yescharacteristic
414C22×C4D4×D4711yescharacteristic
415C22×C4C23×D4711yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—474no—
419C2×C8—9416no—
420C2×C8—942no—
421C2×C8—942no—
422C2×C8Q8×D4714yescomplemented
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—42no—
428C4⋊C4—474no—
429C4⋊C4—472no—
430C4⋊C4—944no—
431C4⋊C4—948no—
432C4⋊C4—948no—
433C4⋊C4—944no—
434C4⋊C4—942no—
435C4⋊C4—941no—
436C4⋊C4—942no—
437C4⋊C4—1882no—
438C4⋊C4—1882no—
439C4⋊C4—1882no—
440C4⋊C4—1882no—
441C4⋊C4D4×D4714yes—
442C4⋊C4Q8×D4712yescomplemented
443C42—22no—
444C42—942no—
445C42—942no—
446C42—942no—
447C23—472no—
448C23—472no—
449C23—472no—
450C23—472no—
451C23—472no—
452C23—472no—
453C23—472no—
454C23C2×D4×D4711yescharacteristic
455Q8—48no—
456Q8—1888no—
457Q8—18816no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—472no—
472C2×C4—472no—
473C2×C4—472no—
474C2×C4—478no—
475C2×C4—478no—
476C2×C4—472no—
477C2×C4—472no—
478C2×C4—948no—
479C2×C4—948no—
480C2×C4—941no—
481C2×C4—941no—
482C2×C4—941no—
483C2×C4—941no—
484C2×C4—944no—
485C2×C4—942no—
486C2×C4—3764no—
487C2×C4—1888no—
488C2×C4—18816no—
489C2×C4—1881no—
490C2×C4—1881no—
491C2×C4—1881no—
492C2×C4—1881no—
493C2×C4—1882no—
494C2×C4—1881no—
495C2×C4—1882no—
496C2×C4SD16×D4712yes—
497C2×C4SD16×D4712yes—
498C2×C4C2×D4×D4712yes—
499C2×C4C2×Q8×D4712yes—
500C2×C4C2×Q8×D4711yescharacteristic
501C2×C4#41×D4711yescharacteristic
502C8—24no—
503C8—944no—
504C22—474no—
505C22—474no—
506C22—474no—
507C22—474no—
508C22—474no—
509C22—474no—
510C22—474no—
511C22#120×D4711yescharacteristic
512C22C22⋊Q8×D4711yescharacteristic
513C22C4⋊Q8×D4711yescharacteristic
514C22C2×SD16×D4711yescharacteristic
515C22C2×SD16×D4711yescharacteristic
516C22AGL(1,ℤ/8)×D4711yescharacteristic
517C22#137×D4711yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—81no—
523C4—474no—
524C4—942no—
525C4—942no—
526C4—3761no—
527C4—1884no—
528C4—1882no—
529C4C22⋊Q8×D4712yes—
530C4C4⋊Q8×D4712yes—
531C2—478no—
532C2#395×D4711yescharacteristic
533C2#450×D4711yescharacteristic
534C2#448×D4711yescharacteristic
535C2#476×D4711yescharacteristic
536C2#475×D4711yescharacteristic
537C2#498×D4711yescharacteristic
538C2#501×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2058C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenter#2058D47
hypocenterC47C2×#2058
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
4. #20244722C2semidirect
5. #20244721C2semidirect
6. #20244720C2semidirect
7. #20244719C2semidirect
8. #20244718C2semidirect
11. C47×#2058C2semidirect
59. C2×C8×D47Q8semidirect
82. C4⋊C4×D47Q8semidirect
148. C2×C8×C47C2×Q8semidirect
155. C4⋊C4×C47C2×Q8semidirect
163. C4⋊Dic47C2×Q8semidirect
175. C2×C47⋊C8C2×Q8semidirect
270. #2058D47direct (N × H)
280. D47#2058direct (N × H)
314. C47C2×#2058semidirect
422. C2×C8Q8×D47semidirect
442. C4⋊C4Q8×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×#106×D472
#389×D472
#202447222
#202447212
#202447202
#202447192
#202447182
#340×D472
#336×D472
C47×#20582
C2×#205847