Finite Group Databasebeta

← D47×#1821 #26216031

Subgroups — D47×#1821 #26216031

Order 12032.

1734 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic
2#407×D47C212yesmaximal
3#20243468C211yesmaximal, characteristic, complemented
4#20243467C214yesmaximal, complemented
5#20243466C212yesmaximal, complemented
6#343×D47C214yesmaximal, complemented
7C47×#1821C211yesmaximal, characteristic, complemented
8C23×C4×D47C412yes—
9C23×C4×D47C2211yescharacteristic
10C2×M16×D47C2214yes—
11C22×C4⋊Dic47C2211yescharacteristic
12C22×Dic47⋊C4C412yes—
13C2×C4⋊C4×D47—22no—
14C2×C4⋊C4×D47—22no—
15C2×C4⋊C4×D47—22no—
16C2×C4⋊C4×D47—22no—
17C2×C4⋊C4×D47C412yes—
18C2×C4⋊C4×D47C412yes—
19C2×C4⋊C4×D47C2212yes—
20C2×C4⋊C4×D47C2212yes—
21#15689087C2212yes—
22#15689086C2214yes—
23#15689085—22no—
24#15689085—22no—
25C22⋊C8×D47—22no—
26C22⋊C8×D47—22no—
27#15688892C2214yescomplemented
28#15688891C2218yescomplemented
29C22×C4⋊C4×C47C2211yescharacteristic
30C47×#407C2212yes—
31C47×#343C2214yescomplemented
32C24×D47C2×C411yescharacteristic
33C23×Dic47C2×C411yescharacteristic
34C23×Dic47C2×C412yes—
35C22×C4×D47—28no—
36C22×C4×D47—22no—
37C22×C4×D47—22no—
38C22×C4×D47—22no—
39C22×C4×D47—22no—
40C22×C4×D47—48no—
41C22×C4×D47C2×C411yescharacteristic
42C22×C4×D47C2×C411yescharacteristic
43C22×C4×D47C2×C414yes—
44C22×C4×D47C2×C414yes—
45C22×C4×D47D412yes—
46C22×C4×D47D412yes—
47C22×C4×D47D412yes—
48C22×C4×D47D412yes—
49C22×C4×D47C2311yescharacteristic
50C22×C4×D47C2311yescharacteristic
51C2×#10625329C2314yes—
52C2×#10625324—24no—
53M16×D47—216no—
54C2×C8×D47—24no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47C2×C412yes—
58C2×C4⋊Dic47C2312yes—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4C2×C414yes—
62C2×Dic47⋊C4C2×C414yes—
63C4⋊C4×D47—24no—
64C4⋊C4×D47—24no—
65C4⋊C4×D47—24no—
66C4⋊C4×D47—24no—
67C4⋊C4×D47—24no—
68C4⋊C4×D47—24no—
69C4⋊C4×D47—24no—
70C4⋊C4×D47—24no—
71C22⋊(C47⋊C8)—22no—
72C22⋊(C47⋊C8)—22no—
73(C2×D47)⋊C8—24no—
74(C2×D47)⋊C8—24no—
75C23×C4×C47C2×C412yes—
76C23×C4×C47C2311yescharacteristic
77C2×M16×C47C2314yes—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47C2×C412yes—
81C2×C4⋊C4×C47C2312yes—
82C22⋊C8×C47—22no—
83C22⋊C8×C47—22no—
84C24×C47C22×C411yescharacteristic
85C23×D47—24no—
86C23×D47—24no—
87C23×D47—24no—
88C23×D47C22⋊C411yescharacteristic
89C23×D47C22⋊C411yescharacteristic
90C23×D47C22⋊C411yescharacteristic
91C23×D47C22⋊C411yescharacteristic
92C23×D47C22×C411yescharacteristic
93C23×D47C22×C411yescharacteristic
94C22×C4×C47—24no—
95C22×C4×C47—22no—
96C22×C4×C47—22no—
97C22×C4×C47—44no—
98C22×C4×C47C22×C411yescharacteristic
99C22×C4×C47C22×C414yes—
100C22×C4×C47C2×D412yes—
101C22×C4×C47C2×D412yes—
102C22×C4×C47C2411yescharacteristic
103C22×Dic47—24no—
104C22×Dic47—22no—
105C22×Dic47—22no—
106C22×Dic47—44no—
107C22×Dic47C22⋊C412yes—
108C22×Dic47C22⋊C412yes—
109C22×Dic47C22×C411yescharacteristic
110C22×Dic47C22×C414yes—
111C22×Dic47C22×C411yescharacteristic
112C2×C4×D47—24no—
113C2×C4×D47—24no—
114C2×C4×D47—24no—
115C2×C4×D47—28no—
116C2×C4×D47—28no—
117C2×C4×D47—28no—
118C2×C4×D47—28no—
119C2×C4×D47—24no—
120C2×C4×D47—24no—
121C2×C4×D47—24no—
122C2×C4×D47—24no—
123C2×C4×D47—48no—
124C2×C4×D47—48no—
125C2×C4×D47—48no—
126C2×C4×D47—48no—
127C2×C4×D47—48no—
128C2×C4×D47—48no—
129C2×C4×D47C22⋊C412yes—
130C2×C4×D47C22⋊C412yes—
131C2×C4×D47C22⋊C412yes—
132C2×C4×D47C22⋊C412yes—
133C2×C4×D47C2×D412yes—
134C2×C4×D47C2×D412yes—
135C2×C4×D47C2×D412yes—
136C2×C4×D47C2×D412yes—
137C2×C4×D47#4118yes—
138M16×C47—28no—
139C2×C8×C47—24no—
140C4⋊C4×C47—24no—
141C4⋊C4×C47—24no—
142C4⋊Dic47—24no—
143C4⋊Dic47—24no—
144Dic47⋊C4—28no—
145Dic47⋊C4—28no—
146#10625329—28no—
147C2×C47⋊C8—24no—
148#10625324—48no—
149C8×D47—48no—
150C23×C47—22no—
151C23×C47—22no—
152C23×C47—22no—
153C23×C47C2×C22⋊C411yescharacteristic
154C23×C47C2×C22⋊C411yescharacteristic
155C23×C47C23×C411yescharacteristic
156C22×D47—232no—
157C22×D47—22no—
158C22×D47—22no—
159C22×D47—22no—
160C22×D47—22no—
161C22×D47—22no—
162C22×D47—22no—
163C22×D47—22no—
164C22×D47—22no—
165C22×D47—22no—
166C22×D47—22no—
167C22×D47—22no—
168C22×D47—22no—
169C22×D47—22no—
170C22×D47—22no—
171C22×D47—22no—
172C22×D47#10014yes—
173C22×D47#10114yes—
174C22×D47C2×C22⋊C411yescharacteristic
175C22×D47C2×C22⋊C411yescharacteristic
176C22×D47C2×C22⋊C411yescharacteristic
177C22×D47C2×C22⋊C411yescharacteristic
178C22×D47#11714yes—
179C2×C4×C47—22no—
180C2×C4×C47—24no—
181C2×C4×C47—24no—
182C2×C4×C47—24no—
183C2×C4×C47—44no—
184C2×C4×C47—44no—
185C2×C4×C47—44no—
186C2×C4×C47C2×C22⋊C412yes—
187C2×C4×C47C22×D412yes—
188C2×C4×C47C2×#4114yes—
189C2×Dic47—22no—
190C2×Dic47—24no—
191C2×Dic47—24no—
192C2×Dic47—24no—
193C2×Dic47—44no—
194C2×Dic47—44no—
195C2×Dic47—44no—
196C2×Dic47C2×C22⋊C412yes—
197C2×Dic47C2×C22⋊C412yes—
198C2×Dic47#11714yes—
199C4×D47—24no—
200C4×D47—24no—
201C4×D47—24no—
202C4×D47—24no—
203C4×D47—24no—
204C4×D47—24no—
205C4×D47—48no—
206C4×D47—48no—
207C4×D47—48no—
208C4×D47—48no—
209C4×D47#12318yes—
210C4×D47#12318yes—
211C8×C47—44no—
212C47⋊C8—44no—
213C2×#1821—471nomaximal, Sylow
214C22×C47—28no—
215C22×C47—21no—
216C22×C47—21no—
217C22×C47—21no—
218C22×C47—21no—
219C22×C47—21no—
220C22×C47—21no—
221C22×C47C2×#10012yes—
222C22×C47C2×#10112yes—
223C22×C47C22×C22⋊C411yescharacteristic
224C22×C47C2×#11712yes—
225C2×D47—28no—
226C2×D47—28no—
227C2×D47—28no—
228C2×D47—21no—
229C2×D47—21no—
230C2×D47—21no—
231C2×D47—21no—
232C2×D47—21no—
233C2×D47—21no—
234C2×D47—28no—
235C2×D47—28no—
236C2×D47—28no—
237C2×D47#38112yes—
238C2×D47#38112yes—
239C2×D47C2×#10012yes—
240C2×D47C2×#10012yes—
241C2×D47C2×#10112yes—
242C2×D47C2×#10112yes—
243C4×C47—22no—
244C4×C47—44no—
245C4×C47C2×#12314yes—
246Dic47—22no—
247Dic47—44no—
248Dic47#38114yes—
249C23×C4⋊C4—471no—
250C2×#407—472no—
251#1821—472no—
252#1821—474no—
253#1821—471no—
254#1821D4711yescharacteristic, direct product factor
255C2×#343—474no—
256C2×C47—22no—
257C2×C47—22no—
258C2×C47—22no—
259C2×C47C2×#38111yescharacteristic
260C2×C47C22×#10011yescharacteristic
261C2×C47C22×#10111yescharacteristic
262D47—22no—
263D47—22no—
264D47—22no—
265D47#182114yesdirect product factor
266C24×C4—471no—
267C24×C4—472no—
268C22×M16—474no—
269C22×C4⋊C4—472no—
270C22×C4⋊C4—471no—
271C22×C4⋊C4—472no—
272C22×C4⋊C4—472no—
273C22×C4⋊C4—472no—
274C22×C4⋊C4—472no—
275C22×C4⋊C4—942no—
276C22×C4⋊C4—942no—
277C22×C4⋊C4—942no—
278C22×C4⋊C4—942no—
279C22×C4⋊C4C2×D4711yescharacteristic
280#407—472no—
281#407—474no—
282#407—942no—
283#407—942no—
284#407C2×D4712yes—
285C2×C22⋊C8—942no—
286C2×C22⋊C8—942no—
287#343—478no—
288#343—474no—
289#343C2×D4714yescomplemented
290C47C2×#182111yescharacteristic, complemented, Sylow
291C25—471no—
292C23×C4—471no—
293C23×C4—471no—
294C23×C4—471no—
295C23×C4—471no—
296C23×C4—472no—
297C23×C4—472no—
298C23×C4—472no—
299C23×C4—472no—
300C23×C4—471no—
301C23×C4—472no—
302C23×C4—474no—
303C23×C4—474no—
304C23×C4—948no—
305C23×C4—942no—
306C23×C4—942no—
307C23×C4—942no—
308C23×C4—942no—
309C23×C4—1888no—
310C23×C4C4×D4712yes—
311C23×C4C22×D4711yescharacteristic
312C2×M16—474no—
313C2×M16—944no—
314C2×M16—9416no—
315C2×M16C22×D4714yes—
316C22×C8—944no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—474no—
320C2×C4⋊C4—474no—
321C2×C4⋊C4—472no—
322C2×C4⋊C4—472no—
323C2×C4⋊C4—944no—
324C2×C4⋊C4—944no—
325C2×C4⋊C4—944no—
326C2×C4⋊C4—944no—
327C2×C4⋊C4—944no—
328C2×C4⋊C4—944no—
329C2×C4⋊C4—944no—
330C2×C4⋊C4—944no—
331C2×C4⋊C4—944no—
332C2×C4⋊C4—944no—
333C2×C4⋊C4—942no—
334C2×C4⋊C4—942no—
335C2×C4⋊C4C4×D4712yes—
336C2×C4⋊C4C22×D4712yes—
337C22⋊C8—22no—
338C22⋊C8—22no—
339C22⋊C8—944no—
340C22⋊C8—944no—
341C22⋊C8—942no—
342C22⋊C8—942no—
343C24—471no—
344C24—471no—
345C24—471no—
346C24—471no—
347C24—471no—
348C24—471no—
349C24—944no—
350C24—944no—
351C24—944no—
352C24C2×C4×D4711yescharacteristic
353C22×C4—24no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—44no—
357C22×C4—471no—
358C22×C4—472no—
359C22×C4—472no—
360C22×C4—478no—
361C22×C4—472no—
362C22×C4—472no—
363C22×C4—471no—
364C22×C4—472no—
365C22×C4—472no—
366C22×C4—472no—
367C22×C4—472no—
368C22×C4—472no—
369C22×C4—472no—
370C22×C4—474no—
371C22×C4—944no—
372C22×C4—948no—
373C22×C4—948no—
374C22×C4—948no—
375C22×C4—948no—
376C22×C4—944no—
377C22×C4—944no—
378C22×C4—944no—
379C22×C4—944no—
380C22×C4—944no—
381C22×C4—944no—
382C22×C4—944no—
383C22×C4—942no—
384C22×C4—942no—
385C22×C4—1888no—
386C22×C4—1888no—
387C22×C4—1888no—
388C22×C4—1888no—
389C22×C4—1888no—
390C22×C4—1888no—
391C22×C4—1884no—
392C22×C4C2×C4×D4711yescharacteristic
393C22×C4C2×C4×D4714yes—
394C22×C4D4×D4712yes—
395C22×C4D4×D4712yes—
396C22×C4C23×D4711yescharacteristic
397M16—28no—
398M16—948no—
399M16—1888no—
400C2×C8—24no—
401C2×C8—944no—
402C2×C8—1888no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—948no—
406C4⋊C4—948no—
407C4⋊C4—944no—
408C4⋊C4—944no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—471no—
413C23—471no—
414C23—471no—
415C23—471no—
416C23—474no—
417C23—474no—
418C23—474no—
419C23—942no—
420C23—942no—
421C23—942no—
422C23—942no—
423C23—942no—
424C23—942no—
425C23—942no—
426C23—942no—
427C23—942no—
428C23—942no—
429C23—942no—
430C23—942no—
431C23—9432no—
432C23—942no—
433C23—942no—
434C23—942no—
435C23C22⋊C4×D4711yescharacteristic
436C23C22⋊C4×D4711yescharacteristic
437C23C22×C4×D4711yescharacteristic
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—472no—
446C2×C4—474no—
447C2×C4—478no—
448C2×C4—478no—
449C2×C4—472no—
450C2×C4—944no—
451C2×C4—944no—
452C2×C4—944no—
453C2×C4—944no—
454C2×C4—944no—
455C2×C4—944no—
456C2×C4—942no—
457C2×C4—944no—
458C2×C4—944no—
459C2×C4—944no—
460C2×C4—1888no—
461C2×C4—1888no—
462C2×C4—1888no—
463C2×C4—1888no—
464C2×C4—1884no—
465C2×C4—1884no—
466C2×C4—1884no—
467C2×C4C22⋊C4×D4712yes—
468C2×C4C2×D4×D4712yes—
469C2×C4#41×D4714yes—
470C8—44no—
471C8—1884no—
472C22—28no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—472no—
480C22—472no—
481C22—472no—
482C22—472no—
483C22—472no—
484C22—472no—
485C22—948no—
486C22—948no—
487C22—948no—
488C22—948no—
489C22—948no—
490C22—948no—
491C22—941no—
492C22—941no—
493C22—941no—
494C22—941no—
495C22—941no—
496C22—941no—
497C22#100×D4712yes—
498C22#101×D4712yes—
499C22C2×C22⋊C4×D4711yescharacteristic
500C22#117×D4712yes—
501C4—22no—
502C4—44no—
503C4—474no—
504C4—942no—
505C4—1884no—
506C4#123×D4714yes—
507C2—22no—
508C2—22no—
509C2—22no—
510C2—474no—
511C2—942no—
512C2—942no—
513C2—942no—
514C2#381×D4711yescharacteristic
515C2C2×#100×D4711yescharacteristic
516C2C2×#101×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1821C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenter#1821D47
hypocenterC47C2×#1821
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #20243468C2semidirect
4. #20243467C2semidirect
5. #20243466C2semidirect
6. #343×D47C2semidirect
7. C47×#1821C2semidirect
27. #15688892C22semidirect
28. #15688891C22semidirect
31. C47×#343C22semidirect
254. #1821D47direct (N × H)
265. D47#1821direct (N × H)
289. #343C2×D47semidirect
290. C47C2×#1821semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
#407×D472
#202434682
#202434672
#202434662
#343×D472
C47×#18212
C2×#182147