Finite Group Databasebeta

← C47×#8449 #26048147

Subgroups — C47×#8449 #26048147

Order 12032.

788 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#556C211yesmaximal, characteristic
2C47×#1990C211yesmaximal, characteristic, complemented
3C47×#1803C211yesmaximal, characteristic, complemented
4C47×#1802C211yesmaximal, characteristic
5C2×C47×#332C211yesmaximal, characteristic, complemented
6C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
7C2×C47×D4⋊C8C211yesmaximal, characteristic
8C47×#556—22no—
9C47×#556—22no—
10C47×#556—22no—
11C47×#556C414yescomplemented
12C2×C4⋊Q8×C47C2211yescharacteristic
13C2×#126×C47—22no—
14C2×#124×C47—21no—
15C2×C22⋊Q8×C47—21no—
16C2×C4×Q8×C47—21no—
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×#117×C47—21no—
20C2×C4⋊C8×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×#103×C47—21no—
23C2×#102×C47—21no—
24C2×C4×C8×C47C2211yescharacteristic
25C47×#384C2211yescharacteristic
26C47×#340—21no—
27C47×#340—21no—
28C47×#340—22no—
29C47×#332—22no—
30C47×Q8⋊C8—22no—
31C47×D4⋊C8—22no—
32C22×Q8×C47—21no—
33C22×Q8×C47D411yescharacteristic
34C22×D4×C47D411yescharacteristic
35C23×C4×C47—21no—
36C22×C8×C47—21no—
37C22×C8×C47—21no—
38C22×C8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47C2×C412yes—
42C4⋊Q8×C47D412yes—
43#126×C47—28no—
44#126×C47—28no—
45#124×C47—24no—
46#124×C47—24no—
47C22⋊Q8×C47—24no—
48C22⋊Q8×C47—24no—
49C4×Q8×C47—24no—
50C4×Q8×C47—24no—
51C4×Q8×C47—21no—
52C4×Q8×C47—21no—
53C4×Q8×C47C2×C412yes—
54C4×Q8×C47D412yes—
55C4×D4×C47—21no—
56C4×D4×C47—21no—
57C4×D4×C47C2×C412yes—
58C4×D4×C47D412yes—
59#117×C47—24no—
60#117×C47—24no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47D411yescharacteristic
68C2×C4⋊C4×C47D411yescharacteristic
69C2×C4⋊C4×C47D412yes—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—21no—
73C2×C42×C47—22no—
74C2×C42×C47—21no—
75C2×C42×C47C2311yescharacteristic
76C4⋊C8×C47—21no—
77C4⋊C8×C47—21no—
78C4⋊C8×C47—21no—
79C4⋊C8×C47—21no—
80#103×C47—42no—
81#102×C47—42no—
82C4×C8×C47—21no—
83C4×C8×C47—21no—
84C24×C47—21no—
85C2×Q8×C47—22no—
86C2×Q8×C47—21no—
87C2×Q8×C47—22no—
88C2×Q8×C47—21no—
89C2×Q8×C47—21no—
90C2×Q8×C47—21no—
91C2×Q8×C47—21no—
92C2×Q8×C47—41no—
93C2×Q8×C47—41no—
94C2×Q8×C47—41no—
95C2×Q8×C47—41no—
96C2×Q8×C47C22⋊C412yes—
97C2×D4×C47—21no—
98C2×D4×C47—21no—
99C2×D4×C47—21no—
100C2×D4×C47—21no—
101C2×D4×C47—21no—
102C2×D4×C47C22⋊C412yes—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—41no—
110C22×C4×C47—41no—
111C22×C4×C47—41no—
112C22×C4×C47—41no—
113C22×C4×C47—41no—
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C2×C8×C47—22no—
118C2×C8×C47—41no—
119C2×C8×C47—41no—
120C2×C8×C47—41no—
121C2×C8×C47—41no—
122C2×C8×C47—41no—
123C2×C8×C47—41no—
124C2×C8×C47—41no—
125C2×C8×C47—41no—
126C4⋊C4×C47—28no—
127C4⋊C4×C47—22no—
128C4⋊C4×C47—22no—
129C4⋊C4×C47—22no—
130C4⋊C4×C47—22no—
131C4⋊C4×C47—21no—
132C4⋊C4×C47—21no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—42no—
135C4⋊C4×C47—41no—
136C4⋊C4×C47—41no—
137C4⋊C4×C47—41no—
138C4⋊C4×C47—41no—
139C4⋊C4×C47C22⋊C412yes—
140C4⋊C4×C47C22⋊C412yes—
141C4⋊C4×C47C22⋊C414yes—
142C22⋊C4×C47—28no—
143C22⋊C4×C47—28no—
144C22⋊C4×C47—22no—
145C22⋊C4×C47—22no—
146C42×C47—28no—
147C42×C47—22no—
148C42×C47—22no—
149C42×C47C22×C411yescharacteristic
150C42×C47C2×D411yescharacteristic
151C42×C47C2×D411yescharacteristic
152C42×C47C2×D411yescharacteristic
153C23×C47—22no—
154C23×C47—41no—
155C23×C47—41no—
156C23×C47—41no—
157C23×C47—41no—
158C23×C47—41no—
159C23×C47—41no—
160C23×C47#12011yescharacteristic
161Q8×C47—22no—
162Q8×C47—22no—
163Q8×C47—42no—
164Q8×C47—42no—
165Q8×C47—41no—
166Q8×C47—42no—
167Q8×C47—41no—
168Q8×C47—42no—
169D4×C47—22no—
170D4×C47—22no—
171D4×C47—41no—
172D4×C47—41no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
175C2×C4×C47—22no—
176C2×C4×C47—22no—
177C2×C4×C47—22no—
178C2×C4×C47—24no—
179C2×C4×C47—41no—
180C2×C4×C47—41no—
181C2×C4×C47—42no—
182C2×C4×C47—41no—
183C2×C4×C47—41no—
184C2×C4×C47—42no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—42no—
190C2×C4×C47—42no—
191C2×C4×C47—81no—
192C2×C4×C47—81no—
193C2×C4×C47—81no—
194C2×C4×C47C2×C22⋊C411yescharacteristic
195C2×C4×C47C2×C22⋊C411yescharacteristic
196C2×C4×C47C2×C22⋊C411yescharacteristic
197C2×C4×C47#12011yescharacteristic
198C2×C4×C47#12011yescharacteristic
199C2×C4×C47#12011yescharacteristic
200C2×C4×C47#13511yescharacteristic
201C2×C4×C47#13511yescharacteristic
202C2×C4×C47#13511yescharacteristic
203C2×C4×C47#13511yescharacteristic
204C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C47#13711yescharacteristic
207C2×C4×C47#13711yescharacteristic
208C8×C47—42no—
209C8×C47—81no—
210C8×C47—81no—
211#8449C4711yesmaximal, characteristic, direct product factor, Sylow
212C22×C47—42no—
213C22×C47—42no—
214C22×C47—42no—
215C22×C47—81no—
216C22×C47—81no—
217C22×C47—81no—
218C22×C47—81no—
219C22×C47#37911yescharacteristic
220C22×C47#44911yescharacteristic
221C22×C47#44911yescharacteristic
222C22×C47#45211yescharacteristic
223C22×C47#45211yescharacteristic
224C22×C47#45411yescharacteristic
225C22×C47#45611yescharacteristic
226C4×C47—21no—
227C4×C47—21no—
228C4×C47—42no—
229C4×C47—42no—
230C4×C47—42no—
231C4×C47—44no—
232C4×C47—161no—
233C4×C47#41611yescharacteristic
234C4×C47#41611yescharacteristic
235C4×C47#41711yescharacteristic
236C4×C47#41711yescharacteristic
237C4×C47#44911yescharacteristic
238C4×C47#44911yescharacteristic
239C4×C47#45211yescharacteristic
240C4×C47#45211yescharacteristic
241C2×#556C2×C4711yescharacteristic
242#1990C2×C4711yescharacteristic, complemented
243#1803C2×C4711yescharacteristic, complemented
244#1802C2×C4711yescharacteristic
245C2×#332C2×C4711yescharacteristic, complemented
246C2×Q8⋊C8C2×C4711yescharacteristic, complemented
247C2×D4⋊C8C2×C4711yescharacteristic
248C2×C47—82no—
249C2×C47#162811yescharacteristic
250C2×C47#163811yescharacteristic
251C2×C47#165011yescharacteristic
252C2×C47#165211yescharacteristic
253C2×C47#178811yescharacteristic
254C2×C47#178811yescharacteristic
255C2×C47#179311yescharacteristic
256#556—22no—
257#556—22no—
258#556—22no—
259#556C4×C4714yescomplemented
260C2×C4⋊Q8C22×C4711yescharacteristic
261C2×#126—22no—
262C2×#124—21no—
263C2×C22⋊Q8—21no—
264C2×C4×Q8—21no—
265C2×C4×Q8C22×C4711yescharacteristic
266C2×C4×D4C22×C4711yescharacteristic
267C2×#117—21no—
268C2×C4⋊C8C22×C4711yescharacteristic
269C2×C4⋊C8C22×C4711yescharacteristic
270C2×#103—21no—
271C2×#102—21no—
272C2×C4×C8C22×C4711yescharacteristic
273#384C22×C4711yescharacteristic
274#340—21no—
275#340—21no—
276#340—22no—
277#332—22no—
278Q8⋊C8—22no—
279D4⋊C8—22no—
280C47#844911yescharacteristic, direct product factor, Sylow
281C22×Q8—21no—
282C22×Q8D4×C4711yescharacteristic
283C22×D4D4×C4711yescharacteristic
284C23×C4—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8C2×C4×C4712yes—
291C4⋊Q8D4×C4712yes—
292#126—28no—
293#126—28no—
294#124—24no—
295#124—24no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C4×Q8—24no—
299C4×Q8—24no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8C2×C4×C4712yes—
303C4×Q8D4×C4712yes—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C2×C4×C4712yes—
307C4×D4D4×C4712yes—
308#117—24no—
309#117—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C4711yescharacteristic
317C2×C4⋊C4D4×C4711yescharacteristic
318C2×C4⋊C4D4×C4712yes—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—21no—
322C2×C42—22no—
323C2×C42—21no—
324C2×C42C23×C4711yescharacteristic
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329#103—42no—
330#102—42no—
331C4×C8—21no—
332C4×C8—21no—
333C24—21no—
334C2×Q8—22no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8C22⋊C4×C4712yes—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4C22⋊C4×C4712yes—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4C2×D4×C4711yescharacteristic
364C22×C4C2×D4×C4711yescharacteristic
365C22×C4C2×D4×C4711yescharacteristic
366C2×C8—22no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—41no—
375C4⋊C4—28no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C22⋊C4×C4712yes—
389C4⋊C4C22⋊C4×C4712yes—
390C4⋊C4C22⋊C4×C4714yes—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C42—28no—
396C42—22no—
397C42—22no—
398C42C22×C4×C4711yescharacteristic
399C42C2×D4×C4711yescharacteristic
400C42C2×D4×C4711yescharacteristic
401C42C2×D4×C4711yescharacteristic
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23#120×C4711yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—42no—
414Q8—41no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418D4—22no—
419D4—22no—
420D4—41no—
421D4—41no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4C2×C22⋊C4×C4711yescharacteristic
444C2×C4C2×C22⋊C4×C4711yescharacteristic
445C2×C4C2×C22⋊C4×C4711yescharacteristic
446C2×C4#120×C4711yescharacteristic
447C2×C4#120×C4711yescharacteristic
448C2×C4#120×C4711yescharacteristic
449C2×C4#135×C4711yescharacteristic
450C2×C4#135×C4711yescharacteristic
451C2×C4#135×C4711yescharacteristic
452C2×C4#135×C4711yescharacteristic
453C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
454C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
455C2×C4#137×C4711yescharacteristic
456C2×C4#137×C4711yescharacteristic
457C8—42no—
458C8—81no—
459C8—81no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C47×#37911yescharacteristic
468C22C47×#44911yescharacteristic
469C22C47×#44911yescharacteristic
470C22C47×#45211yescharacteristic
471C22C47×#45211yescharacteristic
472C22C47×#45411yescharacteristic
473C22C47×#45611yescharacteristic
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—44no—
479C4—42no—
480C4—161no—
481C4C47×#41611yescharacteristic
482C4C47×#41611yescharacteristic
483C4C47×#41711yescharacteristic
484C4C47×#41711yescharacteristic
485C4C47×#44911yescharacteristic
486C4C47×#44911yescharacteristic
487C4C47×#45211yescharacteristic
488C4C47×#45211yescharacteristic
489C2—82no—
490C2C47×#162811yescharacteristic
491C2C47×#163811yescharacteristic
492C2C47×#165011yescharacteristic
493C2C47×#165211yescharacteristic
494C2C47×#178811yescharacteristic
495C2C47×#178811yescharacteristic
496C2C47×#179311yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1990C2semidirect
3. C47×#1803C2semidirect
5. C2×C47×#332C2semidirect
6. C2×C47×Q8⋊C8C2semidirect
11. C47×#556C4semidirect
211. #8449C47direct (N × H)
242. #1990C2×C47semidirect
243. #1803C2×C47semidirect
245. C2×#332C2×C47semidirect
246. C2×Q8⋊C8C2×C47semidirect
259. #556C4×C47semidirect
280. C47#8449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5562
C47×#19902
C47×#18032
C47×#18022
C2×C47×#3322
C2×C47×Q8⋊C82
C2×C47×D4⋊C82
#844947