Finite Group Databasebeta

← C47×#18525 #26058223

Subgroups — C47×#18525 #26058223

Order 12032.

1048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#554C211yesmaximal, characteristic, complemented
2C47×#3152C211yesmaximal, characteristic, complemented
3C47×#3112C211yesmaximal, characteristic, complemented
4C47×#3109C211yesmaximal, characteristic
5C47×#1632C214yesmaximal, complemented
6C47×#1622C214yesmaximal, complemented
7C47×#1558C211yesmaximal, characteristic, complemented
8C47×#1491C211yesmaximal, characteristic, complemented
9C47×#1490C211yesmaximal, characteristic, complemented
10C2×#137×C47—22no—
11C47×#554—22no—
12C47×#554—22no—
13C47×#554—22no—
14C47×#554C2214yes—
15C47×#532C2211yescharacteristic
16C2×C4⋊Q8×C47C2211yescharacteristic
17C2×#125×C47—21no—
18C2×C22⋊Q8×C47—21no—
19C2×C22⋊Q8×C47—22no—
20C2×C4×Q8×C47C2211yescharacteristic
21C2×C4×D4×C47—21no—
22C2×C4×D4×C47C2211yescharacteristic
23C22×C4⋊C4×C47—21no—
24C47×#497—22no—
25C47×#494C2212yescomplemented
26C47×#492C2212yescomplemented
27C47×#481—21no—
28C47×#480—21no—
29C47×#477C2212yescomplemented
30C47×#476C2212yes—
31C47×#460C2212yescomplemented
32C47×#459C2212yes—
33C47×#448—21no—
34C47×#447—21no—
35C47×#442—22no—
36C47×#440—22no—
37C47×#432C2211yescharacteristic
38C47×#432C2211yescharacteristic
39C4×M16×C47C2211yescharacteristic
40C47×#333C2214yescomplemented
41C47×Q8⋊C8C2214yescomplemented
42C47×D4⋊C8C2214yes—
43C2×#41×C47—21no—
44C22×Q8×C47D411yescharacteristic
45C22×Q8×C47D412yes—
46C22×D4×C47D411yescharacteristic
47C23×C4×C47—22no—
48C23×C4×C47—21no—
49#137×C47—48no—
50C2×Q16×C47—24no—
51C2×SD16×C47—22no—
52C2×SD16×C47—24no—
53C2×D8×C47—22no—
54C2×M16×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47D412yes—
58C4⋊Q8×C47C2311yescharacteristic
59C4⋊Q8×C47C2312yes—
60#127×C47C2311yescharacteristic
61#125×C47—24no—
62#125×C47—24no—
63#124×C47—21no—
64C22⋊Q8×C47—24no—
65C22⋊Q8×C47—28no—
66C22⋊Q8×C47—24no—
67C22⋊Q8×C47—28no—
68#121×C47—21no—
69#121×C47—21no—
70C4×Q8×C47—21no—
71C4×Q8×C47—21no—
72C4×Q8×C47D412yes—
73C4×Q8×C47C2312yes—
74C4×D4×C47—24no—
75C4×D4×C47—24no—
76C4×D4×C47—21no—
77C4×D4×C47—21no—
78C4×D4×C47—21no—
79C4×D4×C47—21no—
80C4×D4×C47D412yes—
81C4×D4×C47C2312yes—
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—24no—
84C2×C4⋊C4×C47—22no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—24no—
89C2×C4⋊C4×C47D411yescharacteristic
90C2×C4⋊C4×C47D411yescharacteristic
91C2×C22⋊C4×C47—22no—
92C2×C22⋊C4×C47—21no—
93C2×C42×C47—21no—
94C2×C42×C47C2311yescharacteristic
95#107×C47—22no—
96#106×C47—22no—
97C4⋊C8×C47C2312yes—
98C4⋊C8×C47C2312yes—
99#103×C47—22no—
100#102×C47—22no—
101#102×C47—22no—
102#102×C47—22no—
103C22⋊C8×C47—21no—
104C22⋊C8×C47—21no—
105#97×C47—21no—
106#97×C47—21no—
107#97×C47—21no—
108C4×C8×C47C2312yes—
109C24×C47—21no—
110#41×C47—44no—
111C2×Q8×C47—21no—
112C2×Q8×C47—22no—
113C2×Q8×C47—21no—
114C2×Q8×C47—42no—
115C2×Q8×C47—44no—
116C2×Q8×C47C2×D412yes—
117C2×Q8×C47C2×D414yes—
118C2×D4×C47—24no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—41no—
124C2×D4×C47C2×D412yes—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—28no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—44no—
133C22×C4×C47—41no—
134C22×C4×C47—84no—
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138Q16×C47—48no—
139SD16×C47—48no—
140SD16×C47—44no—
141D8×C47—44no—
142M16×C47—24no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C4⋊C4×C47—28no—
147C4⋊C4×C47—28no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47C2×D412yes—
159C4⋊C4×C47C2×D412yes—
160C22⋊C4×C47—28no—
161C22⋊C4×C47—22no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—41no—
164C22⋊C4×C47—41no—
165C42×C47—22no—
166C42×C47—22no—
167C42×C47C2×D411yescharacteristic
168C42×C47C2×D411yescharacteristic
169C42×C47C2×D411yescharacteristic
170C42×C47C2411yescharacteristic
171C23×C47—24no—
172C23×C47—22no—
173C23×C47—42no—
174C23×C47—42no—
175C23×C47—41no—
176C23×C47#12011yescharacteristic
177Q8×C47—22no—
178Q8×C47—22no—
179Q8×C47—44no—
180Q8×C47—42no—
181Q8×C47—42no—
182Q8×C47—82no—
183D4×C47—24no—
184D4×C47—22no—
185D4×C47—42no—
186D4×C47—42no—
187D4×C47—42no—
188D4×C47—82no—
189D4×C47#13714yescomplemented
190C2×C4×C47—22no—
191C2×C4×C47—22no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—44no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—44no—
202C2×C4×C47—44no—
203C2×C4×C47—41no—
204C2×C4×C47—82no—
205C2×C4×C47—88no—
206C2×C4×C47#12011yescharacteristic
207C2×C4×C47#12011yescharacteristic
208C2×C4×C47#12011yescharacteristic
209C2×C4×C47C22×D411yescharacteristic
210C2×C4×C47C22×D411yescharacteristic
211C2×C4×C47C22×D411yescharacteristic
212C8×C47—24no—
213C8×C47—42no—
214C8×C47—42no—
215#18525C4711yesmaximal, characteristic, direct product factor, Sylow
216C22×C47—21no—
217C22×C47—21no—
218C22×C47—24no—
219C22×C47—48no—
220C22×C47—42no—
221C22×C47—42no—
222C22×C47—81no—
223C22×C47—81no—
224C22×C47—81no—
225C22×C47#45312yes—
226C22×C47C2×#12011yescharacteristic
227C4×C47—21no—
228C4×C47—21no—
229C4×C47—21no—
230C4×C47—21no—
231C4×C47—42no—
232C4×C47—42no—
233C4×C47—42no—
234C4×C47—44no—
235C4×C47—81no—
236C4×C47C2×#13712yes—
237C4×C47#57512yes—
238C2×#554C2×C4711yescharacteristic, complemented
239#3152C2×C4711yescharacteristic, complemented
240#3112C2×C4711yescharacteristic, complemented
241#3109C2×C4711yescharacteristic
242#1632C2×C4714yescomplemented
243#1622C2×C4714yescomplemented
244#1558C2×C4711yescharacteristic, complemented
245#1491C2×C4711yescharacteristic, complemented
246#1490C2×C4711yescharacteristic, complemented
247C2×C47—22no—
248C2×C47—44no—
249C2×C47—161no—
250C2×C47#300411yescharacteristic
251C2×C47#300511yescharacteristic
252C2×C47C2×#45311yescharacteristic
253C2×#137—22no—
254#554—22no—
255#554—22no—
256#554—22no—
257#554C22×C4714yes—
258#532C22×C4711yescharacteristic
259C2×C4⋊Q8C22×C4711yescharacteristic
260C2×#125—21no—
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—22no—
263C2×C4×Q8C22×C4711yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C22×C4711yescharacteristic
266C22×C4⋊C4—21no—
267#497—22no—
268#494C22×C4712yescomplemented
269#492C22×C4712yescomplemented
270#481—21no—
271#480—21no—
272#477C22×C4712yescomplemented
273#476C22×C4712yes—
274#460C22×C4712yescomplemented
275#459C22×C4712yes—
276#448—21no—
277#447—21no—
278#442—22no—
279#440—22no—
280#432C22×C4711yescharacteristic
281#432C22×C4711yescharacteristic
282C4×M16C22×C4711yescharacteristic
283#333C22×C4714yescomplemented
284Q8⋊C8C22×C4714yescomplemented
285D4⋊C8C22×C4714yes—
286C47#1852511yescharacteristic, direct product factor, Sylow
287C2×#41—21no—
288C22×Q8D4×C4711yescharacteristic
289C22×Q8D4×C4712yes—
290C22×D4D4×C4711yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293#137—48no—
294C2×Q16—24no—
295C2×SD16—24no—
296C2×SD16—22no—
297C2×D8—22no—
298C2×M16—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8D4×C4712yes—
302C4⋊Q8C23×C4711yescharacteristic
303C4⋊Q8C23×C4712yes—
304#127C23×C4711yescharacteristic
305#125—24no—
306#125—24no—
307#124—21no—
308C22⋊Q8—24no—
309C22⋊Q8—28no—
310C22⋊Q8—24no—
311C22⋊Q8—28no—
312#121—21no—
313#121—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C4712yes—
317C4×Q8C23×C4712yes—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4D4×C4712yes—
325C4×D4C23×C4712yes—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4D4×C4711yescharacteristic
334C2×C4⋊C4D4×C4711yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C42—21no—
338C2×C42C23×C4711yescharacteristic
339#107—22no—
340#106—22no—
341C4⋊C8C23×C4712yes—
342C4⋊C8C23×C4712yes—
343#103—22no—
344#102—22no—
345#102—22no—
346#102—22no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349#97—21no—
350#97—21no—
351#97—21no—
352C4×C8C23×C4712yes—
353C24—21no—
354#41—44no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—42no—
359C2×Q8—44no—
360C2×Q8C2×D4×C4712yes—
361C2×Q8C2×D4×C4714yes—
362C2×D4—24no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C4712yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—28no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—44no—
377C22×C4—41no—
378C22×C4—84no—
379C22×C4C2×D4×C4711yescharacteristic
380C22×C4C2×D4×C4711yescharacteristic
381C22×C4C2×D4×C4711yescharacteristic
382Q16—48no—
383SD16—48no—
384SD16—44no—
385D8—44no—
386M16—24no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4C2×D4×C4712yes—
403C4⋊C4C2×D4×C4712yes—
404C22⋊C4—28no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C42—22no—
410C42—22no—
411C42C2×D4×C4711yescharacteristic
412C42C2×D4×C4711yescharacteristic
413C42C2×D4×C4711yescharacteristic
414C42C24×C4711yescharacteristic
415C23—24no—
416C23—22no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23#120×C4711yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—44no—
424Q8—42no—
425Q8—42no—
426Q8—82no—
427D4—24no—
428D4—22no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—82no—
433D4#137×C4714yescomplemented
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—88no—
450C2×C4#120×C4711yescharacteristic
451C2×C4#120×C4711yescharacteristic
452C2×C4#120×C4711yescharacteristic
453C2×C4C22×D4×C4711yescharacteristic
454C2×C4C22×D4×C4711yescharacteristic
455C2×C4C22×D4×C4711yescharacteristic
456C8—24no—
457C8—42no—
458C8—42no—
459C22—21no—
460C22—21no—
461C22—24no—
462C22—48no—
463C22—42no—
464C22—42no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C47×#45312yes—
469C22C2×#120×C4711yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—44no—
478C4—81no—
479C4C2×#137×C4712yes—
480C4C47×#57512yes—
481C2—22no—
482C2—44no—
483C2—161no—
484C2C47×#300411yescharacteristic
485C2C47×#300511yescharacteristic
486C2C2×C47×#45311yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#554C2semidirect
2. C47×#3152C2semidirect
3. C47×#3112C2semidirect
5. C47×#1632C2semidirect
6. C47×#1622C2semidirect
7. C47×#1558C2semidirect
8. C47×#1491C2semidirect
9. C47×#1490C2semidirect
25. C47×#494C22semidirect
26. C47×#492C22semidirect
29. C47×#477C22semidirect
31. C47×#460C22semidirect
40. C47×#333C22semidirect
41. C47×Q8⋊C8C22semidirect
189. D4×C47#137semidirect
215. #18525C47direct (N × H)
238. C2×#554C2×C47semidirect
239. #3152C2×C47semidirect
240. #3112C2×C47semidirect
242. #1632C2×C47semidirect
243. #1622C2×C47semidirect
244. #1558C2×C47semidirect
245. #1491C2×C47semidirect
246. #1490C2×C47semidirect
268. #494C22×C47semidirect
269. #492C22×C47semidirect
272. #477C22×C47semidirect
274. #460C22×C47semidirect
283. #333C22×C47semidirect
284. Q8⋊C8C22×C47semidirect
286. C47#18525direct (N × H)
433. D4#137×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5542
C47×#31522
C47×#31122
C47×#31092
C47×#16322
C47×#16222
C47×#15582
C47×#14912
C47×#14902
#1852547