Finite Group Databasebeta

← C47×#18615 #26058313

Subgroups — C47×#18615 #26058313

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3506C211yesmaximal, characteristic
2C47×#3237C211yesmaximal, characteristic, complemented
3C47×#3182C211yesmaximal, characteristic, complemented
4C47×#3101C211yesmaximal, characteristic, complemented
5C47×#1650C212yesmaximal, complemented
6C47×#1642C212yesmaximal, complemented
7C47×#1638C212yesmaximal, complemented
8C47×#1631C212yesmaximal, complemented
9C47×#1553C211yesmaximal, characteristic, complemented
10C47×#1490C211yesmaximal, characteristic, complemented
11C47×#1485C211yesmaximal, characteristic, complemented
12C47×#559—22no—
13C47×#556C2212yes—
14C47×#555—21no—
15C47×#553—22no—
16C47×#550C2212yes—
17C47×#547—21no—
18C47×#538—22no—
19C47×#535—21no—
20C47×#533C2211yescharacteristic
21C47×#533C2211yescharacteristic
22C47×#532C2211yescharacteristic
23C47×#525—22no—
24C47×#520—21no—
25C2×C4×D4×C47C2211yescharacteristic
26C47×#501—21no—
27C47×#500C2211yescharacteristic, complemented
28C47×#492C2211yescharacteristic, complemented
29C47×#491—21no—
30C47×#487C2211yescharacteristic, complemented
31C47×#486C2211yescharacteristic, complemented
32C47×#485—22no—
33C47×#483—21no—
34C47×#477C2212yescomplemented
35C47×#476C2212yes—
36C47×#475C2212yescomplemented
37C47×#468—22no—
38C47×#461C2212yes—
39C47×#450—21no—
40C47×#440—22no—
41C4×SD16×C47—22no—
42C47×#432C2211yescharacteristic
43C47×#431C2211yescharacteristic
44C4×M16×C47C2211yescharacteristic
45C47×#332C2212yescomplemented
46C47×#331C2212yescomplemented
47C47×Q8⋊C8C2212yescomplemented
48C47×Q8⋊C8C2212yescomplemented
49C47×D4⋊C8C2212yes—
50C47×D4⋊C8C2212yes—
51C2×#41×C47—22no—
52C2×#41×C47—21no—
53C22×D4×C47D411yescharacteristic
54C23×C4×C47—21no—
55C2×SD16×C47—22no—
56C2×SD16×C47—22no—
57C2×M16×C47—21no—
58C4⋊Q8×C47D411yescharacteristic
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47C2311yescharacteristic
61C4⋊Q8×C47C2311yescharacteristic
62C4⋊Q8×C47C2311yescharacteristic
63#127×C47—22no—
64#127×C47C2311yescharacteristic
65#126×C47—24no—
66#125×C47—21no—
67#125×C47—21no—
68#124×C47—24no—
69#124×C47—22no—
70#124×C47—21no—
71#123×C47—24no—
72#123×C47—24no—
73C22⋊Q8×C47—22no—
74C22⋊Q8×C47—21no—
75C22⋊Q8×C47—21no—
76C22⋊Q8×C47—21no—
77C22⋊Q8×C47D412yes—
78#121×C47—22no—
79#121×C47—22no—
80#121×C47—24no—
81#121×C47—21no—
82#121×C47—22no—
83#121×C47D412yes—
84#120×C47—24no—
85C4×Q8×C47—22no—
86C4×Q8×C47—21no—
87C4×Q8×C47—21no—
88C4×Q8×C47—21no—
89C4×Q8×C47C2312yes—
90C4×D4×C47—24no—
91C4×D4×C47—24no—
92C4×D4×C47—22no—
93C4×D4×C47—21no—
94C4×D4×C47—21no—
95C4×D4×C47—21no—
96C4×D4×C47D412yes—
97C4×D4×C47D412yes—
98C4×D4×C47C2312yes—
99#117×C47—22no—
100#117×C47—21no—
101#117×C47—22no—
102#117×C47—21no—
103C2×C4⋊C4×C47—22no—
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C42×C47C2311yescharacteristic
107#107×C47—22no—
108#107×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47C2312yes—
112C4⋊C8×C47C2312yes—
113#103×C47—22no—
114#103×C47—22no—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119C22⋊C8×C47—21no—
120C22⋊C8×C47—21no—
121#97×C47—21no—
122#97×C47—21no—
123C4×C8×C47—21no—
124C4×C8×C47C2311yescharacteristic
125C4×C8×C47C2311yescharacteristic
126C24×C47—21no—
127#41×C47—44no—
128#41×C47—84no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47C2×D412yes—
134C2×D4×C47—22no—
135C2×D4×C47—24no—
136C2×D4×C47—24no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—21no—
140C2×D4×C47—42no—
141C2×D4×C47C2×D412yes—
142C2×D4×C47C2×D412yes—
143C22×C4×C47—24no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—82no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152SD16×C47—44no—
153SD16×C47—44no—
154M16×C47—42no—
155C2×C8×C47—21no—
156C2×C8×C47—22no—
157C2×C8×C47—21no—
158C2×C8×C47—22no—
159C4⋊C4×C47—24no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—41no—
172C4⋊C4×C47—41no—
173C4⋊C4×C47C2×D412yes—
174C4⋊C4×C47C2×D412yes—
175C4⋊C4×C47C2×D412yes—
176C22⋊C4×C47—24no—
177C22⋊C4×C47—24no—
178C22⋊C4×C47—24no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—22no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—41no—
185C42×C47—24no—
186C42×C47—22no—
187C42×C47—41no—
188C42×C47C2×D411yescharacteristic
189C42×C47C2×D411yescharacteristic
190C42×C47C2×D411yescharacteristic
191C42×C47C2411yescharacteristic
192C23×C47—22no—
193C23×C47—22no—
194C23×C47—42no—
195C23×C47—81no—
196C23×C47—81no—
197C23×C47#12011yescharacteristic
198Q8×C47—24no—
199Q8×C47—42no—
200Q8×C47—42no—
201Q8×C47—42no—
202Q8×C47—81no—
203D4×C47—22no—
204D4×C47—22no—
205D4×C47—42no—
206D4×C47—42no—
207D4×C47—44no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—84no—
211D4×C47—84no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—41no—
219C2×C4×C47—44no—
220C2×C4×C47—44no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—82no—
224C2×C4×C47—81no—
225C2×C4×C47—84no—
226C2×C4×C47#12011yescharacteristic
227C2×C4×C47#12011yescharacteristic
228C2×C4×C47#12011yescharacteristic
229C2×C4×C47C22×D411yescharacteristic
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C8×C47—22no—
233C8×C47—41no—
234C8×C47—42no—
235C8×C47—42no—
236#18615C4711yesmaximal, characteristic, direct product factor, Sylow
237C22×C47—21no—
238C22×C47—21no—
239C22×C47—21no—
240C22×C47—42no—
241C22×C47—42no—
242C22×C47—42no—
243C22×C47—42no—
244C22×C47—42no—
245C22×C47—42no—
246C22×C47—84no—
247C22×C47C2×#12011yescharacteristic
248C4×C47—21no—
249C4×C47—21no—
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—42no—
253C4×C47—42no—
254C4×C47—42no—
255C4×C47—42no—
256C4×C47—81no—
257C4×C47—81no—
258C4×C47#57512yes—
259C4×C47#57712yes—
260#3506C2×C4711yescharacteristic
261#3237C2×C4711yescharacteristic, complemented
262#3182C2×C4711yescharacteristic, complemented
263#3101C2×C4711yescharacteristic, complemented
264#1650C2×C4712yescomplemented
265#1642C2×C4712yescomplemented
266#1638C2×C4712yescomplemented
267#1631C2×C4712yescomplemented
268#1553C2×C4711yescharacteristic, complemented
269#1490C2×C4711yescharacteristic, complemented
270#1485C2×C4711yescharacteristic, complemented
271C2×C47—41no—
272C2×C47—82no—
273C2×C47—82no—
274C2×C47#300511yescharacteristic
275C2×C47#300911yescharacteristic
276C2×C47#301811yescharacteristic
277#559—22no—
278#556C22×C4712yes—
279#555—21no—
280#553—22no—
281#550C22×C4712yes—
282#547—21no—
283#538—22no—
284#535—21no—
285#533C22×C4711yescharacteristic
286#533C22×C4711yescharacteristic
287#532C22×C4711yescharacteristic
288#525—22no—
289#520—21no—
290C2×C4×D4C22×C4711yescharacteristic
291#501—21no—
292#500C22×C4711yescharacteristic, complemented
293#492C22×C4711yescharacteristic, complemented
294#491—21no—
295#487C22×C4711yescharacteristic, complemented
296#486C22×C4711yescharacteristic, complemented
297#485—22no—
298#483—21no—
299#477C22×C4712yescomplemented
300#476C22×C4712yes—
301#475C22×C4712yescomplemented
302#468—22no—
303#461C22×C4712yes—
304#450—21no—
305#440—22no—
306C4×SD16—22no—
307#432C22×C4711yescharacteristic
308#431C22×C4711yescharacteristic
309C4×M16C22×C4711yescharacteristic
310#332C22×C4712yescomplemented
311#331C22×C4712yescomplemented
312Q8⋊C8C22×C4712yescomplemented
313Q8⋊C8C22×C4712yescomplemented
314D4⋊C8C22×C4712yes—
315D4⋊C8C22×C4712yes—
316C47#1861511yescharacteristic, direct product factor, Sylow
317C2×#41—22no—
318C2×#41—21no—
319C22×D4D4×C4711yescharacteristic
320C23×C4—21no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×M16—21no—
324C4⋊Q8D4×C4711yescharacteristic
325C4⋊Q8D4×C4711yescharacteristic
326C4⋊Q8C23×C4711yescharacteristic
327C4⋊Q8C23×C4711yescharacteristic
328C4⋊Q8C23×C4711yescharacteristic
329#127—22no—
330#127C23×C4711yescharacteristic
331#126—24no—
332#125—21no—
333#125—21no—
334#124—24no—
335#124—22no—
336#124—21no—
337#123—24no—
338#123—24no—
339C22⋊Q8—22no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8D4×C4712yes—
344#121—22no—
345#121—22no—
346#121—24no—
347#121—21no—
348#121—22no—
349#121D4×C4712yes—
350#120—24no—
351C4×Q8—22no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8C23×C4712yes—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—22no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4D4×C4712yes—
363C4×D4D4×C4712yes—
364C4×D4C23×C4712yes—
365#117—22no—
366#117—21no—
367#117—22no—
368#117—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4D4×C4711yescharacteristic
371C2×C22⋊C4—21no—
372C2×C42C23×C4711yescharacteristic
373#107—22no—
374#107—22no—
375#106—22no—
376#106—22no—
377C4⋊C8C23×C4712yes—
378C4⋊C8C23×C4712yes—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—22no—
383#102—22no—
384#102—22no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387#97—21no—
388#97—21no—
389C4×C8—21no—
390C4×C8C23×C4711yescharacteristic
391C4×C8C23×C4711yescharacteristic
392C24—21no—
393#41—44no—
394#41—84no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8C2×D4×C4712yes—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—42no—
407C2×D4C2×D4×C4712yes—
408C2×D4C2×D4×C4712yes—
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—82no—
415C22×C4C2×D4×C4711yescharacteristic
416C22×C4C2×D4×C4711yescharacteristic
417C22×C4C2×D4×C4711yescharacteristic
418SD16—44no—
419SD16—44no—
420M16—42no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8—21no—
424C2×C8—22no—
425C4⋊C4—24no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4C2×D4×C4712yes—
440C4⋊C4C2×D4×C4712yes—
441C4⋊C4C2×D4×C4712yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C42—24no—
452C42—22no—
453C42—41no—
454C42C2×D4×C4711yescharacteristic
455C42C2×D4×C4711yescharacteristic
456C42C2×D4×C4711yescharacteristic
457C42C24×C4711yescharacteristic
458C23—22no—
459C23—22no—
460C23—42no—
461C23—81no—
462C23—81no—
463C23#120×C4711yescharacteristic
464Q8—24no—
465Q8—42no—
466Q8—42no—
467Q8—42no—
468Q8—81no—
469D4—22no—
470D4—22no—
471D4—42no—
472D4—42no—
473D4—44no—
474D4—42no—
475D4—42no—
476D4—84no—
477D4—84no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4#120×C4711yescharacteristic
493C2×C4#120×C4711yescharacteristic
494C2×C4#120×C4711yescharacteristic
495C2×C4C22×D4×C4711yescharacteristic
496C2×C4C22×D4×C4711yescharacteristic
497C2×C4C22×D4×C4711yescharacteristic
498C8—22no—
499C8—41no—
500C8—42no—
501C8—42no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—84no—
512C22C2×#120×C4711yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—42no—
519C4—42no—
520C4—42no—
521C4—81no—
522C4—81no—
523C4C47×#57512yes—
524C4C47×#57712yes—
525C2—41no—
526C2—82no—
527C2—82no—
528C2C47×#300511yescharacteristic
529C2C47×#300911yescharacteristic
530C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3506C2
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
2. C47×#3237C2semidirect
3. C47×#3182C2semidirect
4. C47×#3101C2semidirect
5. C47×#1650C2semidirect
6. C47×#1642C2semidirect
7. C47×#1638C2semidirect
8. C47×#1631C2semidirect
9. C47×#1553C2semidirect
10. C47×#1490C2semidirect
11. C47×#1485C2semidirect
27. C47×#500C22semidirect
28. C47×#492C22semidirect
30. C47×#487C22semidirect
31. C47×#486C22semidirect
34. C47×#477C22semidirect
36. C47×#475C22semidirect
45. C47×#332C22semidirect
46. C47×#331C22semidirect
47. C47×Q8⋊C8C22semidirect
48. C47×Q8⋊C8C22semidirect
236. #18615C47direct (N × H)
261. #3237C2×C47semidirect
262. #3182C2×C47semidirect
263. #3101C2×C47semidirect
264. #1650C2×C47semidirect
265. #1642C2×C47semidirect
266. #1638C2×C47semidirect
267. #1631C2×C47semidirect
268. #1553C2×C47semidirect
269. #1490C2×C47semidirect
270. #1485C2×C47semidirect
292. #500C22×C47semidirect
293. #492C22×C47semidirect
295. #487C22×C47semidirect
296. #486C22×C47semidirect
299. #477C22×C47semidirect
301. #475C22×C47semidirect
310. #332C22×C47semidirect
311. #331C22×C47semidirect
312. Q8⋊C8C22×C47semidirect
313. Q8⋊C8C22×C47semidirect
316. C47#18615direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35062
C47×#32372
C47×#31822
C47×#31012
C47×#16502
C47×#16422
C47×#16382
C47×#16312
C47×#15532
C47×#14902
C47×#14852
#1861547