Finite Group Databasebeta

← C47×#18831 #26058529

Subgroups — C47×#18831 #26058529

Order 12032.

838 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
1C47×#3509C211yesmaximal, characteristic
2C47×#3237C211yesmaximal, characteristic, complemented
3C47×#3230C211yesmaximal, characteristic, complemented
4C47×#3116C211yesmaximal, characteristic
5C47×#1650C212yesmaximal, complemented
6C47×#1648C212yesmaximal, complemented
7C47×#1638C212yesmaximal, complemented
8C47×#1636C212yesmaximal, complemented
9C47×#1556C211yesmaximal, characteristic, complemented
10C47×#1497C211yesmaximal, characteristic, complemented
11C47×#1488C211yesmaximal, characteristic
12C47×#557—21no—
13C47×#557C2212yes—
14C47×#556—21no—
15C47×#556C2212yes—
16C47×#552—22no—
17C47×#552—22no—
18C47×#541—22no—
19C47×#536—21no—
20C47×#533—21no—
21C47×#533—21no—
22C47×#533C2211yescharacteristic
23C47×#533C2211yescharacteristic
24C2×C4⋊Q8×C47C2211yescharacteristic
25C47×#519—21no—
26C4×#41×C47C2211yescharacteristic
27C47×#501—21no—
28C47×#500C2212yes—
29C47×#491—21no—
30C47×#487C2212yes—
31C47×#485—22no—
32C47×#485—21no—
33C47×#484—22no—
34C47×#477—22no—
35C47×#477C2211yescharacteristic
36C47×#477C2212yes—
37C47×#476C2211yescharacteristic
38C47×#475C2212yes—
39C47×#462C2211yescharacteristic
40C47×#461C2211yescharacteristic
41C47×#452—21no—
42C47×#441—21no—
43C47×#440—21no—
44C47×#432C2211yescharacteristic
45C47×#432C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#332C2212yes—
48C47×#332C2212yes—
49C47×Q8⋊C8C2212yes—
50C47×Q8⋊C8C2212yes—
51C47×Q8⋊C8C2212yes—
52C47×D4⋊C8C2212yes—
53C2×#41×C47D411yescharacteristic
54C22×Q8×C47—21no—
55C2×Q16×C47—21no—
56C2×SD16×C47—21no—
57C4⋊Q8×C47—22no—
58C4⋊Q8×C47—21no—
59C4⋊Q8×C47—21no—
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47D412yes—
62C4⋊Q8×C47D411yescharacteristic
63C4⋊Q8×C47C2311yescharacteristic
64C4⋊Q8×C47C2311yescharacteristic
65C4⋊Q8×C47C2312yes—
66#126×C47—24no—
67#126×C47—24no—
68#125×C47—22no—
69#125×C47—24no—
70#125×C47—22no—
71#125×C47—24no—
72#125×C47—21no—
73#125×C47—21no—
74#124×C47—22no—
75#123×C47—24no—
76C22⋊Q8×C47—22no—
77C22⋊Q8×C47—22no—
78C22⋊Q8×C47—22no—
79C22⋊Q8×C47—22no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47D412yes—
84C4×Q8×C47—22no—
85C4×Q8×C47—22no—
86C4×Q8×C47—22no—
87C4×Q8×C47—22no—
88C4×Q8×C47—22no—
89C4×Q8×C47—22no—
90C4×Q8×C47—21no—
91C4×Q8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47D411yescharacteristic
94C4×Q8×C47C2311yescharacteristic
95C4×Q8×C47C2312yes—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47D411yescharacteristic
99C4×D4×C47C2311yescharacteristic
100#117×C47—24no—
101#117×C47—22no—
102#117×C47—21no—
103#117×C47—22no—
104#117×C47—21no—
105#117×C47—21no—
106#117×C47D411yescharacteristic
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47D412yes—
109C2×C42×C47—21no—
110C2×C42×C47C2311yescharacteristic
111#107×C47—24no—
112#107×C47—22no—
113#107×C47—21no—
114#106×C47—22no—
115#106×C47—21no—
116C4⋊C8×C47—21no—
117C4⋊C8×C47C2311yescharacteristic
118C4⋊C8×C47C2311yescharacteristic
119C4⋊C8×C47C2312yes—
120#103×C47—21no—
121#103×C47—22no—
122#103×C47—22no—
123#103×C47—21no—
124#103×C47—21no—
125#103×C47—24no—
126#102×C47—21no—
127C22⋊C8×C47—21no—
128C22⋊C8×C47—21no—
129C22⋊C8×C47—21no—
130#97×C47—21no—
131#97×C47—21no—
132C4×C8×C47C2312yes—
133#41×C47—41no—
134#41×C47—41no—
135C2×Q8×C47—21no—
136C2×Q8×C47—22no—
137C2×Q8×C47—22no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—42no—
141C2×Q8×C47—42no—
142C2×Q8×C47C2×D412yes—
143C2×Q8×C47C2×D411yescharacteristic
144C2×D4×C47—21no—
145C2×D4×C47C2×D411yescharacteristic
146C22×C4×C47—22no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153Q16×C47—42no—
154SD16×C47—42no—
155C2×C8×C47—22no—
156C2×C8×C47—22no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C4⋊C4×C47—24no—
160C4⋊C4×C47—24no—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—24no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—41no—
179C4⋊C4×C47C2×D411yescharacteristic
180C4⋊C4×C47C2×D414yes—
181C4⋊C4×C47C2×D411yescharacteristic
182C4⋊C4×C47C2×D412yes—
183C22⋊C4×C47—24no—
184C22⋊C4×C47—24no—
185C22⋊C4×C47—21no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—21no—
188C22⋊C4×C47—21no—
189C22⋊C4×C47—41no—
190C42×C47—24no—
191C42×C47—24no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—22no—
196C42×C47—41no—
197C42×C47C2×D411yescharacteristic
198C42×C47C2×D411yescharacteristic
199C42×C47C2×D411yescharacteristic
200C42×C47C2411yescharacteristic
201C23×C47—21no—
202C23×C47#12011yescharacteristic
203Q8×C47—21no—
204Q8×C47—21no—
205Q8×C47—24no—
206Q8×C47—42no—
207Q8×C47—44no—
208Q8×C47—42no—
209Q8×C47—42no—
210Q8×C47—42no—
211Q8×C47—41no—
212Q8×C47—41no—
213D4×C47—21no—
214D4×C47—21no—
215D4×C47—42no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—24no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—44no—
229C2×C4×C47—42no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47#12011yescharacteristic
233C2×C4×C47#12011yescharacteristic
234C2×C4×C47#12011yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C8×C47—42no—
239C8×C47—41no—
240C8×C47—41no—
241C8×C47—42no—
242#18831C4711yesmaximal, characteristic, direct product factor, Sylow
243C22×C47—21no—
244C22×C47—21no—
245C22×C47—21no—
246C22×C47—41no—
247C22×C47—41no—
248C22×C47—41no—
249C22×C47C2×#12011yescharacteristic
250C4×C47—21no—
251C4×C47—21no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—41no—
255C4×C47—44no—
256C4×C47—41no—
257C4×C47—42no—
258C4×C47—41no—
259C4×C47—42no—
260C4×C47—81no—
261C4×C47—81no—
262C4×C47#57511yescharacteristic
263C4×C47#57511yescharacteristic
264C4×C47#57812yes—
265#3509C2×C4711yescharacteristic
266#3237C2×C4711yescharacteristic, complemented
267#3230C2×C4711yescharacteristic, complemented
268#3116C2×C4711yescharacteristic
269#1650C2×C4712yescomplemented
270#1648C2×C4712yescomplemented
271#1638C2×C4712yescomplemented
272#1636C2×C4712yescomplemented
273#1556C2×C4711yescharacteristic, complemented
274#1497C2×C4711yescharacteristic, complemented
275#1488C2×C4711yescharacteristic
276C2×C47—41no—
277C2×C47—81no—
278C2×C47#300511yescharacteristic
279C2×C47#301111yescharacteristic
280C2×C47#302011yescharacteristic
281#557—21no—
282#557C22×C4712yes—
283#556—21no—
284#556C22×C4712yes—
285#552—22no—
286#552—22no—
287#541—22no—
288#536—21no—
289#533—21no—
290#533—21no—
291#533C22×C4711yescharacteristic
292#533C22×C4711yescharacteristic
293C2×C4⋊Q8C22×C4711yescharacteristic
294#519—21no—
295C4×#41C22×C4711yescharacteristic
296#501—21no—
297#500C22×C4712yes—
298#491—21no—
299#487C22×C4712yes—
300#485—22no—
301#485—21no—
302#484—22no—
303#477—22no—
304#477C22×C4711yescharacteristic
305#477C22×C4712yes—
306#476C22×C4711yescharacteristic
307#475C22×C4712yes—
308#462C22×C4711yescharacteristic
309#461C22×C4711yescharacteristic
310#452—21no—
311#441—21no—
312#440—21no—
313#432C22×C4711yescharacteristic
314#432C22×C4711yescharacteristic
315#431C22×C4711yescharacteristic
316#332C22×C4712yes—
317#332C22×C4712yes—
318Q8⋊C8C22×C4712yes—
319Q8⋊C8C22×C4712yes—
320Q8⋊C8C22×C4712yes—
321D4⋊C8C22×C4712yes—
322C47#1883111yescharacteristic, direct product factor, Sylow
323C2×#41D4×C4711yescharacteristic
324C22×Q8—21no—
325C2×Q16—21no—
326C2×SD16—21no—
327C4⋊Q8—22no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8D4×C4711yescharacteristic
331C4⋊Q8D4×C4712yes—
332C4⋊Q8D4×C4711yescharacteristic
333C4⋊Q8C23×C4711yescharacteristic
334C4⋊Q8C23×C4711yescharacteristic
335C4⋊Q8C23×C4712yes—
336#126—24no—
337#126—24no—
338#125—22no—
339#125—24no—
340#125—22no—
341#125—24no—
342#125—21no—
343#125—21no—
344#124—22no—
345#123—24no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8D4×C4712yes—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8D4×C4711yescharacteristic
364C4×Q8C23×C4711yescharacteristic
365C4×Q8C23×C4712yes—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4D4×C4711yescharacteristic
369C4×D4C23×C4711yescharacteristic
370#117—24no—
371#117—22no—
372#117—21no—
373#117—22no—
374#117—21no—
375#117—21no—
376#117D4×C4711yescharacteristic
377C2×C4⋊C4—21no—
378C2×C4⋊C4D4×C4712yes—
379C2×C42—21no—
380C2×C42C23×C4711yescharacteristic
381#107—21no—
382#107—24no—
383#107—22no—
384#106—21no—
385#106—22no—
386C4⋊C8—21no—
387C4⋊C8C23×C4712yes—
388C4⋊C8C23×C4711yescharacteristic
389C4⋊C8C23×C4711yescharacteristic
390#103—21no—
391#103—22no—
392#103—22no—
393#103—21no—
394#103—21no—
395#103—24no—
396#102—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400#97—21no—
401#97—21no—
402C4×C8C23×C4712yes—
403#41—41no—
404#41—41no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8C2×D4×C4712yes—
413C2×Q8C2×D4×C4711yescharacteristic
414C2×D4—21no—
415C2×D4C2×D4×C4711yescharacteristic
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4C2×D4×C4711yescharacteristic
421C22×C4C2×D4×C4711yescharacteristic
422C22×C4C2×D4×C4711yescharacteristic
423Q16—42no—
424SD16—42no—
425C2×C8—22no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—21no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4C2×D4×C4711yescharacteristic
450C4⋊C4C2×D4×C4714yes—
451C4⋊C4C2×D4×C4711yescharacteristic
452C4⋊C4C2×D4×C4712yes—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—21no—
456C22⋊C4—22no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C22⋊C4—41no—
460C42—24no—
461C42—24no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—22no—
466C42—41no—
467C42C2×D4×C4711yescharacteristic
468C42C2×D4×C4711yescharacteristic
469C42C2×D4×C4711yescharacteristic
470C42C24×C4711yescharacteristic
471C23—21no—
472C23#120×C4711yescharacteristic
473Q8—21no—
474Q8—21no—
475Q8—24no—
476Q8—42no—
477Q8—44no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—41no—
482Q8—41no—
483D4—21no—
484D4—21no—
485D4—42no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4#120×C4711yescharacteristic
503C2×C4#120×C4711yescharacteristic
504C2×C4#120×C4711yescharacteristic
505C2×C4C22×D4×C4711yescharacteristic
506C2×C4C22×D4×C4711yescharacteristic
507C2×C4C22×D4×C4711yescharacteristic
508C8—42no—
509C8—41no—
510C8—41no—
511C8—42no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22C2×#120×C4711yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—41no—
524C4—44no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—81no—
530C4—81no—
531C4C47×#57511yescharacteristic
532C4C47×#57511yescharacteristic
533C4C47×#57812yes—
534C2—41no—
535C2—81no—
536C2C47×#300511yescharacteristic
537C2C47×#301111yescharacteristic
538C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×#41×C47D4
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×#3230C2semidirect
5. C47×#1650C2semidirect
6. C47×#1648C2semidirect
7. C47×#1638C2semidirect
8. C47×#1636C2semidirect
9. C47×#1556C2semidirect
10. C47×#1497C2semidirect
242. #18831C47direct (N × H)
266. #3237C2×C47semidirect
267. #3230C2×C47semidirect
269. #1650C2×C47semidirect
270. #1648C2×C47semidirect
271. #1638C2×C47semidirect
272. #1636C2×C47semidirect
273. #1556C2×C47semidirect
274. #1497C2×C47semidirect
322. C47#18831direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35092
C47×#32372
C47×#32302
C47×#31162
C47×#16502
C47×#16482
C47×#16382
C47×#16362
C47×#15562
C47×#14972
C47×#14882
#1883147