Finite Group Databasebeta

← C47×#18952 #26058650

Subgroups — C47×#18952 #26058650

Order 12032.

880 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×#3550C211yesmaximal, characteristic, complemented
2C47×#3246C211yesmaximal, characteristic, complemented
3C47×#3228C211yesmaximal, characteristic, complemented
4C47×#3214C211yesmaximal, characteristic
5C47×#1651C212yesmaximal, complemented
6C47×#1650C212yesmaximal, complemented
7C47×#1628C212yesmaximal, complemented
8C47×#1627C212yesmaximal, complemented
9C47×#1552C211yesmaximal, characteristic, complemented
10C47×#1497C211yesmaximal, characteristic, complemented
11C47×#1480C211yesmaximal, characteristic, complemented
12C47×#563—22no—
13C47×#559—21no—
14Q82×C47—21no—
15C47×#556—21no—
16C47×#556C2212yes—
17D4×Q8×C47—21no—
18D4×Q8×C47C2212yes—
19C47×#542—22no—
20C47×#542—22no—
21C47×#536—22no—
22C47×#533C2211yescharacteristic
23C47×#533C2211yescharacteristic
24C47×#532C2211yescharacteristic
25C47×#532C2211yescharacteristic
26C47×#500C2211yescharacteristic
27C47×#498C2211yescharacteristic
28C47×#496—21no—
29C47×#489—21no—
30C47×#486C2211yescharacteristic
31C47×#486C2211yescharacteristic
32C47×#482—22no—
33C47×#478—22no—
34C47×#476—21no—
35C47×#475C2212yes—
36C47×#465—22no—
37C47×#461—21no—
38C47×#461C2212yes—
39C47×#460C2212yes—
40C47×#459C2212yes—
41C47×#449—22no—
42C47×#432C2211yescharacteristic
43C47×#431C2211yescharacteristic
44C2×C4⋊C8×C47C2211yescharacteristic
45C47×#332C2212yes—
46C47×#332C2212yes—
47C47×Q8⋊C8C2212yes—
48C47×Q8⋊C8C2212yes—
49C47×D4⋊C8C2212yes—
50C47×D4⋊C8C2212yes—
51C2×#41×C47—21no—
52C2×#41×C47—21no—
53C22×Q8×C47—22no—
54C2×SD16×C47—22no—
55C2×SD16×C47—22no—
56C2×D8×C47—22no—
57C22×C8×C47—21no—
58C4⋊Q8×C47—24no—
59C4⋊Q8×C47—22no—
60C4⋊Q8×C47—22no—
61C4⋊Q8×C47D411yescharacteristic
62C4⋊Q8×C47D411yescharacteristic
63C4⋊Q8×C47D411yescharacteristic
64C4⋊Q8×C47C2311yescharacteristic
65C4⋊Q8×C47C2311yescharacteristic
66C4⋊Q8×C47C2311yescharacteristic
67#127×C47D411yescharacteristic
68#127×C47C2311yescharacteristic
69#126×C47—24no—
70#126×C47—24no—
71#125×C47—21no—
72#125×C47D412yes—
73#124×C47—24no—
74#124×C47—22no—
75#124×C47—22no—
76#124×C47—21no—
77#124×C47—21no—
78#123×C47—24no—
79#123×C47—24no—
80C22⋊Q8×C47—24no—
81C22⋊Q8×C47—22no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—21no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—24no—
87C22⋊Q8×C47D412yes—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—21no—
91#121×C47D412yes—
92C4×Q8×C47—22no—
93C4×Q8×C47—22no—
94C4×Q8×C47—21no—
95C4×Q8×C47—21no—
96C4×Q8×C47—21no—
97C4×Q8×C47C2312yes—
98C4×D4×C47—22no—
99C4×D4×C47—22no—
100C4×D4×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—21no—
103C4×D4×C47C2312yes—
104#117×C47—21no—
105#117×C47—22no—
106#117×C47D412yes—
107C2×C42×C47C2311yescharacteristic
108#107×C47—22no—
109#106×C47—22no—
110#106×C47—22no—
111C4⋊C8×C47—21no—
112C4⋊C8×C47—21no—
113C4⋊C8×C47C2312yes—
114C4⋊C8×C47C2312yes—
115#103×C47—22no—
116#103×C47—22no—
117#102×C47—22no—
118#102×C47—22no—
119#102×C47—22no—
120#102×C47—22no—
121C22⋊C8×C47—21no—
122C22⋊C8×C47—21no—
123#97×C47—21no—
124C4×C8×C47C2311yescharacteristic
125C4×C8×C47C2311yescharacteristic
126#41×C47—81no—
127#41×C47—81no—
128#41×C47—82no—
129C2×Q8×C47—24no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—82no—
136C2×Q8×C47—82no—
137C2×Q8×C47C2×D412yes—
138C2×D4×C47—22no—
139C2×D4×C47—21no—
140C2×D4×C47—21no—
141C2×D4×C47—21no—
142C2×D4×C47—21no—
143C2×D4×C47—21no—
144C2×D4×C47—41no—
145C2×D4×C47C2×D412yes—
146C22×C4×C47—24no—
147C22×C4×C47—22no—
148C22×C4×C47—41no—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152SD16×C47—82no—
153SD16×C47—82no—
154D8×C47—82no—
155C2×C8×C47—22no—
156C2×C8×C47—22no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—81no—
160C4⋊C4×C47—24no—
161C4⋊C4×C47—24no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—22no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47C2×D412yes—
175C4⋊C4×C47C2×D412yes—
176C4⋊C4×C47C2×D412yes—
177C4⋊C4×C47C2×D412yes—
178C22⋊C4×C47—24no—
179C22⋊C4×C47—24no—
180C22⋊C4×C47—24no—
181C22⋊C4×C47—22no—
182C22⋊C4×C47—22no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C42×C47—24no—
188C42×C47—22no—
189C42×C47—22no—
190C42×C47C2×D411yescharacteristic
191C42×C47C2×D411yescharacteristic
192C42×C47C2×D411yescharacteristic
193C42×C47C2411yescharacteristic
194C23×C47—22no—
195C23×C47—41no—
196C23×C47#12011yescharacteristic
197Q8×C47—22no—
198Q8×C47—22no—
199Q8×C47—42no—
200Q8×C47—41no—
201Q8×C47—42no—
202Q8×C47—41no—
203Q8×C47—42no—
204Q8×C47—81no—
205Q8×C47—84no—
206D4×C47—22no—
207D4×C47—22no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—41no—
211D4×C47—42no—
212D4×C47—41no—
213D4×C47—81no—
214D4×C47—82no—
215D4×C47—82no—
216C2×C4×C47—21no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—41no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—82no—
229C2×C4×C47—84no—
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47#12011yescharacteristic
232C2×C4×C47#12011yescharacteristic
233C2×C4×C47C22×D411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D411yescharacteristic
236C8×C47—41no—
237C8×C47—41no—
238C8×C47—42no—
239C8×C47—42no—
240#18952C4711yesmaximal, characteristic, direct product factor, Sylow
241C22×C47—21no—
242C22×C47—21no—
243C22×C47—21no—
244C22×C47—42no—
245C22×C47—42no—
246C22×C47—42no—
247C22×C47—81no—
248C22×C47—81no—
249C22×C47—81no—
250C22×C47C2×#12011yescharacteristic
251C4×C47—21no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—42no—
256C4×C47—42no—
257C4×C47—42no—
258C4×C47—42no—
259C4×C47—42no—
260C4×C47—81no—
261C4×C47#57611yescharacteristic
262C4×C47#57712yes—
263C4×C47#57711yescharacteristic
264#3550C2×C4711yescharacteristic, complemented
265#3246C2×C4711yescharacteristic, complemented
266#3228C2×C4711yescharacteristic, complemented
267#3214C2×C4711yescharacteristic
268#1651C2×C4712yescomplemented
269#1650C2×C4712yescomplemented
270#1628C2×C4712yescomplemented
271#1627C2×C4712yescomplemented
272#1552C2×C4711yescharacteristic, complemented
273#1497C2×C4711yescharacteristic, complemented
274#1480C2×C4711yescharacteristic, complemented
275C2×C47—41no—
276C2×C47—82no—
277C2×C47—161no—
278C2×C47#301011yescharacteristic
279C2×C47#301211yescharacteristic
280C2×C47#302011yescharacteristic
281#563—22no—
282#559—21no—
283Q82—21no—
284#556—21no—
285#556C22×C4712yes—
286D4×Q8—21no—
287D4×Q8C22×C4712yes—
288#542—22no—
289#542—22no—
290#536—22no—
291#533C22×C4711yescharacteristic
292#533C22×C4711yescharacteristic
293#532C22×C4711yescharacteristic
294#532C22×C4711yescharacteristic
295#500C22×C4711yescharacteristic
296#498C22×C4711yescharacteristic
297#496—21no—
298#489—21no—
299#486C22×C4711yescharacteristic
300#486C22×C4711yescharacteristic
301#482—22no—
302#478—22no—
303#476—21no—
304#475C22×C4712yes—
305#465—22no—
306#461—21no—
307#461C22×C4712yes—
308#460C22×C4712yes—
309#459C22×C4712yes—
310#449—22no—
311#432C22×C4711yescharacteristic
312#431C22×C4711yescharacteristic
313C2×C4⋊C8C22×C4711yescharacteristic
314#332C22×C4712yes—
315#332C22×C4712yes—
316Q8⋊C8C22×C4712yes—
317Q8⋊C8C22×C4712yes—
318D4⋊C8C22×C4712yes—
319D4⋊C8C22×C4712yes—
320C47#1895211yescharacteristic, direct product factor, Sylow
321C2×#41—21no—
322C2×#41—21no—
323C22×Q8—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×D8—22no—
327C22×C8—21no—
328C4⋊Q8—24no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8D4×C4711yescharacteristic
332C4⋊Q8D4×C4711yescharacteristic
333C4⋊Q8D4×C4711yescharacteristic
334C4⋊Q8C23×C4711yescharacteristic
335C4⋊Q8C23×C4711yescharacteristic
336C4⋊Q8C23×C4711yescharacteristic
337#127D4×C4711yescharacteristic
338#127C23×C4711yescharacteristic
339#126—24no—
340#126—24no—
341#125—21no—
342#125D4×C4712yes—
343#124—24no—
344#124—22no—
345#124—22no—
346#124—21no—
347#124—21no—
348#123—24no—
349#123—24no—
350C22⋊Q8—24no—
351C22⋊Q8—22no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8D4×C4712yes—
358#121—21no—
359#121—21no—
360#121—21no—
361#121D4×C4712yes—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C4712yes—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C23×C4712yes—
374#117—21no—
375#117—22no—
376#117D4×C4712yes—
377C2×C42C23×C4711yescharacteristic
378#107—22no—
379#106—22no—
380#106—22no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8C23×C4712yes—
384C4⋊C8C23×C4712yes—
385#103—22no—
386#103—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393#97—21no—
394C4×C8C23×C4711yescharacteristic
395C4×C8C23×C4711yescharacteristic
396#41—81no—
397#41—81no—
398#41—82no—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—82no—
406C2×Q8—82no—
407C2×Q8C2×D4×C4712yes—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—41no—
415C2×D4C2×D4×C4712yes—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4C2×D4×C4711yescharacteristic
420C22×C4C2×D4×C4711yescharacteristic
421C22×C4C2×D4×C4711yescharacteristic
422SD16—82no—
423SD16—82no—
424D8—82no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—81no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4C2×D4×C4712yes—
445C4⋊C4C2×D4×C4712yes—
446C4⋊C4C2×D4×C4712yes—
447C4⋊C4C2×D4×C4712yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C42—24no—
458C42—22no—
459C42—22no—
460C42C2×D4×C4711yescharacteristic
461C42C2×D4×C4711yescharacteristic
462C42C2×D4×C4711yescharacteristic
463C42C24×C4711yescharacteristic
464C23—22no—
465C23—41no—
466C23#120×C4711yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—42no—
470Q8—41no—
471Q8—42no—
472Q8—41no—
473Q8—42no—
474Q8—81no—
475Q8—84no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—42no—
480D4—41no—
481D4—42no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—84no—
500C2×C4#120×C4711yescharacteristic
501C2×C4#120×C4711yescharacteristic
502C2×C4#120×C4711yescharacteristic
503C2×C4C22×D4×C4711yescharacteristic
504C2×C4C22×D4×C4711yescharacteristic
505C2×C4C22×D4×C4711yescharacteristic
506C8—41no—
507C8—41no—
508C8—42no—
509C8—42no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C2×#120×C4711yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—81no—
530C4C47×#57611yescharacteristic
531C4C47×#57712yes—
532C4C47×#57711yescharacteristic
533C2—41no—
534C2—82no—
535C2—161no—
536C2C47×#301011yescharacteristic
537C2C47×#301211yescharacteristic
538C2C47×#302011yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3214C2
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. C47×#3550C2semidirect
2. C47×#3246C2semidirect
3. C47×#3228C2semidirect
5. C47×#1651C2semidirect
6. C47×#1650C2semidirect
7. C47×#1628C2semidirect
8. C47×#1627C2semidirect
9. C47×#1552C2semidirect
10. C47×#1497C2semidirect
11. C47×#1480C2semidirect
240. #18952C47direct (N × H)
264. #3550C2×C47semidirect
265. #3246C2×C47semidirect
266. #3228C2×C47semidirect
268. #1651C2×C47semidirect
269. #1650C2×C47semidirect
270. #1628C2×C47semidirect
271. #1627C2×C47semidirect
272. #1552C2×C47semidirect
273. #1497C2×C47semidirect
274. #1480C2×C47semidirect
320. C47#18952direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35502
C47×#32462
C47×#32282
C47×#32142
C47×#16512
C47×#16502
C47×#16282
C47×#16272
C47×#15522
C47×#14972
C47×#14802
#1895247