Finite Group Databasebeta

← C47×#29761 #26069459

Subgroups — C47×#29761 #26069459

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#484C211yesmaximal, characteristic, complemented
2C2×C47×#481C211yesmaximal, characteristic
3C47×#2850C211yesmaximal, characteristic
4C2×C47×#389C211yesmaximal, characteristic, complemented
5C47×#2085C212yesmaximal, complemented
6C47×#2067C212yesmaximal, complemented
7C47×#2066C212yesmaximal, complemented
8C47×#2042C212yesmaximal, complemented
9C47×#1874C211yesmaximal, characteristic
10C47×#1872C211yesmaximal, characteristic, complemented
11C47×#1797C211yesmaximal, characteristic, complemented
12C2×#124×C47C2211yescharacteristic
13C2×C22⋊Q8×C47C2211yescharacteristic
14C2×#121×C47C2211yescharacteristic
15C22×C4⋊C4×C47—21no—
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C42×C47C2211yescharacteristic
19C47×#484—24no—
20C47×#481—24no—
21C2×#107×C47C2212yes—
22C2×#106×C47C2212yes—
23C2×C4⋊C8×C47C2212yes—
24C2×#103×C47C2212yes—
25C2×#103×C47C2212yes—
26C2×#102×C47C2212yes—
27C2×#102×C47C2212yes—
28C2×C22⋊C8×C47C2211yescharacteristic
29C2×C22⋊C8×C47C2211yescharacteristic
30C47×#391C2211yescharacteristic
31C47×#390C2211yescharacteristic
32C47×#389—21no—
33C47×#389—21no—
34C47×#389C2212yes—
35C47×#389C2212yes—
36C47×#388—21no—
37C47×#388—21no—
38C47×#386—21no—
39C47×#386—21no—
40C47×#382C2211yescharacteristic
41C2×#95×C47—21no—
42C47×#340C2212yes—
43C47×#340C2212yes—
44C47×#336C2212yes—
45C22×Q8×C47C2311yescharacteristic
46C22×D4×C47—21no—
47C22×D4×C47C2311yescharacteristic
48C23×C4×C47—21no—
49C23×C4×C47—21no—
50C23×C4×C47D411yescharacteristic
51C23×C4×C47D411yescharacteristic
52C23×C4×C47C2311yescharacteristic
53C22×C8×C47C2312yes—
54C22×C8×C47C2312yes—
55#124×C47—42no—
56C22⋊Q8×C47—22no—
57C22⋊Q8×C47—22no—
58#121×C47—22no—
59#121×C47—22no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47—21no—
65C2×C4⋊C4×C47—21no—
66C2×C4⋊C4×C47—42no—
67C2×C4⋊C4×C47—44no—
68C2×C4⋊C4×C47D414yes—
69C2×C4⋊C4×C47C2312yes—
70C2×C4⋊C4×C47C2311yescharacteristic
71C2×C4⋊C4×C47C2311yescharacteristic
72C2×C4⋊C4×C47C2312yes—
73C2×C22⋊C4×C47—21no—
74C2×C22⋊C4×C47—21no—
75C2×C22⋊C4×C47—21no—
76C2×C22⋊C4×C47—21no—
77C2×C22⋊C4×C47—21no—
78C2×C22⋊C4×C47—21no—
79C2×C42×C47—42no—
80C2×C42×C47D411yescharacteristic
81C2×C42×C47D411yescharacteristic
82C2×C42×C47C2311yescharacteristic
83C2×C42×C47C2311yescharacteristic
84#107×C47—24no—
85#106×C47—24no—
86C4⋊C8×C47—42no—
87#103×C47—24no—
88#103×C47—42no—
89#102×C47—24no—
90#102×C47—42no—
91C22⋊C8×C47—22no—
92C22⋊C8×C47—22no—
93#95×C47—22no—
94#95×C47—22no—
95#95×C47—21no—
96#95×C47—21no—
97#95×C47—21no—
98#95×C47—21no—
99C24×C47—21no—
100C24×C47C2×D411yescharacteristic
101C2×Q8×C47—21no—
102C2×Q8×C47—21no—
103C2×Q8×C47—22no—
104C2×Q8×C47—22no—
105C2×D4×C47—21no—
106C2×D4×C47—21no—
107C2×D4×C47—22no—
108C2×D4×C47—22no—
109C2×D4×C47—42no—
110C2×D4×C47—42no—
111C2×D4×C47—42no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—24no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47#4112yes—
138C22×C4×C47C2411yescharacteristic
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C4⋊C4×C47—24no—
146C4⋊C4×C47—22no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47—44no—
155C4⋊C4×C47—42no—
156C4⋊C4×C47—44no—
157C4⋊C4×C47C2×D414yes—
158C22⋊C4×C47—42no—
159C22⋊C4×C47—42no—
160C22⋊C4×C47—42no—
161C22⋊C4×C47—42no—
162C22⋊C4×C47—42no—
163C22⋊C4×C47—42no—
164C42×C47—22no—
165C42×C47—22no—
166C42×C47—41no—
167C42×C47—41no—
168C23×C47—21no—
169C23×C47—21no—
170C23×C47—21no—
171C23×C47—21no—
172C23×C47—41no—
173C23×C47—41no—
174C23×C47—41no—
175C23×C47—41no—
176C23×C47—41no—
177C23×C47—41no—
178C23×C47—41no—
179C23×C47#12112yes—
180C23×C47#13512yes—
181C23×C47#13712yes—
182C23×C47C22×D411yescharacteristic
183Q8×C47—42no—
184Q8×C47—42no—
185D4×C47—42no—
186D4×C47—42no—
187D4×C47—84no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—44no—
205C2×C4×C47—44no—
206C2×C4×C47—48no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—42no—
214C2×C4×C47—41no—
215C2×C4×C47—42no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—42no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—84no—
222C2×C4×C47#12112yes—
223C2×C4×C47AGL(1,ℤ/8)12yes—
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C47C2×#4111yescharacteristic
226C2×C4×C47H(5,𝔽2)12yes—
227C2×C4×C472−1+412yes—
228C8×C47—42no—
229C8×C47—42no—
230#29761C4711yesmaximal, characteristic, direct product factor, Sylow
231C22×C47—22no—
232C22×C47—22no—
233C22×C47—22no—
234C22×C47—22no—
235C22×C47—22no—
236C22×C47—22no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47—81no—
244C22×C47#46414yes—
245C22×C47C2×#12111yescharacteristic
246C22×C47#53411yescharacteristic
247C22×C47#53611yescharacteristic
248C22×C47C2×#13511yescharacteristic
249C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C47C2×#13711yescharacteristic
251C22×C47#57511yescharacteristic
252C4×C47—22no—
253C4×C47—22no—
254C4×C47—41no—
255C4×C47—41no—
256C4×C47—41no—
257C4×C47—44no—
258C4×C47—81no—
259C4×C47—82no—
260C4×C47—81no—
261C4×C47—81no—
262C4×C47#53712yes—
263C4×C47#53912yes—
264C2×#484C2×C4711yescharacteristic, complemented
265C2×#481C2×C4711yescharacteristic
266#2850C2×C4711yescharacteristic
267C2×#389C2×C4711yescharacteristic, complemented
268#2085C2×C4712yescomplemented
269#2067C2×C4712yescomplemented
270#2066C2×C4712yescomplemented
271#2042C2×C4712yescomplemented
272#1874C2×C4711yescharacteristic
273#1872C2×C4711yescharacteristic, complemented
274#1797C2×C4711yescharacteristic, complemented
275C2×C47—24no—
276C2×C47—161no—
277C2×C47#261811yescharacteristic
278C2×C47C2×#46411yescharacteristic
279C2×C47#303611yescharacteristic
280C2×C47#318811yescharacteristic
281C2×C47#319611yescharacteristic
282C2×C47#323211yescharacteristic
283C2×C47#323911yescharacteristic
284C2×#124C22×C4711yescharacteristic
285C2×C22⋊Q8C22×C4711yescharacteristic
286C2×#121C22×C4711yescharacteristic
287C22×C4⋊C4—21no—
288C22×C4⋊C4C22×C4711yescharacteristic
289C22×C4⋊C4C22×C4711yescharacteristic
290C22×C42C22×C4711yescharacteristic
291#484—24no—
292#481—24no—
293C2×#107C22×C4712yes—
294C2×#106C22×C4712yes—
295C2×C4⋊C8C22×C4712yes—
296C2×#103C22×C4712yes—
297C2×#103C22×C4712yes—
298C2×#102C22×C4712yes—
299C2×#102C22×C4712yes—
300C2×C22⋊C8C22×C4711yescharacteristic
301C2×C22⋊C8C22×C4711yescharacteristic
302#391C22×C4711yescharacteristic
303#390C22×C4711yescharacteristic
304#389—21no—
305#389—21no—
306#389C22×C4712yes—
307#389C22×C4712yes—
308#388—21no—
309#388—21no—
310#386—21no—
311#386—21no—
312#382C22×C4711yescharacteristic
313C2×#95—21no—
314#340C22×C4712yes—
315#340C22×C4712yes—
316#336C22×C4712yes—
317C47#2976111yescharacteristic, direct product factor, Sylow
318C22×Q8C23×C4711yescharacteristic
319C22×D4—21no—
320C22×D4C23×C4711yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4D4×C4711yescharacteristic
324C23×C4D4×C4711yescharacteristic
325C23×C4C23×C4711yescharacteristic
326C22×C8C23×C4712yes—
327C22×C8C23×C4712yes—
328#124—42no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331#121—22no—
332#121—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4D4×C4714yes—
342C2×C4⋊C4C23×C4712yes—
343C2×C4⋊C4C23×C4711yescharacteristic
344C2×C4⋊C4C23×C4711yescharacteristic
345C2×C4⋊C4C23×C4712yes—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—42no—
353C2×C42D4×C4711yescharacteristic
354C2×C42D4×C4711yescharacteristic
355C2×C42C23×C4711yescharacteristic
356C2×C42C23×C4711yescharacteristic
357#107—24no—
358#106—24no—
359C4⋊C8—42no—
360#103—24no—
361#103—42no—
362#102—24no—
363#102—42no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366#95—22no—
367#95—22no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372C24—21no—
373C24C2×D4×C4711yescharacteristic
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4C2×D4×C4711yescharacteristic
405C22×C4C2×D4×C4711yescharacteristic
406C22×C4C2×D4×C4711yescharacteristic
407C22×C4C2×D4×C4711yescharacteristic
408C22×C4C2×D4×C4712yes—
409C22×C4C2×D4×C4711yescharacteristic
410C22×C4#41×C4712yes—
411C22×C4C24×C4711yescharacteristic
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—44no—
428C4⋊C4—42no—
429C4⋊C4—44no—
430C4⋊C4C2×D4×C4714yes—
431C22⋊C4—42no—
432C22⋊C4—42no—
433C22⋊C4—42no—
434C22⋊C4—42no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C42—22no—
438C42—22no—
439C42—41no—
440C42—41no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23#121×C4712yes—
453C23#135×C4712yes—
454C23#137×C4712yes—
455C23C22×D4×C4711yescharacteristic
456Q8—42no—
457Q8—42no—
458D4—42no—
459D4—42no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—44no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—84no—
495C2×C4#121×C4712yes—
496C2×C4AGL(1,ℤ/8)×C4712yes—
497C2×C4C22×D4×C4711yescharacteristic
498C2×C4C2×#41×C4711yescharacteristic
499C2×C4H(5,𝔽2)×C4712yes—
500C2×C42−1+4×C4712yes—
501C8—42no—
502C8—42no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22C47×#46414yes—
517C22C2×#121×C4711yescharacteristic
518C22C47×#53411yescharacteristic
519C22C47×#53611yescharacteristic
520C22C2×#135×C4711yescharacteristic
521C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
522C22C2×#137×C4711yescharacteristic
523C22C47×#57511yescharacteristic
524C4—22no—
525C4—22no—
526C4—44no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—82no—
534C4C47×#53712yes—
535C4C47×#53912yes—
536C2—24no—
537C2—161no—
538C2C47×#261811yescharacteristic
539C2C2×C47×#46411yescharacteristic
540C2C47×#303611yescharacteristic
541C2C47×#318811yescharacteristic
542C2C47×#319611yescharacteristic
543C2C47×#323211yescharacteristic
544C2C47×#323911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#484C2semidirect
4. C2×C47×#389C2semidirect
5. C47×#2085C2semidirect
6. C47×#2067C2semidirect
7. C47×#2066C2semidirect
8. C47×#2042C2semidirect
10. C47×#1872C2semidirect
11. C47×#1797C2semidirect
230. #29761C47direct (N × H)
264. C2×#484C2×C47semidirect
267. C2×#389C2×C47semidirect
268. #2085C2×C47semidirect
269. #2067C2×C47semidirect
270. #2066C2×C47semidirect
271. #2042C2×C47semidirect
273. #1872C2×C47semidirect
274. #1797C2×C47semidirect
317. C47#29761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4842
C2×C47×#4812
C47×#28502
C2×C47×#3892
C47×#20852
C47×#20672
C47×#20662
C47×#20422
C47×#18742
C47×#18722
C47×#17972
#2976147