Finite Group Databasebeta

← C47×#9259 #26048957

Subgroups — C47×#9259 #26048957

Order 12032.

966 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#447C211yesmaximal, characteristic
2D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
3C47×#1964C211yesmaximal, characteristic, complemented
4C47×#1786C211yesmaximal, characteristic, complemented
5C47×#1519C211yesmaximal, characteristic, complemented
6C47×#1289C211yesmaximal, characteristic, complemented
7C47×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C47C2211yescharacteristic
9C22×D8×C47C412yescomplemented
10C2×#121×C47C2211yescharacteristic
11C2×C4×D4×C47—21no—
12C22×C22⋊C4×C47—21no—
13C47×#447—21no—
14C47×#447—22no—
15C47×#447—21no—
16C2×#102×C47—22no—
17C2×#102×C47C412yescomplemented
18C2×#99×C47—21no—
19C2×#99×C47—21no—
20C2×C22⋊C8×C47C2211yescharacteristic
21C2×C22⋊C8×C47C2211yescharacteristic
22C47×#390—21no—
23C47×#386—22no—
24C47×#380C2211yescharacteristic
25C47×#380C2211yescharacteristic
26C47×#379—21no—
27C4×C22⋊C4×C47C2211yescharacteristic
28C47×#327—22no—
29C25×C47—21no—
30C22×D4×C47—21no—
31C22×D4×C47—21no—
32C22×D4×C47—21no—
33C22×D4×C47—21no—
34C22×D4×C47—44no—
35C22×D4×C47C2×C412yes—
36C22×D4×C47C2×C411yescharacteristic, complemented
37C22×D4×C47D411yescharacteristic
38C22×D4×C47D412yes—
39C22×D4×C47D411yescharacteristic
40C23×C4×C47—22no—
41C23×C4×C47C2311yescharacteristic
42C2×D8×C47—22no—
43C2×D8×C47—22no—
44C2×D8×C47—44no—
45C22×C8×C47—21no—
46C22×C8×C47C2×C412yescomplemented
47#121×C47—21no—
48#121×C47—21no—
49#121×C47—21no—
50#121×C47—21no—
51C4×D4×C47—44no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
55C2×C22⋊C4×C47—22no—
56C2×C22⋊C4×C47—22no—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59C2×C22⋊C4×C47—21no—
60C2×C22⋊C4×C47—22no—
61C2×C22⋊C4×C47—42no—
62C2×C22⋊C4×C47—42no—
63C2×C22⋊C4×C47D411yescharacteristic
64C2×C22⋊C4×C47D411yescharacteristic
65C2×C42×C47—21no—
66#102×C47—22no—
67#102×C47—22no—
68#102×C47—44no—
69#99×C47—42no—
70#99×C47—42no—
71C22⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47—21no—
75#95×C47—21no—
76#95×C47—21no—
77#95×C47D412yes—
78C24×C47—21no—
79C24×C47—21no—
80C24×C47—22no—
81C24×C47—22no—
82C24×C47—21no—
83C24×C47—44no—
84C24×C47—41no—
85C24×C47—41no—
86C24×C47—41no—
87C24×C47—41no—
88C24×C47—82no—
89C24×C47C2×D411yescharacteristic
90C2×D4×C47—24no—
91C2×D4×C47—24no—
92C2×D4×C47—24no—
93C2×D4×C47—21no—
94C2×D4×C47—22no—
95C2×D4×C47—21no—
96C2×D4×C47—22no—
97C2×D4×C47—21no—
98C2×D4×C47—21no—
99C2×D4×C47—42no—
100C2×D4×C47—42no—
101C2×D4×C47—42no—
102C2×D4×C47—42no—
103C2×D4×C47—44no—
104C2×D4×C47—44no—
105C2×D4×C47—44no—
106C2×D4×C47—41no—
107C2×D4×C47—41no—
108C2×D4×C47—41no—
109C2×D4×C47—41no—
110C2×D4×C47—41no—
111C2×D4×C47—41no—
112C2×D4×C47C22⋊C412yes—
113C2×D4×C47C22⋊C412yes—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—42no—
119C22×C4×C47—44no—
120C22×C4×C47—44no—
121C22×C4×C47—41no—
122C22×C4×C47—82no—
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47#4111yescharacteristic
128C22×C4×C47#4111yescharacteristic
129D8×C47—44no—
130D8×C47—44no—
131C2×C8×C47—22no—
132C2×C8×C47—42no—
133C2×C8×C47—42no—
134C2×C8×C47—41no—
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—42no—
138C4⋊C4×C47—42no—
139C22⋊C4×C47—21no—
140C22⋊C4×C47—21no—
141C22⋊C4×C47—21no—
142C22⋊C4×C47—44no—
143C22⋊C4×C47—44no—
144C22⋊C4×C47—41no—
145C22⋊C4×C47—41no—
146C22⋊C4×C47—41no—
147C22⋊C4×C47—41no—
148C22⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C22⋊C4×C47—82no—
151C22⋊C4×C47D812yescomplemented
152C42×C47—42no—
153C23×C47—24no—
154C23×C47—22no—
155C23×C47—22no—
156C23×C47—41no—
157C23×C47—41no—
158C23×C47—44no—
159C23×C47—44no—
160C23×C47—42no—
161C23×C47—42no—
162C23×C47—42no—
163C23×C47—41no—
164C23×C47—41no—
165C23×C47—42no—
166C23×C47—42no—
167C23×C47—41no—
168C23×C47—41no—
169C23×C47—42no—
170C23×C47—42no—
171C23×C47—41no—
172C23×C47—41no—
173C23×C47—41no—
174C23×C47—82no—
175C23×C47—82no—
176C23×C47—81no—
177C23×C47—81no—
178C23×C47—84no—
179C23×C47—84no—
180C23×C47—84no—
181C23×C47—84no—
182C23×C47C4×D411yescharacteristic
183C23×C47#12011yescharacteristic
184C23×C47#12111yescharacteristic
185C23×C47C2×D811yescharacteristic
186C23×C47#13511yescharacteristic
187C23×C47AGL(1,ℤ/8)11yescharacteristic
188C23×C47AGL(1,ℤ/8)11yescharacteristic
189D4×C47—24no—
190D4×C47—22no—
191D4×C47—22no—
192D4×C47—22no—
193D4×C47—44no—
194D4×C47—44no—
195D4×C47—42no—
196D4×C47—42no—
197D4×C47—81no—
198D4×C47—81no—
199D4×C47—81no—
200D4×C47—81no—
201D4×C47—81no—
202D4×C47#9914yescomplemented
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
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—41no—
219C2×C4×C47—42no—
220C2×C4×C47—41no—
221C2×C4×C47—88no—
222C2×C4×C47—81no—
223C2×C4×C47—81no—
224C2×C4×C47—81no—
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47#12111yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C8×C47—42no—
230C8×C47—81no—
231#9259C4711yesmaximal, characteristic, direct product factor, Sylow
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—21no—
237C22×C47—21no—
238C22×C47—24no—
239C22×C47—41no—
240C22×C47—41no—
241C22×C47—41no—
242C22×C47—41no—
243C22×C47—44no—
244C22×C47—44no—
245C22×C47—42no—
246C22×C47—42no—
247C22×C47—42no—
248C22×C47—42no—
249C22×C47—42no—
250C22×C47—84no—
251C22×C47—84no—
252C22×C47—84no—
253C22×C47—84no—
254C22×C47—82no—
255C22×C47—82no—
256C22×C47—81no—
257C22×C47—81no—
258C22×C47—81no—
259C22×C47—161no—
260C22×C47—161no—
261C22×C47#38611yescharacteristic
262C22×C47C4×D811yescharacteristic
263C22×C47#44211yescharacteristic
264C22×C47#44711yescharacteristic
265C22×C47#44911yescharacteristic
266C22×C47#45911yescharacteristic
267C22×C47#46311yescharacteristic
268C4×C47—21no—
269C4×C47—21no—
270C4×C47—21no—
271C4×C47—42no—
272C4×C47—81no—
273C4×C47—82no—
274C4×C47—81no—
275C4×C47—161no—
276C4×C47C2×#9912yes—
277C2×#447C2×C4711yescharacteristic
278D4×C22⋊C4C2×C4711yescharacteristic, complemented
279#1964C2×C4711yescharacteristic, complemented
280#1786C2×C4711yescharacteristic, complemented
281#1519C2×C4711yescharacteristic, complemented
282#1289C2×C4711yescharacteristic, complemented
283#1282C2×C4711yescharacteristic, complemented
284C2×C47—21no—
285C2×C47—21no—
286C2×C47—21no—
287C2×C47—21no—
288C2×C47—21no—
289C2×C47—21no—
290C2×C47—44no—
291C2×C47—82no—
292C2×C47—161no—
293C2×C47#187911yescharacteristic
294C2×C47#189811yescharacteristic
295C2×C47#190411yescharacteristic
296C23×D4C22×C4711yescharacteristic
297C22×D8C4×C4712yescomplemented
298C2×#121C22×C4711yescharacteristic
299C2×C4×D4—21no—
300C22×C22⋊C4—21no—
301#447—21no—
302#447—22no—
303#447—21no—
304C2×#102—22no—
305C2×#102C4×C4712yescomplemented
306C2×#99—21no—
307C2×#99—21no—
308C2×C22⋊C8C22×C4711yescharacteristic
309C2×C22⋊C8C22×C4711yescharacteristic
310#390—21no—
311#386—22no—
312#380C22×C4711yescharacteristic
313#380C22×C4711yescharacteristic
314#379—21no—
315C4×C22⋊C4C22×C4711yescharacteristic
316#327—22no—
317C47#925911yescharacteristic, direct product factor, Sylow
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—44no—
324C22×D4C2×C4×C4712yes—
325C22×D4C2×C4×C4711yescharacteristic, complemented
326C22×D4D4×C4711yescharacteristic
327C22×D4D4×C4712yes—
328C22×D4D4×C4711yescharacteristic
329C23×C4—22no—
330C23×C4C23×C4711yescharacteristic
331C2×D8—22no—
332C2×D8—22no—
333C2×D8—44no—
334C22×C8—21no—
335C22×C8C2×C4×C4712yescomplemented
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C2×C4×C4711yescharacteristic, complemented
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4D4×C4711yescharacteristic
353C2×C22⋊C4D4×C4711yescharacteristic
354C2×C42—21no—
355#102—22no—
356#102—22no—
357#102—44no—
358#99—42no—
359#99—42no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364#95—21no—
365#95—21no—
366#95D4×C4712yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—44no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—82no—
378C24C2×D4×C4711yescharacteristic
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C22⋊C4×C4712yes—
402C2×D4C22⋊C4×C4712yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—44no—
409C22×C4—44no—
410C22×C4—41no—
411C22×C4—82no—
412C22×C4C22×C4×C4711yescharacteristic
413C22×C4C2×D4×C4711yescharacteristic
414C22×C4C2×D4×C4711yescharacteristic
415C22×C4C2×D4×C4711yescharacteristic
416C22×C4#41×C4711yescharacteristic
417C22×C4#41×C4711yescharacteristic
418D8—44no—
419D8—44no—
420C2×C8—22no—
421C2×C8—42no—
422C2×C8—42no—
423C2×C8—41no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—82no—
440C22⋊C4D8×C4712yescomplemented
441C42—42no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—82no—
464C23—82no—
465C23—81no—
466C23—81no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23C4×D4×C4711yescharacteristic
472C23#120×C4711yescharacteristic
473C23#121×C4711yescharacteristic
474C23C2×D8×C4711yescharacteristic
475C23#135×C4711yescharacteristic
476C23AGL(1,ℤ/8)×C4711yescharacteristic
477C23AGL(1,ℤ/8)×C4711yescharacteristic
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—44no—
483D4—44no—
484D4—42no—
485D4—42no—
486D4—81no—
487D4—81no—
488D4—81no—
489D4—81no—
490D4—81no—
491D4#99×C4714yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—88no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4C2×C22⋊C4×C4711yescharacteristic
515C2×C4C4×D4×C4711yescharacteristic
516C2×C4#121×C4711yescharacteristic
517C2×C4#123×C4711yescharacteristic
518C8—42no—
519C8—81no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—161no—
548C22—161no—
549C22C47×#38611yescharacteristic
550C22C4×D8×C4711yescharacteristic
551C22C47×#44211yescharacteristic
552C22C47×#44711yescharacteristic
553C22C47×#44911yescharacteristic
554C22C47×#45911yescharacteristic
555C22C47×#46311yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—161no—
564C4C2×#99×C4712yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—44no—
572C2—82no—
573C2—161no—
574C2C47×#187911yescharacteristic
575C2C47×#189811yescharacteristic
576C2C47×#190411yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC2×C47×#447C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×C22⋊C4×C47C2semidirect
3. C47×#1964C2semidirect
4. C47×#1786C2semidirect
5. C47×#1519C2semidirect
6. C47×#1289C2semidirect
7. C47×#1282C2semidirect
9. C22×D8×C47C4semidirect
17. C2×#102×C47C4semidirect
36. C22×D4×C47C2×C4semidirect
46. C22×C8×C47C2×C4semidirect
54. C2×C4⋊C4×C47C2×C4semidirect
151. C22⋊C4×C47D8semidirect
202. D4×C47#99semidirect
231. #9259C47direct (N × H)
278. D4×C22⋊C4C2×C47semidirect
279. #1964C2×C47semidirect
280. #1786C2×C47semidirect
281. #1519C2×C47semidirect
282. #1289C2×C47semidirect
283. #1282C2×C47semidirect
297. C22×D8C4×C47semidirect
305. C2×#102C4×C47semidirect
317. C47#9259direct (N × H)
325. C22×D4C2×C4×C47semidirect
335. C22×C8C2×C4×C47semidirect
343. C2×C4⋊C4C2×C4×C47semidirect
440. C22⋊C4D8×C47semidirect
491. D4#99×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4472
D4×C22⋊C4×C472
C47×#19642
C47×#17862
C47×#15192
C47×#12892
C47×#12822
#925947