Finite Group Databasebeta

← C47×#29091 #26068789

Subgroups — C47×#29091 #26068789

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2514C211yesmaximal, characteristic, complemented
2C47×#2452C211yesmaximal, characteristic
3C47×#2087C211yesmaximal, characteristic, complemented
4C47×#2073C211yesmaximal, characteristic
5C47×#2055C211yesmaximal, characteristic
6C47×#2024C211yesmaximal, characteristic, complemented
7C47×#1993C211yesmaximal, characteristic, complemented
8C47×#1973C211yesmaximal, characteristic
9C47×#1936C211yesmaximal, characteristic
10C47×#1935C211yesmaximal, characteristic, complemented
11C47×#1933C211yesmaximal, characteristic, complemented
12C47×#1918C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic
14C47×#1771C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic
16C22×SD16×C47C2211yescharacteristic
17C2×C4⋊Q8×C47C2211yescharacteristic
18C2×C22⋊Q8×C47—21no—
19C2×C4×D4×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×C4⋊C8×C47C2211yescharacteristic
22C2×#103×C47C2211yescharacteristic
23C2×#103×C47C2211yescharacteristic
24C2×#103×C47C2211yescharacteristic
25C2×#102×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#97×C47C2211yescharacteristic
29C2×#97×C47C2211yescharacteristic
30C2×C4×C8×C47C2211yescharacteristic
31C47×#401—21no—
32C47×#400—21no—
33C47×#396—21no—
34C47×#393—21no—
35C47×#391C2211yescharacteristic
36C47×#391C2211yescharacteristic
37C47×#391C2211yescharacteristic
38C47×#390C2211yescharacteristic
39C47×#390C2211yescharacteristic
40C47×#389C2211yescharacteristic
41C47×#389C2211yescharacteristic
42C47×#389C2211yescharacteristic
43C47×#387—21no—
44C47×#385—21no—
45C47×#383—21no—
46C47×#382C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47—21no—
60C22×Q8×C47C2311yescharacteristic
61C22×D4×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C2×SD16×C47—22no—
64C2×SD16×C47—22no—
65C2×SD16×C47—41no—
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C4⋊Q8×C47—22no—
71C4⋊Q8×C47—41no—
72C22⋊Q8×C47—44no—
73C4×D4×C47—22no—
74C4×D4×C47—41no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47D411yescharacteristic
80C2×C4⋊C4×C47D411yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C42×C47—21no—
93C2×C42×C47C2311yescharacteristic
94C2×C42×C47C2311yescharacteristic
95C2×C42×C47C2311yescharacteristic
96#107×C47—22no—
97C4⋊C8×C47—22no—
98#103×C47—22no—
99#103×C47—22no—
100#103×C47—41no—
101#102×C47—22no—
102#102×C47—22no—
103#102×C47—22no—
104#97×C47—22no—
105#97×C47—41no—
106C4×C8×C47—41no—
107#95×C47—21no—
108#95×C47—21no—
109#95×C47—21no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47D411yescharacteristic
120#95×C47D411yescharacteristic
121C24×C47—21no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—42no—
129C2×Q8×C47—42no—
130C2×Q8×C47—81no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47#4112yes—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47—81no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2411yescharacteristic
154SD16×C47—44no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47#4112yes—
166C2×C8×C47#4112yes—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—41no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—42no—
182C4⋊C4×C47—42no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47#4112yes—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—42no—
187C22⋊C4×C47—42no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—81no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—42no—
197C23×C47—22no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47C22×D411yescharacteristic
205Q8×C47—41no—
206Q8×C47—41no—
207Q8×C47—41no—
208Q8×C47—41no—
209Q8×C47—84no—
210D4×C47—22no—
211D4×C47—22no—
212D4×C47—41no—
213D4×C47—41no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—84no—
253C2×C4×C47AGL(1,ℤ/8)12yes—
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47H(5,𝔽2)11yescharacteristic
259C2×C4×C472−1+411yescharacteristic
260C8×C47—22no—
261C8×C47—22no—
262C8×C47—41no—
263C8×C47—41no—
264#29091C4711yesmaximal, characteristic, direct product factor, Sylow
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47#53211yescharacteristic
273C22×C47#54611yescharacteristic
274C22×C47#54811yescharacteristic
275C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C47#57511yescharacteristic
277C22×C47#57711yescharacteristic
278C22×C47#57811yescharacteristic
279C4×C47—22no—
280C4×C47—41no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—42no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47#52911yescharacteristic
293C4×C47#53911yescharacteristic
294C4×C47#55111yescharacteristic
295C4×C47#55611yescharacteristic
296#2514C2×C4711yescharacteristic, complemented
297#2452C2×C4711yescharacteristic
298#2087C2×C4711yescharacteristic, complemented
299#2073C2×C4711yescharacteristic
300#2055C2×C4711yescharacteristic
301#2024C2×C4711yescharacteristic, complemented
302#1993C2×C4711yescharacteristic, complemented
303#1973C2×C4711yescharacteristic
304#1936C2×C4711yescharacteristic
305#1935C2×C4711yescharacteristic, complemented
306#1933C2×C4711yescharacteristic, complemented
307#1918C2×C4711yescharacteristic, complemented
308#1877C2×C4711yescharacteristic
309#1771C2×C4711yescharacteristic, complemented
310C4×#102C2×C4711yescharacteristic
311C2×C47—82no—
312C2×C47#256011yescharacteristic
313C2×C47#317111yescharacteristic
314C2×C47#317811yescharacteristic
315C2×C47#331011yescharacteristic
316C2×C47#331311yescharacteristic
317C2×C47#336711yescharacteristic
318C2×C47#337611yescharacteristic
319C22×SD16C22×C4711yescharacteristic
320C2×C4⋊Q8C22×C4711yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C4×D4C22×C4711yescharacteristic
323C2×#107C22×C4711yescharacteristic
324C2×C4⋊C8C22×C4711yescharacteristic
325C2×#103C22×C4711yescharacteristic
326C2×#103C22×C4711yescharacteristic
327C2×#103C22×C4711yescharacteristic
328C2×#102C22×C4711yescharacteristic
329C2×#102C22×C4711yescharacteristic
330C2×#102C22×C4711yescharacteristic
331C2×#97C22×C4711yescharacteristic
332C2×#97C22×C4711yescharacteristic
333C2×C4×C8C22×C4711yescharacteristic
334#401—21no—
335#400—21no—
336#396—21no—
337#393—21no—
338#391C22×C4711yescharacteristic
339#391C22×C4711yescharacteristic
340#391C22×C4711yescharacteristic
341#390C22×C4711yescharacteristic
342#390C22×C4711yescharacteristic
343#389C22×C4711yescharacteristic
344#389C22×C4711yescharacteristic
345#389C22×C4711yescharacteristic
346#387—21no—
347#385—21no—
348#383—21no—
349#382C22×C4711yescharacteristic
350C4×C4⋊C4C22×C4711yescharacteristic
351C4×C4⋊C4C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#340C22×C4711yescharacteristic
355#340C22×C4711yescharacteristic
356#340C22×C4711yescharacteristic
357#340C22×C4711yescharacteristic
358#340C22×C4711yescharacteristic
359#340C22×C4711yescharacteristic
360#336C22×C4711yescharacteristic
361#336C22×C4711yescharacteristic
362C47#2909111yescharacteristic, direct product factor, Sylow
363C22×Q8—21no—
364C22×Q8C23×C4711yescharacteristic
365C22×D4C23×C4711yescharacteristic
366C23×C4—21no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—41no—
370C22×C8C23×C4711yescharacteristic
371C22×C8C23×C4711yescharacteristic
372C22×C8C23×C4711yescharacteristic
373C22×C8C23×C4711yescharacteristic
374C4⋊Q8—22no—
375C4⋊Q8—41no—
376C22⋊Q8—44no—
377C4×D4—22no—
378C4×D4—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C4711yescharacteristic
384C2×C4⋊C4D4×C4711yescharacteristic
385C2×C4⋊C4C23×C4711yescharacteristic
386C2×C4⋊C4C23×C4711yescharacteristic
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C4⋊C4C23×C4711yescharacteristic
390C2×C4⋊C4C23×C4711yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42C23×C4711yescharacteristic
398C2×C42C23×C4711yescharacteristic
399C2×C42C23×C4711yescharacteristic
400#107—22no—
401C4⋊C8—22no—
402#103—22no—
403#103—22no—
404#103—41no—
405#102—22no—
406#102—22no—
407#102—22no—
408#97—22no—
409#97—41no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95D4×C4711yescharacteristic
424#95D4×C4711yescharacteristic
425C24—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4#41×C4712yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—81no—
451C22×C4C2×D4×C4711yescharacteristic
452C22×C4C2×D4×C4711yescharacteristic
453C22×C4C2×D4×C4711yescharacteristic
454C22×C4C2×D4×C4711yescharacteristic
455C22×C4C2×D4×C4711yescharacteristic
456C22×C4C2×D4×C4711yescharacteristic
457C22×C4C24×C4711yescharacteristic
458SD16—44no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8#41×C4712yes—
470C2×C8#41×C4712yes—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4#41×C4712yes—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—81no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—42no—
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C22×D4×C4711yescharacteristic
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—84no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—84no—
557C2×C4AGL(1,ℤ/8)×C4712yes—
558C2×C4C2×#41×C4711yescharacteristic
559C2×C4C2×#41×C4711yescharacteristic
560C2×C4C2×#41×C4711yescharacteristic
561C2×C4C2×#41×C4711yescharacteristic
562C2×C4H(5,𝔽2)×C4711yescharacteristic
563C2×C42−1+4×C4711yescharacteristic
564C8—22no—
565C8—22no—
566C8—41no—
567C8—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22C47×#53211yescharacteristic
576C22C47×#54611yescharacteristic
577C22C47×#54811yescharacteristic
578C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
579C22C47×#57511yescharacteristic
580C22C47×#57711yescharacteristic
581C22C47×#57811yescharacteristic
582C4—22no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C47×#52911yescharacteristic
596C4C47×#53911yescharacteristic
597C4C47×#55111yescharacteristic
598C4C47×#55611yescharacteristic
599C2—82no—
600C2C47×#256011yescharacteristic
601C2C47×#317111yescharacteristic
602C2C47×#317811yescharacteristic
603C2C47×#331011yescharacteristic
604C2C47×#331311yescharacteristic
605C2C47×#336711yescharacteristic
606C2C47×#337611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2514C2semidirect
3. C47×#2087C2semidirect
6. C47×#2024C2semidirect
7. C47×#1993C2semidirect
10. C47×#1935C2semidirect
11. C47×#1933C2semidirect
12. C47×#1918C2semidirect
14. C47×#1771C2semidirect
264. #29091C47direct (N × H)
296. #2514C2×C47semidirect
298. #2087C2×C47semidirect
301. #2024C2×C47semidirect
302. #1993C2×C47semidirect
305. #1935C2×C47semidirect
306. #1933C2×C47semidirect
307. #1918C2×C47semidirect
309. #1771C2×C47semidirect
362. C47#29091direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#25142
C47×#24522
C47×#20872
C47×#20732
C47×#20552
C47×#20242
C47×#19932
C47×#19732
C47×#19362
C47×#19352
C47×#19332
C47×#19182
C47×#18772
C47×#17712
C4×#102×C472
#2909147