Finite Group Databasebeta

← C47×#25486 #26065184

Subgroups — C47×#25486 #26065184

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#478C211yesmaximal, characteristic
2C2×C47×#446C211yesmaximal, characteristic, complemented
3C47×#2584C211yesmaximal, characteristic, complemented
4C47×#2538C211yesmaximal, characteristic
5C47×#2088C211yesmaximal, characteristic, complemented
6C47×#2086C211yesmaximal, characteristic, complemented
7C47×#2065C211yesmaximal, characteristic
8C47×#2065C211yesmaximal, characteristic
9C47×#1992C211yesmaximal, characteristic, complemented
10C47×#1948C211yesmaximal, characteristic, complemented
11C47×#1944C211yesmaximal, characteristic, complemented
12C47×#1941C211yesmaximal, characteristic, complemented
13C47×#1936C211yesmaximal, characteristic
14C47×#1934C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×#125×C47C2211yescharacteristic
17C2×C22⋊Q8×C47—21no—
18C2×C4×Q8×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C47×#478—24no—
21C47×#446—24no—
22C2×#107×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#97×C47C2211yescharacteristic
34C2×#97×C47C2211yescharacteristic
35C2×C4×C8×C47C2211yescharacteristic
36C47×#398—21no—
37C47×#396—21no—
38C47×#396—21no—
39C47×#395—21no—
40C47×#390C2211yescharacteristic
41C47×#390C2211yescharacteristic
42C47×#389—21no—
43C47×#389—21no—
44C47×#389C2211yescharacteristic
45C47×#389C2211yescharacteristic
46C47×#389C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#384C2211yescharacteristic
51C47×#380—21no—
52C4×C4⋊C4×C47C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C22×Q8×C47D411yescharacteristic
62C22×D4×C47C2311yescharacteristic
63C23×C4×C47—21no—
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68#125×C47—22no—
69#125×C47—22no—
70C22⋊Q8×C47—44no—
71C4×Q8×C47—22no—
72C4×Q8×C47—22no—
73C4×D4×C47—22no—
74C4×D4×C47—22no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47D411yescharacteristic
86C2×C4⋊C4×C47D411yescharacteristic
87C2×C4⋊C4×C47D411yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C42×C47—21no—
101C2×C42×C47C2311yescharacteristic
102C2×C42×C47C2311yescharacteristic
103C2×C42×C47C2311yescharacteristic
104#107×C47—22no—
105#106×C47—22no—
106#106×C47—22no—
107#106×C47—22no—
108C4⋊C8×C47—22no—
109C4⋊C8×C47—22no—
110C4⋊C8×C47D414yes—
111#102×C47—22no—
112#102×C47—22no—
113#102×C47—22no—
114#102×C47Q814yescomplemented
115#97×C47—22no—
116#97×C47—22no—
117C4×C8×C47—22no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125C24×C47—21no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—41no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47—21no—
134C2×D4×C47C2×Q812yes—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2411yescharacteristic
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
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×C47C2×D412yes—
162C2×C8×C47C2×D412yes—
163C2×C8×C47C2×Q812yes—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—21no—
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—42no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—42no—
182C4⋊C4×C47—42no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47—42no—
185C4⋊C4×C47—42no—
186C4⋊C4×C47—81no—
187C4⋊C4×C47—81no—
188C4⋊C4×C47—81no—
189C4⋊C4×C47C2×Q812yes—
190C4⋊C4×C47#4112yes—
191C22⋊C4×C47—42no—
192C22⋊C4×C47—42no—
193C22⋊C4×C47—42no—
194C22⋊C4×C47—81no—
195C22⋊C4×C47—81no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—81no—
201C42×C47C2×D412yes—
202C42×C47#4112yes—
203C23×C47—22no—
204C23×C47—41no—
205C23×C47—41no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47C22×D411yescharacteristic
211Q8×C47—44no—
212D4×C47—22no—
213D4×C47—22no—
214D4×C47—41no—
215D4×C47—41no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
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×C47#12112yes—
254C2×C4×C47#12112yes—
255C2×C4×C47AGL(1,ℤ/8)12yes—
256C2×C4×C47C22×D411yescharacteristic
257C2×C4×C47C22×Q811yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C472−1+411yescharacteristic
261C2×C4×C472−1+411yescharacteristic
262C8×C47—22no—
263C8×C47—22no—
264C8×C47—22no—
265C8×C47—41no—
266#25486C4711yesmaximal, characteristic, direct product factor, Sylow
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47—81no—
274C22×C47C2×#12111yescharacteristic
275C22×C47#54811yescharacteristic
276C22×C47D4×Q811yescharacteristic
277C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
278C22×C47#57511yescharacteristic
279C22×C47#57711yescharacteristic
280C22×C47#57711yescharacteristic
281C4×C47—22no—
282C4×C47—22no—
283C4×C47—22no—
284C4×C47—42no—
285C4×C47—42no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—81no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47#53311yescharacteristic
295C4×C47#54111yescharacteristic
296C4×C47#54711yescharacteristic
297C4×C47D4×Q811yescharacteristic
298C2×#478C2×C4711yescharacteristic
299C2×#446C2×C4711yescharacteristic, complemented
300#2584C2×C4711yescharacteristic, complemented
301#2538C2×C4711yescharacteristic
302#2088C2×C4711yescharacteristic, complemented
303#2086C2×C4711yescharacteristic, complemented
304#2065C2×C4711yescharacteristic
305#2065C2×C4711yescharacteristic
306#1992C2×C4711yescharacteristic, complemented
307#1948C2×C4711yescharacteristic, complemented
308#1944C2×C4711yescharacteristic, complemented
309#1941C2×C4711yescharacteristic, complemented
310#1936C2×C4711yescharacteristic
311#1934C2×C4711yescharacteristic
312#1762C2×C4711yescharacteristic
313C2×C47—82no—
314C2×C47#242911yescharacteristic
315C2×C47#305511yescharacteristic
316C2×C47#306011yescharacteristic
317C2×C47#336811yescharacteristic
318C2×C47#337611yescharacteristic
319C2×C47#338411yescharacteristic
320C2×C47#338811yescharacteristic
321C2×#125C22×C4711yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C4×Q8C22×C4711yescharacteristic
324C2×C4×D4C22×C4711yescharacteristic
325#478—24no—
326#446—24no—
327C2×#107C22×C4711yescharacteristic
328C2×#106C22×C4711yescharacteristic
329C2×#106C22×C4711yescharacteristic
330C2×#106C22×C4711yescharacteristic
331C2×C4⋊C8C22×C4711yescharacteristic
332C2×C4⋊C8C22×C4711yescharacteristic
333C2×C4⋊C8C22×C4711yescharacteristic
334C2×#102C22×C4711yescharacteristic
335C2×#102C22×C4711yescharacteristic
336C2×#102C22×C4711yescharacteristic
337C2×#102C22×C4711yescharacteristic
338C2×#97C22×C4711yescharacteristic
339C2×#97C22×C4711yescharacteristic
340C2×C4×C8C22×C4711yescharacteristic
341#398—21no—
342#396—21no—
343#396—21no—
344#395—21no—
345#390C22×C4711yescharacteristic
346#390C22×C4711yescharacteristic
347#389—21no—
348#389—21no—
349#389C22×C4711yescharacteristic
350#389C22×C4711yescharacteristic
351#389C22×C4711yescharacteristic
352#389C22×C4711yescharacteristic
353#389C22×C4711yescharacteristic
354#389C22×C4711yescharacteristic
355#384C22×C4711yescharacteristic
356#380—21no—
357C4×C4⋊C4C22×C4711yescharacteristic
358#340C22×C4711yescharacteristic
359#340C22×C4711yescharacteristic
360#340C22×C4711yescharacteristic
361#340C22×C4711yescharacteristic
362#340C22×C4711yescharacteristic
363#340C22×C4711yescharacteristic
364#340C22×C4711yescharacteristic
365#340C22×C4711yescharacteristic
366C47#2548611yescharacteristic, direct product factor, Sylow
367C22×Q8D4×C4711yescharacteristic
368C22×D4C23×C4711yescharacteristic
369C23×C4—21no—
370C22×C8C23×C4711yescharacteristic
371C22×C8C23×C4711yescharacteristic
372C22×C8C23×C4711yescharacteristic
373C22×C8C23×C4711yescharacteristic
374#125—22no—
375#125—22no—
376C22⋊Q8—44no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4D4×C4711yescharacteristic
392C2×C4⋊C4D4×C4711yescharacteristic
393C2×C4⋊C4D4×C4711yescharacteristic
394C2×C4⋊C4C23×C4711yescharacteristic
395C2×C4⋊C4C23×C4711yescharacteristic
396C2×C4⋊C4C23×C4711yescharacteristic
397C2×C4⋊C4C23×C4711yescharacteristic
398C2×C4⋊C4C23×C4711yescharacteristic
399C2×C4⋊C4C23×C4711yescharacteristic
400C2×C4⋊C4C23×C4711yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42C23×C4711yescharacteristic
408C2×C42C23×C4711yescharacteristic
409C2×C42C23×C4711yescharacteristic
410#107—22no—
411#106—22no—
412#106—22no—
413#106—22no—
414C4⋊C8—22no—
415C4⋊C8—22no—
416C4⋊C8D4×C4714yes—
417#102—22no—
418#102—22no—
419#102—22no—
420#102Q8×C4714yescomplemented
421#97—22no—
422#97—22no—
423C4×C8—22no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431C24—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—41no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×Q8×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—42no—
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
458C2×C8—21no—
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×C8C2×D4×C4712yes—
468C2×C8C2×D4×C4712yes—
469C2×C8C2×Q8×C4712yes—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
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—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4C2×Q8×C4712yes—
496C4⋊C4#41×C4712yes—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—81no—
507C42C2×D4×C4712yes—
508C42#41×C4712yes—
509C23—22no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23C22×D4×C4711yescharacteristic
517Q8—44no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
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—41no—
557C2×C4—41no—
558C2×C4—84no—
559C2×C4#121×C4712yes—
560C2×C4#121×C4712yes—
561C2×C4AGL(1,ℤ/8)×C4712yes—
562C2×C4C22×D4×C4711yescharacteristic
563C2×C4C22×Q8×C4711yescharacteristic
564C2×C4C2×#41×C4711yescharacteristic
565C2×C4C2×#41×C4711yescharacteristic
566C2×C42−1+4×C4711yescharacteristic
567C2×C42−1+4×C4711yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×#121×C4711yescharacteristic
580C22C47×#54811yescharacteristic
581C22D4×Q8×C4711yescharacteristic
582C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
583C22C47×#57511yescharacteristic
584C22C47×#57711yescharacteristic
585C22C47×#57711yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4C47×#53311yescharacteristic
600C4C47×#54111yescharacteristic
601C4C47×#54711yescharacteristic
602C4D4×Q8×C4711yescharacteristic
603C2—82no—
604C2C47×#242911yescharacteristic
605C2C47×#305511yescharacteristic
606C2C47×#306011yescharacteristic
607C2C47×#336811yescharacteristic
608C2C47×#337611yescharacteristic
609C2C47×#338411yescharacteristic
610C2C47×#338811yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#446C2semidirect
3. C47×#2584C2semidirect
5. C47×#2088C2semidirect
6. C47×#2086C2semidirect
9. C47×#1992C2semidirect
10. C47×#1948C2semidirect
11. C47×#1944C2semidirect
12. C47×#1941C2semidirect
114. #102×C47Q8semidirect
266. #25486C47direct (N × H)
299. C2×#446C2×C47semidirect
300. #2584C2×C47semidirect
302. #2088C2×C47semidirect
303. #2086C2×C47semidirect
306. #1992C2×C47semidirect
307. #1948C2×C47semidirect
308. #1944C2×C47semidirect
309. #1941C2×C47semidirect
366. C47#25486direct (N × H)
420. #102Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4782
C2×C47×#4462
C47×#25842
C47×#25382
C47×#20882
C47×#20862
C47×#20652
C47×#19922
C47×#19482
C47×#19442
C47×#19412
C47×#19362
C47×#19342
C47×#17622
#2548647