Finite Group Databasebeta

← C47×#24619 #26064317

Subgroups — C47×#24619 #26064317

Order 12032.

756 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#485C211yesmaximal, characteristic
2C2×C47×#433C211yesmaximal, characteristic
3C47×#2625C211yesmaximal, characteristic
4C47×#2316C211yesmaximal, characteristic
5C47×#2088C211yesmaximal, characteristic, complemented
6C47×#2087C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2066C211yesmaximal, characteristic, complemented
9C47×#1944C211yesmaximal, characteristic, complemented
10C47×#1941C211yesmaximal, characteristic, complemented
11C47×#1935C211yesmaximal, characteristic, complemented
12C47×#1933C211yesmaximal, characteristic, complemented
13C47×#1872C211yesmaximal, characteristic
14C47×#1853C211yesmaximal, characteristic
15C47×#1825C211yesmaximal, characteristic
16C2×C22⋊Q8×C47C2211yescharacteristic
17C2×#117×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C47×#485—24no—
21C47×#433—24no—
22C2×#107×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×#97×C47C2211yescharacteristic
35C2×C4×C8×C47C2211yescharacteristic
36C47×#400—21no—
37C47×#398—21no—
38C47×#397—21no—
39C47×#397—21no—
40C47×#391C2211yescharacteristic
41C47×#391C2211yescharacteristic
42C47×#389—21no—
43C47×#389—21no—
44C47×#389C2211yescharacteristic
45C47×#389C2211yescharacteristic
46C47×#389C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#380—21no—
51C47×#380—21no—
52C47×#380C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C22×Q8×C47C2311yescharacteristic
62C23×C4×C47—21no—
63C23×C4×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22⋊Q8×C47—22no—
69C22⋊Q8×C47—22no—
70#117×C47—22no—
71#117×C47—22no—
72#117×C47—22no—
73#117×C47—22no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—22no—
76C2×C4⋊C4×C47—22no—
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×C47D411yescharacteristic
85C2×C4⋊C4×C47D411yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C4⋊C4×C47C2311yescharacteristic
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47D411yescharacteristic
97C2×C22⋊C4×C47D411yescharacteristic
98C2×C42×C47—21no—
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101#107×C47—22no—
102#106×C47—22no—
103#106×C47—22no—
104#106×C47—22no—
105C4⋊C8×C47—22no—
106C4⋊C8×C47—22no—
107#103×C47—22no—
108#103×C47—22no—
109#103×C47—22no—
110#103×C47—22no—
111C22⋊C8×C47—22no—
112C22⋊C8×C47D414yes—
113#97×C47—22no—
114C4×C8×C47—22no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
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—
125#95×C47—21no—
126C24×C47C2×D411yescharacteristic
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—24no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—81no—
147C22×C4×C47—81no—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D412yes—
154C22×C4×C47#4112yes—
155C22×C4×C47C2411yescharacteristic
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—21no—
166C2×C8×C47C2×D412yes—
167C2×C8×C47C2×D412yes—
168C4⋊C4×C47—24no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
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—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47—81no—
185C4⋊C4×C47—81no—
186C4⋊C4×C47—81no—
187C4⋊C4×C47—81no—
188C4⋊C4×C47—81no—
189C4⋊C4×C47—81no—
190C4⋊C4×C47#4112yes—
191C4⋊C4×C47#4112yes—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—42no—
195C22⋊C4×C47—42no—
196C22⋊C4×C47—81no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—42no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47#12112yes—
209C23×C47C22×D411yescharacteristic
210Q8×C47—41no—
211Q8×C47—41no—
212Q8×C47—41no—
213Q8×C47—41no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
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—21no—
233C2×C4×C47—21no—
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—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—84no—
257C2×C4×C47#12112yes—
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C472−1+411yescharacteristic
263C2×C4×C472−1+411yescharacteristic
264C8×C47—22no—
265C8×C47—22no—
266C8×C47—41no—
267C8×C47—41no—
268#24619C4711yesmaximal, characteristic, direct product factor, Sylow
269C22×C47—22no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47C2×#12111yescharacteristic
277C22×C47#52511yescharacteristic
278C22×C47#53611yescharacteristic
279C22×C47#57711yescharacteristic
280C22×C47#57711yescharacteristic
281C22×C47#57711yescharacteristic
282C22×C47#57811yescharacteristic
283C4×C47—22no—
284C4×C47—42no—
285C4×C47—42no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—81no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47#54711yescharacteristic
297C4×C47#54711yescharacteristic
298C4×C47#55211yescharacteristic
299C4×C47#55211yescharacteristic
300C2×#485C2×C4711yescharacteristic
301C2×#433C2×C4711yescharacteristic
302#2625C2×C4711yescharacteristic
303#2316C2×C4711yescharacteristic
304#2088C2×C4711yescharacteristic, complemented
305#2087C2×C4711yescharacteristic, complemented
306#2066C2×C4711yescharacteristic, complemented
307#2066C2×C4711yescharacteristic, complemented
308#1944C2×C4711yescharacteristic, complemented
309#1941C2×C4711yescharacteristic, complemented
310#1935C2×C4711yescharacteristic, complemented
311#1933C2×C4711yescharacteristic, complemented
312#1872C2×C4711yescharacteristic
313#1853C2×C4711yescharacteristic
314#1825C2×C4711yescharacteristic
315C2×C47—42no—
316C2×C47#241311yescharacteristic
317C2×C47#306011yescharacteristic
318C2×C47#306311yescharacteristic
319C2×C47#312111yescharacteristic
320C2×C47#312311yescharacteristic
321C2×C47#324211yescharacteristic
322C2×C47#324411yescharacteristic
323C2×C22⋊Q8C22×C4711yescharacteristic
324C2×#117C22×C4711yescharacteristic
325C2×#117C22×C4711yescharacteristic
326C22×C4⋊C4C22×C4711yescharacteristic
327#485—24no—
328#433—24no—
329C2×#107C22×C4711yescharacteristic
330C2×#106C22×C4711yescharacteristic
331C2×#106C22×C4711yescharacteristic
332C2×#106C22×C4711yescharacteristic
333C2×C4⋊C8C22×C4711yescharacteristic
334C2×C4⋊C8C22×C4711yescharacteristic
335C2×#103C22×C4711yescharacteristic
336C2×#103C22×C4711yescharacteristic
337C2×#103C22×C4711yescharacteristic
338C2×#103C22×C4711yescharacteristic
339C2×C22⋊C8C22×C4711yescharacteristic
340C2×C22⋊C8C22×C4711yescharacteristic
341C2×#97C22×C4711yescharacteristic
342C2×C4×C8C22×C4711yescharacteristic
343#400—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#391C22×C4711yescharacteristic
348#391C22×C4711yescharacteristic
349#389—21no—
350#389—21no—
351#389C22×C4711yescharacteristic
352#389C22×C4711yescharacteristic
353#389C22×C4711yescharacteristic
354#389C22×C4711yescharacteristic
355#389C22×C4711yescharacteristic
356#389C22×C4711yescharacteristic
357#380—21no—
358#380—21no—
359#380C22×C4711yescharacteristic
360#340C22×C4711yescharacteristic
361#340C22×C4711yescharacteristic
362#340C22×C4711yescharacteristic
363#340C22×C4711yescharacteristic
364#340C22×C4711yescharacteristic
365#340C22×C4711yescharacteristic
366#340C22×C4711yescharacteristic
367#340C22×C4711yescharacteristic
368C47#2461911yescharacteristic, direct product factor, Sylow
369C22×Q8C23×C4711yescharacteristic
370C23×C4—21no—
371C23×C4C23×C4711yescharacteristic
372C22×C8C23×C4711yescharacteristic
373C22×C8C23×C4711yescharacteristic
374C22×C8C23×C4711yescharacteristic
375C22×C8C23×C4711yescharacteristic
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378#117—22no—
379#117—22no—
380#117—22no—
381#117—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
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⋊C4—21no—
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⋊C4D4×C4711yescharacteristic
405C2×C22⋊C4D4×C4711yescharacteristic
406C2×C42—21no—
407C2×C42C23×C4711yescharacteristic
408C2×C42C23×C4711yescharacteristic
409#107—22no—
410#106—22no—
411#106—22no—
412#106—22no—
413C4⋊C8—22no—
414C4⋊C8—22no—
415#103—22no—
416#103—22no—
417#103—22no—
418#103—22no—
419C22⋊C8—22no—
420C22⋊C8D4×C4714yes—
421#97—22no—
422C4×C8—22no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434C24C2×D4×C4711yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4C2×D4×C4711yescharacteristic
457C22×C4C2×D4×C4711yescharacteristic
458C22×C4C2×D4×C4711yescharacteristic
459C22×C4C2×D4×C4711yescharacteristic
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4C2×D4×C4712yes—
462C22×C4#41×C4712yes—
463C22×C4C24×C4711yescharacteristic
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8C2×D4×C4712yes—
475C2×C8C2×D4×C4712yes—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4#41×C4712yes—
499C4⋊C4#41×C4712yes—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—42no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23#121×C4712yes—
517C23C22×D4×C4711yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
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—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4#121×C4712yes—
566C2×C4C22×D4×C4711yescharacteristic
567C2×C4C2×#41×C4711yescharacteristic
568C2×C4C2×#41×C4711yescharacteristic
569C2×C4C2×#41×C4711yescharacteristic
570C2×C42−1+4×C4711yescharacteristic
571C2×C42−1+4×C4711yescharacteristic
572C8—22no—
573C8—22no—
574C8—41no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×#121×C4711yescharacteristic
584C22C47×#52511yescharacteristic
585C22C47×#53611yescharacteristic
586C22C47×#57711yescharacteristic
587C22C47×#57711yescharacteristic
588C22C47×#57711yescharacteristic
589C22C47×#57811yescharacteristic
590C4—22no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C47×#54711yescharacteristic
604C4C47×#54711yescharacteristic
605C4C47×#55211yescharacteristic
606C4C47×#55211yescharacteristic
607C2—42no—
608C2C47×#241311yescharacteristic
609C2C47×#306011yescharacteristic
610C2C47×#306311yescharacteristic
611C2C47×#312111yescharacteristic
612C2C47×#312311yescharacteristic
613C2C47×#324211yescharacteristic
614C2C47×#324411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
5. C47×#2088C2semidirect
6. C47×#2087C2semidirect
7. C47×#2066C2semidirect
8. C47×#2066C2semidirect
9. C47×#1944C2semidirect
10. C47×#1941C2semidirect
11. C47×#1935C2semidirect
12. C47×#1933C2semidirect
268. #24619C47direct (N × H)
304. #2088C2×C47semidirect
305. #2087C2×C47semidirect
306. #2066C2×C47semidirect
307. #2066C2×C47semidirect
308. #1944C2×C47semidirect
309. #1941C2×C47semidirect
310. #1935C2×C47semidirect
311. #1933C2×C47semidirect
368. C47#24619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4852
C2×C47×#4332
C47×#26252
C47×#23162
C47×#20882
C47×#20872
C47×#20662
C47×#19442
C47×#19412
C47×#19352
C47×#19332
C47×#18722
C47×#18532
C47×#18252
#2461947