Finite Group Databasebeta

← C47×#22945 #26062643

Subgroups — C47×#22945 #26062643

Order 12032.

818 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×#483C211yesmaximal, characteristic
2C47×#2362C211yesmaximal, characteristic
3C47×#2345C211yesmaximal, characteristic
4C47×#1944C211yesmaximal, characteristic, complemented
5C47×#1933C211yesmaximal, characteristic, complemented
6C47×#1928C211yesmaximal, characteristic, complemented
7C47×#1920C211yesmaximal, characteristic, complemented
8C47×#1920C211yesmaximal, characteristic, complemented
9C47×#1894C211yesmaximal, characteristic
10C47×#1865C211yesmaximal, characteristic, complemented
11C47×#1854C211yesmaximal, characteristic
12C4×#106×C47C211yesmaximal, characteristic, complemented
13C47×#1763C211yesmaximal, characteristic, complemented
14C47×#1753C211yesmaximal, characteristic
15C47×#1736C211yesmaximal, characteristic
16C22×M16×C47C2211yescharacteristic
17C2×C22⋊Q8×C47C2211yescharacteristic
18C2×C4×Q8×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C47×#483C418yescomplemented
22C2×#107×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×#97×C47C2211yescharacteristic
32C2×C4×C8×C47C2211yescharacteristic
33C47×#391C2211yescharacteristic
34C47×#389C2211yescharacteristic
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#388—21no—
38C47×#388—21no—
39C47×#387—21no—
40C47×#387—21no—
41C47×#387—21no—
42C47×#380—21no—
43C47×#380C2211yescharacteristic
44C4×C4⋊C4×C47—21no—
45C4×C4⋊C4×C47C2211yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C22⋊C4×C47—21no—
49C4×C22⋊C4×C47C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C22×Q8×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C23×C4×C47C2311yescharacteristic
63C2×M16×C47—22no—
64C2×M16×C47—22no—
65C2×M16×C47—41no—
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22⋊Q8×C47—22no—
71C22⋊Q8×C47C2×C414yes—
72C4×Q8×C47—22no—
73C4×Q8×C47—41no—
74#117×C47—22no—
75#117×C47—41no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47C2×C414yes—
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47D411yescharacteristic
95C2×C22⋊C4×C47D411yescharacteristic
96C2×C42×C47—21no—
97C2×C42×C47—21no—
98C2×C42×C47—21no—
99C2×C42×C47—21no—
100C2×C42×C47—21no—
101C2×C42×C47C2311yescharacteristic
102C2×C42×C47C2311yescharacteristic
103#107×C47—41no—
104#106×C47—22no—
105#106×C47C2×C414yes—
106#106×C47C2×C414yes—
107#103×C47—22no—
108#103×C47—41no—
109#103×C47C2×C414yes—
110#103×C47C2×C414yes—
111C22⋊C8×C47C2×C414yes—
112#97×C47—41no—
113C4×C8×C47—22no—
114#95×C47—21no—
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×C47D411yescharacteristic
124#95×C47D411yescharacteristic
125C24×C47C2×D411yescharacteristic
126C2×Q8×C47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47C22×C412yes—
132C22×C4×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—21no—
140C22×C4×C47—21no—
141C22×C4×C47—24no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—81no—
146C22×C4×C47—81no—
147C22×C4×C47C22×C412yes—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4112yes—
154C22×C4×C47C2411yescharacteristic
155M16×C47—44no—
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×C47C22×C412yes—
166C2×C8×C47C22×C412yes—
167C2×C8×C47#4112yes—
168C4⋊C4×C47—24no—
169C4⋊C4×C47—24no—
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—21no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—42no—
182C4⋊C4×C47—81no—
183C4⋊C4×C47—81no—
184C4⋊C4×C47C22×C412yes—
185C4⋊C4×C47C22×C412yes—
186C4⋊C4×C47C22×C412yes—
187C4⋊C4×C47#4112yes—
188C22⋊C4×C47—24no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—41no—
191C22⋊C4×C47—42no—
192C22⋊C4×C47—42no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—42no—
198C42×C47—42no—
199C42×C47—42no—
200C42×C47—81no—
201C42×C47—81no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47C4×D412yes—
209C23×C47C22×D411yescharacteristic
210Q8×C47—22no—
211Q8×C47—22no—
212Q8×C47—41no—
213Q8×C47—41no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—22no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
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—84no—
256C2×C4×C47C4×D412yes—
257C2×C4×C47#13712yes—
258C2×C4×C47C23×C411yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47H(5,𝔽2)11yescharacteristic
263C2×C4×C472−1+411yescharacteristic
264C8×C47—22no—
265C8×C47—22no—
266C8×C47—22no—
267C8×C47—41no—
268#22945C4711yesmaximal, 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×C4×D411yescharacteristic
277C22×C47#54611yescharacteristic
278C22×C47#54711yescharacteristic
279C22×C47C2×#13711yescharacteristic
280C22×C47#57511yescharacteristic
281C22×C47#57711yescharacteristic
282C22×C47#57711yescharacteristic
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—41no—
286C4×C47—42no—
287C4×C47—41no—
288C4×C47—42no—
289C4×C47—42no—
290C4×C47—42no—
291C4×C47—42no—
292C4×C47—41no—
293C4×C47—81no—
294C4×C47—81no—
295C4×C47—81no—
296C4×C47C4×#4111yescharacteristic
297C4×C47#52011yescharacteristic
298C4×C47#55111yescharacteristic
299C4×C47#55211yescharacteristic
300C2×#483C2×C4711yescharacteristic
301#2362C2×C4711yescharacteristic
302#2345C2×C4711yescharacteristic
303#1944C2×C4711yescharacteristic, complemented
304#1933C2×C4711yescharacteristic, complemented
305#1928C2×C4711yescharacteristic, complemented
306#1920C2×C4711yescharacteristic, complemented
307#1920C2×C4711yescharacteristic, complemented
308#1894C2×C4711yescharacteristic
309#1865C2×C4711yescharacteristic, complemented
310#1854C2×C4711yescharacteristic
311C4×#106C2×C4711yescharacteristic, complemented
312#1763C2×C4711yescharacteristic, complemented
313#1753C2×C4711yescharacteristic
314#1736C2×C4711yescharacteristic
315C2×C47—42no—
316C2×C47#235911yescharacteristic
317C2×C47C4×#13711yescharacteristic
318C2×C47#294911yescharacteristic
319C2×C47#332611yescharacteristic
320C2×C47#333111yescharacteristic
321C2×C47#334411yescharacteristic
322C2×C47#335011yescharacteristic
323C22×M16C22×C4711yescharacteristic
324C2×C22⋊Q8C22×C4711yescharacteristic
325C2×C4×Q8C22×C4711yescharacteristic
326C2×#117C22×C4711yescharacteristic
327C22×C4⋊C4C22×C4711yescharacteristic
328#483C4×C4718yescomplemented
329C2×#107C22×C4711yescharacteristic
330C2×#106C22×C4711yescharacteristic
331C2×#106C22×C4711yescharacteristic
332C2×#106C22×C4711yescharacteristic
333C2×#103C22×C4711yescharacteristic
334C2×#103C22×C4711yescharacteristic
335C2×#103C22×C4711yescharacteristic
336C2×#103C22×C4711yescharacteristic
337C2×C22⋊C8C22×C4711yescharacteristic
338C2×#97C22×C4711yescharacteristic
339C2×C4×C8C22×C4711yescharacteristic
340#391C22×C4711yescharacteristic
341#389C22×C4711yescharacteristic
342#389C22×C4711yescharacteristic
343#389C22×C4711yescharacteristic
344#388—21no—
345#388—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#380—21no—
350#380C22×C4711yescharacteristic
351C4×C4⋊C4—21no—
352C4×C4⋊C4C22×C4711yescharacteristic
353C4×C4⋊C4C22×C4711yescharacteristic
354C4×C4⋊C4C22×C4711yescharacteristic
355C4×C22⋊C4—21no—
356C4×C22⋊C4C22×C4711yescharacteristic
357#340C22×C4711yescharacteristic
358#340C22×C4711yescharacteristic
359#340C22×C4711yescharacteristic
360#340C22×C4711yescharacteristic
361#340C22×C4711yescharacteristic
362#340C22×C4711yescharacteristic
363#340C22×C4711yescharacteristic
364#340C22×C4711yescharacteristic
365#336C22×C4711yescharacteristic
366#336C22×C4711yescharacteristic
367C47#2294511yescharacteristic, direct product factor, Sylow
368C22×Q8C23×C4711yescharacteristic
369C23×C4—21no—
370C23×C4C23×C4711yescharacteristic
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—41no—
374C22×C8C23×C4711yescharacteristic
375C22×C8C23×C4711yescharacteristic
376C22×C8C23×C4711yescharacteristic
377C22×C8C23×C4711yescharacteristic
378C22⋊Q8—22no—
379C22⋊Q8C2×C4×C4714yes—
380C4×Q8—22no—
381C4×Q8—41no—
382#117—22no—
383#117—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C2×C4×C4714yes—
392C2×C4⋊C4C23×C4711yescharacteristic
393C2×C4⋊C4C23×C4711yescharacteristic
394C2×C4⋊C4C23×C4711yescharacteristic
395C2×C4⋊C4C23×C4711yescharacteristic
396C2×C4⋊C4C23×C4711yescharacteristic
397C2×C4⋊C4C23×C4711yescharacteristic
398C2×C4⋊C4C23×C4711yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4D4×C4711yescharacteristic
403C2×C22⋊C4D4×C4711yescharacteristic
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C23×C4711yescharacteristic
410C2×C42C23×C4711yescharacteristic
411#107—41no—
412#106—22no—
413#106C2×C4×C4714yes—
414#106C2×C4×C4714yes—
415#103—22no—
416#103—41no—
417#103C2×C4×C4714yes—
418#103C2×C4×C4714yes—
419C22⋊C8C2×C4×C4714yes—
420#97—41no—
421C4×C8—22no—
422#95—21no—
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#95D4×C4711yescharacteristic
432#95D4×C4711yescharacteristic
433C24C2×D4×C4711yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C22×C4×C4712yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C22×C4×C4712yes—
456C22×C4C2×D4×C4711yescharacteristic
457C22×C4C2×D4×C4711yescharacteristic
458C22×C4C2×D4×C4711yescharacteristic
459C22×C4C2×D4×C4711yescharacteristic
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4#41×C4712yes—
462C22×C4C24×C4711yescharacteristic
463M16—44no—
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×C8C22×C4×C4712yes—
474C2×C8C22×C4×C4712yes—
475C2×C8#41×C4712yes—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—21no—
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—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4C22×C4×C4712yes—
493C4⋊C4C22×C4×C4712yes—
494C4⋊C4C22×C4×C4712yes—
495C4⋊C4#41×C4712yes—
496C22⋊C4—24no—
497C22⋊C4—22no—
498C22⋊C4—41no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—42no—
507C42—42no—
508C42—81no—
509C42—81no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C4×D4×C4712yes—
517C23C22×D4×C4711yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
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—84no—
564C2×C4C4×D4×C4712yes—
565C2×C4#137×C4712yes—
566C2×C4C23×C4×C4711yescharacteristic
567C2×C4C2×#41×C4711yescharacteristic
568C2×C4C2×#41×C4711yescharacteristic
569C2×C4C2×#41×C4711yescharacteristic
570C2×C4H(5,𝔽2)×C4711yescharacteristic
571C2×C42−1+4×C4711yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—41no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×C4×D4×C4711yescharacteristic
584C22C47×#54611yescharacteristic
585C22C47×#54711yescharacteristic
586C22C2×#137×C4711yescharacteristic
587C22C47×#57511yescharacteristic
588C22C47×#57711yescharacteristic
589C22C47×#57711yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4C4×#41×C4711yescharacteristic
604C4C47×#52011yescharacteristic
605C4C47×#55111yescharacteristic
606C4C47×#55211yescharacteristic
607C2—42no—
608C2C47×#235911yescharacteristic
609C2C4×#137×C4711yescharacteristic
610C2C47×#294911yescharacteristic
611C2C47×#332611yescharacteristic
612C2C47×#333111yescharacteristic
613C2C47×#334411yescharacteristic
614C2C47×#335011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
4. C47×#1944C2semidirect
5. C47×#1933C2semidirect
6. C47×#1928C2semidirect
7. C47×#1920C2semidirect
8. C47×#1920C2semidirect
10. C47×#1865C2semidirect
12. C4×#106×C47C2semidirect
13. C47×#1763C2semidirect
21. C47×#483C4semidirect
268. #22945C47direct (N × H)
303. #1944C2×C47semidirect
304. #1933C2×C47semidirect
305. #1928C2×C47semidirect
306. #1920C2×C47semidirect
307. #1920C2×C47semidirect
309. #1865C2×C47semidirect
311. C4×#106C2×C47semidirect
312. #1763C2×C47semidirect
328. #483C4×C47semidirect
367. C47#22945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4832
C47×#23622
C47×#23452
C47×#19442
C47×#19332
C47×#19282
C47×#19202
C47×#18942
C47×#18652
C47×#18542
C4×#106×C472
C47×#17632
C47×#17532
C47×#17362
#2294547