Finite Group Databasebeta

← C47×#29463 #26069161

Subgroups — C47×#29463 #26069161

Order 12032.

766 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2855C211yesmaximal, characteristic
2C4×C22⋊Q8×C47C211yesmaximal, characteristic
3C47×#2075C211yesmaximal, characteristic
4C47×#2035C211yesmaximal, characteristic
5C47×#2035C211yesmaximal, characteristic
6C47×#2001C211yesmaximal, characteristic
7C47×#1969C211yesmaximal, characteristic, complemented
8C47×#1941C211yesmaximal, characteristic, complemented
9C47×#1933C211yesmaximal, characteristic, complemented
10C47×#1933C211yesmaximal, characteristic, complemented
11C47×#1927C211yesmaximal, characteristic, complemented
12C47×#1918C211yesmaximal, characteristic, complemented
13C47×#1878C211yesmaximal, characteristic, complemented
14C47×#1865C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C47C211yesmaximal, characteristic
16C22×Q16×C47C2211yescharacteristic
17C2×C22⋊Q8×C47C2211yescharacteristic
18C2×C22⋊Q8×C47C2211yescharacteristic
19C2×C4×Q8×C47C2211yescharacteristic
20C22×C42×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#103×C47C2211yescharacteristic
25C2×#103×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#103×C47C2211yescharacteristic
28C2×#103×C47C2211yescharacteristic
29C2×#103×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C4×C8×C47C2211yescharacteristic
33C2×C4×C8×C47C2211yescharacteristic
34C47×#391C2211yescharacteristic
35C47×#391C2211yescharacteristic
36C47×#391C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#389C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#387—21no—
41C47×#387—21no—
42C47×#387—21no—
43C47×#385—21no—
44C47×#385—21no—
45C47×#381—21no—
46C47×#380C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C4×C4⋊C4×C47—21no—
49C4×C4⋊C4×C47C2211yescharacteristic
50C4×C22⋊C4×C47—21no—
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47C2311yescharacteristic
60C22×Q8×C47C2311yescharacteristic
61C23×C4×C47D411yescharacteristic
62C23×C4×C47D411yescharacteristic
63C23×C4×C47C2311yescharacteristic
64C2×Q16×C47—22no—
65C2×Q16×C47—22no—
66C2×Q16×C47—41no—
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22⋊Q8×C47—22no—
72C22⋊Q8×C47—22no—
73C22⋊Q8×C47—41no—
74C22⋊Q8×C47—41no—
75C4×Q8×C47—41no—
76C4×Q8×C47—41no—
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×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47C2311yescharacteristic
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C42×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—41no—
96C2×C42×C47—41no—
97C2×C42×C47D411yescharacteristic
98C2×C42×C47D411yescharacteristic
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101#107×C47—22no—
102#106×C47—22no—
103#106×C47—41no—
104#103×C47—22no—
105#103×C47—22no—
106#103×C47—22no—
107#103×C47—22no—
108#103×C47—41no—
109#103×C47—41no—
110C22⋊C8×C47—22no—
111C22⋊C8×C47—22no—
112C4×C8×C47—41no—
113C4×C8×C47—41no—
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×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—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—21no—
138C2×Q8×C47#4112yes—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—41no—
158C22×C4×C47—41no—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2411yescharacteristic
165Q16×C47—44no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C2×C8×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47#4112yes—
177C2×C8×C47#4112yes—
178C4⋊C4×C47—24no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—42no—
191C4⋊C4×C47—42no—
192C4⋊C4×C47—42no—
193C4⋊C4×C47—42no—
194C4⋊C4×C47—42no—
195C4⋊C4×C47#4112yes—
196C22⋊C4×C47—24no—
197C22⋊C4×C47—42no—
198C22⋊C4×C47—42no—
199C22⋊C4×C47—42no—
200C42×C47—21no—
201C42×C47—21no—
202C42×C47—21no—
203C42×C47—21no—
204C42×C47—41no—
205C42×C47—41no—
206C42×C47—42no—
207C42×C47—42no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47#13512yes—
215C23×C47C22×D411yescharacteristic
216Q8×C47—22no—
217Q8×C47—22no—
218Q8×C47—41no—
219Q8×C47—41no—
220Q8×C47—41no—
221Q8×C47—41no—
222Q8×C47—41no—
223Q8×C47—41no—
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—22no—
231C2×C4×C47—22no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—44no—
239C2×C4×C47—44no—
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—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47#13512yes—
267C2×C4×C47#13712yes—
268C2×C4×C47#13712yes—
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C47C2×#4111yescharacteristic
271C2×C4×C47C2×#4111yescharacteristic
272C2×C4×C47C2×#4111yescharacteristic
273C2×C4×C47H(5,𝔽2)11yescharacteristic
274C2×C4×C47H(5,𝔽2)11yescharacteristic
275C8×C47—22no—
276C8×C47—22no—
277C8×C47—41no—
278C8×C47—41no—
279#29463C4711yesmaximal, characteristic, direct product factor, Sylow
280C22×C47—22no—
281C22×C47—22no—
282C22×C47—22no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47#52511yescharacteristic
288C22×C47#53211yescharacteristic
289C22×C47#53411yescharacteristic
290C22×C47C2×#13511yescharacteristic
291C22×C47C2×#13511yescharacteristic
292C22×C47C2×#13711yescharacteristic
293C22×C47C2×#13711yescharacteristic
294C4×C47—22no—
295C4×C47—22no—
296C4×C47—22no—
297C4×C47—42no—
298C4×C47—41no—
299C4×C47—42no—
300C4×C47—41no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47—81no—
304C4×C47—81no—
305C4×C47—81no—
306C4×C47—81no—
307C4×C47#55111yescharacteristic
308C4×C47#55311yescharacteristic
309C4×C47#55311yescharacteristic
310C4×C47#55911yescharacteristic
311#2855C2×C4711yescharacteristic
312C4×C22⋊Q8C2×C4711yescharacteristic
313#2075C2×C4711yescharacteristic
314#2035C2×C4711yescharacteristic
315#2035C2×C4711yescharacteristic
316#2001C2×C4711yescharacteristic
317#1969C2×C4711yescharacteristic, complemented
318#1941C2×C4711yescharacteristic, complemented
319#1933C2×C4711yescharacteristic, complemented
320#1933C2×C4711yescharacteristic, complemented
321#1927C2×C4711yescharacteristic, complemented
322#1918C2×C4711yescharacteristic, complemented
323#1878C2×C4711yescharacteristic, complemented
324#1865C2×C4711yescharacteristic, complemented
325C4×C22⋊C8C2×C4711yescharacteristic
326C2×C47—42no—
327C2×C47#260211yescharacteristic
328C2×C47#310711yescharacteristic
329C2×C47#310811yescharacteristic
330C2×C47#316811yescharacteristic
331C2×C47#318511yescharacteristic
332C2×C47#319011yescharacteristic
333C2×C47#319011yescharacteristic
334C22×Q16C22×C4711yescharacteristic
335C2×C22⋊Q8C22×C4711yescharacteristic
336C2×C22⋊Q8C22×C4711yescharacteristic
337C2×C4×Q8C22×C4711yescharacteristic
338C22×C42C22×C4711yescharacteristic
339C2×#107C22×C4711yescharacteristic
340C2×#106C22×C4711yescharacteristic
341C2×#106C22×C4711yescharacteristic
342C2×#103C22×C4711yescharacteristic
343C2×#103C22×C4711yescharacteristic
344C2×#103C22×C4711yescharacteristic
345C2×#103C22×C4711yescharacteristic
346C2×#103C22×C4711yescharacteristic
347C2×#103C22×C4711yescharacteristic
348C2×C22⋊C8C22×C4711yescharacteristic
349C2×C22⋊C8C22×C4711yescharacteristic
350C2×C4×C8C22×C4711yescharacteristic
351C2×C4×C8C22×C4711yescharacteristic
352#391C22×C4711yescharacteristic
353#391C22×C4711yescharacteristic
354#391C22×C4711yescharacteristic
355#389C22×C4711yescharacteristic
356#389C22×C4711yescharacteristic
357#389C22×C4711yescharacteristic
358#387—21no—
359#387—21no—
360#387—21no—
361#385—21no—
362#385—21no—
363#381—21no—
364#380C22×C4711yescharacteristic
365#380C22×C4711yescharacteristic
366C4×C4⋊C4—21no—
367C4×C4⋊C4C22×C4711yescharacteristic
368C4×C22⋊C4—21no—
369#340C22×C4711yescharacteristic
370#340C22×C4711yescharacteristic
371#340C22×C4711yescharacteristic
372#340C22×C4711yescharacteristic
373#340C22×C4711yescharacteristic
374#340C22×C4711yescharacteristic
375#336C22×C4711yescharacteristic
376#336C22×C4711yescharacteristic
377C47#2946311yescharacteristic, direct product factor, Sylow
378C22×Q8C23×C4711yescharacteristic
379C22×Q8C23×C4711yescharacteristic
380C23×C4D4×C4711yescharacteristic
381C23×C4D4×C4711yescharacteristic
382C23×C4C23×C4711yescharacteristic
383C2×Q16—22no—
384C2×Q16—22no—
385C2×Q16—41no—
386C22×C8C23×C4711yescharacteristic
387C22×C8C23×C4711yescharacteristic
388C22×C8C23×C4711yescharacteristic
389C22×C8C23×C4711yescharacteristic
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—41no—
393C22⋊Q8—41no—
394C4×Q8—41no—
395C4×Q8—41no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4C23×C4711yescharacteristic
403C2×C4⋊C4C23×C4711yescharacteristic
404C2×C4⋊C4C23×C4711yescharacteristic
405C2×C4⋊C4C23×C4711yescharacteristic
406C2×C4⋊C4C23×C4711yescharacteristic
407C2×C4⋊C4C23×C4711yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—41no—
415C2×C42—41no—
416C2×C42D4×C4711yescharacteristic
417C2×C42D4×C4711yescharacteristic
418C2×C42C23×C4711yescharacteristic
419C2×C42C23×C4711yescharacteristic
420#107—22no—
421#106—22no—
422#106—41no—
423#103—22no—
424#103—22no—
425#103—22no—
426#103—22no—
427#103—41no—
428#103—41no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C4×C8—41no—
432C4×C8—41no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445C24C2×D4×C4711yescharacteristic
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8#41×C4712yes—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4C2×D4×C4711yescharacteristic
479C22×C4C2×D4×C4711yescharacteristic
480C22×C4C2×D4×C4711yescharacteristic
481C22×C4C2×D4×C4711yescharacteristic
482C22×C4C2×D4×C4711yescharacteristic
483C22×C4C24×C4711yescharacteristic
484Q16—44no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8#41×C4712yes—
496C2×C8#41×C4712yes—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4#41×C4712yes—
515C22⋊C4—24no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—41no—
524C42—41no—
525C42—42no—
526C42—42no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23#135×C4712yes—
534C23C22×D4×C4711yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4#135×C4712yes—
586C2×C4#137×C4712yes—
587C2×C4#137×C4712yes—
588C2×C4C2×#41×C4711yescharacteristic
589C2×C4C2×#41×C4711yescharacteristic
590C2×C4C2×#41×C4711yescharacteristic
591C2×C4C2×#41×C4711yescharacteristic
592C2×C4H(5,𝔽2)×C4711yescharacteristic
593C2×C4H(5,𝔽2)×C4711yescharacteristic
594C8—22no—
595C8—22no—
596C8—41no—
597C8—41no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22C47×#52511yescharacteristic
606C22C47×#53211yescharacteristic
607C22C47×#53411yescharacteristic
608C22C2×#135×C4711yescharacteristic
609C22C2×#135×C4711yescharacteristic
610C22C2×#137×C4711yescharacteristic
611C22C2×#137×C4711yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4C47×#55111yescharacteristic
626C4C47×#55311yescharacteristic
627C4C47×#55311yescharacteristic
628C4C47×#55911yescharacteristic
629C2—42no—
630C2C47×#260211yescharacteristic
631C2C47×#310711yescharacteristic
632C2C47×#310811yescharacteristic
633C2C47×#316811yescharacteristic
634C2C47×#318511yescharacteristic
635C2C47×#319011yescharacteristic
636C2C47×#319011yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
7. C47×#1969C2semidirect
8. C47×#1941C2semidirect
9. C47×#1933C2semidirect
10. C47×#1933C2semidirect
11. C47×#1927C2semidirect
12. C47×#1918C2semidirect
13. C47×#1878C2semidirect
14. C47×#1865C2semidirect
279. #29463C47direct (N × H)
317. #1969C2×C47semidirect
318. #1941C2×C47semidirect
319. #1933C2×C47semidirect
320. #1933C2×C47semidirect
321. #1927C2×C47semidirect
322. #1918C2×C47semidirect
323. #1878C2×C47semidirect
324. #1865C2×C47semidirect
377. C47#29463direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28552
C4×C22⋊Q8×C472
C47×#20752
C47×#20352
C47×#20012
C47×#19692
C47×#19412
C47×#19332
C47×#19272
C47×#19182
C47×#18782
C47×#18652
C4×C22⋊C8×C472
#2946347