Finite Group Databasebeta

← C47×#25992 #26065690

Subgroups — C47×#25992 #26065690

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2440C211yesmaximal, characteristic
2C47×#2345C211yesmaximal, characteristic
3C47×#2099C211yesmaximal, characteristic, complemented
4C47×#2088C211yesmaximal, characteristic, complemented
5C47×#2088C211yesmaximal, characteristic, complemented
6C47×#2058C211yesmaximal, characteristic, complemented
7C47×#1988C211yesmaximal, characteristic, complemented
8C47×#1948C211yesmaximal, characteristic, complemented
9C47×#1919C211yesmaximal, characteristic, complemented
10C47×#1919C211yesmaximal, characteristic, complemented
11C47×#1853C211yesmaximal, characteristic
12C47×#1850C211yesmaximal, characteristic
13C47×#1824C211yesmaximal, characteristic
14C47×#1807C211yesmaximal, characteristic
15C2×C47×#340C211yesmaximal, characteristic
16C23×C8×C47C2211yescharacteristic
17C2×C4⋊Q8×C47C2211yescharacteristic
18C2×C22⋊Q8×C47—21no—
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C22⋊C8×C47C2211yescharacteristic
28C47×#398—21no—
29C47×#395—21no—
30C47×#389C2211yescharacteristic
31C47×#389C2211yescharacteristic
32C47×#389C2211yescharacteristic
33C47×#389C2211yescharacteristic
34C47×#387—21no—
35C47×#387—21no—
36C47×#385—21no—
37C47×#384C2211yescharacteristic
38C47×#380—21no—
39C47×#380C2211yescharacteristic
40C47×#380C2211yescharacteristic
41C4×C4⋊C4×C47C2211yescharacteristic
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C22⋊C4×C47—21no—
44C4×C22⋊C4×C47C2211yescharacteristic
45C47×#340C2211yescharacteristic
46C47×#340C2211yescharacteristic
47C47×#340C2211yescharacteristic
48C47×#340C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47—21no—
60C23×C4×C47—21no—
61C23×C4×C47—21no—
62C23×C4×C47C2311yescharacteristic
63C22×C8×C47—22no—
64C22×C8×C47—22no—
65C22×C8×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—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—22no—
75C2×C4⋊C4×C47—22no—
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—41no—
85C2×C4⋊C4×C47Q814yescomplemented
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×C4⋊C4×C47C2311yescharacteristic
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47D411yescharacteristic
97C2×C22⋊C4×C47D411yescharacteristic
98C2×C42×C47—21no—
99C2×C42×C47—21no—
100C2×C42×C47C2311yescharacteristic
101C2×C42×C47C2311yescharacteristic
102#106×C47—22no—
103#106×C47—22no—
104#106×C47—41no—
105#106×C47—41no—
106C4⋊C8×C47—22no—
107C4⋊C8×C47—41no—
108C22⋊C8×C47—22no—
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×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119C24×C47C2×D411yescharacteristic
120C2×Q8×C47—42no—
121C2×Q8×C47—42no—
122C2×Q8×C47—81no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—24no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—42no—
137C22×C4×C47—42no—
138C22×C4×C47—81no—
139C22×C4×C47—81no—
140C22×C4×C47—81no—
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×Q812yes—
147C22×C4×C47#4112yes—
148C22×C4×C47C2411yescharacteristic
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
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—44no—
161C2×C8×C47#4112yes—
162C4⋊C4×C47—24no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
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—42no—
177C4⋊C4×C47—42no—
178C4⋊C4×C47—42no—
179C4⋊C4×C47—42no—
180C4⋊C4×C47—42no—
181C4⋊C4×C47—81no—
182C4⋊C4×C47—81no—
183C4⋊C4×C47—81no—
184C4⋊C4×C47C2×Q812yes—
185C4⋊C4×C47C2×Q812yes—
186C4⋊C4×C47#4112yes—
187C22⋊C4×C47—22no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—42no—
190C22⋊C4×C47SD1614yes—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—81no—
196C42×C47—81no—
197C23×C47—21no—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47C22⋊Q812yes—
202C23×C47C2×SD1612yes—
203C23×C47#13712yes—
204C23×C47C22×D411yescharacteristic
205Q8×C47—84no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
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—84no—
247C2×C4×C47—84no—
248C2×C4×C47C22⋊Q812yes—
249C2×C4×C47C2×SD1612yes—
250C2×C4×C47C2×SD1612yes—
251C2×C4×C47C22×Q811yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47H(5,𝔽2)11yescharacteristic
256C2×C4×C472−1+411yescharacteristic
257C8×C47—22no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261#25992C4711yesmaximal, characteristic, direct product factor, Sylow
262C22×C47—22no—
263C22×C47—22no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47#47514yes—
269C22×C47C2×C22⋊Q811yescharacteristic
270C22×C47#54611yescharacteristic
271C22×C47#54711yescharacteristic
272C22×C47C22×SD1611yescharacteristic
273C22×C47C2×#13711yescharacteristic
274C22×C47#57611yescharacteristic
275C22×C47#57711yescharacteristic
276C4×C47—22no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—42no—
280C4×C47—42no—
281C4×C47—41no—
282C4×C47—42no—
283C4×C47—41no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47#53311yescharacteristic
290C4×C47#54411yescharacteristic
291C4×C47#55111yescharacteristic
292C4×C47#55211yescharacteristic
293#2440C2×C4711yescharacteristic
294#2345C2×C4711yescharacteristic
295#2099C2×C4711yescharacteristic, complemented
296#2088C2×C4711yescharacteristic, complemented
297#2088C2×C4711yescharacteristic, complemented
298#2058C2×C4711yescharacteristic, complemented
299#1988C2×C4711yescharacteristic, complemented
300#1948C2×C4711yescharacteristic, complemented
301#1919C2×C4711yescharacteristic, complemented
302#1919C2×C4711yescharacteristic, complemented
303#1853C2×C4711yescharacteristic
304#1850C2×C4711yescharacteristic
305#1824C2×C4711yescharacteristic
306#1807C2×C4711yescharacteristic
307C2×#340C2×C4711yescharacteristic
308C2×C47—24no—
309C2×C47#243811yescharacteristic
310C2×C47C2×#47511yescharacteristic
311C2×C47#308111yescharacteristic
312C2×C47#329511yescharacteristic
313C2×C47#332011yescharacteristic
314C2×C47#333511yescharacteristic
315C2×C47#334611yescharacteristic
316C23×C8C22×C4711yescharacteristic
317C2×C4⋊Q8C22×C4711yescharacteristic
318C2×C22⋊Q8—21no—
319C22×C4⋊C4C22×C4711yescharacteristic
320C22×C4⋊C4C22×C4711yescharacteristic
321C2×#106C22×C4711yescharacteristic
322C2×#106C22×C4711yescharacteristic
323C2×#106C22×C4711yescharacteristic
324C2×#106C22×C4711yescharacteristic
325C2×C4⋊C8C22×C4711yescharacteristic
326C2×C4⋊C8C22×C4711yescharacteristic
327C2×C22⋊C8C22×C4711yescharacteristic
328#398—21no—
329#395—21no—
330#389C22×C4711yescharacteristic
331#389C22×C4711yescharacteristic
332#389C22×C4711yescharacteristic
333#389C22×C4711yescharacteristic
334#387—21no—
335#387—21no—
336#385—21no—
337#384C22×C4711yescharacteristic
338#380—21no—
339#380C22×C4711yescharacteristic
340#380C22×C4711yescharacteristic
341C4×C4⋊C4C22×C4711yescharacteristic
342C4×C4⋊C4C22×C4711yescharacteristic
343C4×C22⋊C4—21no—
344C4×C22⋊C4C22×C4711yescharacteristic
345#340C22×C4711yescharacteristic
346#340C22×C4711yescharacteristic
347#340C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#340C22×C4711yescharacteristic
355#340C22×C4711yescharacteristic
356#340C22×C4711yescharacteristic
357#336C22×C4711yescharacteristic
358#336C22×C4711yescharacteristic
359C47#2599211yescharacteristic, direct product factor, Sylow
360C22×Q8—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C23×C4711yescharacteristic
364C22×C8—22no—
365C22×C8—22no—
366C22×C8—41no—
367C22×C8C23×C4711yescharacteristic
368C22×C8C23×C4711yescharacteristic
369C22×C8C23×C4711yescharacteristic
370C22×C8C23×C4711yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C22⋊Q8—44no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4Q8×C4714yescomplemented
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C4⋊C4C23×C4711yescharacteristic
390C2×C4⋊C4C23×C4711yescharacteristic
391C2×C4⋊C4C23×C4711yescharacteristic
392C2×C4⋊C4C23×C4711yescharacteristic
393C2×C4⋊C4C23×C4711yescharacteristic
394C2×C4⋊C4C23×C4711yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4D4×C4711yescharacteristic
398C2×C22⋊C4D4×C4711yescharacteristic
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C4711yescharacteristic
402C2×C42C23×C4711yescharacteristic
403#106—22no—
404#106—22no—
405#106—41no—
406#106—41no—
407C4⋊C8—22no—
408C4⋊C8—41no—
409C22⋊C8—22no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C4711yescharacteristic
419#95D4×C4711yescharacteristic
420C24C2×D4×C4711yescharacteristic
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—81no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—81no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4C2×D4×C4711yescharacteristic
443C22×C4C2×D4×C4711yescharacteristic
444C22×C4C2×D4×C4711yescharacteristic
445C22×C4C2×D4×C4711yescharacteristic
446C22×C4C2×D4×C4711yescharacteristic
447C22×C4C2×Q8×C4712yes—
448C22×C4#41×C4712yes—
449C22×C4C24×C4711yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—44no—
462C2×C8#41×C4712yes—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4C2×Q8×C4712yes—
486C4⋊C4C2×Q8×C4712yes—
487C4⋊C4#41×C4712yes—
488C22⋊C4—22no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4SD16×C4714yes—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—81no—
497C42—81no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22⋊Q8×C4712yes—
503C23C2×SD16×C4712yes—
504C23#137×C4712yes—
505C23C22×D4×C4711yescharacteristic
506Q8—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
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—84no—
548C2×C4—84no—
549C2×C4C22⋊Q8×C4712yes—
550C2×C4C2×SD16×C4712yes—
551C2×C4C2×SD16×C4712yes—
552C2×C4C22×Q8×C4711yescharacteristic
553C2×C4C2×#41×C4711yescharacteristic
554C2×C4C2×#41×C4711yescharacteristic
555C2×C4C2×#41×C4711yescharacteristic
556C2×C4H(5,𝔽2)×C4711yescharacteristic
557C2×C42−1+4×C4711yescharacteristic
558C8—22no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22C47×#47514yes—
569C22C2×C22⋊Q8×C4711yescharacteristic
570C22C47×#54611yescharacteristic
571C22C47×#54711yescharacteristic
572C22C22×SD16×C4711yescharacteristic
573C22C2×#137×C4711yescharacteristic
574C22C47×#57611yescharacteristic
575C22C47×#57711yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C47×#53311yescharacteristic
590C4C47×#54411yescharacteristic
591C4C47×#55111yescharacteristic
592C4C47×#55211yescharacteristic
593C2—24no—
594C2C47×#243811yescharacteristic
595C2C2×C47×#47511yescharacteristic
596C2C47×#308111yescharacteristic
597C2C47×#329511yescharacteristic
598C2C47×#332011yescharacteristic
599C2C47×#333511yescharacteristic
600C2C47×#334611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×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
3. C47×#2099C2semidirect
4. C47×#2088C2semidirect
5. C47×#2088C2semidirect
6. C47×#2058C2semidirect
7. C47×#1988C2semidirect
8. C47×#1948C2semidirect
9. C47×#1919C2semidirect
10. C47×#1919C2semidirect
85. C2×C4⋊C4×C47Q8semidirect
261. #25992C47direct (N × H)
295. #2099C2×C47semidirect
296. #2088C2×C47semidirect
297. #2088C2×C47semidirect
298. #2058C2×C47semidirect
299. #1988C2×C47semidirect
300. #1948C2×C47semidirect
301. #1919C2×C47semidirect
302. #1919C2×C47semidirect
359. C47#25992direct (N × H)
386. C2×C4⋊C4Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#24402
C47×#23452
C47×#20992
C47×#20882
C47×#20582
C47×#19882
C47×#19482
C47×#19192
C47×#18532
C47×#18502
C47×#18242
C47×#18072
C2×C47×#3402
#2599247