Finite Group Databasebeta

← C47×#25068 #26064766

Subgroups — C47×#25068 #26064766

Order 12032.

732 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2580C211yesmaximal, characteristic
2Q8×C4⋊C4×C47C211yesmaximal, characteristic, complemented
3C47×#2094C211yesmaximal, characteristic
4C47×#2093C211yesmaximal, characteristic
5C47×#2084C211yesmaximal, characteristic, complemented
6C47×#2083C211yesmaximal, characteristic, complemented
7C47×#1985C211yesmaximal, characteristic, complemented
8C47×#1949C211yesmaximal, characteristic, complemented
9C47×#1926C211yesmaximal, characteristic
10C47×#1925C211yesmaximal, characteristic
11C47×#1921C211yesmaximal, characteristic, complemented
12C47×#1920C211yesmaximal, characteristic, complemented
13C47×#1847C211yesmaximal, characteristic, complemented
14C47×#1802C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×C4×Q8×C47—21no—
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×#97×C47C2211yescharacteristic
31C47×#399—21no—
32C47×#393—21no—
33C47×#390C2211yescharacteristic
34C47×#390C2211yescharacteristic
35C47×#389—21no—
36C47×#389—21no—
37C47×#389—21no—
38C47×#389C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#385—21no—
41C47×#385—21no—
42C47×#384C2211yescharacteristic
43C47×#384C2211yescharacteristic
44C47×#384C2211yescharacteristic
45C47×#382C2211yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C4×C4⋊C4×C47C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47D411yescharacteristic
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C22×C8×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C4×Q8×C47—22no—
67C4×Q8×C47—22no—
68C4×Q8×C47—44no—
69C4×D4×C47—22no—
70C4×D4×C47—22no—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47D411yescharacteristic
80C2×C4⋊C4×C47D411yescharacteristic
81C2×C4⋊C4×C47D411yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99C2×C42×C47C2311yescharacteristic
100#107×C47—22no—
101#107×C47—41no—
102#107×C47—41no—
103#106×C47—22no—
104#106×C47—41no—
105#106×C47—41no—
106C4⋊C8×C47—22no—
107#102×C47—22no—
108#102×C47—41no—
109#102×C47—41no—
110#102×C47Q814yescomplemented
111#97×C47—22no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119C24×C47—21no—
120C2×Q8×C47—22no—
121C2×Q8×C47—22no—
122C2×Q8×C47—22no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47C2×Q812yes—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
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—81no—
138C22×C4×C47—81no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2411yescharacteristic
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
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×C47C2×Q812yes—
157C2×C8×C47#4112yes—
158C4⋊C4×C47—22no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
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—42no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—42no—
177C4⋊C4×C47—81no—
178C4⋊C4×C47—81no—
179C4⋊C4×C47—81no—
180C4⋊C4×C47—81no—
181C4⋊C4×C47—81no—
182C4⋊C4×C47C2×Q812yes—
183C22⋊C4×C47—42no—
184C22⋊C4×C47—42no—
185C22⋊C4×C47—42no—
186C22⋊C4×C47—81no—
187C22⋊C4×C47—81no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—42no—
193C42×C47—42no—
194C42×C47—42no—
195C42×C47#4112yes—
196C42×C47#4112yes—
197C23×C47—22no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47C22×D411yescharacteristic
205Q8×C47—28no—
206D4×C47—22no—
207D4×C47—22no—
208D4×C47—41no—
209D4×C47—41no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—22no—
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—84no—
246C2×C4×C47#12312yes—
247C2×C4×C47#12312yes—
248C2×C4×C47AGL(1,ℤ/8)12yes—
249C2×C4×C47#13712yes—
250C2×C4×C47C22×Q811yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47H(5,𝔽2)11yescharacteristic
255C2×C4×C472−1+411yescharacteristic
256C8×C47—22no—
257C8×C47—22no—
258C8×C47—41no—
259C8×C47—41no—
260#25068C4711yesmaximal, characteristic, direct product factor, Sylow
261C22×C47—42no—
262C22×C47—42no—
263C22×C47—42no—
264C22×C47—81no—
265C22×C47—81no—
266C22×C47—81no—
267C22×C47—81no—
268C22×C47C2×#12311yescharacteristic
269C22×C47D4×Q811yescharacteristic
270C22×C47#55011yescharacteristic
271C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C47C2×#13711yescharacteristic
273C22×C47#57611yescharacteristic
274C22×C47#57711yescharacteristic
275C4×C47—22no—
276C4×C47—22no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—42no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47#53311yescharacteristic
289C4×C47#54211yescharacteristic
290C4×C47#55211yescharacteristic
291C4×C47#55411yescharacteristic
292#2580C2×C4711yescharacteristic
293Q8×C4⋊C4C2×C4711yescharacteristic, complemented
294#2094C2×C4711yescharacteristic
295#2093C2×C4711yescharacteristic
296#2084C2×C4711yescharacteristic, complemented
297#2083C2×C4711yescharacteristic, complemented
298#1985C2×C4711yescharacteristic, complemented
299#1949C2×C4711yescharacteristic, complemented
300#1926C2×C4711yescharacteristic
301#1925C2×C4711yescharacteristic
302#1921C2×C4711yescharacteristic, complemented
303#1920C2×C4711yescharacteristic, complemented
304#1847C2×C4711yescharacteristic, complemented
305#1802C2×C4711yescharacteristic
306#1762C2×C4711yescharacteristic
307C2×C47—82no—
308C2×C47#242311yescharacteristic
309C2×C47#309211yescharacteristic
310C2×C47#309611yescharacteristic
311C2×C47#338411yescharacteristic
312C2×C47#338511yescharacteristic
313C2×C47#339911yescharacteristic
314C2×C47#340011yescharacteristic
315C2×C4×Q8—21no—
316C2×C4×Q8C22×C4711yescharacteristic
317C2×C4×D4C22×C4711yescharacteristic
318C2×#107C22×C4711yescharacteristic
319C2×#107C22×C4711yescharacteristic
320C2×#107C22×C4711yescharacteristic
321C2×#106C22×C4711yescharacteristic
322C2×#106C22×C4711yescharacteristic
323C2×#106C22×C4711yescharacteristic
324C2×C4⋊C8C22×C4711yescharacteristic
325C2×#102C22×C4711yescharacteristic
326C2×#102C22×C4711yescharacteristic
327C2×#102C22×C4711yescharacteristic
328C2×#102C22×C4711yescharacteristic
329C2×#97C22×C4711yescharacteristic
330#399—21no—
331#393—21no—
332#390C22×C4711yescharacteristic
333#390C22×C4711yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389C22×C4711yescharacteristic
338#389C22×C4711yescharacteristic
339#385—21no—
340#385—21no—
341#384C22×C4711yescharacteristic
342#384C22×C4711yescharacteristic
343#384C22×C4711yescharacteristic
344#382C22×C4711yescharacteristic
345C4×C4⋊C4C22×C4711yescharacteristic
346C4×C4⋊C4C22×C4711yescharacteristic
347C4×C4⋊C4C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#340C22×C4711yescharacteristic
352#340C22×C4711yescharacteristic
353#340C22×C4711yescharacteristic
354#336C22×C4711yescharacteristic
355#336C22×C4711yescharacteristic
356#336C22×C4711yescharacteristic
357#336C22×C4711yescharacteristic
358C47#2506811yescharacteristic, direct product factor, Sylow
359C22×Q8D4×C4711yescharacteristic
360C22×D4C23×C4711yescharacteristic
361C23×C4—21no—
362C22×C8C23×C4711yescharacteristic
363C22×C8C23×C4711yescharacteristic
364C22×C8C23×C4711yescharacteristic
365C22×C8C23×C4711yescharacteristic
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—44no—
369C4×D4—22no—
370C4×D4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C4711yescharacteristic
380C2×C4⋊C4D4×C4711yescharacteristic
381C2×C4⋊C4D4×C4711yescharacteristic
382C2×C4⋊C4C23×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C4⋊C4C23×C4711yescharacteristic
386C2×C4⋊C4C23×C4711yescharacteristic
387C2×C4⋊C4C23×C4711yescharacteristic
388C2×C4⋊C4C23×C4711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C23×C4711yescharacteristic
398C2×C42C23×C4711yescharacteristic
399C2×C42C23×C4711yescharacteristic
400#107—22no—
401#107—41no—
402#107—41no—
403#106—22no—
404#106—41no—
405#106—41no—
406C4⋊C8—22no—
407#102—22no—
408#102—41no—
409#102—41no—
410#102Q8×C4714yescomplemented
411#97—22no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C24—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4C2×Q8×C4712yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C2×D4×C4711yescharacteristic
442C22×C4C2×D4×C4711yescharacteristic
443C22×C4C2×D4×C4711yescharacteristic
444C22×C4C2×D4×C4711yescharacteristic
445C22×C4C24×C4711yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8C2×Q8×C4712yes—
457C2×C8#41×C4712yes—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
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—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4C2×Q8×C4712yes—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C42—42no—
494C42—42no—
495C42#41×C4712yes—
496C42#41×C4712yes—
497C23—22no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23C22×D4×C4711yescharacteristic
505Q8—28no—
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
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—84no—
546C2×C4#123×C4712yes—
547C2×C4#123×C4712yes—
548C2×C4AGL(1,ℤ/8)×C4712yes—
549C2×C4#137×C4712yes—
550C2×C4C22×Q8×C4711yescharacteristic
551C2×C4C2×#41×C4711yescharacteristic
552C2×C4C2×#41×C4711yescharacteristic
553C2×C4C2×#41×C4711yescharacteristic
554C2×C4H(5,𝔽2)×C4711yescharacteristic
555C2×C42−1+4×C4711yescharacteristic
556C8—22no—
557C8—22no—
558C8—41no—
559C8—41no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C2×#123×C4711yescharacteristic
568C22D4×Q8×C4711yescharacteristic
569C22C47×#55011yescharacteristic
570C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
571C22C2×#137×C4711yescharacteristic
572C22C47×#57611yescharacteristic
573C22C47×#57711yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C47×#53311yescharacteristic
588C4C47×#54211yescharacteristic
589C4C47×#55211yescharacteristic
590C4C47×#55411yescharacteristic
591C2—82no—
592C2C47×#242311yescharacteristic
593C2C47×#309211yescharacteristic
594C2C47×#309611yescharacteristic
595C2C47×#338411yescharacteristic
596C2C47×#338511yescharacteristic
597C2C47×#339911yescharacteristic
598C2C47×#340011yescharacteristic
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. Q8×C4⋊C4×C47C2semidirect
5. C47×#2084C2semidirect
6. C47×#2083C2semidirect
7. C47×#1985C2semidirect
8. C47×#1949C2semidirect
11. C47×#1921C2semidirect
12. C47×#1920C2semidirect
13. C47×#1847C2semidirect
110. #102×C47Q8semidirect
260. #25068C47direct (N × H)
293. Q8×C4⋊C4C2×C47semidirect
296. #2084C2×C47semidirect
297. #2083C2×C47semidirect
298. #1985C2×C47semidirect
299. #1949C2×C47semidirect
302. #1921C2×C47semidirect
303. #1920C2×C47semidirect
304. #1847C2×C47semidirect
358. C47#25068direct (N × H)
410. #102Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#25802
Q8×C4⋊C4×C472
C47×#20942
C47×#20932
C47×#20842
C47×#20832
C47×#19852
C47×#19492
C47×#19262
C47×#19252
C47×#19212
C47×#19202
C47×#18472
C47×#18022
C47×#17622
#2506847