Finite Group Databasebeta

← C47×#29547 #26069245

Subgroups — C47×#29547 #26069245

Order 12032.

698 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×#2320C211yesmaximal, characteristic, complemented
2C47×#2319C211yesmaximal, characteristic
3C47×#2088C211yesmaximal, characteristic, complemented
4C47×#2068C211yesmaximal, characteristic, complemented
5C47×#2067C211yesmaximal, characteristic
6C47×#2055C211yesmaximal, characteristic
7C47×#1927C211yesmaximal, characteristic, complemented
8C47×#1926C211yesmaximal, characteristic
9C47×#1921C211yesmaximal, characteristic, complemented
10C47×#1918C211yesmaximal, characteristic, complemented
11C47×#1880C211yesmaximal, characteristic
12C47×#1877C211yesmaximal, characteristic
13C47×#1863C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic
15C47×#1832C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C2×C4⋊C8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#103×C47C2211yescharacteristic
25C2×#103×C47C2211yescharacteristic
26C2×#103×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C47×#391C2211yescharacteristic
31C47×#391C2211yescharacteristic
32C47×#390C2211yescharacteristic
33C47×#390C2211yescharacteristic
34C47×#389C2211yescharacteristic
35C47×#389C2211yescharacteristic
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#388—21no—
39C47×#388—21no—
40C47×#387—21no—
41C47×#387—21no—
42C47×#383—21no—
43C47×#382—21no—
44C47×#381—21no—
45C47×#380—21no—
46C4×C4⋊C4×C47C2211yescharacteristic
47C4×C4⋊C4×C47C2211yescharacteristic
48C47×#376C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47C2311yescharacteristic
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C2×SD16×C47—22no—
63C2×SD16×C47—22no—
64C2×SD16×C47—41no—
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C22×C8×C47C2311yescharacteristic
69C4×Q8×C47—22no—
70C4×Q8×C47—22no—
71C4×D4×C47—22no—
72C4×D4×C47—22no—
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×C47C2311yescharacteristic
79C2×C4⋊C4×C47C2311yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C22⋊C4×C47—21no—
85C2×C22⋊C4×C47—21no—
86C2×C22⋊C4×C47—21no—
87C2×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
89C2×C42×C47—21no—
90C2×C42×C47—21no—
91C2×C42×C47—21no—
92C2×C42×C47C2311yescharacteristic
93C2×C42×C47C2311yescharacteristic
94C2×C42×C47C2311yescharacteristic
95#107×C47—22no—
96#107×C47—22no—
97#106×C47—41no—
98C4⋊C8×C47—41no—
99C4⋊C8×C47—41no—
100#103×C47—22no—
101#103×C47—22no—
102#103×C47—41no—
103#102×C47—22no—
104#102×C47—22no—
105#102×C47—41no—
106#95×C47—21no—
107#95×C47—21no—
108#95×C47—21no—
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×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47—21no—
121C2×Q8×C47—21no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47#4112yes—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47#4112yes—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—24no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—81no—
142C22×C4×C47—81no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2411yescharacteristic
150SD16×C47—44no—
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—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C4⋊C4×C47—24no—
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—81no—
175C4⋊C4×C47—81no—
176C4⋊C4×C47—81no—
177C4⋊C4×C47—81no—
178C4⋊C4×C47#4112yes—
179C4⋊C4×C47#4112yes—
180C22⋊C4×C47—24no—
181C22⋊C4×C47—81no—
182C22⋊C4×C47—81no—
183C22⋊C4×C47—81no—
184C22⋊C4×C47—81no—
185C42×C47—24no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—81no—
193C42×C47—81no—
194C23×C47—22no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47C22×D411yescharacteristic
202Q8×C47—22no—
203Q8×C47—22no—
204Q8×C47—41no—
205Q8×C47—41no—
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—22no—
214C2×C4×C47—22no—
215C2×C4×C47—21no—
216C2×C4×C47—22no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
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—21no—
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—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—84no—
250C2×C4×C47C2×#4111yescharacteristic
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—41no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260#29547C4711yesmaximal, 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×C47#52511yescharacteristic
269C22×C47#52511yescharacteristic
270C22×C47#53711yescharacteristic
271C22×C47#57611yescharacteristic
272C22×C47#57711yescharacteristic
273C22×C47#57711yescharacteristic
274C22×C47#57811yescharacteristic
275C4×C47—41no—
276C4×C47—42no—
277C4×C47—41no—
278C4×C47—42no—
279C4×C47—41no—
280C4×C47—42no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—81no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47#55111yescharacteristic
289C4×C47#55211yescharacteristic
290C4×C47#55211yescharacteristic
291C4×C47#55511yescharacteristic
292#2320C2×C4711yescharacteristic, complemented
293#2319C2×C4711yescharacteristic
294#2088C2×C4711yescharacteristic, complemented
295#2068C2×C4711yescharacteristic, complemented
296#2067C2×C4711yescharacteristic
297#2055C2×C4711yescharacteristic
298#1927C2×C4711yescharacteristic, complemented
299#1926C2×C4711yescharacteristic
300#1921C2×C4711yescharacteristic, complemented
301#1918C2×C4711yescharacteristic, complemented
302#1880C2×C4711yescharacteristic
303#1877C2×C4711yescharacteristic
304#1863C2×C4711yescharacteristic, complemented
305#1862C2×C4711yescharacteristic
306#1832C2×C4711yescharacteristic, complemented
307C2×C47—82no—
308C2×C47#260911yescharacteristic
309C2×C47#311811yescharacteristic
310C2×C47#311911yescharacteristic
311C2×C47#312011yescharacteristic
312C2×C47#312111yescharacteristic
313C2×C47#326011yescharacteristic
314C2×C47#326211yescharacteristic
315C22×SD16C22×C4711yescharacteristic
316C2×C4×Q8C22×C4711yescharacteristic
317C2×C4×D4C22×C4711yescharacteristic
318C2×#107C22×C4711yescharacteristic
319C2×#107C22×C4711yescharacteristic
320C2×#106C22×C4711yescharacteristic
321C2×C4⋊C8C22×C4711yescharacteristic
322C2×C4⋊C8C22×C4711yescharacteristic
323C2×#103C22×C4711yescharacteristic
324C2×#103C22×C4711yescharacteristic
325C2×#103C22×C4711yescharacteristic
326C2×#102C22×C4711yescharacteristic
327C2×#102C22×C4711yescharacteristic
328C2×#102C22×C4711yescharacteristic
329#391C22×C4711yescharacteristic
330#391C22×C4711yescharacteristic
331#390C22×C4711yescharacteristic
332#390C22×C4711yescharacteristic
333#389C22×C4711yescharacteristic
334#389C22×C4711yescharacteristic
335#389C22×C4711yescharacteristic
336#389C22×C4711yescharacteristic
337#388—21no—
338#388—21no—
339#387—21no—
340#387—21no—
341#383—21no—
342#382—21no—
343#381—21no—
344#380—21no—
345C4×C4⋊C4C22×C4711yescharacteristic
346C4×C4⋊C4C22×C4711yescharacteristic
347#376C22×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#2954711yescharacteristic, direct product factor, Sylow
359C22×Q8C23×C4711yescharacteristic
360C22×D4C23×C4711yescharacteristic
361C23×C4—21no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×SD16—41no—
365C22×C8C23×C4711yescharacteristic
366C22×C8C23×C4711yescharacteristic
367C22×C8C23×C4711yescharacteristic
368C22×C8C23×C4711yescharacteristic
369C4×Q8—22no—
370C4×Q8—22no—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C23×C4711yescharacteristic
379C2×C4⋊C4C23×C4711yescharacteristic
380C2×C4⋊C4C23×C4711yescharacteristic
381C2×C4⋊C4C23×C4711yescharacteristic
382C2×C4⋊C4C23×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C4711yescharacteristic
393C2×C42C23×C4711yescharacteristic
394C2×C42C23×C4711yescharacteristic
395#107—22no—
396#107—22no—
397#106—41no—
398C4⋊C8—41no—
399C4⋊C8—41no—
400#103—22no—
401#103—22no—
402#103—41no—
403#102—22no—
404#102—22no—
405#102—41no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95D4×C4711yescharacteristic
417#95D4×C4711yescharacteristic
418#95D4×C4711yescharacteristic
419#95D4×C4711yescharacteristic
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#41×C4712yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4#41×C4712yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—81no—
442C22×C4—81no—
443C22×C4C2×D4×C4711yescharacteristic
444C22×C4C2×D4×C4711yescharacteristic
445C22×C4C2×D4×C4711yescharacteristic
446C22×C4C2×D4×C4711yescharacteristic
447C22×C4C2×D4×C4711yescharacteristic
448C22×C4C2×D4×C4711yescharacteristic
449C22×C4C24×C4711yescharacteristic
450SD16—44no—
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—21no—
462C2×C8—21no—
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—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4#41×C4712yes—
479C4⋊C4#41×C4712yes—
480C22⋊C4—24no—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C42—24no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—81no—
493C42—81no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23C22×D4×C4711yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
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—41no—
548C2×C4—41no—
549C2×C4—84no—
550C2×C4C2×#41×C4711yescharacteristic
551C2×C4C2×#41×C4711yescharacteristic
552C2×C4C2×#41×C4711yescharacteristic
553C2×C4C2×#41×C4711yescharacteristic
554C2×C4H(5,𝔽2)×C4711yescharacteristic
555C2×C42−1+4×C4711yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22C47×#52511yescharacteristic
568C22C47×#52511yescharacteristic
569C22C47×#53711yescharacteristic
570C22C47×#57611yescharacteristic
571C22C47×#57711yescharacteristic
572C22C47×#57711yescharacteristic
573C22C47×#57811yescharacteristic
574C4—41no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C47×#55111yescharacteristic
588C4C47×#55211yescharacteristic
589C4C47×#55211yescharacteristic
590C4C47×#55511yescharacteristic
591C2—82no—
592C2C47×#260911yescharacteristic
593C2C47×#311811yescharacteristic
594C2C47×#311911yescharacteristic
595C2C47×#312011yescharacteristic
596C2C47×#312111yescharacteristic
597C2C47×#326011yescharacteristic
598C2C47×#326211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C47×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2320C2semidirect
3. C47×#2088C2semidirect
4. C47×#2068C2semidirect
7. C47×#1927C2semidirect
9. C47×#1921C2semidirect
10. C47×#1918C2semidirect
13. C47×#1863C2semidirect
15. C47×#1832C2semidirect
260. #29547C47direct (N × H)
292. #2320C2×C47semidirect
294. #2088C2×C47semidirect
295. #2068C2×C47semidirect
298. #1927C2×C47semidirect
300. #1921C2×C47semidirect
301. #1918C2×C47semidirect
304. #1863C2×C47semidirect
306. #1832C2×C47semidirect
358. C47#29547direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#23202
C47×#23192
C47×#20882
C47×#20682
C47×#20672
C47×#20552
C47×#19272
C47×#19262
C47×#19212
C47×#19182
C47×#18802
C47×#18772
C47×#18632
C47×#18622
C47×#18322
#2954747