Finite Group Databasebeta

← C47×#15122 #26054820

Subgroups — C47×#15122 #26054820

Order 12032.

1238 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#389C211yesmaximal, characteristic
2C2×C47×#387C212yesmaximal
3C2×C47×#376C211yesmaximal, characteristic
4C47×#1445C211yesmaximal, characteristic
5C47×#1445C211yesmaximal, characteristic
6C47×#1444C211yesmaximal, characteristic
7C47×#1443C212yesmaximal
8C47×#1442C212yesmaximal
9C47×#1442C211yesmaximal, characteristic
10C47×#1436C212yesmaximal
11C47×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C47C2212yes—
13C22×C4⋊C4×C47C2212yes—
14C22×C4⋊C4×C47C2211yescharacteristic
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C42×C47C2211yescharacteristic
17C22×C42×C47C2211yescharacteristic
18C22×C42×C47C2211yescharacteristic
19C47×#389—24no—
20C47×#387—28no—
21C47×#376—24no—
22C2×#95×C47C2211yescharacteristic
23C2×#95×C47C2211yescharacteristic
24C2×#95×C47C2211yescharacteristic
25C2×#95×C47C2211yescharacteristic
26C2×#95×C47C2212yes—
27C2×#95×C47C2212yes—
28C2×#95×C47C2212yes—
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2212yes—
32C2×#95×C47C2211yescharacteristic
33C2×#95×C47C2211yescharacteristic
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C23×C4×C47C2312yes—
39C23×C4×C47C2312yes—
40C23×C4×C47C2311yescharacteristic
41C23×C4×C47C2311yescharacteristic
42C23×C4×C47C2311yescharacteristic
43C23×C4×C47C2311yescharacteristic
44C23×C4×C47C2311yescharacteristic
45C23×C4×C47C2312yes—
46C23×C4×C47C2312yes—
47C23×C4×C47C2311yescharacteristic
48C23×C4×C47C2311yescharacteristic
49C2×C4⋊C4×C47—24no—
50C2×C4⋊C4×C47—22no—
51C2×C4⋊C4×C47—24no—
52C2×C4⋊C4×C47—24no—
53C2×C4⋊C4×C47—24no—
54C2×C4⋊C4×C47—24no—
55C2×C4⋊C4×C47—24no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—24no—
58C2×C4⋊C4×C47—22no—
59C2×C4⋊C4×C47—22no—
60C2×C42×C47—22no—
61C2×C42×C47—22no—
62C2×C42×C47—22no—
63C2×C42×C47—22no—
64C2×C42×C47—22no—
65C2×C42×C47—22no—
66C2×C42×C47—22no—
67C2×C42×C47D414yes—
68C2×C42×C47D414yes—
69#95×C47—22no—
70#95×C47—22no—
71#95×C47—22no—
72#95×C47—22no—
73#95×C47—24no—
74#95×C47—24no—
75#95×C47—24no—
76#95×C47—24no—
77#95×C47—24no—
78#95×C47—24no—
79#95×C47—22no—
80#95×C47—24no—
81#95×C47—24no—
82#95×C47—24no—
83#95×C47—24no—
84#95×C47—22no—
85C24×C47C2411yescharacteristic
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—22no—
97C22×C4×C47—22no—
98C22×C4×C47—22no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D412yes—
144C22×C4×C47#4112yes—
145C22×C4×C47#4112yes—
146C22×C4×C47#4114yes—
147C22×C4×C47#4114yes—
148C22×C4×C47#4112yes—
149C22×C4×C47#4112yes—
150C22×C4×C47#4112yes—
151C4⋊C4×C47—28no—
152C4⋊C4×C47—216no—
153C4⋊C4×C47—48no—
154C4⋊C4×C47—44no—
155C42×C47—28no—
156C42×C47—28no—
157C42×C47—28no—
158C23×C47C22×D411yescharacteristic
159C23×C47C22×D411yescharacteristic
160C23×C47C2×#4111yescharacteristic
161C23×C47C2×#4111yescharacteristic
162C23×C47C2×#4111yescharacteristic
163C23×C47C2×#4112yes—
164C23×C47C2×#4111yescharacteristic
165C23×C47C2×#4112yes—
166C23×C47C2×#4111yescharacteristic
167C23×C472−1+412yes—
168C23×C472−1+412yes—
169C2×C4×C47—22no—
170C2×C4×C47—22no—
171C2×C4×C47—22no—
172C2×C4×C47—22no—
173C2×C4×C47—22no—
174C2×C4×C47—22no—
175C2×C4×C47—22no—
176C2×C4×C47—22no—
177C2×C4×C47—24no—
178C2×C4×C47—24no—
179C2×C4×C47—22no—
180C2×C4×C47—22no—
181C2×C4×C47—22no—
182C2×C4×C47—22no—
183C2×C4×C47—22no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—22no—
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—42no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—42no—
206C2×C4×C47—41no—
207C2×C4×C47—42no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47#12114yes—
233C2×C4×C47#12314yes—
234#15122C4711yesmaximal, characteristic, direct product factor, Sylow
235C22×C47C2×#12111yescharacteristic
236C22×C47C2×#12311yescharacteristic
237C22×C47#52511yescharacteristic
238C22×C47#52511yescharacteristic
239C22×C47#52512yes—
240C22×C47#52911yescharacteristic
241C22×C47#52911yescharacteristic
242C22×C47#52912yes—
243C22×C47#53211yescharacteristic
244C22×C47#53211yescharacteristic
245C22×C47#53211yescharacteristic
246C22×C47#53611yescharacteristic
247C22×C47#53612yes—
248C22×C47#53611yescharacteristic
249C22×C47#54112yes—
250C22×C47#55212yes—
251C22×C47#55212yes—
252C22×C47#55212yes—
253C22×C47#55212yes—
254C22×C47#55212yes—
255C22×C47#55212yes—
256C22×C47#55612yes—
257C22×C47#55612yes—
258C4×C47—24no—
259C4×C47—24no—
260C4×C47—42no—
261C4×C47—42no—
262C4×C47—44no—
263C4×C47—42no—
264C4×C47—42no—
265C4×C47—44no—
266C4×C47—42no—
267C4×C47—82no—
268C4×C47—82no—
269C2×#389C2×C4711yescharacteristic
270C2×#387C2×C4712yes—
271C2×#376C2×C4711yescharacteristic
272#1445C2×C4711yescharacteristic
273#1445C2×C4711yescharacteristic
274#1444C2×C4711yescharacteristic
275#1443C2×C4712yes—
276#1442C2×C4712yes—
277#1442C2×C4711yescharacteristic
278#1436C2×C4712yes—
279#1434C2×C4711yescharacteristic
280C2×C47#239211yescharacteristic
281C2×C47#248411yescharacteristic
282C2×C47#249911yescharacteristic
283C2×C47#252812yes—
284C2×C47#253312yes—
285C2×C47#259911yescharacteristic
286C2×C47#260412yes—
287C2×C47#261111yescharacteristic
288C2×C47#261112yes—
289C2×C47#262111yescharacteristic
290C2×C47#285411yescharacteristic
291C22×C4⋊C4C22×C4712yes—
292C22×C4⋊C4C22×C4712yes—
293C22×C4⋊C4C22×C4711yescharacteristic
294C22×C4⋊C4C22×C4711yescharacteristic
295C22×C42C22×C4711yescharacteristic
296C22×C42C22×C4711yescharacteristic
297C22×C42C22×C4711yescharacteristic
298#389—24no—
299#387—28no—
300#376—24no—
301C2×#95C22×C4712yes—
302C2×#95C22×C4712yes—
303C2×#95C22×C4711yescharacteristic
304C2×#95C22×C4711yescharacteristic
305C2×#95C22×C4712yes—
306C2×#95C22×C4712yes—
307C2×#95C22×C4712yes—
308C2×#95C22×C4712yes—
309C2×#95C22×C4711yescharacteristic
310C2×#95C22×C4712yes—
311C2×#95C22×C4712yes—
312C2×#95C22×C4711yescharacteristic
313C2×#95C22×C4712yes—
314C2×#95C22×C4711yescharacteristic
315C2×#95C22×C4712yes—
316C2×#95C22×C4711yescharacteristic
317C47#1512211yescharacteristic, direct product factor, Sylow
318C23×C4C23×C4712yes—
319C23×C4C23×C4712yes—
320C23×C4C23×C4711yescharacteristic
321C23×C4C23×C4711yescharacteristic
322C23×C4C23×C4711yescharacteristic
323C23×C4C23×C4712yes—
324C23×C4C23×C4712yes—
325C23×C4C23×C4711yescharacteristic
326C23×C4C23×C4711yescharacteristic
327C23×C4C23×C4711yescharacteristic
328C23×C4C23×C4711yescharacteristic
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42D4×C4714yes—
348C2×C42D4×C4714yes—
349#95—22no—
350#95—22no—
351#95—22no—
352#95—22no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—22no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—22no—
365C24C24×C4711yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C2×D4×C4712yes—
419C22×C4C2×D4×C4712yes—
420C22×C4C2×D4×C4712yes—
421C22×C4C2×D4×C4712yes—
422C22×C4C2×D4×C4712yes—
423C22×C4C2×D4×C4712yes—
424C22×C4#41×C4712yes—
425C22×C4#41×C4712yes—
426C22×C4#41×C4714yes—
427C22×C4#41×C4714yes—
428C22×C4#41×C4712yes—
429C22×C4#41×C4712yes—
430C22×C4#41×C4712yes—
431C4⋊C4—28no—
432C4⋊C4—216no—
433C4⋊C4—48no—
434C4⋊C4—44no—
435C42—28no—
436C42—28no—
437C42—28no—
438C23C22×D4×C4711yescharacteristic
439C23C22×D4×C4711yescharacteristic
440C23C2×#41×C4711yescharacteristic
441C23C2×#41×C4711yescharacteristic
442C23C2×#41×C4711yescharacteristic
443C23C2×#41×C4712yes—
444C23C2×#41×C4711yescharacteristic
445C23C2×#41×C4712yes—
446C23C2×#41×C4711yescharacteristic
447C232−1+4×C4712yes—
448C232−1+4×C4712yes—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4#121×C4714yes—
513C2×C4#123×C4714yes—
514C22C2×#121×C4711yescharacteristic
515C22C2×#123×C4711yescharacteristic
516C22C47×#52511yescharacteristic
517C22C47×#52511yescharacteristic
518C22C47×#52512yes—
519C22C47×#52911yescharacteristic
520C22C47×#52912yes—
521C22C47×#52911yescharacteristic
522C22C47×#53211yescharacteristic
523C22C47×#53211yescharacteristic
524C22C47×#53211yescharacteristic
525C22C47×#53611yescharacteristic
526C22C47×#53612yes—
527C22C47×#53611yescharacteristic
528C22C47×#54112yes—
529C22C47×#55212yes—
530C22C47×#55212yes—
531C22C47×#55212yes—
532C22C47×#55212yes—
533C22C47×#55212yes—
534C22C47×#55212yes—
535C22C47×#55612yes—
536C22C47×#55612yes—
537C4—24no—
538C4—24no—
539C4—42no—
540C4—42no—
541C4—44no—
542C4—42no—
543C4—42no—
544C4—44no—
545C4—42no—
546C4—82no—
547C4—82no—
548C2C47×#239211yescharacteristic
549C2C47×#248411yescharacteristic
550C2C47×#249911yescharacteristic
551C2C47×#252812yes—
552C2C47×#253312yes—
553C2C47×#259911yescharacteristic
554C2C47×#260412yes—
555C2C47×#261111yescharacteristic
556C2C47×#261112yes—
557C2C47×#262111yescharacteristic
558C2C47×#285411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C47C24
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
234. #15122C47direct (N × H)
317. C47#15122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3892
C2×C47×#3872
C2×C47×#3762
C47×#14452
C47×#14442
C47×#14432
C47×#14422
C47×#14362
C47×#14342
#1512247