Finite Group Databasebeta

← C47×#8538 #26048236

Subgroups — C47×#8538 #26048236

Order 12032.

820 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3505C211yesmaximal, characteristic
2C47×#1901C211yesmaximal, characteristic, complemented
3C47×#1900C211yesmaximal, characteristic, complemented
4C47×#1870C211yesmaximal, characteristic, complemented
5C47×#1472C211yesmaximal, characteristic, complemented
6C47×#1471C211yesmaximal, characteristic, complemented
7C47×#1465C211yesmaximal, characteristic, complemented
8C22×M16×C47C2211yescharacteristic
9C47×#553—22no—
10C47×#553—21no—
11C47×#552—21no—
12C47×#551—22no—
13C47×#548—21no—
14C47×#546—21no—
15C47×#539—21no—
16C47×#538—21no—
17C47×#534C412yes—
18C47×#529—21no—
19C47×#525—21no—
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C47×#518C412yes—
23C2×C4×D4×C47C2211yescharacteristic
24C2×#101×C47—21no—
25C2×#100×C47—21no—
26C47×#407C2211yescharacteristic
27C47×#407C2211yescharacteristic
28C2×C22⋊C8×C47—21no—
29C2×C22⋊C8×C47C2211yescharacteristic
30C47×#343—21no—
31C47×#343—21no—
32C47×#336—21no—
33C47×#324—21no—
34C47×#324—22no—
35C47×#323—21no—
36C47×#323—22no—
37C2×#41×C47—21no—
38C22×Q8×C47D411yescharacteristic
39C22×D4×C47C2×C411yescharacteristic
40C22×D4×C47C2×C412yes—
41C22×D4×C47D411yescharacteristic
42C23×C4×C47D411yescharacteristic
43C23×C4×C47C2311yescharacteristic
44C2×M16×C47—21no—
45C2×M16×C47—21no—
46C2×M16×C47—21no—
47C2×M16×C47—21no—
48C2×M16×C47—42no—
49C22×C8×C47—21no—
50C22×C8×C47—21no—
51#126×C47—22no—
52#126×C47—22no—
53#126×C47—22no—
54#125×C47—21no—
55#125×C47—22no—
56#124×C47—21no—
57#124×C47—22no—
58#123×C47—22no—
59#123×C47—22no—
60#123×C47—22no—
61#123×C47—22no—
62#123×C47—22no—
63C22⋊Q8×C47—21no—
64C22⋊Q8×C47—22no—
65C22⋊Q8×C47—21no—
66C22⋊Q8×C47—21no—
67C22⋊Q8×C47—21no—
68C22⋊Q8×C47—21no—
69#121×C47—21no—
70#121×C47—22no—
71#121×C47—22no—
72#121×C47—22no—
73#121×C47—21no—
74#121×C47—21no—
75#121×C47—21no—
76#121×C47—21no—
77#120×C47—22no—
78#120×C47—22no—
79C4×Q8×C47—21no—
80C4×D4×C47—22no—
81C4×D4×C47—21no—
82C4×D4×C47—22no—
83C4×D4×C47—22no—
84C4×D4×C47—22no—
85C4×D4×C47—22no—
86C4×D4×C47—21no—
87C4×D4×C47—21no—
88C4×D4×C47—21no—
89C4×D4×C47—21no—
90#117×C47—21no—
91#117×C47—22no—
92#117×C47—22no—
93C2×C4⋊C4×C47D411yescharacteristic
94C2×C4⋊C4×C47D411yescharacteristic
95C2×C4⋊C4×C47D412yes—
96C2×C4⋊C4×C47D411yescharacteristic
97C2×C22⋊C4×C47—22no—
98C2×C22⋊C4×C47C2×C411yescharacteristic
99C2×C22⋊C4×C47C2×C412yes—
100C2×C22⋊C4×C47D411yescharacteristic
101C2×C22⋊C4×C47D412yes—
102C2×C42×C47D411yescharacteristic
103#101×C47—42no—
104#100×C47—42no—
105C22⋊C8×C47—21no—
106C22⋊C8×C47—21no—
107C22⋊C8×C47—21no—
108C22⋊C8×C47—21no—
109C22⋊C8×C47—21no—
110C22⋊C8×C47—21no—
111C22⋊C8×C47—42no—
112C24×C47C22⋊C411yescharacteristic
113C24×C47C22⋊C412yes—
114C24×C47C22×C411yescharacteristic
115#41×C47—81no—
116#41×C47—81no—
117C2×Q8×C47—21no—
118C2×Q8×C47—21no—
119C2×Q8×C47—41no—
120C2×Q8×C47—41no—
121C2×D4×C47—21no—
122C2×D4×C47—22no—
123C2×D4×C47—22no—
124C2×D4×C47—21no—
125C2×D4×C47—22no—
126C2×D4×C47—22no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47—42no—
134C2×D4×C47—42no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47—41no—
142C22×C4×C47—41no—
143C22×C4×C47C22⋊C411yescharacteristic
144C22×C4×C47C22⋊C411yescharacteristic
145C22×C4×C47C22⋊C412yes—
146C22×C4×C47C22⋊C411yescharacteristic
147C22×C4×C47C22⋊C412yes—
148C22×C4×C47C22⋊C412yes—
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155M16×C47—22no—
156M16×C47—22no—
157M16×C47—41no—
158M16×C47—41no—
159M16×C47—41no—
160M16×C47—41no—
161M16×C47—41no—
162M16×C47—41no—
163C2×C8×C47—22no—
164C2×C8×C47—41no—
165C2×C8×C47—41no—
166C2×C8×C47—41no—
167C2×C8×C47—41no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—21no—
183C22⋊C4×C47—22no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47—22no—
187C22⋊C4×C47—22no—
188C22⋊C4×C47—22no—
189C22⋊C4×C47—21no—
190C22⋊C4×C47—22no—
191C22⋊C4×C47—21no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C22⋊C4×C47—22no—
197C42×C47—22no—
198C42×C47—22no—
199C42×C47—21no—
200C42×C47—21no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—22no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—42no—
212C23×C47—42no—
213C23×C47—42no—
214C23×C47C2×C22⋊C411yescharacteristic
215C23×C47C2×C22⋊C411yescharacteristic
216C23×C47C2×C22⋊C411yescharacteristic
217Q8×C47—41no—
218Q8×C47—41no—
219Q8×C47—81no—
220D4×C47—42no—
221D4×C47—42no—
222D4×C47—44no—
223D4×C47—42no—
224D4×C47—42no—
225D4×C47—41no—
226D4×C47—41no—
227D4×C47—81no—
228D4×C47—82no—
229D4×C47—82no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
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—22no—
239C2×C4×C47—21no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
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—42no—
252C2×C4×C47—42no—
253C2×C4×C47—42no—
254C2×C4×C47—81no—
255C2×C4×C47—82no—
256C2×C4×C47—82no—
257C2×C4×C47#12011yescharacteristic
258C2×C4×C47#12011yescharacteristic
259C2×C4×C47#12011yescharacteristic
260C2×C4×C47#12011yescharacteristic
261C8×C47—42no—
262C8×C47—81no—
263C8×C47—81no—
264C8×C47—81no—
265#8538C4711yesmaximal, characteristic, direct product factor, Sylow
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—42no—
275C22×C47—41no—
276C22×C47—42no—
277C22×C47—41no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—41no—
281C22×C47—81no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—162no—
285C22×C47#37911yescharacteristic
286C22×C47#41311yescharacteristic
287C22×C47#41311yescharacteristic
288C4×C47—21no—
289C4×C47—21no—
290C4×C47—21no—
291C4×C47—41no—
292C4×C47—42no—
293C4×C47—41no—
294C4×C47—42no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47B(4,𝔽2)11yescharacteristic
298C4×C47#45811yescharacteristic
299#3505C2×C4711yescharacteristic
300#1901C2×C4711yescharacteristic, complemented
301#1900C2×C4711yescharacteristic, complemented
302#1870C2×C4711yescharacteristic, complemented
303#1472C2×C4711yescharacteristic, complemented
304#1471C2×C4711yescharacteristic, complemented
305#1465C2×C4711yescharacteristic, complemented
306C2×C47—21no—
307C2×C47—21no—
308C2×C47—41no—
309C2×C47—41no—
310C2×C47—81no—
311C2×C47—82no—
312C2×C47#178511yescharacteristic
313C2×C47#179011yescharacteristic
314C2×C47#179111yescharacteristic
315C22×M16C22×C4711yescharacteristic
316#553—22no—
317#553—21no—
318#552—21no—
319#551—22no—
320#548—21no—
321#546—21no—
322#539—21no—
323#538—21no—
324#534C4×C4712yes—
325#529—21no—
326#525—21no—
327C2×C22⋊Q8C22×C4711yescharacteristic
328C2×#121C22×C4711yescharacteristic
329#518C4×C4712yes—
330C2×C4×D4C22×C4711yescharacteristic
331C2×#101—21no—
332C2×#100—21no—
333#407C22×C4711yescharacteristic
334#407C22×C4711yescharacteristic
335C2×C22⋊C8—21no—
336C2×C22⋊C8C22×C4711yescharacteristic
337#343—21no—
338#343—21no—
339#336—21no—
340#324—21no—
341#324—22no—
342#323—21no—
343#323—22no—
344C47#853811yescharacteristic, direct product factor, Sylow
345C2×#41—21no—
346C22×Q8D4×C4711yescharacteristic
347C22×D4C2×C4×C4711yescharacteristic
348C22×D4C2×C4×C4712yes—
349C22×D4D4×C4711yescharacteristic
350C23×C4D4×C4711yescharacteristic
351C23×C4C23×C4711yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—42no—
357C22×C8—21no—
358C22×C8—21no—
359#126—22no—
360#126—22no—
361#126—22no—
362#125—21no—
363#125—22no—
364#124—21no—
365#124—22no—
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370#123—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377#121—21no—
378#121—22no—
379#121—22no—
380#121—22no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#120—22no—
386#120—22no—
387C4×Q8—21no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398#117—21no—
399#117—22no—
400#117—22no—
401C2×C4⋊C4D4×C4711yescharacteristic
402C2×C4⋊C4D4×C4711yescharacteristic
403C2×C4⋊C4D4×C4712yes—
404C2×C4⋊C4D4×C4711yescharacteristic
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×C4×C4711yescharacteristic
407C2×C22⋊C4C2×C4×C4712yes—
408C2×C22⋊C4D4×C4711yescharacteristic
409C2×C22⋊C4D4×C4712yes—
410C2×C42D4×C4711yescharacteristic
411#101—42no—
412#100—42no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—42no—
420C24C22⋊C4×C4711yescharacteristic
421C24C22⋊C4×C4712yes—
422C24C22×C4×C4711yescharacteristic
423#41—81no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C22⋊C4×C4711yescharacteristic
452C22×C4C22⋊C4×C4711yescharacteristic
453C22×C4C22⋊C4×C4712yes—
454C22×C4C22⋊C4×C4711yescharacteristic
455C22×C4C22⋊C4×C4712yes—
456C22×C4C22⋊C4×C4712yes—
457C22×C4C2×D4×C4711yescharacteristic
458C22×C4C2×D4×C4711yescharacteristic
459C22×C4C2×D4×C4711yescharacteristic
460C22×C4C2×D4×C4711yescharacteristic
461C22×C4C2×D4×C4711yescharacteristic
462C22×C4C2×D4×C4711yescharacteristic
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471C2×C8—22no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C42—22no—
506C42—22no—
507C42—21no—
508C42—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—21no—
514C23—21no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23C2×C22⋊C4×C4711yescharacteristic
523C23C2×C22⋊C4×C4711yescharacteristic
524C23C2×C22⋊C4×C4711yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—81no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—81no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4#120×C4711yescharacteristic
566C2×C4#120×C4711yescharacteristic
567C2×C4#120×C4711yescharacteristic
568C2×C4#120×C4711yescharacteristic
569C8—42no—
570C8—81no—
571C8—81no—
572C8—81no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—42no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—162no—
592C22C47×#37911yescharacteristic
593C22C47×#41311yescharacteristic
594C22C47×#41311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—42no—
604C4C47×B(4,𝔽2)11yescharacteristic
605C4C47×#45811yescharacteristic
606C2—21no—
607C2—21no—
608C2—41no—
609C2—41no—
610C2—81no—
611C2—82no—
612C2C47×#178511yescharacteristic
613C2C47×#179011yescharacteristic
614C2C47×#179111yescharacteristic
subgroupG/H
center, socleC22×C47#379
commutatorC24C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC47×#3505C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#1901C2semidirect
3. C47×#1900C2semidirect
4. C47×#1870C2semidirect
5. C47×#1472C2semidirect
6. C47×#1471C2semidirect
7. C47×#1465C2semidirect
265. #8538C47direct (N × H)
300. #1901C2×C47semidirect
301. #1900C2×C47semidirect
302. #1870C2×C47semidirect
303. #1472C2×C47semidirect
304. #1471C2×C47semidirect
305. #1465C2×C47semidirect
344. C47#8538direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35052
C47×#19012
C47×#19002
C47×#18702
C47×#14722
C47×#14712
C47×#14652
#853847