Finite Group Databasebeta

← C47×#18426 #26058124

Subgroups — C47×#18426 #26058124

Order 12032.

1168 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3558C211yesmaximal, characteristic, complemented
2C47×#3217C211yesmaximal, characteristic, complemented
3C47×#3205C211yesmaximal, characteristic, complemented
4C47×#2657C211yesmaximal, characteristic, complemented
5C47×#1600C214yesmaximal, complemented
6C47×#1595C214yesmaximal, complemented
7C47×#1505C211yesmaximal, characteristic, complemented
8C47×#1500C211yesmaximal, characteristic, complemented
9C47×#1469C211yesmaximal, characteristic, complemented
10C47×#562—21no—
11C47×H(3,𝔽4)—21no—
12C47×#559—21no—
13C47×#548—21no—
14C47×#546—21no—
15C47×#546—22no—
16D42×C47—21no—
17C47×#542—21no—
18C47×#538—22no—
19C47×#538C2212yes—
20C47×#535—21no—
21C47×#534C2212yes—
22C47×#532C2211yescharacteristic
23C2×#127×C47—21no—
24C2×#127×C47C2211yescharacteristic, complemented
25C47×#529C2211yescharacteristic
26C2×#124×C47—21no—
27C2×#124×C47C2211yescharacteristic
28C47×#496—21no—
29C47×#493—21no—
30C47×#490—21no—
31C47×#486—21no—
32C47×#460—21no—
33C47×#459—22no—
34C47×#459—21no—
35C47×#450C2212yescomplemented
36C47×#447C2212yes—
37C47×#447C2214yescomplemented
38C47×#432C2211yescharacteristic, complemented
39C47×#431C2211yescharacteristic, complemented
40C47×#392—22no—
41C47×#392C2214yescomplemented
42C47×#376C2211yescharacteristic, complemented
43C47×#328C2212yescomplemented
44C47×#327C2212yes—
45C47×#327C2214yescomplemented
46C47×#323C2214yescomplemented
47C2×#41×C47—21no—
48C2×#41×C47—21no—
49C22×Q8×C47D411yescharacteristic
50C22×D4×C47—21no—
51C22×D4×C47—22no—
52C22×D4×C47—24no—
53C22×D4×C47—21no—
54C22×D4×C47—21no—
55C22×D4×C47D411yescharacteristic
56C22×D4×C47C2312yes—
57C2×SD16×C47—22no—
58C2×D8×C47—24no—
59C2×D8×C47—22no—
60C4⋊Q8×C47D411yescharacteristic, complemented
61#127×C47—21no—
62#127×C47—21no—
63#127×C47—21no—
64#127×C47—21no—
65#127×C47—21no—
66#127×C47—44no—
67#127×C47D411yescharacteristic, complemented
68#126×C47—22no—
69#126×C47—21no—
70#125×C47D411yescharacteristic, complemented
71#124×C47—21no—
72#124×C47—22no—
73#124×C47—22no—
74#124×C47—22no—
75#124×C47—21no—
76#124×C47—21no—
77#124×C47—21no—
78#124×C47—21no—
79#124×C47—21no—
80#124×C47—44no—
81#124×C47D411yescharacteristic, complemented
82#123×C47—22no—
83#123×C47—21no—
84#123×C47—22no—
85#123×C47—22no—
86#123×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—21no—
89C22⋊Q8×C47—22no—
90C22⋊Q8×C47C2311yescharacteristic
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—21no—
95#121×C47—22no—
96#121×C47—21no—
97#121×C47—22no—
98#121×C47C2311yescharacteristic
99#121×C47C2312yes—
100#120×C47—22no—
101#120×C47—22no—
102#120×C47—22no—
103#120×C47—22no—
104#120×C47—22no—
105C4×Q8×C47—21no—
106C4×Q8×C47D411yescharacteristic, complemented
107C4×D4×C47—22no—
108C4×D4×C47—21no—
109C4×D4×C47—21no—
110C4×D4×C47—22no—
111C4×D4×C47—21no—
112C4×D4×C47D411yescharacteristic, complemented
113C4×D4×C47D412yescomplemented
114#117×C47—21no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—24no—
117C2×C22⋊C4×C47D412yes—
118C2×C22⋊C4×C47C2312yes—
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123#102×C47—22no—
124#102×C47—24no—
125#102×C47—22no—
126C22⋊C8×C47C2312yes—
127C22⋊C8×C47C2312yes—
128#97×C47—21no—
129C4×C8×C47—21no—
130#95×C47—21no—
131#95×C47C2312yes—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47C2×D412yes—
135#41×C47—82no—
136#41×C47—82no—
137C2×Q8×C47—21no—
138C2×Q8×C47—21no—
139C2×Q8×C47—21no—
140C2×Q8×C47—42no—
141C2×Q8×C47C2×D411yescharacteristic
142C2×D4×C47—22no—
143C2×D4×C47—21no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47—22no—
148C2×D4×C47—22no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47—42no—
158C2×D4×C47—48no—
159C2×D4×C47—41no—
160C2×D4×C47—41no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—82no—
164C2×D4×C47—82no—
165C2×D4×C47—82no—
166C2×D4×C47—84no—
167C2×D4×C47—84no—
168C2×D4×C47—84no—
169C2×D4×C47C2×D411yescharacteristic
170C2×D4×C47C2×D412yes—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—21no—
175C22×C4×C47—22no—
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2411yescharacteristic
180SD16×C47—82no—
181D8×C47—84no—
182D8×C47—82no—
183C2×C8×C47—22no—
184C2×C8×C47—22no—
185C4⋊C4×C47—22no—
186C4⋊C4×C47—22no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47C2×D412yes—
193C4⋊C4×C47C2×D411yescharacteristic
194C4⋊C4×C47C2×D411yescharacteristic
195C22⋊C4×C47—22no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—22no—
199C22⋊C4×C47—22no—
200C22⋊C4×C47—21no—
201C22⋊C4×C47—21no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—22no—
204C22⋊C4×C47—21no—
205C22⋊C4×C47—21no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—21no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—48no—
212C42×C47—24no—
213C42×C47—22no—
214C42×C47—21no—
215C42×C47C2×D411yescharacteristic
216C42×C47C2×D411yescharacteristic
217C42×C47C2×D411yescharacteristic
218C42×C47C2×D411yescharacteristic
219C23×C47—22no—
220C23×C47—21no—
221C23×C47—22no—
222C23×C47—24no—
223C23×C47—42no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—44no—
228C23×C47—42no—
229C23×C47—44no—
230C23×C47—82no—
231C23×C47—82no—
232C23×C47—82no—
233C23×C47C22×D411yescharacteristic
234Q8×C47—41no—
235Q8×C47—42no—
236Q8×C47—81no—
237Q8×C47—81no—
238D4×C47—42no—
239D4×C47—41no—
240D4×C47—44no—
241D4×C47—42no—
242D4×C47—42no—
243D4×C47—42no—
244D4×C47—44no—
245D4×C47—42no—
246D4×C47—42no—
247D4×C47—81no—
248D4×C47—81no—
249D4×C47—82no—
250D4×C47—82no—
251D4×C47—82no—
252D4×C47—82no—
253D4×C47—82no—
254D4×C47—82no—
255D4×C47—82no—
256D4×C47—82no—
257D4×C47—816no—
258D4×C47—82no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—24no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—41no—
268C2×C4×C47—42no—
269C2×C4×C47—42no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—82no—
273C2×C4×C47—82no—
274C2×C4×C47—82no—
275C2×C4×C47#12011yescharacteristic
276C2×C4×C47#12011yescharacteristic
277C2×C4×C47#12011yescharacteristic
278C2×C4×C47#12011yescharacteristic
279C2×C4×C47C22×D411yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C8×C47—42no—
282C8×C47—42no—
283#18426C4711yesmaximal, characteristic, direct product factor, Sylow
284C22×C47—21no—
285C22×C47—21no—
286C22×C47—42no—
287C22×C47—42no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—42no—
291C22×C47—42no—
292C22×C47—42no—
293C22×C47—41no—
294C22×C47—42no—
295C22×C47—84no—
296C22×C47—84no—
297C22×C47—84no—
298C22×C47—82no—
299C22×C47—82no—
300C22×C47—82no—
301C22×C47—164no—
302C22×C47C2×#12011yescharacteristic
303C22×C47#57612yes—
304C4×C47—21no—
305C4×C47—21no—
306C4×C47—21no—
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—44no—
310C4×C47—41no—
311C4×C47—42no—
312C4×C47—41no—
313C4×C47—42no—
314C4×C47—41no—
315C4×C47#45312yes—
316#3558C2×C4711yescharacteristic, complemented
317#3217C2×C4711yescharacteristic, complemented
318#3205C2×C4711yescharacteristic, complemented
319#2657C2×C4711yescharacteristic, complemented
320#1600C2×C4714yescomplemented
321#1595C2×C4714yescomplemented
322#1505C2×C4711yescharacteristic, complemented
323#1500C2×C4711yescharacteristic, complemented
324#1469C2×C4711yescharacteristic, complemented
325C2×C47—22no—
326C2×C47—82no—
327C2×C47—82no—
328C2×C47—81no—
329C2×C47—162no—
330C2×C47#300811yescharacteristic
331C2×C47C2×#45311yescharacteristic
332C2×C47#302711yescharacteristic
333#562—21no—
334H(3,𝔽4)—21no—
335#559—21no—
336#548—21no—
337#546—21no—
338#546—22no—
339D42—21no—
340#542—21no—
341#538—22no—
342#538C22×C4712yes—
343#535—21no—
344#534C22×C4712yes—
345#532C22×C4711yescharacteristic
346C2×#127—21no—
347C2×#127C22×C4711yescharacteristic, complemented
348#529C22×C4711yescharacteristic
349C2×#124—21no—
350C2×#124C22×C4711yescharacteristic
351#496—21no—
352#493—21no—
353#490—21no—
354#486—21no—
355#460—21no—
356#459—22no—
357#459—21no—
358#450C22×C4712yescomplemented
359#447C22×C4712yes—
360#447C22×C4714yescomplemented
361#432C22×C4711yescharacteristic, complemented
362#431C22×C4711yescharacteristic, complemented
363#392—22no—
364#392C22×C4714yescomplemented
365#376C22×C4711yescharacteristic, complemented
366#328C22×C4712yescomplemented
367#327C22×C4712yes—
368#327C22×C4714yescomplemented
369#323C22×C4714yescomplemented
370C47#1842611yescharacteristic, direct product factor, Sylow
371C2×#41—21no—
372C2×#41—21no—
373C22×Q8D4×C4711yescharacteristic
374C22×D4—21no—
375C22×D4—22no—
376C22×D4—24no—
377C22×D4—21no—
378C22×D4—21no—
379C22×D4D4×C4711yescharacteristic
380C22×D4C23×C4712yes—
381C2×SD16—22no—
382C2×D8—22no—
383C2×D8—24no—
384C4⋊Q8D4×C4711yescharacteristic, complemented
385#127—21no—
386#127—21no—
387#127—21no—
388#127—21no—
389#127—21no—
390#127—44no—
391#127D4×C4711yescharacteristic, complemented
392#126—22no—
393#126—21no—
394#125D4×C4711yescharacteristic, complemented
395#124—21no—
396#124—22no—
397#124—22no—
398#124—22no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124—21no—
403#124—21no—
404#124—44no—
405#124D4×C4711yescharacteristic, complemented
406#123—22no—
407#123—21no—
408#123—22no—
409#123—22no—
410#123—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8C23×C4711yescharacteristic
415#121—22no—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—22no—
420#121—21no—
421#121—22no—
422#121C23×C4711yescharacteristic
423#121C23×C4712yes—
424#120—22no—
425#120—22no—
426#120—22no—
427#120—22no—
428#120—22no—
429C4×Q8—21no—
430C4×Q8D4×C4711yescharacteristic, complemented
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4D4×C4711yescharacteristic, complemented
437C4×D4D4×C4712yescomplemented
438#117—21no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4D4×C4712yes—
442C2×C22⋊C4C23×C4712yes—
443C2×C42—21no—
444C2×C42C23×C4711yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—21no—
447#102—22no—
448#102—24no—
449#102—22no—
450C22⋊C8C23×C4712yes—
451C22⋊C8C23×C4712yes—
452#97—21no—
453C4×C8—21no—
454#95—21no—
455#95C23×C4712yes—
456C24—22no—
457C24—22no—
458C24C2×D4×C4712yes—
459#41—82no—
460#41—82no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8C2×D4×C4711yescharacteristic
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—48no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—82no—
488C2×D4—82no—
489C2×D4—82no—
490C2×D4—84no—
491C2×D4—84no—
492C2×D4—84no—
493C2×D4C2×D4×C4711yescharacteristic
494C2×D4C2×D4×C4712yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4C2×D4×C4711yescharacteristic
501C22×C4C2×D4×C4711yescharacteristic
502C22×C4C2×D4×C4712yes—
503C22×C4C24×C4711yescharacteristic
504SD16—82no—
505D8—84no—
506D8—82no—
507C2×C8—22no—
508C2×C8—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4C2×D4×C4712yes—
517C4⋊C4C2×D4×C4711yescharacteristic
518C4⋊C4C2×D4×C4711yescharacteristic
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—48no—
536C42—24no—
537C42—22no—
538C42—21no—
539C42C2×D4×C4711yescharacteristic
540C42C2×D4×C4711yescharacteristic
541C42C2×D4×C4711yescharacteristic
542C42C2×D4×C4711yescharacteristic
543C23—22no—
544C23—21no—
545C23—22no—
546C23—24no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—44no—
552C23—42no—
553C23—44no—
554C23—82no—
555C23—82no—
556C23—82no—
557C23C22×D4×C4711yescharacteristic
558Q8—41no—
559Q8—42no—
560Q8—81no—
561Q8—81no—
562D4—42no—
563D4—41no—
564D4—44no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—44no—
569D4—42no—
570D4—42no—
571D4—81no—
572D4—81no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—816no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4#120×C4711yescharacteristic
600C2×C4#120×C4711yescharacteristic
601C2×C4#120×C4711yescharacteristic
602C2×C4#120×C4711yescharacteristic
603C2×C4C22×D4×C4711yescharacteristic
604C2×C4C22×D4×C4711yescharacteristic
605C8—42no—
606C8—42no—
607C22—21no—
608C22—21no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—84no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—164no—
625C22C2×#120×C4711yescharacteristic
626C22C47×#57612yes—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—41no—
638C4C47×#45312yes—
639C2—22no—
640C2—82no—
641C2—81no—
642C2—82no—
643C2—162no—
644C2C47×#300811yescharacteristic
645C2C2×C47×#45311yescharacteristic
646C2C47×#302711yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3558C2semidirect
2. C47×#3217C2semidirect
3. C47×#3205C2semidirect
4. C47×#2657C2semidirect
5. C47×#1600C2semidirect
6. C47×#1595C2semidirect
7. C47×#1505C2semidirect
8. C47×#1500C2semidirect
9. C47×#1469C2semidirect
24. C2×#127×C47C22semidirect
35. C47×#450C22semidirect
37. C47×#447C22semidirect
38. C47×#432C22semidirect
39. C47×#431C22semidirect
41. C47×#392C22semidirect
42. C47×#376C22semidirect
43. C47×#328C22semidirect
45. C47×#327C22semidirect
46. C47×#323C22semidirect
60. C4⋊Q8×C47D4semidirect
67. #127×C47D4semidirect
70. #125×C47D4semidirect
81. #124×C47D4semidirect
106. C4×Q8×C47D4semidirect
112. C4×D4×C47D4semidirect
113. C4×D4×C47D4semidirect
283. #18426C47direct (N × H)
316. #3558C2×C47semidirect
317. #3217C2×C47semidirect
318. #3205C2×C47semidirect
319. #2657C2×C47semidirect
320. #1600C2×C47semidirect
321. #1595C2×C47semidirect
322. #1505C2×C47semidirect
323. #1500C2×C47semidirect
324. #1469C2×C47semidirect
347. C2×#127C22×C47semidirect
358. #450C22×C47semidirect
360. #447C22×C47semidirect
361. #432C22×C47semidirect
362. #431C22×C47semidirect
364. #392C22×C47semidirect
365. #376C22×C47semidirect
366. #328C22×C47semidirect
368. #327C22×C47semidirect
369. #323C22×C47semidirect
370. C47#18426direct (N × H)
384. C4⋊Q8D4×C47semidirect
391. #127D4×C47semidirect
394. #125D4×C47semidirect
405. #124D4×C47semidirect
430. C4×Q8D4×C47semidirect
436. C4×D4D4×C47semidirect
437. C4×D4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35582
C47×#32172
C47×#32052
C47×#26572
C47×#16002
C47×#15952
C47×#15052
C47×#15002
C47×#14692
#1842647