Finite Group Databasebeta

← C47×#61958 #26101656

Subgroups — C47×#61958 #26101656

Order 12032.

1922 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3517C211yesmaximal, characteristic, complemented
2C47×#3483C211yesmaximal, characteristic, complemented
3C47×#3392C211yesmaximal, characteristic, complemented
4C47×#3391C211yesmaximal, characteristic, complemented
5C47×#3363C211yesmaximal, characteristic, complemented
6C47×#3362C211yesmaximal, characteristic, complemented
7C47×#3305C213yesmaximal, complemented
8C47×#3303C213yesmaximal, complemented
9C47×#3287C213yesmaximal, complemented
10C47×#3284C213yesmaximal, complemented
11C47×#3247C213yesmaximal, complemented
12C47×#3207C213yesmaximal, complemented
13C47×#3102C213yesmaximal, complemented
14C47×#3035C213yesmaximal, complemented
15C47×#2988C211yesmaximal, characteristic, complemented
16C2×#135×C47C2216yes—
17Q82×C47C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#555—23no—
20C47×#555C2213yes—
21C47×#553—23no—
22C47×#550—21no—
23C47×#550—21no—
24C47×#550C2213yes—
25C47×#550C2213yes—
26C47×#550C2211yescharacteristic
27C47×#550C2211yescharacteristic
28C47×#547C2213yes—
29C47×#540—23no—
30C47×#532—23no—
31C47×#532C2213yes—
32C47×#532C2213yes—
33C47×#529C2213yes—
34C47×#520—21no—
35C4×#41×C47—21no—
36C4×#41×C47C2213yes—
37C4×#41×C47C2211yescharacteristic
38C47×#493C2213yes—
39C47×#492C2213yes—
40C47×#487C2213yes—
41C47×#486C2213yes—
42C47×#485C2213yes—
43C47×#482C2213yes—
44C47×#479C2211yescharacteristic
45C47×#478C2213yes—
46C47×#477C2213yes—
47C47×#476C2213yes—
48C47×#466C2216yes—
49C47×#465C2216yes—
50C47×#464C2213yes—
51C47×#463C2216yes—
52C47×#463C2213yes—
53C47×#462C2213yes—
54C47×#461C2213yes—
55C47×#460C2213yes—
56C47×#460C2213yes—
57C47×#459C2213yes—
58C47×#459C2213yes—
59C47×#452C2213yes—
60C47×#449C2213yes—
61C47×#449C2216yes—
62C47×#449C2216yes—
63C8×Q8×C47C2211yescharacteristic
64C8×Q8×C47C2211yescharacteristic
65C4×Q16×C47C2213yes—
66C4×SD16×C47C2213yes—
67C4×SD16×C47C2213yes—
68C4×D8×C47C2213yes—
69C8×D4×C47C2213yes—
70C8×D4×C47C2213yes—
71C47×#431C2213yes—
72C2×C4⋊C8×C47C2213yes—
73C47×#416C2216yes—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47—23no—
77C2×#41×C47D411yescharacteristic
78C2×#41×C47C2313yes—
79C2×#41×C47C2316yes—
80#135×C47—412no—
81C2×Q16×C47C2313yes—
82C2×SD16×C47C2313yes—
83C2×SD16×C47C2313yes—
84C2×SD16×C47C2316yes—
85C2×D8×C47C2313yes—
86C2×D8×C47C2316yes—
87C22×C8×C47C2316yes—
88C4⋊Q8×C47—23no—
89C4⋊Q8×C47C2313yes—
90C4⋊Q8×C47C2313yes—
91#127×C47—23no—
92#127×C47—23no—
93#127×C47C2313yes—
94#127×C47C2313yes—
95#126×C47—23no—
96#125×C47—23no—
97#125×C47C2311yescharacteristic
98#124×C47—26no—
99#124×C47—23no—
100#124×C47C2313yes—
101#123×C47—23no—
102#123×C47—26no—
103C22⋊Q8×C47C2313yes—
104#121×C47—23no—
105#121×C47—23no—
106#121×C47—23no—
107#121×C47—23no—
108#121×C47—23no—
109#121×C47—23no—
110#121×C47—23no—
111#121×C47—26no—
112#121×C47—26no—
113#121×C47C2316yes—
114#121×C47C2313yes—
115C4×Q8×C47—21no—
116C4×Q8×C47—21no—
117C4×Q8×C47D411yescharacteristic
118C4×Q8×C47C2313yes—
119C4×Q8×C47C2313yes—
120C4×Q8×C47C2311yescharacteristic
121C4×Q8×C47C2311yescharacteristic
122C4×D4×C47—23no—
123C4×D4×C47—23no—
124C4×D4×C47—23no—
125C4×D4×C47—23no—
126C4×D4×C47—23no—
127C4×D4×C47—23no—
128C4×D4×C47—23no—
129C4×D4×C47—23no—
130C4×D4×C47D413yes—
131C4×D4×C47C2313yes—
132C4×D4×C47C2313yes—
133C4×D4×C47C2313yes—
134C4×D4×C47C2313yes—
135#117×C47—23no—
136#117×C47—23no—
137#117×C47—23no—
138#117×C47D413yes—
139#117×C47C2313yes—
140C2×C4⋊C4×C47—23no—
141C2×C42×C47—23no—
142C2×C42×C47C2313yes—
143#107×C47C2313yes—
144#107×C47C2311yescharacteristic
145#106×C47C2313yes—
146#106×C47C2311yescharacteristic
147C4⋊C8×C47C2313yes—
148C4⋊C8×C47C2313yes—
149C4⋊C8×C47C2311yescharacteristic
150C4⋊C8×C47C2313yes—
151#103×C47C2311yescharacteristic
152#103×C47C2313yes—
153#103×C47C2316yes—
154#103×C47C2311yescharacteristic
155#103×C47C2313yes—
156#102×C47C2313yes—
157#102×C47C2313yes—
158#102×C47C2316yes—
159#102×C47C2313yes—
160#102×C47C2313yes—
161C22⋊C8×C47C2313yes—
162C22⋊C8×C47C2313yes—
163C4×C8×C47C2313yes—
164C4×C8×C47C2313yes—
165#41×C47—24no—
166#41×C47—26no—
167#41×C47—43no—
168#41×C47—46no—
169#41×C47—46no—
170#41×C47—44no—
171#41×C47—44no—
172#41×C47—86no—
173C2×Q8×C47—23no—
174C2×Q8×C47C2×D411yescharacteristic
175C2×Q8×C47C2413yes—
176C2×Q8×C47C2411yescharacteristic
177C2×D4×C47—23no—
178C2×D4×C47—23no—
179C2×D4×C47—26no—
180C2×D4×C47—26no—
181C2×D4×C47—23no—
182C2×D4×C47—23no—
183C2×D4×C47—23no—
184C2×D4×C47—23no—
185C2×D4×C47C2×D413yes—
186C2×D4×C47C2413yes—
187C2×D4×C47C2413yes—
188C22×C4×C47—23no—
189C22×C4×C47—23no—
190C22×C4×C47—23no—
191C22×C4×C47—23no—
192C22×C4×C47—26no—
193C22×C4×C47C2×D413yes—
194C22×C4×C47C2×D413yes—
195C22×C4×C47C2413yes—
196Q16×C47—26no—
197SD16×C47—26no—
198SD16×C47—43no—
199SD16×C47—46no—
200D8×C47—43no—
201D8×C47—46no—
202C2×C8×C47—46no—
203C2×C8×C47C2411yescharacteristic
204C2×C8×C47C2413yes—
205C2×C8×C47C2413yes—
206C2×C8×C47C2411yescharacteristic
207C4⋊C4×C47—23no—
208C4⋊C4×C47—23no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—23no—
212C4⋊C4×C47—23no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—23no—
215C4⋊C4×C47—23no—
216C4⋊C4×C47C2×D413yes—
217C4⋊C4×C47C2×D413yes—
218C4⋊C4×C47C2411yescharacteristic
219C4⋊C4×C47C2413yes—
220C4⋊C4×C47C2411yescharacteristic
221C4⋊C4×C47C2411yescharacteristic
222C22⋊C4×C47—23no—
223C22⋊C4×C47—23no—
224C22⋊C4×C47—23no—
225C22⋊C4×C47—23no—
226C22⋊C4×C47—26no—
227C22⋊C4×C47—23no—
228C22⋊C4×C47—23no—
229C22⋊C4×C47—23no—
230C22⋊C4×C47—23no—
231C22⋊C4×C47C2×D416yes—
232C42×C47—21no—
233C42×C47—23no—
234C42×C47—23no—
235C42×C47—23no—
236C42×C47C2×D413yes—
237C42×C47C2×D413yes—
238C42×C47C2411yescharacteristic
239C42×C47C2413yes—
240C23×C47—23no—
241C23×C47—23no—
242C23×C47C22×D413yes—
243Q8×C47—21no—
244Q8×C47—23no—
245Q8×C47—23no—
246Q8×C47—83no—
247Q8×C47#13514yescomplemented
248Q8×C47H(5,𝔽2)12yes—
249D4×C47—26no—
250D4×C47—23no—
251D4×C47—23no—
252D4×C47—23no—
253D4×C47—23no—
254D4×C47—46no—
255D4×C47—46no—
256D4×C47—46no—
257D4×C47—83no—
258D4×C47—83no—
259D4×C47—83no—
260D4×C47—86no—
261D4×C47—86no—
262C2×C4×C47—21no—
263C2×C4×C47—26no—
264C2×C4×C47—23no—
265C2×C4×C47—23no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—23no—
269C2×C4×C47—23no—
270C2×C4×C47—21no—
271C2×C4×C47—43no—
272C2×C4×C47—46no—
273C2×C4×C47—46no—
274C2×C4×C47—46no—
275C2×C4×C47—46no—
276C2×C4×C47—86no—
277C2×C4×C47C22×D411yescharacteristic
278C2×C4×C47C22×D413yes—
279C2×C4×C47C22×D411yescharacteristic
280C2×C4×C47C22×D413yes—
281C2×C4×C47C22×D413yes—
282C2×C4×C47C2511yescharacteristic
283C8×C47—23no—
284C8×C47—23no—
285C8×C47—21no—
286C8×C47—21no—
287#61958C4711yesmaximal, characteristic, direct product factor, Sylow
288C22×C47—23no—
289C22×C47—23no—
290C22×C47—23no—
291C22×C47—43no—
292C22×C47—43no—
293C22×C47—43no—
294C22×C47—43no—
295C22×C47—43no—
296C22×C47—43no—
297C22×C47C23×D411yescharacteristic
298C4×C47—21no—
299C4×C47—23no—
300C4×C47—23no—
301C4×C47—22no—
302C4×C47—21no—
303C4×C47—43no—
304C4×C47—41no—
305C4×C47—43no—
306C4×C47—41no—
307C4×C47—41no—
308C4×C47C2×#13516yes—
309C4×C47C2×H(5,𝔽2)11yescharacteristic
310C4×C47#58511yescharacteristic
311#3517C2×C4711yescharacteristic, complemented
312#3483C2×C4711yescharacteristic, complemented
313#3392C2×C4711yescharacteristic, complemented
314#3391C2×C4711yescharacteristic, complemented
315#3363C2×C4711yescharacteristic, complemented
316#3362C2×C4711yescharacteristic, complemented
317#3305C2×C4713yescomplemented
318#3303C2×C4713yescomplemented
319#3287C2×C4713yescomplemented
320#3284C2×C4713yescomplemented
321#3247C2×C4713yescomplemented
322#3207C2×C4713yescomplemented
323#3102C2×C4713yescomplemented
324#3035C2×C4713yescomplemented
325#2988C2×C4711yescharacteristic, complemented
326C2×C47—43no—
327C2×C47—83no—
328C2×C47—83no—
329C2×C47#348811yescharacteristic
330C2×C47C22×#13511yescharacteristic
331C2×C47#358511yescharacteristic
332C2×#135C22×C4716yes—
333Q82C22×C4711yescharacteristic
334#557C22×C4711yescharacteristic
335#555—23no—
336#555C22×C4713yes—
337#553—23no—
338#550—21no—
339#550—21no—
340#550C22×C4713yes—
341#550C22×C4713yes—
342#550C22×C4711yescharacteristic
343#550C22×C4711yescharacteristic
344#547C22×C4713yes—
345#540—23no—
346#532—23no—
347#532C22×C4713yes—
348#532C22×C4713yes—
349#529C22×C4713yes—
350#520—21no—
351C4×#41—21no—
352C4×#41C22×C4713yes—
353C4×#41C22×C4711yescharacteristic
354#493C22×C4713yes—
355#492C22×C4713yes—
356#487C22×C4713yes—
357#486C22×C4713yes—
358#485C22×C4713yes—
359#482C22×C4713yes—
360#479C22×C4711yescharacteristic
361#478C22×C4713yes—
362#477C22×C4713yes—
363#476C22×C4713yes—
364#466C22×C4716yes—
365#465C22×C4716yes—
366#464C22×C4713yes—
367#463C22×C4713yes—
368#463C22×C4716yes—
369#462C22×C4713yes—
370#461C22×C4713yes—
371#460C22×C4713yes—
372#460C22×C4713yes—
373#459C22×C4713yes—
374#459C22×C4713yes—
375#452C22×C4713yes—
376#449C22×C4713yes—
377#449C22×C4716yes—
378#449C22×C4716yes—
379C8×Q8C22×C4711yescharacteristic
380C8×Q8C22×C4711yescharacteristic
381C4×Q16C22×C4713yes—
382C4×SD16C22×C4713yes—
383C4×SD16C22×C4713yes—
384C4×D8C22×C4713yes—
385C8×D4C22×C4713yes—
386C8×D4C22×C4713yes—
387#431C22×C4713yes—
388C2×C4⋊C8C22×C4713yes—
389#416C22×C4716yes—
390C47#6195811yescharacteristic, direct product factor, Sylow
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—23no—
394C2×#41D4×C4711yescharacteristic
395C2×#41C23×C4713yes—
396C2×#41C23×C4716yes—
397#135—412no—
398C2×Q16C23×C4713yes—
399C2×SD16C23×C4713yes—
400C2×SD16C23×C4716yes—
401C2×SD16C23×C4713yes—
402C2×D8C23×C4716yes—
403C2×D8C23×C4713yes—
404C22×C8C23×C4716yes—
405C4⋊Q8—23no—
406C4⋊Q8C23×C4713yes—
407C4⋊Q8C23×C4713yes—
408#127—23no—
409#127—23no—
410#127C23×C4713yes—
411#127C23×C4713yes—
412#126—23no—
413#125—23no—
414#125C23×C4711yescharacteristic
415#124—26no—
416#124—23no—
417#124C23×C4713yes—
418#123—23no—
419#123—26no—
420C22⋊Q8C23×C4713yes—
421#121—23no—
422#121—23no—
423#121—23no—
424#121—23no—
425#121—23no—
426#121—23no—
427#121—23no—
428#121—26no—
429#121—26no—
430#121C23×C4713yes—
431#121C23×C4716yes—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8D4×C4711yescharacteristic
435C4×Q8C23×C4711yescharacteristic
436C4×Q8C23×C4713yes—
437C4×Q8C23×C4713yes—
438C4×Q8C23×C4711yescharacteristic
439C4×D4—23no—
440C4×D4—23no—
441C4×D4—23no—
442C4×D4—23no—
443C4×D4—23no—
444C4×D4—23no—
445C4×D4—23no—
446C4×D4—23no—
447C4×D4D4×C4713yes—
448C4×D4C23×C4713yes—
449C4×D4C23×C4713yes—
450C4×D4C23×C4713yes—
451C4×D4C23×C4713yes—
452#117—23no—
453#117—23no—
454#117—23no—
455#117D4×C4713yes—
456#117C23×C4713yes—
457C2×C4⋊C4—23no—
458C2×C42—23no—
459C2×C42C23×C4713yes—
460#107C23×C4711yescharacteristic
461#107C23×C4713yes—
462#106C23×C4711yescharacteristic
463#106C23×C4713yes—
464C4⋊C8C23×C4713yes—
465C4⋊C8C23×C4713yes—
466C4⋊C8C23×C4713yes—
467C4⋊C8C23×C4711yescharacteristic
468#103C23×C4713yes—
469#103C23×C4716yes—
470#103C23×C4711yescharacteristic
471#103C23×C4711yescharacteristic
472#103C23×C4713yes—
473#102C23×C4713yes—
474#102C23×C4716yes—
475#102C23×C4713yes—
476#102C23×C4713yes—
477#102C23×C4713yes—
478C22⋊C8C23×C4713yes—
479C22⋊C8C23×C4713yes—
480C4×C8C23×C4713yes—
481C4×C8C23×C4713yes—
482#41—24no—
483#41—26no—
484#41—43no—
485#41—46no—
486#41—46no—
487#41—44no—
488#41—44no—
489#41—86no—
490C2×Q8—23no—
491C2×Q8C2×D4×C4711yescharacteristic
492C2×Q8C24×C4713yes—
493C2×Q8C24×C4711yescharacteristic
494C2×D4—23no—
495C2×D4—23no—
496C2×D4—26no—
497C2×D4—26no—
498C2×D4—23no—
499C2×D4—23no—
500C2×D4—23no—
501C2×D4—23no—
502C2×D4C2×D4×C4713yes—
503C2×D4C24×C4713yes—
504C2×D4C24×C4713yes—
505C22×C4—23no—
506C22×C4—23no—
507C22×C4—23no—
508C22×C4—23no—
509C22×C4—26no—
510C22×C4C2×D4×C4713yes—
511C22×C4C2×D4×C4713yes—
512C22×C4C24×C4713yes—
513Q16—26no—
514SD16—26no—
515SD16—43no—
516SD16—46no—
517D8—43no—
518D8—46no—
519C2×C8—46no—
520C2×C8C24×C4711yescharacteristic
521C2×C8C24×C4711yescharacteristic
522C2×C8C24×C4713yes—
523C2×C8C24×C4713yes—
524C4⋊C4—23no—
525C4⋊C4—23no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—23no—
529C4⋊C4—23no—
530C4⋊C4—21no—
531C4⋊C4—23no—
532C4⋊C4—23no—
533C4⋊C4C2×D4×C4713yes—
534C4⋊C4C2×D4×C4713yes—
535C4⋊C4C24×C4711yescharacteristic
536C4⋊C4C24×C4713yes—
537C4⋊C4C24×C4711yescharacteristic
538C4⋊C4C24×C4711yescharacteristic
539C22⋊C4—23no—
540C22⋊C4—23no—
541C22⋊C4—23no—
542C22⋊C4—23no—
543C22⋊C4—26no—
544C22⋊C4—23no—
545C22⋊C4—23no—
546C22⋊C4—23no—
547C22⋊C4—23no—
548C22⋊C4C2×D4×C4716yes—
549C42—21no—
550C42—23no—
551C42—23no—
552C42—23no—
553C42C2×D4×C4713yes—
554C42C2×D4×C4713yes—
555C42C24×C4713yes—
556C42C24×C4711yescharacteristic
557C23—23no—
558C23—23no—
559C23C22×D4×C4713yes—
560Q8—21no—
561Q8—23no—
562Q8—23no—
563Q8—83no—
564Q8#135×C4714yescomplemented
565Q8H(5,𝔽2)×C4712yes—
566D4—26no—
567D4—23no—
568D4—23no—
569D4—23no—
570D4—23no—
571D4—46no—
572D4—46no—
573D4—46no—
574D4—83no—
575D4—83no—
576D4—83no—
577D4—86no—
578D4—86no—
579C2×C4—21no—
580C2×C4—26no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—23no—
587C2×C4—21no—
588C2×C4—43no—
589C2×C4—46no—
590C2×C4—46no—
591C2×C4—46no—
592C2×C4—46no—
593C2×C4—86no—
594C2×C4C22×D4×C4711yescharacteristic
595C2×C4C22×D4×C4713yes—
596C2×C4C22×D4×C4711yescharacteristic
597C2×C4C22×D4×C4713yes—
598C2×C4C22×D4×C4713yes—
599C2×C4C25×C4711yescharacteristic
600C8—23no—
601C8—23no—
602C8—21no—
603C8—21no—
604C22—23no—
605C22—23no—
606C22—23no—
607C22—43no—
608C22—43no—
609C22—43no—
610C22—43no—
611C22—43no—
612C22—43no—
613C22C23×D4×C4711yescharacteristic
614C4—21no—
615C4—21no—
616C4—23no—
617C4—23no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—43no—
622C4—41no—
623C4—43no—
624C4C2×#135×C4716yes—
625C4C2×H(5,𝔽2)×C4711yescharacteristic
626C4C47×#58511yescharacteristic
627C2—43no—
628C2—83no—
629C2—83no—
630C2C47×#348811yescharacteristic
631C2C22×#135×C4711yescharacteristic
632C2C47×#358511yescharacteristic
subgroupG/H
center, socleC22×C47C23×D4
commutator, Frattini, cosocleC2×C4C25×C47
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3517C2semidirect
2. C47×#3483C2semidirect
3. C47×#3392C2semidirect
4. C47×#3391C2semidirect
5. C47×#3363C2semidirect
6. C47×#3362C2semidirect
7. C47×#3305C2semidirect
8. C47×#3303C2semidirect
9. C47×#3287C2semidirect
10. C47×#3284C2semidirect
11. C47×#3247C2semidirect
12. C47×#3207C2semidirect
13. C47×#3102C2semidirect
14. C47×#3035C2semidirect
15. C47×#2988C2semidirect
247. Q8×C47#135semidirect
287. #61958C47direct (N × H)
311. #3517C2×C47semidirect
312. #3483C2×C47semidirect
313. #3392C2×C47semidirect
314. #3391C2×C47semidirect
315. #3363C2×C47semidirect
316. #3362C2×C47semidirect
317. #3305C2×C47semidirect
318. #3303C2×C47semidirect
319. #3287C2×C47semidirect
320. #3284C2×C47semidirect
321. #3247C2×C47semidirect
322. #3207C2×C47semidirect
323. #3102C2×C47semidirect
324. #3035C2×C47semidirect
325. #2988C2×C47semidirect
390. C47#61958direct (N × H)
564. Q8#135×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35172
C47×#34832
C47×#33922
C47×#33912
C47×#33632
C47×#33622
C47×#33052
C47×#33032
C47×#32872
C47×#32842
C47×#32472
C47×#32072
C47×#31022
C47×#30352
C47×#29882
#6195847