Finite Group Databasebeta

← C47×#61434 #26101132

Subgroups — C47×#61434 #26101132

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3483C211yesmaximal, characteristic, complemented
2C47×#3482C211yesmaximal, characteristic, complemented
3C47×#3392C211yesmaximal, characteristic, complemented
4Q8×SD16×C47C211yesmaximal, characteristic, complemented
5C47×#3363C211yesmaximal, characteristic, complemented
6C47×#3358C211yesmaximal, characteristic, complemented
7C47×#3340C213yesmaximal, complemented
8C47×#3304C213yesmaximal, complemented
9C47×#3303C213yesmaximal, complemented
10C47×#3284C213yesmaximal, complemented
11C47×#3167C213yesmaximal, complemented
12C47×#3107C213yesmaximal, complemented
13C47×#3106C213yesmaximal, complemented
14C8×#41×C47C211yesmaximal, characteristic, complemented
15C4×#135×C47C213yesmaximal, complemented
16C2×#135×C47C2213yes—
17Q82×C47C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#556C2213yes—
20C47×#555—23no—
21C47×#555C2213yes—
22C47×#552—23no—
23C47×#550—21no—
24C47×#550C2213yes—
25C47×#550C2211yescharacteristic
26D4×Q8×C47C2211yescharacteristic
27C47×#548—21no—
28C47×#547C2213yes—
29C47×#533C2213yes—
30C47×#532—23no—
31C47×#532C2213yes—
32C47×#529—23no—
33C4×#41×C47—21no—
34C4×#41×C47C2213yes—
35C4×#41×C47C2213yes—
36C4×#41×C47C2211yescharacteristic
37C2×C4×Q8×C47—21no—
38C47×#498C2213yes—
39C47×#492C2213yes—
40C47×#487C2213yes—
41C47×#486C2213yes—
42C47×#485C2216yes—
43C47×#482C2216yes—
44C47×#477C2213yes—
45C47×#476C2213yes—
46C47×#475C2213yes—
47C47×#474C2213yes—
48C47×#465C2216yes—
49C47×#465C2216yes—
50C47×#462C2213yes—
51C47×#461C2213yes—
52C47×#460C2213yes—
53C47×#459C2213yes—
54C47×#452C2216yes—
55C47×#449C2216yes—
56C8×Q8×C47C2211yescharacteristic
57C8×Q8×C47C2211yescharacteristic
58C4×Q16×C47C2213yes—
59C4×Q16×C47C2213yes—
60C4×SD16×C47C2213yes—
61C4×SD16×C47C2216yes—
62C4×SD16×C47C2213yes—
63C4×SD16×C47C2213yes—
64C4×SD16×C47C2211yescharacteristic
65C4×D8×C47C2213yes—
66C4×D8×C47C2213yes—
67C8×D4×C47C2213yes—
68C8×D4×C47C2213yes—
69C47×#431C2213yes—
70C47×#427C2213yes—
71C47×#416C2213yes—
72C47×#416C2213yes—
73C2×C4×C8×C47C2213yes—
74C2×#41×C47—21no—
75C2×#41×C47—23no—
76C2×#41×C47D411yescharacteristic
77C2×#41×C47C2313yes—
78C2×#41×C47C2313yes—
79C22×Q8×C47—21no—
80#135×C47—212no—
81C2×Q16×C47C2313yes—
82C2×SD16×C47C2313yes—
83C2×SD16×C47C2316yes—
84C2×SD16×C47C2311yescharacteristic
85C2×D8×C47C2313yes—
86C22×C8×C47C2313yes—
87C22×C8×C47C2313yes—
88C4⋊Q8×C47—23no—
89C4⋊Q8×C47C2313yes—
90C4⋊Q8×C47C2313yes—
91C4⋊Q8×C47C2313yes—
92#127×C47—23no—
93#127×C47C2313yes—
94#126×C47—26no—
95#125×C47—23no—
96#125×C47—23no—
97#124×C47—23no—
98#124×C47—26no—
99#124×C47—23no—
100#123×C47—26no—
101C22⋊Q8×C47—23no—
102C22⋊Q8×C47—23no—
103C22⋊Q8×C47C2316yes—
104#121×C47—23no—
105#121×C47—23no—
106#121×C47—23no—
107#121×C47—23no—
108#121×C47—26no—
109#121×C47C2316yes—
110C4×Q8×C47—21no—
111C4×Q8×C47—21no—
112C4×Q8×C47—23no—
113C4×Q8×C47—23no—
114C4×Q8×C47D411yescharacteristic
115C4×Q8×C47C2313yes—
116C4×Q8×C47C2313yes—
117C4×Q8×C47C2311yescharacteristic
118C4×Q8×C47C2313yes—
119C4×Q8×C47C2311yescharacteristic
120C4×D4×C47—23no—
121C4×D4×C47—23no—
122C4×D4×C47—23no—
123C4×D4×C47—23no—
124C4×D4×C47—23no—
125C4×D4×C47—23no—
126C4×D4×C47D413yes—
127C4×D4×C47C2313yes—
128C4×D4×C47C2313yes—
129C4×D4×C47C2311yescharacteristic
130C4×D4×C47C2313yes—
131C4×D4×C47C2313yes—
132#117×C47—23no—
133#117×C47—23no—
134#117×C47—23no—
135#117×C47—23no—
136#117×C47D413yes—
137#117×C47C2313yes—
138#117×C47C2313yes—
139C2×C4⋊C4×C47—23no—
140C2×C42×C47—23no—
141C2×C42×C47—23no—
142C2×C42×C47C2313yes—
143#107×C47C2313yes—
144#107×C47C2313yes—
145#106×C47C2313yes—
146#106×C47C2316yes—
147#106×C47C2311yescharacteristic
148C4⋊C8×C47C2313yes—
149C4⋊C8×C47C2313yes—
150#103×C47C2316yes—
151#103×C47C2313yes—
152#103×C47C2313yes—
153#103×C47C2313yes—
154#103×C47C2311yescharacteristic
155#102×C47C2313yes—
156#102×C47C2316yes—
157#102×C47C2313yes—
158#102×C47C2313yes—
159#102×C47C2311yescharacteristic
160C22⋊C8×C47C2316yes—
161C4×C8×C47C2313yes—
162C4×C8×C47C2313yes—
163C4×C8×C47C2311yescharacteristic
164C4×C8×C47C2313yes—
165#41×C47—24no—
166#41×C47—26no—
167#41×C47—26no—
168#41×C47—43no—
169#41×C47—43no—
170#41×C47—44no—
171#41×C47—86no—
172C2×Q8×C47—23no—
173C2×Q8×C47—23no—
174C2×Q8×C47—44no—
175C2×Q8×C47C2×D411yescharacteristic
176C2×Q8×C47C2413yes—
177C2×Q8×C47C2411yescharacteristic
178C2×D4×C47—23no—
179C2×D4×C47—23no—
180C2×D4×C47—26no—
181C2×D4×C47—23no—
182C2×D4×C47—23no—
183C2×D4×C47C2×D413yes—
184C2×D4×C47C2413yes—
185C2×D4×C47C2411yescharacteristic
186C22×C4×C47—23no—
187C22×C4×C47—23no—
188C22×C4×C47—23no—
189C22×C4×C47—23no—
190C22×C4×C47—21no—
191C22×C4×C47—23no—
192C22×C4×C47C2×D413yes—
193C22×C4×C47C2×D413yes—
194C22×C4×C47C2413yes—
195Q16×C47—26no—
196SD16×C47—26no—
197SD16×C47—46no—
198SD16×C47#4114yescomplemented
199D8×C47—26no—
200C2×C8×C47—26no—
201C2×C8×C47—43no—
202C2×C8×C47C2411yescharacteristic
203C2×C8×C47C2413yes—
204C2×C8×C47C2413yes—
205C2×C8×C47C2411yescharacteristic
206C4⋊C4×C47—23no—
207C4⋊C4×C47—26no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—23no—
210C4⋊C4×C47—23no—
211C4⋊C4×C47—23no—
212C4⋊C4×C47—23no—
213C4⋊C4×C47—23no—
214C4⋊C4×C47—23no—
215C4⋊C4×C47C2×D413yes—
216C4⋊C4×C47C2×D413yes—
217C4⋊C4×C47C2413yes—
218C4⋊C4×C47C2411yescharacteristic
219C4⋊C4×C47C2413yes—
220C4⋊C4×C47C2411yescharacteristic
221C22⋊C4×C47—26no—
222C22⋊C4×C47—23no—
223C22⋊C4×C47—23no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—26no—
226C22⋊C4×C47—23no—
227C22⋊C4×C47—23no—
228C22⋊C4×C47—23no—
229C22⋊C4×C47C2×D416yes—
230C42×C47—23no—
231C42×C47—23no—
232C42×C47—23no—
233C42×C47—23no—
234C42×C47—21no—
235C42×C47—23no—
236C42×C47C2×D413yes—
237C42×C47C2×D413yes—
238C42×C47C2413yes—
239C42×C47C2411yescharacteristic
240C23×C47—21no—
241C23×C47—23no—
242C23×C47C22×D413yes—
243Q8×C47—21no—
244Q8×C47—23no—
245Q8×C47—23no—
246Q8×C47—46no—
247Q8×C47—83no—
248Q8×C47#13514yescomplemented
249Q8×C47C2×#4112yes—
250D4×C47—26no—
251D4×C47—23no—
252D4×C47—21no—
253D4×C47—23no—
254D4×C47—46no—
255D4×C47—46no—
256D4×C47—46no—
257D4×C47—83no—
258D4×C47—86no—
259D4×C47C2×#4112yes—
260C2×C4×C47—21no—
261C2×C4×C47—26no—
262C2×C4×C47—26no—
263C2×C4×C47—23no—
264C2×C4×C47—23no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—23no—
268C2×C4×C47—23no—
269C2×C4×C47—23no—
270C2×C4×C47—46no—
271C2×C4×C47—46no—
272C2×C4×C47—46no—
273C2×C4×C47—46no—
274C2×C4×C47—42no—
275C2×C4×C47—46no—
276C2×C4×C47C22×D413yes—
277C2×C4×C47C22×D411yescharacteristic
278C2×C4×C47C22×D413yes—
279C2×C4×C47C22×D413yes—
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C2511yescharacteristic
282C8×C47—23no—
283C8×C47—21no—
284C8×C47—23no—
285C8×C47C2×#4112yes—
286#61434C4711yesmaximal, characteristic, direct product factor, Sylow
287C22×C47—23no—
288C22×C47—22no—
289C22×C47—23no—
290C22×C47—23no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—43no—
294C22×C47—43no—
295C22×C47—43no—
296C22×C47C23×D411yescharacteristic
297C4×C47—23no—
298C4×C47—22no—
299C4×C47—21no—
300C4×C47—23no—
301C4×C47—43no—
302C4×C47—41no—
303C4×C47—43no—
304C4×C47—41no—
305C4×C47—43no—
306C4×C47C2×#13516yes—
307C4×C47#57712yes—
308C4×C47C22×#4111yescharacteristic
309C4×C47#58511yescharacteristic
310#3483C2×C4711yescharacteristic, complemented
311#3482C2×C4711yescharacteristic, complemented
312#3392C2×C4711yescharacteristic, complemented
313Q8×SD16C2×C4711yescharacteristic, complemented
314#3363C2×C4711yescharacteristic, complemented
315#3358C2×C4711yescharacteristic, complemented
316#3340C2×C4713yescomplemented
317#3304C2×C4713yescomplemented
318#3303C2×C4713yescomplemented
319#3284C2×C4713yescomplemented
320#3167C2×C4713yescomplemented
321#3107C2×C4713yescomplemented
322#3106C2×C4713yescomplemented
323C8×#41C2×C4711yescharacteristic, complemented
324C4×#135C2×C4713yescomplemented
325C2×C47—43no—
326C2×C47—42no—
327C2×C47—83no—
328C2×C47D4×#4111yescharacteristic
329C2×C47C22×#13511yescharacteristic
330C2×C47C2×#57711yescharacteristic
331C2×#135C22×C4713yes—
332Q82C22×C4711yescharacteristic
333#557C22×C4711yescharacteristic
334#556C22×C4713yes—
335#555—23no—
336#555C22×C4713yes—
337#552—23no—
338#550—21no—
339#550C22×C4713yes—
340#550C22×C4711yescharacteristic
341D4×Q8C22×C4711yescharacteristic
342#548—21no—
343#547C22×C4713yes—
344#533C22×C4713yes—
345#532—23no—
346#532C22×C4713yes—
347#529—23no—
348C4×#41—21no—
349C4×#41C22×C4713yes—
350C4×#41C22×C4713yes—
351C4×#41C22×C4711yescharacteristic
352C2×C4×Q8—21no—
353#498C22×C4713yes—
354#492C22×C4713yes—
355#487C22×C4713yes—
356#486C22×C4713yes—
357#485C22×C4716yes—
358#482C22×C4716yes—
359#477C22×C4713yes—
360#476C22×C4713yes—
361#475C22×C4713yes—
362#474C22×C4713yes—
363#465C22×C4716yes—
364#465C22×C4716yes—
365#462C22×C4713yes—
366#461C22×C4713yes—
367#460C22×C4713yes—
368#459C22×C4713yes—
369#452C22×C4716yes—
370#449C22×C4716yes—
371C8×Q8C22×C4711yescharacteristic
372C8×Q8C22×C4711yescharacteristic
373C4×Q16C22×C4713yes—
374C4×Q16C22×C4713yes—
375C4×SD16C22×C4713yes—
376C4×SD16C22×C4716yes—
377C4×SD16C22×C4713yes—
378C4×SD16C22×C4713yes—
379C4×SD16C22×C4711yescharacteristic
380C4×D8C22×C4713yes—
381C4×D8C22×C4713yes—
382C8×D4C22×C4713yes—
383C8×D4C22×C4713yes—
384#431C22×C4713yes—
385#427C22×C4713yes—
386#416C22×C4713yes—
387#416C22×C4713yes—
388C2×C4×C8C22×C4713yes—
389C47#6143411yescharacteristic, direct product factor, Sylow
390C2×#41—21no—
391C2×#41—23no—
392C2×#41D4×C4711yescharacteristic
393C2×#41C23×C4713yes—
394C2×#41C23×C4713yes—
395C22×Q8—21no—
396#135—212no—
397C2×Q16C23×C4713yes—
398C2×SD16C23×C4713yes—
399C2×SD16C23×C4716yes—
400C2×SD16C23×C4711yescharacteristic
401C2×D8C23×C4713yes—
402C22×C8C23×C4713yes—
403C22×C8C23×C4713yes—
404C4⋊Q8—23no—
405C4⋊Q8C23×C4713yes—
406C4⋊Q8C23×C4713yes—
407C4⋊Q8C23×C4713yes—
408#127—23no—
409#127C23×C4713yes—
410#126—26no—
411#125—23no—
412#125—23no—
413#124—23no—
414#124—26no—
415#124—23no—
416#123—26no—
417C22⋊Q8—23no—
418C22⋊Q8—23no—
419C22⋊Q8C23×C4716yes—
420#121—23no—
421#121—23no—
422#121—23no—
423#121—23no—
424#121—26no—
425#121C23×C4716yes—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—23no—
429C4×Q8—23no—
430C4×Q8D4×C4711yescharacteristic
431C4×Q8C23×C4711yescharacteristic
432C4×Q8C23×C4713yes—
433C4×Q8C23×C4713yes—
434C4×Q8C23×C4713yes—
435C4×Q8C23×C4711yescharacteristic
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4—23no—
441C4×D4—23no—
442C4×D4D4×C4713yes—
443C4×D4C23×C4711yescharacteristic
444C4×D4C23×C4713yes—
445C4×D4C23×C4713yes—
446C4×D4C23×C4713yes—
447C4×D4C23×C4713yes—
448#117—23no—
449#117—23no—
450#117—23no—
451#117—23no—
452#117D4×C4713yes—
453#117C23×C4713yes—
454#117C23×C4713yes—
455C2×C4⋊C4—23no—
456C2×C42—23no—
457C2×C42—23no—
458C2×C42C23×C4713yes—
459#107C23×C4713yes—
460#107C23×C4713yes—
461#106C23×C4711yescharacteristic
462#106C23×C4713yes—
463#106C23×C4716yes—
464C4⋊C8C23×C4713yes—
465C4⋊C8C23×C4713yes—
466#103C23×C4711yescharacteristic
467#103C23×C4713yes—
468#103C23×C4713yes—
469#103C23×C4713yes—
470#103C23×C4716yes—
471#102C23×C4711yescharacteristic
472#102C23×C4713yes—
473#102C23×C4713yes—
474#102C23×C4713yes—
475#102C23×C4716yes—
476C22⋊C8C23×C4716yes—
477C4×C8C23×C4711yescharacteristic
478C4×C8C23×C4713yes—
479C4×C8C23×C4713yes—
480C4×C8C23×C4713yes—
481#41—24no—
482#41—26no—
483#41—26no—
484#41—43no—
485#41—43no—
486#41—44no—
487#41—86no—
488C2×Q8—23no—
489C2×Q8—23no—
490C2×Q8—44no—
491C2×Q8C2×D4×C4711yescharacteristic
492C2×Q8C24×C4713yes—
493C2×Q8C24×C4711yescharacteristic
494C2×D4—23no—
495C2×D4—23no—
496C2×D4—26no—
497C2×D4—23no—
498C2×D4—23no—
499C2×D4C2×D4×C4713yes—
500C2×D4C24×C4713yes—
501C2×D4C24×C4711yescharacteristic
502C22×C4—21no—
503C22×C4—23no—
504C22×C4—23no—
505C22×C4—23no—
506C22×C4—23no—
507C22×C4—23no—
508C22×C4C2×D4×C4713yes—
509C22×C4C2×D4×C4713yes—
510C22×C4C24×C4713yes—
511Q16—26no—
512SD16—26no—
513SD16—46no—
514SD16#41×C4714yescomplemented
515D8—26no—
516C2×C8—26no—
517C2×C8—43no—
518C2×C8C24×C4711yescharacteristic
519C2×C8C24×C4713yes—
520C2×C8C24×C4713yes—
521C2×C8C24×C4711yescharacteristic
522C4⋊C4—23no—
523C4⋊C4—26no—
524C4⋊C4—21no—
525C4⋊C4—23no—
526C4⋊C4—23no—
527C4⋊C4—23no—
528C4⋊C4—23no—
529C4⋊C4—23no—
530C4⋊C4—23no—
531C4⋊C4C2×D4×C4713yes—
532C4⋊C4C2×D4×C4713yes—
533C4⋊C4C24×C4713yes—
534C4⋊C4C24×C4711yescharacteristic
535C4⋊C4C24×C4713yes—
536C4⋊C4C24×C4711yescharacteristic
537C22⋊C4—26no—
538C22⋊C4—23no—
539C22⋊C4—23no—
540C22⋊C4—21no—
541C22⋊C4—26no—
542C22⋊C4—23no—
543C22⋊C4—23no—
544C22⋊C4—23no—
545C22⋊C4C2×D4×C4716yes—
546C42—21no—
547C42—23no—
548C42—23no—
549C42—23no—
550C42—23no—
551C42—23no—
552C42C2×D4×C4713yes—
553C42C2×D4×C4713yes—
554C42C24×C4711yescharacteristic
555C42C24×C4713yes—
556C23—21no—
557C23—23no—
558C23C22×D4×C4713yes—
559Q8—21no—
560Q8—23no—
561Q8—23no—
562Q8—46no—
563Q8—83no—
564Q8#135×C4714yescomplemented
565Q8C2×#41×C4712yes—
566D4—26no—
567D4—23no—
568D4—21no—
569D4—23no—
570D4—46no—
571D4—46no—
572D4—46no—
573D4—83no—
574D4—86no—
575D4C2×#41×C4712yes—
576C2×C4—21no—
577C2×C4—26no—
578C2×C4—26no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—23no—
586C2×C4—46no—
587C2×C4—46no—
588C2×C4—46no—
589C2×C4—46no—
590C2×C4—42no—
591C2×C4—46no—
592C2×C4C22×D4×C4713yes—
593C2×C4C22×D4×C4711yescharacteristic
594C2×C4C22×D4×C4713yes—
595C2×C4C22×D4×C4713yes—
596C2×C4C22×D4×C4711yescharacteristic
597C2×C4C25×C4711yescharacteristic
598C8—23no—
599C8—21no—
600C8—23no—
601C8C2×#41×C4712yes—
602C22—23no—
603C22—23no—
604C22—23no—
605C22—22no—
606C22—41no—
607C22—41no—
608C22—43no—
609C22—43no—
610C22—43no—
611C22C23×D4×C4711yescharacteristic
612C4—21no—
613C4—23no—
614C4—23no—
615C4—22no—
616C4—41no—
617C4—43no—
618C4—43no—
619C4—41no—
620C4—43no—
621C4C2×#135×C4716yes—
622C4C47×#57712yes—
623C4C22×#41×C4711yescharacteristic
624C4C47×#58511yescharacteristic
625C2—43no—
626C2—42no—
627C2—83no—
628C2D4×#41×C4711yescharacteristic
629C2C22×#135×C4711yescharacteristic
630C2C2×C47×#57711yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
socleC22×C47C23×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C4×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3483C2semidirect
2. C47×#3482C2semidirect
3. C47×#3392C2semidirect
4. Q8×SD16×C47C2semidirect
5. C47×#3363C2semidirect
6. C47×#3358C2semidirect
7. C47×#3340C2semidirect
8. C47×#3304C2semidirect
9. C47×#3303C2semidirect
10. C47×#3284C2semidirect
11. C47×#3167C2semidirect
12. C47×#3107C2semidirect
13. C47×#3106C2semidirect
14. C8×#41×C47C2semidirect
15. C4×#135×C47C2semidirect
198. SD16×C47#41semidirect
248. Q8×C47#135semidirect
286. #61434C47direct (N × H)
310. #3483C2×C47semidirect
311. #3482C2×C47semidirect
312. #3392C2×C47semidirect
313. Q8×SD16C2×C47semidirect
314. #3363C2×C47semidirect
315. #3358C2×C47semidirect
316. #3340C2×C47semidirect
317. #3304C2×C47semidirect
318. #3303C2×C47semidirect
319. #3284C2×C47semidirect
320. #3167C2×C47semidirect
321. #3107C2×C47semidirect
322. #3106C2×C47semidirect
323. C8×#41C2×C47semidirect
324. C4×#135C2×C47semidirect
389. C47#61434direct (N × H)
514. SD16#41×C47semidirect
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×#34832
C47×#34822
C47×#33922
Q8×SD16×C472
C47×#33632
C47×#33582
C47×#33402
C47×#33042
C47×#33032
C47×#32842
C47×#31672
C47×#31072
C47×#31062
C8×#41×C472
C4×#135×C472
#6143447