Finite Group Databasebeta

← C47×#19760 #26059458

Subgroups — C47×#19760 #26059458

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3358C211yesmaximal, characteristic, complemented
2C47×#3334C211yesmaximal, characteristic, complemented
3C47×#3284C211yesmaximal, characteristic, complemented
4C47×#3276C211yesmaximal, characteristic, complemented
5C47×#1722C211yesmaximal, characteristic, complemented
6C47×#1685C211yesmaximal, characteristic, complemented
7C47×#1681C211yesmaximal, characteristic, complemented
8C47×#1674C211yesmaximal, characteristic, complemented
9C47×#1669C211yesmaximal, characteristic, complemented
10C47×#1649C211yesmaximal, characteristic, complemented
11C47×#1647C211yesmaximal, characteristic, complemented
12C47×#1641C211yesmaximal, characteristic, complemented
13C47×#1625C211yesmaximal, characteristic, complemented
14C47×#1581C211yesmaximal, characteristic, complemented
15C47×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#137×C47—21no—
17C2×#135×C47—21no—
18C47×#550C2211yescharacteristic
19D4×Q8×C47C2211yescharacteristic
20C47×#547C2211yescharacteristic
21C47×#547C2211yescharacteristic
22C47×#500C2211yescharacteristic
23C47×#500C2211yescharacteristic
24C47×#494C2211yescharacteristic
25C47×#492C2211yescharacteristic
26C47×#486—21no—
27C47×#486C2211yescharacteristic
28C47×#486C2211yescharacteristic
29C47×#480—21no—
30C47×#480—21no—
31C47×#474—21no—
32C47×#474C2211yescharacteristic
33C47×#474C2211yescharacteristic
34C47×#474C2211yescharacteristic
35C47×#470—21no—
36C47×#466—21no—
37C47×#465—21no—
38C47×#462C2211yescharacteristic
39C47×#462C2211yescharacteristic
40C47×#461C2211yescharacteristic
41C47×#459—21no—
42C47×#459C2211yescharacteristic
43C47×#459C2211yescharacteristic
44C47×#452—21no—
45C47×#452—21no—
46C47×#451—21no—
47C47×#449—21no—
48C8×Q8×C47C2211yescharacteristic
49C4×SD16×C47C2211yescharacteristic
50C4×D8×C47—21no—
51C4×D8×C47C2211yescharacteristic
52C47×#436C2211yescharacteristic
53C8×D4×C47C2211yescharacteristic
54C8×D4×C47C2211yescharacteristic
55C2×#107×C47—21no—
56C47×#335C2211yescharacteristic
57C47×#335C2211yescharacteristic
58C47×#332C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×Q8⋊C8C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—21no—
70C22×Q8×C47—21no—
71#137×C47—44no—
72#135×C47—44no—
73C2×Q16×C47—21no—
74C2×Q16×C47—21no—
75C2×Q16×C47—21no—
76C2×Q16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47D411yescharacteristic
81C2×D8×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47D411yescharacteristic
84C2×M16×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C4⋊Q8×C47—21no—
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90C4⋊Q8×C47C2311yescharacteristic
91#127×C47—21no—
92#127×C47C2311yescharacteristic
93#123×C47—41no—
94#123×C47—41no—
95C22⋊Q8×C47—21no—
96C22⋊Q8×C47—21no—
97C22⋊Q8×C47—21no—
98C22⋊Q8×C47—41no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—21no—
102#121×C47—41no—
103C4×Q8×C47C2311yescharacteristic
104C4×D4×C47—21no—
105C4×D4×C47—21no—
106C4×D4×C47C2311yescharacteristic
107C4×D4×C47C2311yescharacteristic
108C4×D4×C47C2311yescharacteristic
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111#107×C47—21no—
112#107×C47—21no—
113#107×C47—21no—
114#107×C47—21no—
115#107×C47—21no—
116#107×C47—41no—
117#107×C47D411yescharacteristic
118#106×C47D411yescharacteristic
119C4⋊C8×C47—21no—
120C4⋊C8×C47C2311yescharacteristic
121C4⋊C8×C47C2311yescharacteristic
122C4⋊C8×C47C2311yescharacteristic
123C4⋊C8×C47C2311yescharacteristic
124#103×C47—21no—
125#103×C47—21no—
126#103×C47—21no—
127#103×C47D411yescharacteristic
128#102×C47—21no—
129#102×C47—21no—
130#102×C47—21no—
131#102×C47—21no—
132#102×C47—21no—
133#102×C47—21no—
134#102×C47—21no—
135#102×C47—41no—
136#102×C47D411yescharacteristic
137#102×C47D411yescharacteristic
138#102×C47D411yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C4×C8×C47—21no—
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C4×C8×C47C2311yescharacteristic
146#41×C47—42no—
147#41×C47—42no—
148#41×C47—42no—
149#41×C47—81no—
150#41×C47—81no—
151#41×C47—81no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—41no—
156C2×Q8×C47—42no—
157C2×Q8×C47—81no—
158C2×Q8×C47C2×D411yescharacteristic
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47—41no—
166C2×D4×C47C2×D411yescharacteristic
167C2×D4×C47C2×D411yescharacteristic
168C2×D4×C47C2×D411yescharacteristic
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47—41no—
176Q16×C47—42no—
177Q16×C47—42no—
178Q16×C47—42no—
179Q16×C47—81no—
180SD16×C47—42no—
181SD16×C47—42no—
182SD16×C47—81no—
183SD16×C47D814yescomplemented
184D8×C47—41no—
185D8×C47—42no—
186D8×C47—42no—
187M16×C47—42no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—42no—
194C2×C8×C47—42no—
195C2×C8×C47C2×D411yescharacteristic
196C2×C8×C47C2×D411yescharacteristic
197C2×C8×C47C2×D411yescharacteristic
198C2×C8×C47C2×D411yescharacteristic
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—41no—
207C4⋊C4×C47—41no—
208C4⋊C4×C47—41no—
209C4⋊C4×C47C2×D411yescharacteristic
210C4⋊C4×C47C2×D411yescharacteristic
211C4⋊C4×C47C2×D411yescharacteristic
212C4⋊C4×C47C2×D411yescharacteristic
213C22⋊C4×C47—21no—
214C22⋊C4×C47—21no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—41no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—41no—
219C22⋊C4×C47—41no—
220C42×C47—21no—
221C42×C47C2411yescharacteristic
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—41no—
226Q8×C47—21no—
227Q8×C47—41no—
228Q8×C47—41no—
229Q8×C47—41no—
230Q8×C47—41no—
231Q8×C47—41no—
232Q8×C47—41no—
233Q8×C47—82no—
234Q8×C47C2×D812yes—
235D4×C47—21no—
236D4×C47—21no—
237D4×C47—21no—
238D4×C47—21no—
239D4×C47—21no—
240D4×C47—41no—
241D4×C47—41no—
242D4×C47—41no—
243D4×C47—41no—
244D4×C47—82no—
245D4×C47—81no—
246D4×C47—82no—
247D4×C47—82no—
248D4×C47—161no—
249D4×C47C2×D812yes—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—82no—
265C2×C4×C47—82no—
266C2×C4×C47—82no—
267C2×C4×C47—82no—
268C2×C4×C47C22×D411yescharacteristic
269C2×C4×C47C22×D411yescharacteristic
270C2×C4×C47H(5,𝔽2)11yescharacteristic
271C8×C47—21no—
272C8×C47—21no—
273C8×C47—21no—
274C8×C47—41no—
275C8×C47—41no—
276C8×C47—41no—
277C8×C47—41no—
278C8×C47—41no—
279C8×C47C2×D812yes—
280#19760C4711yesmaximal, characteristic, direct product factor, Sylow
281C22×C47—22no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47—41no—
290C22×C47—81no—
291C22×C47—81no—
292C22×C47—81no—
293C22×C47D4211yescharacteristic
294C4×C47—22no—
295C4×C47—21no—
296C4×C47—41no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—41no—
300C4×C47—81no—
301C4×C47—81no—
302C4×C47—81no—
303C4×C47C22×D811yescharacteristic
304C4×C47#57511yescharacteristic
305C4×C47#57611yescharacteristic
306C4×C47#57811yescharacteristic
307#3358C2×C4711yescharacteristic, complemented
308#3334C2×C4711yescharacteristic, complemented
309#3284C2×C4711yescharacteristic, complemented
310#3276C2×C4711yescharacteristic, complemented
311#1722C2×C4711yescharacteristic, complemented
312#1685C2×C4711yescharacteristic, complemented
313#1681C2×C4711yescharacteristic, complemented
314#1674C2×C4711yescharacteristic, complemented
315#1669C2×C4711yescharacteristic, complemented
316#1649C2×C4711yescharacteristic, complemented
317#1647C2×C4711yescharacteristic, complemented
318#1641C2×C4711yescharacteristic, complemented
319#1625C2×C4711yescharacteristic, complemented
320#1581C2×C4711yescharacteristic, complemented
321SD16⋊C8C2×C4711yescharacteristic, complemented
322C2×C47—42no—
323C2×C47—81no—
324C2×C47—81no—
325C2×C47—161no—
326C2×C47#326911yescharacteristic
327C2×C47D4×D811yescharacteristic
328C2×C47#328911yescharacteristic
329C2×#137—21no—
330C2×#135—21no—
331#550C22×C4711yescharacteristic
332D4×Q8C22×C4711yescharacteristic
333#547C22×C4711yescharacteristic
334#547C22×C4711yescharacteristic
335#500C22×C4711yescharacteristic
336#500C22×C4711yescharacteristic
337#494C22×C4711yescharacteristic
338#492C22×C4711yescharacteristic
339#486—21no—
340#486C22×C4711yescharacteristic
341#486C22×C4711yescharacteristic
342#480—21no—
343#480—21no—
344#474—21no—
345#474C22×C4711yescharacteristic
346#474C22×C4711yescharacteristic
347#474C22×C4711yescharacteristic
348#470—21no—
349#466—21no—
350#465—21no—
351#462C22×C4711yescharacteristic
352#462C22×C4711yescharacteristic
353#461C22×C4711yescharacteristic
354#459—21no—
355#459C22×C4711yescharacteristic
356#459C22×C4711yescharacteristic
357#452—21no—
358#452—21no—
359#451—21no—
360#449—21no—
361C8×Q8C22×C4711yescharacteristic
362C4×SD16C22×C4711yescharacteristic
363C4×D8—21no—
364C4×D8C22×C4711yescharacteristic
365#436C22×C4711yescharacteristic
366C8×D4C22×C4711yescharacteristic
367C8×D4C22×C4711yescharacteristic
368C2×#107—21no—
369#335C22×C4711yescharacteristic
370#335C22×C4711yescharacteristic
371#332C22×C4711yescharacteristic
372#332C22×C4711yescharacteristic
373#332C22×C4711yescharacteristic
374#331C22×C4711yescharacteristic
375Q8⋊C8C22×C4711yescharacteristic
376D4⋊C8C22×C4711yescharacteristic
377D4⋊C8C22×C4711yescharacteristic
378D4⋊C8C22×C4711yescharacteristic
379#322C22×C4711yescharacteristic
380C47#1976011yescharacteristic, direct product factor, Sylow
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C22×Q8—21no—
385#137—44no—
386#135—44no—
387C2×Q16—21no—
388C2×Q16—21no—
389C2×Q16—21no—
390C2×Q16—21no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16D4×C4711yescharacteristic
395C2×D8—21no—
396C2×D8—21no—
397C2×D8D4×C4711yescharacteristic
398C2×M16—21no—
399C22×C8—21no—
400C22×C8—21no—
401C4⋊Q8—21no—
402C4⋊Q8C23×C4711yescharacteristic
403C4⋊Q8C23×C4711yescharacteristic
404C4⋊Q8C23×C4711yescharacteristic
405#127—21no—
406#127C23×C4711yescharacteristic
407#123—41no—
408#123—41no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—41no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—41no—
417C4×Q8C23×C4711yescharacteristic
418C4×D4—21no—
419C4×D4—21no—
420C4×D4C23×C4711yescharacteristic
421C4×D4C23×C4711yescharacteristic
422C4×D4C23×C4711yescharacteristic
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425#107—21no—
426#107—21no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107—41no—
431#107D4×C4711yescharacteristic
432#106D4×C4711yescharacteristic
433C4⋊C8—21no—
434C4⋊C8C23×C4711yescharacteristic
435C4⋊C8C23×C4711yescharacteristic
436C4⋊C8C23×C4711yescharacteristic
437C4⋊C8C23×C4711yescharacteristic
438#103—21no—
439#103—21no—
440#103—21no—
441#103D4×C4711yescharacteristic
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—41no—
450#102D4×C4711yescharacteristic
451#102D4×C4711yescharacteristic
452#102D4×C4711yescharacteristic
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C4×C8—21no—
457C4×C8C23×C4711yescharacteristic
458C4×C8C23×C4711yescharacteristic
459C4×C8C23×C4711yescharacteristic
460#41—42no—
461#41—42no—
462#41—42no—
463#41—81no—
464#41—81no—
465#41—81no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8C2×D4×C4711yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4C2×D4×C4711yescharacteristic
481C2×D4C2×D4×C4711yescharacteristic
482C2×D4C2×D4×C4711yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490Q16—42no—
491Q16—42no—
492Q16—42no—
493Q16—81no—
494SD16—42no—
495SD16—42no—
496SD16—81no—
497SD16D8×C4714yescomplemented
498D8—41no—
499D8—42no—
500D8—42no—
501M16—42no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—42no—
508C2×C8—42no—
509C2×C8C2×D4×C4711yescharacteristic
510C2×C8C2×D4×C4711yescharacteristic
511C2×C8C2×D4×C4711yescharacteristic
512C2×C8C2×D4×C4711yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4C2×D4×C4711yescharacteristic
524C4⋊C4C2×D4×C4711yescharacteristic
525C4⋊C4C2×D4×C4711yescharacteristic
526C4⋊C4C2×D4×C4711yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C42—21no—
535C42C24×C4711yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—41no—
540Q8—21no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—82no—
548Q8C2×D8×C4712yes—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—82no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—161no—
563D4C2×D8×C4712yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4C22×D4×C4711yescharacteristic
583C2×C4C22×D4×C4711yescharacteristic
584C2×C4H(5,𝔽2)×C4711yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—41no—
593C8C2×D8×C4712yes—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22D42×C4711yescharacteristic
607C4—21no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4C22×D8×C4711yescharacteristic
617C4C47×#57511yescharacteristic
618C4C47×#57611yescharacteristic
619C4C47×#57811yescharacteristic
620C2—42no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C47×#326911yescharacteristic
625C2D4×D8×C4711yescharacteristic
626C2C47×#328911yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC42C24×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3358C2semidirect
2. C47×#3334C2semidirect
3. C47×#3284C2semidirect
4. C47×#3276C2semidirect
5. C47×#1722C2semidirect
6. C47×#1685C2semidirect
7. C47×#1681C2semidirect
8. C47×#1674C2semidirect
9. C47×#1669C2semidirect
10. C47×#1649C2semidirect
11. C47×#1647C2semidirect
12. C47×#1641C2semidirect
13. C47×#1625C2semidirect
14. C47×#1581C2semidirect
15. C47×SD16⋊C8C2semidirect
183. SD16×C47D8semidirect
280. #19760C47direct (N × H)
307. #3358C2×C47semidirect
308. #3334C2×C47semidirect
309. #3284C2×C47semidirect
310. #3276C2×C47semidirect
311. #1722C2×C47semidirect
312. #1685C2×C47semidirect
313. #1681C2×C47semidirect
314. #1674C2×C47semidirect
315. #1669C2×C47semidirect
316. #1649C2×C47semidirect
317. #1647C2×C47semidirect
318. #1641C2×C47semidirect
319. #1625C2×C47semidirect
320. #1581C2×C47semidirect
321. SD16⋊C8C2×C47semidirect
380. C47#19760direct (N × H)
497. SD16D8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#33582
C47×#33342
C47×#32842
C47×#32762
C47×#17222
C47×#16852
C47×#16812
C47×#16742
C47×#16692
C47×#16492
C47×#16472
C47×#16412
C47×#16252
C47×#15812
C47×SD16⋊C82
#1976047