Finite Group Databasebeta

← C47×#18969 #26058667

Subgroups — C47×#18969 #26058667

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3547C211yesmaximal, characteristic
2C47×#3230C211yesmaximal, characteristic, complemented
3C47×#3226C211yesmaximal, characteristic, complemented
4C47×#3218C211yesmaximal, characteristic, complemented
5C47×#1649C212yesmaximal, complemented
6C47×#1647C212yesmaximal, complemented
7C47×#1646C212yesmaximal, complemented
8C47×#1644C212yesmaximal, complemented
9C47×#1554C211yesmaximal, characteristic, complemented
10C47×#1496C211yesmaximal, characteristic, complemented
11C47×#1482C211yesmaximal, characteristic, complemented
12C47×#562—22no—
13C47×#555—21no—
14C47×#555C2211yescharacteristic
15C47×#554C2211yescharacteristic
16C47×#553—21no—
17C47×#552—21no—
18D4×Q8×C47C2211yescharacteristic
19C47×#548—21no—
20C47×#547C2211yescharacteristic
21C47×#544—21no—
22C47×#542—22no—
23C47×#540—21no—
24C47×#537—21no—
25C47×#536—21no—
26C47×#533C2211yescharacteristic
27C47×#532C2211yescharacteristic
28C2×C4⋊Q8×C47C2211yescharacteristic
29C47×#529C2211yescharacteristic
30C47×#500—21no—
31C47×#500C2212yes—
32C47×#497—21no—
33C47×#491—21no—
34C47×#487C2212yes—
35C47×#486—21no—
36C47×#484—22no—
37C47×#480—21no—
38C47×#480—21no—
39C47×#477—22no—
40C47×#474C2212yes—
41C47×#474C2212yes—
42C47×#462C2212yes—
43C47×#461C2212yes—
44C47×#451—21no—
45C47×#448—21no—
46C47×#432C2211yescharacteristic
47C47×#431C2211yescharacteristic
48C47×#431C2211yescharacteristic
49C47×#333C2212yes—
50C47×#332C2212yes—
51C47×Q8⋊C8C2212yes—
52C47×D4⋊C8C2212yes—
53C47×D4⋊C8C2212yes—
54C47×D4⋊C8C2212yes—
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C22×Q8×C47—21no—
58C22×Q8×C47—21no—
59C2×Q16×C47—22no—
60C2×SD16×C47—22no—
61C4⋊Q8×C47—22no—
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47D411yescharacteristic
67C4⋊Q8×C47C2312yes—
68C4⋊Q8×C47C2311yescharacteristic
69C4⋊Q8×C47C2311yescharacteristic
70#127×C47D411yescharacteristic
71#126×C47—22no—
72#126×C47—21no—
73#125×C47—22no—
74#125×C47—21no—
75#125×C47—21no—
76#125×C47D411yescharacteristic
77#124×C47—22no—
78#124×C47—22no—
79#124×C47—22no—
80#124×C47—21no—
81#124×C47D411yescharacteristic
82#123×C47—22no—
83#123×C47—22no—
84#123×C47—22no—
85#123×C47—21no—
86#123×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—22no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47—22no—
95C22⋊Q8×C47D411yescharacteristic
96C22⋊Q8×C47D412yes—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—21no—
102#121×C47—21no—
103#121×C47—21no—
104#121×C47—21no—
105#121×C47D411yescharacteristic
106#121×C47D411yescharacteristic
107#121×C47D411yescharacteristic
108C4×Q8×C47—21no—
109C4×Q8×C47D412yes—
110C4×Q8×C47C2311yescharacteristic
111C4×D4×C47—22no—
112C4×D4×C47—21no—
113C4×D4×C47—21no—
114C4×D4×C47—21no—
115C4×D4×C47—21no—
116C4×D4×C47C2311yescharacteristic
117C4×D4×C47C2311yescharacteristic
118C4×D4×C47C2311yescharacteristic
119#117×C47—22no—
120#117×C47—21no—
121#117×C47—21no—
122#117×C47—21no—
123#117×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C42×C47C2311yescharacteristic
129#107×C47—22no—
130#107×C47—22no—
131#107×C47—24no—
132C4⋊C8×C47—21no—
133C4⋊C8×C47C2312yes—
134C4⋊C8×C47C2312yes—
135#103×C47—24no—
136#103×C47—22no—
137#103×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C22⋊C8×C47—21no—
143#97×C47—21no—
144C4×C8×C47—21no—
145C4×C8×C47C2312yes—
146#41×C47—82no—
147#41×C47—82no—
148C2×Q8×C47—22no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—22no—
152C2×Q8×C47—41no—
153C2×Q8×C47—82no—
154C2×Q8×C47—82no—
155C2×Q8×C47C2×D411yescharacteristic
156C2×Q8×C47C2×D412yes—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47C2×D411yescharacteristic
165C2×D4×C47C2×D411yescharacteristic
166C2×D4×C47C2×D411yescharacteristic
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—41no—
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177Q16×C47—82no—
178SD16×C47—82no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47—22no—
185C4⋊C4×C47—22no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—22no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47—22no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C4⋊C4×C47C2×D411yescharacteristic
201C4⋊C4×C47C2×D411yescharacteristic
202C4⋊C4×C47C2×D411yescharacteristic
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D412yes—
205C22⋊C4×C47—22no—
206C22⋊C4×C47—22no—
207C22⋊C4×C47—22no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—21no—
212C22⋊C4×C47—21no—
213C22⋊C4×C47—21no—
214C22⋊C4×C47—21no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—21no—
217C22⋊C4×C47—21no—
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C42×C47—22no—
221C42×C47—22no—
222C42×C47—21no—
223C42×C47C2×D411yescharacteristic
224C42×C47C2×D411yescharacteristic
225C42×C47C2×D411yescharacteristic
226C42×C47C2411yescharacteristic
227C23×C47—21no—
228C23×C47—21no—
229C23×C47—21no—
230C23×C47#12011yescharacteristic
231Q8×C47—22no—
232Q8×C47—42no—
233Q8×C47—42no—
234Q8×C47—42no—
235Q8×C47—42no—
236Q8×C47—81no—
237Q8×C47—82no—
238Q8×C47—82no—
239D4×C47—22no—
240D4×C47—22no—
241D4×C47—22no—
242D4×C47—81no—
243D4×C47—81no—
244D4×C47—81no—
245D4×C47—81no—
246D4×C47—81no—
247D4×C47—82no—
248D4×C47—82no—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—21no—
252C2×C4×C47—22no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—22no—
257C2×C4×C47—21no—
258C2×C4×C47—41no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—82no—
264C2×C4×C47—82no—
265C2×C4×C47—82no—
266C2×C4×C47—82no—
267C2×C4×C47#12011yescharacteristic
268C2×C4×C47#12011yescharacteristic
269C2×C4×C47#12011yescharacteristic
270C2×C4×C47C22×D411yescharacteristic
271C2×C4×C47C22×D411yescharacteristic
272C2×C4×C47C22×D411yescharacteristic
273C8×C47—42no—
274C8×C47—42no—
275C8×C47—42no—
276#18969C4711yesmaximal, characteristic, direct product factor, Sylow
277C22×C47—21no—
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47—41no—
289C22×C47C2×#12011yescharacteristic
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—21no—
293C4×C47—21no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—41no—
300C4×C47—42no—
301C4×C47—82no—
302C4×C47#57612yes—
303C4×C47#57812yes—
304#3547C2×C4711yescharacteristic
305#3230C2×C4711yescharacteristic, complemented
306#3226C2×C4711yescharacteristic, complemented
307#3218C2×C4711yescharacteristic, complemented
308#1649C2×C4712yescomplemented
309#1647C2×C4712yescomplemented
310#1646C2×C4712yescomplemented
311#1644C2×C4712yescomplemented
312#1554C2×C4711yescharacteristic, complemented
313#1496C2×C4711yescharacteristic, complemented
314#1482C2×C4711yescharacteristic, complemented
315C2×C47—41no—
316C2×C47—81no—
317C2×C47—81no—
318C2×C47—81no—
319C2×C47#300811yescharacteristic
320C2×C47#301111yescharacteristic
321C2×C47#302211yescharacteristic
322#562—22no—
323#555—21no—
324#555C22×C4711yescharacteristic
325#554C22×C4711yescharacteristic
326#553—21no—
327#552—21no—
328D4×Q8C22×C4711yescharacteristic
329#548—21no—
330#547C22×C4711yescharacteristic
331#544—21no—
332#542—22no—
333#540—21no—
334#537—21no—
335#536—21no—
336#533C22×C4711yescharacteristic
337#532C22×C4711yescharacteristic
338C2×C4⋊Q8C22×C4711yescharacteristic
339#529C22×C4711yescharacteristic
340#500—21no—
341#500C22×C4712yes—
342#497—21no—
343#491—21no—
344#487C22×C4712yes—
345#486—21no—
346#484—22no—
347#480—21no—
348#480—21no—
349#477—22no—
350#474C22×C4712yes—
351#474C22×C4712yes—
352#462C22×C4712yes—
353#461C22×C4712yes—
354#451—21no—
355#448—21no—
356#432C22×C4711yescharacteristic
357#431C22×C4711yescharacteristic
358#431C22×C4711yescharacteristic
359#333C22×C4712yes—
360#332C22×C4712yes—
361Q8⋊C8C22×C4712yes—
362D4⋊C8C22×C4712yes—
363D4⋊C8C22×C4712yes—
364D4⋊C8C22×C4712yes—
365C47#1896911yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C2×#41—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C2×Q16—22no—
371C2×SD16—22no—
372C4⋊Q8—22no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8D4×C4711yescharacteristic
378C4⋊Q8C23×C4712yes—
379C4⋊Q8C23×C4711yescharacteristic
380C4⋊Q8C23×C4711yescharacteristic
381#127D4×C4711yescharacteristic
382#126—22no—
383#126—21no—
384#125—22no—
385#125—21no—
386#125—21no—
387#125D4×C4711yescharacteristic
388#124—22no—
389#124—22no—
390#124—22no—
391#124—21no—
392#124D4×C4711yescharacteristic
393#123—22no—
394#123—22no—
395#123—22no—
396#123—21no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8D4×C4711yescharacteristic
407C22⋊Q8D4×C4712yes—
408#121—22no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121D4×C4711yescharacteristic
417#121D4×C4711yescharacteristic
418#121D4×C4711yescharacteristic
419C4×Q8—21no—
420C4×Q8D4×C4712yes—
421C4×Q8C23×C4711yescharacteristic
422C4×D4—22no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4C23×C4711yescharacteristic
428C4×D4C23×C4711yescharacteristic
429C4×D4C23×C4711yescharacteristic
430#117—22no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C42C23×C4711yescharacteristic
440#107—22no—
441#107—22no—
442#107—24no—
443C4⋊C8—21no—
444C4⋊C8C23×C4712yes—
445C4⋊C8C23×C4712yes—
446#103—24no—
447#103—22no—
448#103—22no—
449#102—22no—
450#102—22no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454#97—21no—
455C4×C8—21no—
456C4×C8C23×C4712yes—
457#41—82no—
458#41—82no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—82no—
465C2×Q8—82no—
466C2×Q8C2×D4×C4711yescharacteristic
467C2×Q8C2×D4×C4712yes—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×D4×C4711yescharacteristic
476C2×D4C2×D4×C4711yescharacteristic
477C2×D4C2×D4×C4711yescharacteristic
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4C2×D4×C4711yescharacteristic
486C22×C4C2×D4×C4711yescharacteristic
487C22×C4C2×D4×C4711yescharacteristic
488Q16—82no—
489SD16—82no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4C2×D4×C4711yescharacteristic
512C4⋊C4C2×D4×C4711yescharacteristic
513C4⋊C4C2×D4×C4711yescharacteristic
514C4⋊C4C2×D4×C4711yescharacteristic
515C4⋊C4C2×D4×C4712yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C42—22no—
532C42—22no—
533C42—21no—
534C42C2×D4×C4711yescharacteristic
535C42C2×D4×C4711yescharacteristic
536C42C2×D4×C4711yescharacteristic
537C42C24×C4711yescharacteristic
538C23—21no—
539C23—21no—
540C23—21no—
541C23#120×C4711yescharacteristic
542Q8—22no—
543Q8—42no—
544Q8—42no—
545Q8—42no—
546Q8—42no—
547Q8—81no—
548Q8—82no—
549Q8—82no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4—81no—
554D4—81no—
555D4—81no—
556D4—81no—
557D4—81no—
558D4—82no—
559D4—82no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4#120×C4711yescharacteristic
579C2×C4#120×C4711yescharacteristic
580C2×C4#120×C4711yescharacteristic
581C2×C4C22×D4×C4711yescharacteristic
582C2×C4C22×D4×C4711yescharacteristic
583C2×C4C22×D4×C4711yescharacteristic
584C8—42no—
585C8—42no—
586C8—42no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×#120×C4711yescharacteristic
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—41no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—82no—
612C4C47×#57612yes—
613C4C47×#57812yes—
614C2—41no—
615C2—81no—
616C2—81no—
617C2—81no—
618C2C47×#300811yescharacteristic
619C2C47×#301111yescharacteristic
620C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3547C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#3230C2semidirect
3. C47×#3226C2semidirect
4. C47×#3218C2semidirect
5. C47×#1649C2semidirect
6. C47×#1647C2semidirect
7. C47×#1646C2semidirect
8. C47×#1644C2semidirect
9. C47×#1554C2semidirect
10. C47×#1496C2semidirect
11. C47×#1482C2semidirect
276. #18969C47direct (N × H)
305. #3230C2×C47semidirect
306. #3226C2×C47semidirect
307. #3218C2×C47semidirect
308. #1649C2×C47semidirect
309. #1647C2×C47semidirect
310. #1646C2×C47semidirect
311. #1644C2×C47semidirect
312. #1554C2×C47semidirect
313. #1496C2×C47semidirect
314. #1482C2×C47semidirect
365. C47#18969direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35472
C47×#32302
C47×#32262
C47×#32182
C47×#16492
C47×#16472
C47×#16462
C47×#16442
C47×#15542
C47×#14962
C47×#14822
#1896947