Finite Group Databasebeta

← C47×#18842 #26058540

Subgroups — C47×#18842 #26058540

Order 12032.

960 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3514C211yesmaximal, characteristic
2C47×#3239C211yesmaximal, characteristic, complemented
3C47×#3227C211yesmaximal, characteristic, complemented
4C47×#3039C211yesmaximal, characteristic, complemented
5C47×#1652C212yesmaximal, complemented
6C47×#1651C212yesmaximal, complemented
7C47×#1640C212yesmaximal, complemented
8C47×#1639C212yesmaximal, complemented
9C47×#1557C211yesmaximal, characteristic, complemented
10C47×#1495C211yesmaximal, characteristic, complemented
11C47×#1488C211yesmaximal, characteristic, complemented
12C2×#137×C47—21no—
13C47×#559C2211yescharacteristic
14C47×#556C2211yescharacteristic
15C47×#555—21no—
16C47×#551—22no—
17D4×Q8×C47C2211yescharacteristic
18C47×#548—21no—
19C47×#546—21no—
20C47×#546—21no—
21D42×C47C2211yescharacteristic
22C47×#542—21no—
23C47×#538—22no—
24C47×#532C2211yescharacteristic
25C2×C4⋊Q8×C47C2211yescharacteristic, complemented
26C47×#529—21no—
27C47×#529C2211yescharacteristic
28C2×#124×C47—21no—
29C47×#518—21no—
30C4×#41×C47C2211yescharacteristic
31C47×#501—21no—
32C47×#498C2212yescomplemented
33C47×#489—21no—
34C47×#486C2212yes—
35C47×#484—21no—
36C47×#481—22no—
37C47×#481—21no—
38C47×#476—22no—
39C47×#475C2212yescomplemented
40C47×#474C2212yes—
41C47×#462—21no—
42C47×#462C2212yescomplemented
43C47×#461—21no—
44C47×#461C2212yes—
45C47×#432C2211yescharacteristic, complemented
46C47×#431C2211yescharacteristic, complemented
47C47×#423C2211yescharacteristic, complemented
48C47×#419—21no—
49C47×#332C2212yescomplemented
50C47×#331C2212yes—
51C47×Q8⋊C8C2212yescomplemented
52C47×Q8⋊C8C2212yescomplemented
53C47×D4⋊C8C2212yes—
54C47×D4⋊C8C2212yes—
55C2×#41×C47—21no—
56C2×#41×C47D411yescharacteristic
57C22×Q8×C47—21no—
58C22×Q8×C47—21no—
59C22×D4×C47—21no—
60C22×D4×C47—21no—
61#137×C47—44no—
62C2×Q16×C47—22no—
63C2×SD16×C47—22no—
64C2×M16×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47—21no—
67C4⋊Q8×C47—21no—
68C4⋊Q8×C47—21no—
69C4⋊Q8×C47C2312yes—
70C4⋊Q8×C47C2311yescharacteristic
71#127×C47C2311yescharacteristic
72#126×C47—22no—
73#126×C47—22no—
74#126×C47—21no—
75#125×C47D411yescharacteristic
76#124×C47—22no—
77#124×C47—22no—
78#124×C47—22no—
79#124×C47—21no—
80#124×C47—21no—
81#124×C47—21no—
82#124×C47—21no—
83#124×C47D411yescharacteristic
84#123×C47—22no—
85#123×C47—22no—
86#123×C47—22no—
87#123×C47—21no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—21no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—22no—
92C22⋊Q8×C47D411yescharacteristic
93#121×C47—22no—
94#121×C47—22no—
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—21no—
98#121×C47D411yescharacteristic
99#121×C47D412yes—
100#120×C47—22no—
101#120×C47—22no—
102C4×Q8×C47—21no—
103C4×Q8×C47D411yescharacteristic
104C4×Q8×C47C2311yescharacteristic
105C4×Q8×C47C2311yescharacteristic
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C4×D4×C47—21no—
109C4×D4×C47—21no—
110C4×D4×C47—21no—
111C4×D4×C47—21no—
112C4×D4×C47—21no—
113C4×D4×C47—21no—
114C4×D4×C47—21no—
115C4×D4×C47D411yescharacteristic
116C4×D4×C47D412yes—
117C4×D4×C47C2311yescharacteristic
118C4×D4×C47C2311yescharacteristic
119#117×C47—22no—
120#117×C47—21no—
121#117×C47—21no—
122#117×C47—21no—
123#117×C47D411yescharacteristic
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C22⋊C4×C47—22no—
127C2×C22⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131#107×C47—22no—
132#106×C47—22no—
133#106×C47—24no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2312yes—
137C4⋊C8×C47C2312yes—
138#103×C47—22no—
139#103×C47—22no—
140#103×C47—22no—
141#102×C47—22no—
142#102×C47—24no—
143C22⋊C8×C47—21no—
144C22⋊C8×C47—21no—
145#97×C47—21no—
146C4×C8×C47C2312yes—
147C24×C47—22no—
148#41×C47—22no—
149#41×C47—41no—
150#41×C47—82no—
151C2×Q8×C47—22no—
152C2×Q8×C47—21no—
153C2×Q8×C47—22no—
154C2×Q8×C47—42no—
155C2×Q8×C47—42no—
156C2×Q8×C47—41no—
157C2×Q8×C47—82no—
158C2×Q8×C47C2×D411yescharacteristic
159C2×Q8×C47C2×D411yescharacteristic
160C2×D4×C47—22no—
161C2×D4×C47—21no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—22no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—42no—
168C2×D4×C47—42no—
169C2×D4×C47—82no—
170C2×D4×C47C2×D411yescharacteristic
171C2×D4×C47C2×D411yescharacteristic
172C2×D4×C47C2×D412yes—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—22no—
180C22×C4×C47—41no—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184Q16×C47—44no—
185SD16×C47—44no—
186M16×C47—42no—
187C2×C8×C47—22no—
188C2×C8×C47—22no—
189C2×C8×C47—22no—
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—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—22no—
200C4⋊C4×C47—22no—
201C4⋊C4×C47—41no—
202C4⋊C4×C47—41no—
203C4⋊C4×C47C2×D411yescharacteristic
204C4⋊C4×C47C2×D411yescharacteristic
205C4⋊C4×C47C2×D411yescharacteristic
206C4⋊C4×C47C2×D412yes—
207C4⋊C4×C47C2×D411yescharacteristic
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—22no—
211C22⋊C4×C47—22no—
212C22⋊C4×C47—22no—
213C22⋊C4×C47—22no—
214C22⋊C4×C47—22no—
215C22⋊C4×C47—21no—
216C22⋊C4×C47—21no—
217C22⋊C4×C47—21no—
218C22⋊C4×C47—21no—
219C22⋊C4×C47—21no—
220C22⋊C4×C47—21no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C42×C47—22no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47—21no—
229C42×C47—21no—
230C42×C47C2×D411yescharacteristic
231C42×C47C2×D411yescharacteristic
232C42×C47C2×D411yescharacteristic
233C42×C47C2411yescharacteristic
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—22no—
237C23×C47—44no—
238C23×C47—82no—
239C23×C47—82no—
240C23×C47#12011yescharacteristic
241Q8×C47—21no—
242Q8×C47—21no—
243Q8×C47—22no—
244Q8×C47—42no—
245Q8×C47—42no—
246Q8×C47—42no—
247Q8×C47—82no—
248Q8×C47—82no—
249D4×C47—21no—
250D4×C47—22no—
251D4×C47—42no—
252D4×C47—42no—
253D4×C47—44no—
254D4×C47—41no—
255D4×C47—41no—
256D4×C47—42no—
257D4×C47—81no—
258D4×C47—82no—
259D4×C47—82no—
260D4×C47AGL(1,ℤ/8)12yes—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—41no—
272C2×C4×C47—42no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—81no—
278C2×C4×C47—82no—
279C2×C4×C47—82no—
280C2×C4×C47—82no—
281C2×C4×C47—82no—
282C2×C4×C47#12011yescharacteristic
283C2×C4×C47#12011yescharacteristic
284C2×C4×C47#12011yescharacteristic
285C2×C4×C47C22×D411yescharacteristic
286C2×C4×C47C22×D411yescharacteristic
287C2×C4×C47C22×D411yescharacteristic
288C8×C47—42no—
289C8×C47—42no—
290C8×C47—42no—
291#18842C4711yesmaximal, characteristic, direct product factor, Sylow
292C22×C47—21no—
293C22×C47—22no—
294C22×C47—21no—
295C22×C47—21no—
296C22×C47—41no—
297C22×C47—41no—
298C22×C47—41no—
299C22×C47—42no—
300C22×C47—42no—
301C22×C47—41no—
302C22×C47—42no—
303C22×C47—41no—
304C22×C47—164no—
305C22×C47C2×#12011yescharacteristic
306C4×C47—21no—
307C4×C47—21no—
308C4×C47—21no—
309C4×C47—21no—
310C4×C47—41no—
311C4×C47—41no—
312C4×C47—41no—
313C4×C47—42no—
314C4×C47—41no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—82no—
318C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
319C4×C47#57511yescharacteristic
320C4×C47#57712yes—
321#3514C2×C4711yescharacteristic
322#3239C2×C4711yescharacteristic, complemented
323#3227C2×C4711yescharacteristic, complemented
324#3039C2×C4711yescharacteristic, complemented
325#1652C2×C4712yescomplemented
326#1651C2×C4712yescomplemented
327#1640C2×C4712yescomplemented
328#1639C2×C4712yescomplemented
329#1557C2×C4711yescharacteristic, complemented
330#1495C2×C4711yescharacteristic, complemented
331#1488C2×C4711yescharacteristic, complemented
332C2×C47—41no—
333C2×C47—42no—
334C2×C47—82no—
335C2×C47—81no—
336C2×C47#300611yescharacteristic
337C2×C47#300911yescharacteristic
338C2×C47#302211yescharacteristic
339C2×#137—21no—
340#559C22×C4711yescharacteristic
341#556C22×C4711yescharacteristic
342#555—21no—
343#551—22no—
344D4×Q8C22×C4711yescharacteristic
345#548—21no—
346#546—21no—
347#546—21no—
348D42C22×C4711yescharacteristic
349#542—21no—
350#538—22no—
351#532C22×C4711yescharacteristic
352C2×C4⋊Q8C22×C4711yescharacteristic, complemented
353#529—21no—
354#529C22×C4711yescharacteristic
355C2×#124—21no—
356#518—21no—
357C4×#41C22×C4711yescharacteristic
358#501—21no—
359#498C22×C4712yescomplemented
360#489—21no—
361#486C22×C4712yes—
362#484—21no—
363#481—22no—
364#481—21no—
365#476—22no—
366#475C22×C4712yescomplemented
367#474C22×C4712yes—
368#462—21no—
369#462C22×C4712yescomplemented
370#461—21no—
371#461C22×C4712yes—
372#432C22×C4711yescharacteristic, complemented
373#431C22×C4711yescharacteristic, complemented
374#423C22×C4711yescharacteristic, complemented
375#419—21no—
376#332C22×C4712yescomplemented
377#331C22×C4712yes—
378Q8⋊C8C22×C4712yescomplemented
379Q8⋊C8C22×C4712yescomplemented
380D4⋊C8C22×C4712yes—
381D4⋊C8C22×C4712yes—
382C47#1884211yescharacteristic, direct product factor, Sylow
383C2×#41—21no—
384C2×#41D4×C4711yescharacteristic
385C22×Q8—21no—
386C22×Q8—21no—
387C22×D4—21no—
388C22×D4—21no—
389#137—44no—
390C2×Q16—22no—
391C2×SD16—22no—
392C2×M16—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C4712yes—
398C4⋊Q8C23×C4711yescharacteristic
399#127C23×C4711yescharacteristic
400#126—22no—
401#126—22no—
402#126—21no—
403#125D4×C4711yescharacteristic
404#124—22no—
405#124—22no—
406#124—22no—
407#124—21no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124D4×C4711yescharacteristic
412#123—22no—
413#123—22no—
414#123—22no—
415#123—21no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8D4×C4711yescharacteristic
421#121—22no—
422#121—22no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121D4×C4711yescharacteristic
427#121D4×C4712yes—
428#120—22no—
429#120—22no—
430C4×Q8—21no—
431C4×Q8D4×C4711yescharacteristic
432C4×Q8C23×C4711yescharacteristic
433C4×Q8C23×C4711yescharacteristic
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4D4×C4711yescharacteristic
444C4×D4D4×C4712yes—
445C4×D4C23×C4711yescharacteristic
446C4×D4C23×C4711yescharacteristic
447#117—22no—
448#117—21no—
449#117—21no—
450#117—21no—
451#117D4×C4711yescharacteristic
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C42—21no—
458C2×C42C23×C4711yescharacteristic
459#107—22no—
460#106—22no—
461#106—24no—
462C4⋊C8—21no—
463C4⋊C8—21no—
464C4⋊C8C23×C4712yes—
465C4⋊C8C23×C4712yes—
466#103—22no—
467#103—22no—
468#103—22no—
469#102—22no—
470#102—24no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473#97—21no—
474C4×C8C23×C4712yes—
475C24—22no—
476#41—22no—
477#41—41no—
478#41—82no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—41no—
485C2×Q8—82no—
486C2×Q8C2×D4×C4711yescharacteristic
487C2×Q8C2×D4×C4711yescharacteristic
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—82no—
498C2×D4C2×D4×C4711yescharacteristic
499C2×D4C2×D4×C4711yescharacteristic
500C2×D4C2×D4×C4712yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—41no—
509C22×C4C2×D4×C4711yescharacteristic
510C22×C4C2×D4×C4711yescharacteristic
511C22×C4C2×D4×C4711yescharacteristic
512Q16—44no—
513SD16—44no—
514M16—42no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4C2×D4×C4711yescharacteristic
532C4⋊C4C2×D4×C4711yescharacteristic
533C4⋊C4C2×D4×C4711yescharacteristic
534C4⋊C4C2×D4×C4712yes—
535C4⋊C4C2×D4×C4711yescharacteristic
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C42—22no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42C2×D4×C4711yescharacteristic
559C42C2×D4×C4711yescharacteristic
560C42C2×D4×C4711yescharacteristic
561C42C24×C4711yescharacteristic
562C23—21no—
563C23—21no—
564C23—22no—
565C23—44no—
566C23—82no—
567C23—82no—
568C23#120×C4711yescharacteristic
569Q8—21no—
570Q8—21no—
571Q8—22no—
572Q8—42no—
573Q8—42no—
574Q8—42no—
575Q8—82no—
576Q8—82no—
577D4—21no—
578D4—22no—
579D4—42no—
580D4—42no—
581D4—44no—
582D4—41no—
583D4—41no—
584D4—42no—
585D4—81no—
586D4—82no—
587D4—82no—
588D4AGL(1,ℤ/8)×C4712yes—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4#120×C4711yescharacteristic
611C2×C4#120×C4711yescharacteristic
612C2×C4#120×C4711yescharacteristic
613C2×C4C22×D4×C4711yescharacteristic
614C2×C4C22×D4×C4711yescharacteristic
615C2×C4C22×D4×C4711yescharacteristic
616C8—42no—
617C8—42no—
618C8—42no—
619C22—21no—
620C22—22no—
621C22—21no—
622C22—21no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—41no—
629C22—42no—
630C22—41no—
631C22—164no—
632C22C2×#120×C4711yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—82no—
645C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
646C4C47×#57511yescharacteristic
647C4C47×#57712yes—
648C2—41no—
649C2—42no—
650C2—81no—
651C2—82no—
652C2C47×#300611yescharacteristic
653C2C47×#300911yescharacteristic
654C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3514C2
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×#3239C2semidirect
3. C47×#3227C2semidirect
4. C47×#3039C2semidirect
5. C47×#1652C2semidirect
6. C47×#1651C2semidirect
7. C47×#1640C2semidirect
8. C47×#1639C2semidirect
9. C47×#1557C2semidirect
10. C47×#1495C2semidirect
11. C47×#1488C2semidirect
25. C2×C4⋊Q8×C47C22semidirect
32. C47×#498C22semidirect
39. C47×#475C22semidirect
42. C47×#462C22semidirect
45. C47×#432C22semidirect
46. C47×#431C22semidirect
47. C47×#423C22semidirect
49. C47×#332C22semidirect
51. C47×Q8⋊C8C22semidirect
52. C47×Q8⋊C8C22semidirect
291. #18842C47direct (N × H)
322. #3239C2×C47semidirect
323. #3227C2×C47semidirect
324. #3039C2×C47semidirect
325. #1652C2×C47semidirect
326. #1651C2×C47semidirect
327. #1640C2×C47semidirect
328. #1639C2×C47semidirect
329. #1557C2×C47semidirect
330. #1495C2×C47semidirect
331. #1488C2×C47semidirect
352. C2×C4⋊Q8C22×C47semidirect
359. #498C22×C47semidirect
366. #475C22×C47semidirect
369. #462C22×C47semidirect
372. #432C22×C47semidirect
373. #431C22×C47semidirect
374. #423C22×C47semidirect
376. #332C22×C47semidirect
378. Q8⋊C8C22×C47semidirect
379. Q8⋊C8C22×C47semidirect
382. C47#18842direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35142
C47×#32392
C47×#32272
C47×#30392
C47×#16522
C47×#16512
C47×#16402
C47×#16392
C47×#15572
C47×#14952
C47×#14882
#1884247