Finite Group Databasebeta

← C47×#18559 #26058257

Subgroups — C47×#18559 #26058257

Order 12032.

922 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3480C211yesmaximal, characteristic
2C47×#3182C211yesmaximal, characteristic, complemented
3C47×#3116C211yesmaximal, characteristic, complemented
4C47×#3078C211yesmaximal, characteristic, complemented
5C47×#1650C211yesmaximal, characteristic, complemented
6C47×#1648C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1640C211yesmaximal, characteristic, complemented
9C47×#1638C211yesmaximal, characteristic, complemented
10C47×#1636C211yesmaximal, characteristic, complemented
11C47×#1631C211yesmaximal, characteristic, complemented
12C47×#1630C211yesmaximal, characteristic, complemented
13C47×#1557C211yesmaximal, characteristic, complemented
14C47×#1491C211yesmaximal, characteristic, complemented
15C47×#1489C211yesmaximal, characteristic, complemented
16C47×#559—21no—
17C47×#559C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#556—21no—
20C47×#556C2211yescharacteristic
21C47×#553—22no—
22C47×#553—21no—
23C47×#550C2211yescharacteristic
24C47×#548—21no—
25C47×#533C2211yescharacteristic
26C47×#532—21no—
27C47×#532C2211yescharacteristic
28C47×#529—21no—
29C47×#529—22no—
30C4×#41×C47—21no—
31C4×#41×C47—21no—
32C4×#41×C47C2211yescharacteristic
33C2×C4×Q8×C47C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#485—21no—
39C47×#479—21no—
40C47×#479—21no—
41C47×#477C2211yescharacteristic
42C47×#477C2211yescharacteristic
43C47×#477C2211yescharacteristic
44C47×#476C2211yescharacteristic
45C47×#475C2211yescharacteristic
46C47×#475C2211yescharacteristic
47C47×#468—22no—
48C47×#462C2211yescharacteristic
49C47×#461C2211yescharacteristic
50C47×#452—21no—
51C47×#441—21no—
52C47×#440—21no—
53C47×#440—22no—
54C47×#432C2211yescharacteristic
55C47×#428—21no—
56C47×#423C2211yescharacteristic
57C47×#419—21no—
58C4×M16×C47C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#331C2211yescharacteristic
62C47×#331C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×Q8⋊C8C2211yescharacteristic
68C47×Q8⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47D411yescharacteristic
74C22×Q8×C47D411yescharacteristic
75C2×Q16×C47—21no—
76C2×SD16×C47—21no—
77C2×SD16×C47—22no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C4⋊Q8×C47—21no—
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83C4⋊Q8×C47C2311yescharacteristic
84#127×C47—21no—
85#127×C47C2311yescharacteristic
86#126×C47—22no—
87#126×C47—22no—
88#126×C47—22no—
89#125×C47—22no—
90#125×C47—21no—
91#125×C47—21no—
92#124×C47—22no—
93#124×C47—21no—
94#124×C47—21no—
95#124×C47—21no—
96#124×C47—21no—
97#123×C47—22no—
98#123×C47—22no—
99#123×C47—22no—
100C22⋊Q8×C47—22no—
101C22⋊Q8×C47—21no—
102C22⋊Q8×C47—21no—
103C22⋊Q8×C47—21no—
104#121×C47—22no—
105#121×C47—22no—
106#121×C47—22no—
107#121×C47—21no—
108#121×C47—21no—
109#121×C47D412yes—
110C4×Q8×C47—21no—
111C4×Q8×C47—21no—
112C4×Q8×C47—21no—
113C4×Q8×C47—21no—
114C4×Q8×C47—21no—
115C4×Q8×C47—21no—
116C4×Q8×C47—21no—
117C4×Q8×C47D411yescharacteristic
118C4×Q8×C47D411yescharacteristic
119C4×Q8×C47D411yescharacteristic
120C4×Q8×C47C2311yescharacteristic
121C4×Q8×C47C2311yescharacteristic
122C4×Q8×C47C2311yescharacteristic
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47D411yescharacteristic
135C4×D4×C47D412yes—
136C4×D4×C47C2311yescharacteristic
137#117×C47—22no—
138#117×C47—22no—
139#117×C47—21no—
140#117×C47—21no—
141#117×C47—21no—
142#117×C47D411yescharacteristic
143C2×C4⋊C4×C47—21no—
144C2×C4⋊C4×C47D411yescharacteristic
145C2×C42×C47—22no—
146C2×C42×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—22no—
150#107×C47—21no—
151#107×C47—21no—
152#107×C47—21no—
153#106×C47—21no—
154#106×C47—21no—
155#106×C47—21no—
156C4⋊C8×C47—21no—
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161#103×C47—21no—
162#103×C47—21no—
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—22no—
169#102×C47—21no—
170#102×C47—22no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173#97×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—41no—
177#41×C47—41no—
178#41×C47—42no—
179#41×C47—42no—
180#41×C47—42no—
181#41×C47—42no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—22no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—41no—
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D411yescharacteristic
190C2×Q8×C47C2×D411yescharacteristic
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47C2×D411yescharacteristic
198C2×D4×C47C2×D412yes—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—22no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210Q16×C47—42no—
211SD16×C47—44no—
212SD16×C47—42no—
213M16×C47—42no—
214M16×C47—42no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—22no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—41no—
238C4⋊C4×C47—41no—
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D412yes—
242C4⋊C4×C47C2×D411yescharacteristic
243C4⋊C4×C47C2×D411yescharacteristic
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—21no—
255C22⋊C4×C47—41no—
256C42×C47—22no—
257C42×C47—22no—
258C42×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—41no—
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2411yescharacteristic
270C23×C47—21no—
271C23×C47—22no—
272C23×C47#12011yescharacteristic
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47—42no—
279Q8×C47—42no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—41no—
283Q8×C47—41no—
284Q8×C47#13712yes—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—42no—
288D4×C47—44no—
289D4×C47—42no—
290D4×C47—44no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—82no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—41no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—44no—
312C2×C4×C47—44no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—81no—
318C2×C4×C47—81no—
319C2×C4×C47—82no—
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C8×C47—22no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331C8×C47—41no—
332#18559C4711yesmaximal, characteristic, direct product factor, Sylow
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—41no—
337C22×C47—42no—
338C22×C47—42no—
339C22×C47—41no—
340C22×C47—42no—
341C22×C47—41no—
342C22×C47C2×#12011yescharacteristic
343C4×C47—21no—
344C4×C47—21no—
345C4×C47—22no—
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—41no—
349C4×C47—42no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—81no—
356C4×C47—81no—
357C4×C47C2×#13711yescharacteristic
358C4×C47#57511yescharacteristic
359C4×C47#57511yescharacteristic
360C4×C47#57511yescharacteristic
361#3480C2×C4711yescharacteristic
362#3182C2×C4711yescharacteristic, complemented
363#3116C2×C4711yescharacteristic, complemented
364#3078C2×C4711yescharacteristic, complemented
365#1650C2×C4711yescharacteristic, complemented
366#1648C2×C4711yescharacteristic, complemented
367#1642C2×C4711yescharacteristic, complemented
368#1640C2×C4711yescharacteristic, complemented
369#1638C2×C4711yescharacteristic, complemented
370#1636C2×C4711yescharacteristic, complemented
371#1631C2×C4711yescharacteristic, complemented
372#1630C2×C4711yescharacteristic, complemented
373#1557C2×C4711yescharacteristic, complemented
374#1491C2×C4711yescharacteristic, complemented
375#1489C2×C4711yescharacteristic, complemented
376C2×C47—41no—
377C2×C47—81no—
378C2×C47—82no—
379C2×C47#300511yescharacteristic
380C2×C47#300711yescharacteristic
381C2×C47#301811yescharacteristic
382#559—21no—
383#559C22×C4711yescharacteristic
384#557C22×C4711yescharacteristic
385#556—21no—
386#556C22×C4711yescharacteristic
387#553—22no—
388#553—21no—
389#550C22×C4711yescharacteristic
390#548—21no—
391#533C22×C4711yescharacteristic
392#532—21no—
393#532C22×C4711yescharacteristic
394#529—21no—
395#529—22no—
396C4×#41—21no—
397C4×#41—21no—
398C4×#41C22×C4711yescharacteristic
399C2×C4×Q8C22×C4711yescharacteristic
400#500C22×C4711yescharacteristic
401#492C22×C4711yescharacteristic
402#487C22×C4711yescharacteristic
403#486C22×C4711yescharacteristic
404#485—21no—
405#479—21no—
406#479—21no—
407#477C22×C4711yescharacteristic
408#477C22×C4711yescharacteristic
409#477C22×C4711yescharacteristic
410#476C22×C4711yescharacteristic
411#475C22×C4711yescharacteristic
412#475C22×C4711yescharacteristic
413#468—22no—
414#462C22×C4711yescharacteristic
415#461C22×C4711yescharacteristic
416#452—21no—
417#441—21no—
418#440—21no—
419#440—22no—
420#432C22×C4711yescharacteristic
421#428—21no—
422#423C22×C4711yescharacteristic
423#419—21no—
424C4×M16C22×C4711yescharacteristic
425#332C22×C4711yescharacteristic
426#332C22×C4711yescharacteristic
427#331C22×C4711yescharacteristic
428#331C22×C4711yescharacteristic
429Q8⋊C8C22×C4711yescharacteristic
430Q8⋊C8C22×C4711yescharacteristic
431Q8⋊C8C22×C4711yescharacteristic
432Q8⋊C8C22×C4711yescharacteristic
433Q8⋊C8C22×C4711yescharacteristic
434Q8⋊C8C22×C4711yescharacteristic
435D4⋊C8C22×C4711yescharacteristic
436D4⋊C8C22×C4711yescharacteristic
437C47#1855911yescharacteristic, direct product factor, Sylow
438C2×#41—21no—
439C2×#41—21no—
440C2×#41D4×C4711yescharacteristic
441C22×Q8D4×C4711yescharacteristic
442C2×Q16—21no—
443C2×SD16—21no—
444C2×SD16—22no—
445C2×M16—21no—
446C2×M16—21no—
447C4⋊Q8—21no—
448C4⋊Q8C23×C4711yescharacteristic
449C4⋊Q8C23×C4711yescharacteristic
450C4⋊Q8C23×C4711yescharacteristic
451#127—21no—
452#127C23×C4711yescharacteristic
453#126—22no—
454#126—22no—
455#126—22no—
456#125—22no—
457#125—21no—
458#125—21no—
459#124—22no—
460#124—21no—
461#124—21no—
462#124—21no—
463#124—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8—22no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471#121—22no—
472#121—22no—
473#121—22no—
474#121—21no—
475#121—21no—
476#121D4×C4712yes—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8D4×C4711yescharacteristic
485C4×Q8D4×C4711yescharacteristic
486C4×Q8D4×C4711yescharacteristic
487C4×Q8C23×C4711yescharacteristic
488C4×Q8C23×C4711yescharacteristic
489C4×Q8C23×C4711yescharacteristic
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4D4×C4711yescharacteristic
502C4×D4D4×C4712yes—
503C4×D4C23×C4711yescharacteristic
504#117—22no—
505#117—22no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117D4×C4711yescharacteristic
510C2×C4⋊C4—21no—
511C2×C4⋊C4D4×C4711yescharacteristic
512C2×C42—22no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42C23×C4711yescharacteristic
516#107—21no—
517#107—21no—
518#107—22no—
519#107—21no—
520#106—21no—
521#106—21no—
522#106—21no—
523C4⋊C8—21no—
524C4⋊C8C23×C4711yescharacteristic
525C4⋊C8C23×C4711yescharacteristic
526C4⋊C8C23×C4711yescharacteristic
527C4⋊C8C23×C4711yescharacteristic
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—22no—
535#103—21no—
536#102—21no—
537#102—22no—
538C22⋊C8—21no—
539#97—21no—
540#97—21no—
541C4×C8C23×C4711yescharacteristic
542C4×C8C23×C4711yescharacteristic
543#41—41no—
544#41—41no—
545#41—42no—
546#41—42no—
547#41—42no—
548#41—42no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—41no—
555C2×Q8C2×D4×C4711yescharacteristic
556C2×Q8C2×D4×C4711yescharacteristic
557C2×Q8C2×D4×C4711yescharacteristic
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4C2×D4×C4711yescharacteristic
565C2×D4C2×D4×C4712yes—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4C2×D4×C4711yescharacteristic
575C22×C4C2×D4×C4711yescharacteristic
576C22×C4C2×D4×C4711yescharacteristic
577Q16—42no—
578SD16—44no—
579SD16—42no—
580M16—42no—
581M16—42no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4C2×D4×C4711yescharacteristic
607C4⋊C4C2×D4×C4711yescharacteristic
608C4⋊C4C2×D4×C4712yes—
609C4⋊C4C2×D4×C4711yescharacteristic
610C4⋊C4C2×D4×C4711yescharacteristic
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—41no—
623C42—22no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42C2×D4×C4711yescharacteristic
634C42C2×D4×C4711yescharacteristic
635C42C2×D4×C4711yescharacteristic
636C42C24×C4711yescharacteristic
637C23—21no—
638C23—22no—
639C23#120×C4711yescharacteristic
640Q8—21no—
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—21no—
645Q8—42no—
646Q8—42no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8#137×C4712yes—
652D4—21no—
653D4—21no—
654D4—42no—
655D4—44no—
656D4—42no—
657D4—44no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—82no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—82no—
687C2×C4#120×C4711yescharacteristic
688C2×C4#120×C4711yescharacteristic
689C2×C4#120×C4711yescharacteristic
690C2×C4C22×D4×C4711yescharacteristic
691C2×C4C22×D4×C4711yescharacteristic
692C2×C4C22×D4×C4711yescharacteristic
693C8—22no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—41no—
706C22—42no—
707C22—41no—
708C22C2×#120×C4711yescharacteristic
709C4—21no—
710C4—21no—
711C4—22no—
712C4—21no—
713C4—21no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4C2×#137×C4711yescharacteristic
724C4C47×#57511yescharacteristic
725C4C47×#57511yescharacteristic
726C4C47×#57511yescharacteristic
727C2—41no—
728C2—81no—
729C2—82no—
730C2C47×#300511yescharacteristic
731C2C47×#300711yescharacteristic
732C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3480C2
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×#3182C2semidirect
3. C47×#3116C2semidirect
4. C47×#3078C2semidirect
5. C47×#1650C2semidirect
6. C47×#1648C2semidirect
7. C47×#1642C2semidirect
8. C47×#1640C2semidirect
9. C47×#1638C2semidirect
10. C47×#1636C2semidirect
11. C47×#1631C2semidirect
12. C47×#1630C2semidirect
13. C47×#1557C2semidirect
14. C47×#1491C2semidirect
15. C47×#1489C2semidirect
332. #18559C47direct (N × H)
362. #3182C2×C47semidirect
363. #3116C2×C47semidirect
364. #3078C2×C47semidirect
365. #1650C2×C47semidirect
366. #1648C2×C47semidirect
367. #1642C2×C47semidirect
368. #1640C2×C47semidirect
369. #1638C2×C47semidirect
370. #1636C2×C47semidirect
371. #1631C2×C47semidirect
372. #1630C2×C47semidirect
373. #1557C2×C47semidirect
374. #1491C2×C47semidirect
375. #1489C2×C47semidirect
437. C47#18559direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34802
C47×#31822
C47×#31162
C47×#30782
C47×#16502
C47×#16482
C47×#16422
C47×#16402
C47×#16382
C47×#16362
C47×#16312
C47×#16302
C47×#15572
C47×#14912
C47×#14892
#1855947