Finite Group Databasebeta

← C47×#18901 #26058599

Subgroups — C47×#18901 #26058599

Order 12032.

866 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3515C211yesmaximal, characteristic
2C47×#3248C211yesmaximal, characteristic, complemented
3C47×#3231C211yesmaximal, characteristic, complemented
4C47×#3107C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1653C211yesmaximal, characteristic, complemented
7C47×#1648C211yesmaximal, characteristic, complemented
8C47×#1647C211yesmaximal, characteristic, complemented
9C47×#1644C211yesmaximal, characteristic, complemented
10C47×#1644C211yesmaximal, characteristic, complemented
11C47×#1643C211yesmaximal, characteristic, complemented
12C47×#1643C211yesmaximal, characteristic, complemented
13C47×#1542C211yesmaximal, characteristic, complemented
14C47×#1482C211yesmaximal, characteristic, complemented
15C47×#1477C211yesmaximal, characteristic, complemented
16C47×#557C2211yescharacteristic
17C47×#554C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#553—21no—
20C47×#552—21no—
21C47×#552—22no—
22C47×#552—21no—
23C47×#547—21no—
24C47×#547C2211yescharacteristic
25C47×#541—21no—
26C47×#539—22no—
27C47×#533C2211yescharacteristic
28C47×#533C2211yescharacteristic
29C47×#529—21no—
30C47×#529C2211yescharacteristic
31C2×#125×C47—21no—
32C47×#520—21no—
33C4×#41×C47C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#498C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#487C2211yescharacteristic
38C47×#485—22no—
39C47×#485—21no—
40C47×#479—21no—
41C47×#479—22no—
42C47×#475C2211yescharacteristic
43C47×#475C2211yescharacteristic
44C47×#474C2211yescharacteristic
45C47×#474C2211yescharacteristic
46C47×#467—21no—
47C47×#465—21no—
48C47×#464—21no—
49C47×#462C2211yescharacteristic
50C47×#462C2211yescharacteristic
51C47×#461C2211yescharacteristic
52C47×#461C2211yescharacteristic
53C47×#452—21no—
54C4×Q16×C47—21no—
55C4×SD16×C47—21no—
56C47×#431C2211yescharacteristic
57C47×#431C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47D411yescharacteristic
73C2×Q16×C47—21no—
74C2×Q16×C47—21no—
75C2×SD16×C47—21no—
76C2×SD16×C47—21no—
77C22×C8×C47—21no—
78C4⋊Q8×C47—21no—
79C4⋊Q8×C47C2311yescharacteristic
80C4⋊Q8×C47C2311yescharacteristic
81C4⋊Q8×C47C2311yescharacteristic
82C4⋊Q8×C47C2311yescharacteristic
83#126×C47—22no—
84#126×C47—22no—
85#126×C47—22no—
86#126×C47—21no—
87#125×C47—22no—
88#125×C47—22no—
89#125×C47—22no—
90#125×C47—21no—
91#125×C47—21no—
92#125×C47—22no—
93#125×C47—21no—
94#125×C47—21no—
95#125×C47—21no—
96#125×C47D411yescharacteristic
97#124×C47D411yescharacteristic
98#123×C47—22no—
99#123×C47—22no—
100#123×C47—22no—
101#123×C47—21no—
102#123×C47—22no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47D411yescharacteristic
112C22⋊Q8×C47D412yes—
113#121×C47—22no—
114#121×C47—21no—
115#121×C47D411yescharacteristic
116C4×Q8×C47—21no—
117C4×Q8×C47—21no—
118C4×Q8×C47—21no—
119C4×Q8×C47—21no—
120C4×Q8×C47—21no—
121C4×Q8×C47D412yes—
122C4×Q8×C47D411yescharacteristic
123C4×Q8×C47C2311yescharacteristic
124C4×Q8×C47C2311yescharacteristic
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47D411yescharacteristic
133C4×D4×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135#117×C47—22no—
136#117×C47—22no—
137#117×C47—21no—
138#117×C47—21no—
139#117×C47—21no—
140#117×C47—21no—
141#117×C47D411yescharacteristic
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—22no—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47—21no—
146C2×C4⋊C4×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47C2311yescharacteristic
149#107×C47—21no—
150#107×C47—21no—
151#107×C47—22no—
152#106×C47—21no—
153#106×C47—21no—
154#106×C47—22no—
155C4⋊C8×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—22no—
164#103×C47—22no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172C22⋊C8×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—22no—
177#41×C47—41no—
178#41×C47—42no—
179#41×C47—42no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47C2×D411yescharacteristic
184C2×Q8×C47C2×D411yescharacteristic
185C2×Q8×C47C2×D412yes—
186C2×D4×C47—22no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47C2×D411yescharacteristic
190C2×D4×C47C2×D411yescharacteristic
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201Q16×C47—42no—
202Q16×C47—81no—
203SD16×C47—42no—
204SD16×C47—81no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—81no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—22no—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—21no—
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—41no—
236C4⋊C4×C47—41no—
237C4⋊C4×C47C2×D411yescharacteristic
238C4⋊C4×C47C2×D411yescharacteristic
239C4⋊C4×C47C2×D411yescharacteristic
240C4⋊C4×C47C2×D411yescharacteristic
241C4⋊C4×C47C2×D412yes—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—21no—
247C22⋊C4×C47—21no—
248C22⋊C4×C47—21no—
249C22⋊C4×C47—21no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—41no—
255C42×C47—22no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—22no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—41no—
262C42×C47C2×D411yescharacteristic
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2411yescharacteristic
266C23×C47—21no—
267C23×C47—21no—
268C23×C47#12011yescharacteristic
269Q8×C47—21no—
270Q8×C47—21no—
271Q8×C47—21no—
272Q8×C47—21no—
273Q8×C47—42no—
274Q8×C47—41no—
275Q8×C47—41no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—41no—
280D4×C47—21no—
281D4×C47—21no—
282D4×C47—21no—
283D4×C47—42no—
284D4×C47—44no—
285D4×C47—81no—
286D4×C47#13512yes—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—41no—
300C2×C4×C47—42no—
301C2×C4×C47—44no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—81no—
309C2×C4×C47—82no—
310C2×C4×C47—82no—
311C2×C4×C47#12011yescharacteristic
312C2×C4×C47#12011yescharacteristic
313C2×C4×C47#12011yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C8×C47—41no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322C8×C47—41no—
323#18901C4711yesmaximal, characteristic, direct product factor, Sylow
324C22×C47—21no—
325C22×C47—22no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—41no—
332C22×C47—41no—
333C22×C47C2×#12011yescharacteristic
334C4×C47—21no—
335C4×C47—21no—
336C4×C47—21no—
337C4×C47—21no—
338C4×C47—41no—
339C4×C47—41no—
340C4×C47—42no—
341C4×C47—41no—
342C4×C47—41no—
343C4×C47—41no—
344C4×C47—41no—
345C4×C47—42no—
346C4×C47—81no—
347C4×C47—81no—
348C4×C47C2×#13511yescharacteristic
349C4×C47#57511yescharacteristic
350C4×C47#57711yescharacteristic
351C4×C47#57811yescharacteristic
352#3515C2×C4711yescharacteristic
353#3248C2×C4711yescharacteristic, complemented
354#3231C2×C4711yescharacteristic, complemented
355#3107C2×C4711yescharacteristic, complemented
356#1654C2×C4711yescharacteristic, complemented
357#1653C2×C4711yescharacteristic, complemented
358#1648C2×C4711yescharacteristic, complemented
359#1647C2×C4711yescharacteristic, complemented
360#1644C2×C4711yescharacteristic, complemented
361#1644C2×C4711yescharacteristic, complemented
362#1643C2×C4711yescharacteristic, complemented
363#1643C2×C4711yescharacteristic, complemented
364#1542C2×C4711yescharacteristic, complemented
365#1482C2×C4711yescharacteristic, complemented
366#1477C2×C4711yescharacteristic, complemented
367C2×C47—41no—
368C2×C47—42no—
369C2×C47—81no—
370C2×C47#300211yescharacteristic
371C2×C47#301311yescharacteristic
372C2×C47#302211yescharacteristic
373#557C22×C4711yescharacteristic
374#554C22×C4711yescharacteristic
375#554C22×C4711yescharacteristic
376#553—21no—
377#552—21no—
378#552—22no—
379#552—21no—
380#547—21no—
381#547C22×C4711yescharacteristic
382#541—21no—
383#539—22no—
384#533C22×C4711yescharacteristic
385#533C22×C4711yescharacteristic
386#529—21no—
387#529C22×C4711yescharacteristic
388C2×#125—21no—
389#520—21no—
390C4×#41C22×C4711yescharacteristic
391#500C22×C4711yescharacteristic
392#498C22×C4711yescharacteristic
393#487C22×C4711yescharacteristic
394#487C22×C4711yescharacteristic
395#485—22no—
396#485—21no—
397#479—21no—
398#479—22no—
399#475C22×C4711yescharacteristic
400#475C22×C4711yescharacteristic
401#474C22×C4711yescharacteristic
402#474C22×C4711yescharacteristic
403#467—21no—
404#465—21no—
405#464—21no—
406#462C22×C4711yescharacteristic
407#462C22×C4711yescharacteristic
408#461C22×C4711yescharacteristic
409#461C22×C4711yescharacteristic
410#452—21no—
411C4×Q16—21no—
412C4×SD16—21no—
413#431C22×C4711yescharacteristic
414#431C22×C4711yescharacteristic
415C2×C4⋊C8C22×C4711yescharacteristic
416#333C22×C4711yescharacteristic
417#333C22×C4711yescharacteristic
418#332C22×C4711yescharacteristic
419#332C22×C4711yescharacteristic
420Q8⋊C8C22×C4711yescharacteristic
421Q8⋊C8C22×C4711yescharacteristic
422Q8⋊C8C22×C4711yescharacteristic
423Q8⋊C8C22×C4711yescharacteristic
424D4⋊C8C22×C4711yescharacteristic
425D4⋊C8C22×C4711yescharacteristic
426D4⋊C8C22×C4711yescharacteristic
427D4⋊C8C22×C4711yescharacteristic
428C47#1890111yescharacteristic, direct product factor, Sylow
429C2×#41—21no—
430C2×#41D4×C4711yescharacteristic
431C2×Q16—21no—
432C2×Q16—21no—
433C2×SD16—21no—
434C2×SD16—21no—
435C22×C8—21no—
436C4⋊Q8—21no—
437C4⋊Q8C23×C4711yescharacteristic
438C4⋊Q8C23×C4711yescharacteristic
439C4⋊Q8C23×C4711yescharacteristic
440C4⋊Q8C23×C4711yescharacteristic
441#126—22no—
442#126—22no—
443#126—22no—
444#126—21no—
445#125—22no—
446#125—22no—
447#125—22no—
448#125—21no—
449#125—21no—
450#125—22no—
451#125—21no—
452#125—21no—
453#125—21no—
454#125D4×C4711yescharacteristic
455#124D4×C4711yescharacteristic
456#123—22no—
457#123—22no—
458#123—22no—
459#123—21no—
460#123—22no—
461C22⋊Q8—21no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8D4×C4711yescharacteristic
470C22⋊Q8D4×C4712yes—
471#121—22no—
472#121—21no—
473#121D4×C4711yescharacteristic
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8D4×C4711yescharacteristic
480C4×Q8D4×C4712yes—
481C4×Q8C23×C4711yescharacteristic
482C4×Q8C23×C4711yescharacteristic
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4D4×C4711yescharacteristic
491C4×D4C23×C4711yescharacteristic
492C4×D4C23×C4711yescharacteristic
493#117—22no—
494#117—22no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117D4×C4711yescharacteristic
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C42—21no—
506C2×C42C23×C4711yescharacteristic
507#107—21no—
508#107—21no—
509#107—22no—
510#106—21no—
511#106—21no—
512#106—22no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8C23×C4711yescharacteristic
516C4⋊C8C23×C4711yescharacteristic
517C4⋊C8C23×C4711yescharacteristic
518C4⋊C8C23×C4711yescharacteristic
519#103—21no—
520#103—21no—
521#103—22no—
522#103—22no—
523#103—21no—
524#103—21no—
525#103—21no—
526#103—21no—
527#102—21no—
528#102—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C4×C8—21no—
532C4×C8C23×C4711yescharacteristic
533C4×C8C23×C4711yescharacteristic
534#41—22no—
535#41—41no—
536#41—42no—
537#41—42no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×D4×C4711yescharacteristic
542C2×Q8C2×D4×C4711yescharacteristic
543C2×Q8C2×D4×C4712yes—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4C2×D4×C4711yescharacteristic
548C2×D4C2×D4×C4711yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C4711yescharacteristic
557C22×C4C2×D4×C4711yescharacteristic
558C22×C4C2×D4×C4711yescharacteristic
559Q16—42no—
560Q16—81no—
561SD16—42no—
562SD16—81no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—81no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4C2×D4×C4711yescharacteristic
596C4⋊C4C2×D4×C4711yescharacteristic
597C4⋊C4C2×D4×C4711yescharacteristic
598C4⋊C4C2×D4×C4711yescharacteristic
599C4⋊C4C2×D4×C4712yes—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—41no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—22no—
617C42—21no—
618C42—21no—
619C42—41no—
620C42C2×D4×C4711yescharacteristic
621C42C2×D4×C4711yescharacteristic
622C42C2×D4×C4711yescharacteristic
623C42C24×C4711yescharacteristic
624C23—21no—
625C23—21no—
626C23#120×C4711yescharacteristic
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—42no—
642D4—44no—
643D4—81no—
644D4#135×C4712yes—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—81no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4#120×C4711yescharacteristic
670C2×C4#120×C4711yescharacteristic
671C2×C4#120×C4711yescharacteristic
672C2×C4C22×D4×C4711yescharacteristic
673C2×C4C22×D4×C4711yescharacteristic
674C2×C4C22×D4×C4711yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C22—21no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×#120×C4711yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4C2×#135×C4711yescharacteristic
706C4C47×#57511yescharacteristic
707C4C47×#57711yescharacteristic
708C4C47×#57811yescharacteristic
709C2—41no—
710C2—42no—
711C2—81no—
712C2C47×#300211yescharacteristic
713C2C47×#301311yescharacteristic
714C2C47×#302211yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3515C2
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×#3248C2semidirect
3. C47×#3231C2semidirect
4. C47×#3107C2semidirect
5. C47×#1654C2semidirect
6. C47×#1653C2semidirect
7. C47×#1648C2semidirect
8. C47×#1647C2semidirect
9. C47×#1644C2semidirect
10. C47×#1644C2semidirect
11. C47×#1643C2semidirect
12. C47×#1643C2semidirect
13. C47×#1542C2semidirect
14. C47×#1482C2semidirect
15. C47×#1477C2semidirect
323. #18901C47direct (N × H)
353. #3248C2×C47semidirect
354. #3231C2×C47semidirect
355. #3107C2×C47semidirect
356. #1654C2×C47semidirect
357. #1653C2×C47semidirect
358. #1648C2×C47semidirect
359. #1647C2×C47semidirect
360. #1644C2×C47semidirect
361. #1644C2×C47semidirect
362. #1643C2×C47semidirect
363. #1643C2×C47semidirect
364. #1542C2×C47semidirect
365. #1482C2×C47semidirect
366. #1477C2×C47semidirect
428. C47#18901direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35152
C47×#32482
C47×#32312
C47×#31072
C47×#16542
C47×#16532
C47×#16482
C47×#16472
C47×#16442
C47×#16432
C47×#15422
C47×#14822
C47×#14772
#1890147