Finite Group Databasebeta

← C47×#18649 #26058347

Subgroups — C47×#18649 #26058347

Order 12032.

868 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3523C211yesmaximal, characteristic
2C47×#3248C211yesmaximal, characteristic
3C47×#3160C211yesmaximal, characteristic, complemented
4C47×#3113C211yesmaximal, characteristic, complemented
5C47×#1653C211yesmaximal, characteristic, complemented
6C47×#1653C211yesmaximal, characteristic, complemented
7C47×#1652C211yesmaximal, characteristic, complemented
8C47×#1651C211yesmaximal, characteristic, complemented
9C47×#1650C211yesmaximal, characteristic, complemented
10C47×#1649C211yesmaximal, characteristic, complemented
11C47×#1648C211yesmaximal, characteristic, complemented
12C47×#1648C211yesmaximal, characteristic, complemented
13C47×#1552C211yesmaximal, characteristic, complemented
14C47×#1494C211yesmaximal, characteristic
15C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
16C47×#557—21no—
17C47×#557C2211yescharacteristic
18C47×#557C2211yescharacteristic
19C47×#556—21no—
20C47×#556C2211yescharacteristic
21C47×#552—22no—
22C47×#552—21no—
23D4×Q8×C47—21no—
24D4×Q8×C47C2211yescharacteristic
25C47×#541—22no—
26C47×#541—21no—
27C47×#533—21no—
28C47×#533C2211yescharacteristic
29C47×#533C2211yescharacteristic
30C47×#529—21no—
31C47×#529C2211yescharacteristic
32C47×#519—21no—
33C2×C4×Q8×C47C2211yescharacteristic
34C47×#500C2211yescharacteristic
35C47×#500C2211yescharacteristic
36C47×#499—22no—
37C47×#498C2211yescharacteristic
38C47×#498C2211yescharacteristic
39C47×#483—21no—
40C47×#479—21no—
41C47×#475C2211yescharacteristic
42C47×#475C2211yescharacteristic
43C47×#475C2211yescharacteristic
44C47×#474C2211yescharacteristic
45C47×#467—21no—
46C47×#465—21no—
47C47×#464—21no—
48C47×#462C2211yescharacteristic
49C47×#462C2211yescharacteristic
50C47×#462C2211yescharacteristic
51C47×#461C2211yescharacteristic
52C47×#451—21no—
53C47×#441—21no—
54C47×#441—21no—
55C47×#432C2211yescharacteristic
56C47×#427—22no—
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C47×#332C2211yescharacteristic
60C47×#332C2211yescharacteristic
61C47×#332C2211yescharacteristic
62C47×#332C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C47×Q8⋊C8C2211yescharacteristic
68C47×Q8⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C22×Q8×C47—21no—
72C22×Q8×C47D411yescharacteristic
73C2×Q16×C47—21no—
74C2×Q16×C47—21no—
75C2×Q16×C47—21no—
76C2×SD16×C47—21no—
77C22×C8×C47—21no—
78C22×C8×C47—21no—
79C4⋊Q8×C47—22no—
80C4⋊Q8×C47—21no—
81C4⋊Q8×C47—21no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47C2311yescharacteristic
84C4⋊Q8×C47C2311yescharacteristic
85C4⋊Q8×C47C2311yescharacteristic
86C4⋊Q8×C47C2311yescharacteristic
87#126×C47—22no—
88#126×C47—22no—
89#126×C47—22no—
90#126×C47—22no—
91#126×C47—21no—
92#125×C47—22no—
93#125×C47—22no—
94#125×C47—22no—
95#125×C47—21no—
96#125×C47—22no—
97#125×C47—22no—
98#125×C47—21no—
99#125×C47—21no—
100#125×C47D411yescharacteristic
101#125×C47D412yes—
102#124×C47—21no—
103#124×C47D411yescharacteristic
104#123×C47—22no—
105#123×C47—21no—
106C22⋊Q8×C47—22no—
107C22⋊Q8×C47—22no—
108C22⋊Q8×C47—21no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47—21no—
111C22⋊Q8×C47—21no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47D411yescharacteristic
116#121×C47D411yescharacteristic
117C4×Q8×C47—22no—
118C4×Q8×C47—22no—
119C4×Q8×C47—21no—
120C4×Q8×C47—21no—
121C4×Q8×C47—21no—
122C4×Q8×C47—21no—
123C4×Q8×C47—21no—
124C4×Q8×C47—21no—
125C4×Q8×C47—21no—
126C4×Q8×C47—21no—
127C4×Q8×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47—21no—
130C4×Q8×C47D411yescharacteristic
131C4×Q8×C47D411yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C4×Q8×C47C2311yescharacteristic
134C4×Q8×C47C2311yescharacteristic
135C4×D4×C47—22no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47C2311yescharacteristic
139#117×C47—22no—
140#117×C47—22no—
141#117×C47—22no—
142#117×C47—21no—
143#117×C47—21no—
144#117×C47—21no—
145#117×C47D412yes—
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47D411yescharacteristic
148C2×C42×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—21no—
151#107×C47—22no—
152#107×C47—22no—
153#106×C47—21no—
154#106×C47—21no—
155#106×C47—21no—
156#106×C47—22no—
157#106×C47—22no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163#103×C47—21no—
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#103×C47—21no—
168#103×C47—21no—
169#103×C47—21no—
170#102×C47—21no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176C2×Q8×C47—22no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—22no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—41no—
184C2×Q8×C47—42no—
185C2×Q8×C47—42no—
186C2×Q8×C47C2×D411yescharacteristic
187C2×Q8×C47C2×D411yescharacteristic
188C2×Q8×C47C2×D411yescharacteristic
189C2×D4×C47—21no—
190C2×D4×C47C2×D411yescharacteristic
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198Q16×C47—42no—
199Q16×C47—42no—
200Q16×C47—81no—
201SD16×C47—81no—
202C2×C8×C47—24no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—81no—
210C4⋊C4×C47—22no—
211C4⋊C4×C47—22no—
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—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—22no—
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—
242C4⋊C4×C47C2×D412yes—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—21no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—21no—
249C22⋊C4×C47—21no—
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—41no—
253C42×C47—22no—
254C42×C47—22no—
255C42×C47—22no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—22no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—21no—
262C42×C47—41no—
263C42×C47C2×D411yescharacteristic
264C42×C47C2×D411yescharacteristic
265C42×C47C2×D411yescharacteristic
266C42×C47C2411yescharacteristic
267C23×C47—21no—
268C23×C47#12011yescharacteristic
269Q8×C47—21no—
270Q8×C47—21no—
271Q8×C47—21no—
272Q8×C47—21no—
273Q8×C47—21no—
274Q8×C47—42no—
275Q8×C47—44no—
276Q8×C47—41no—
277Q8×C47—41no—
278Q8×C47—41no—
279Q8×C47—41no—
280Q8×C47—41no—
281Q8×C47—41no—
282Q8×C47—41no—
283Q8×C47—41no—
284Q8×C47#13512yes—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—42no—
288C2×C4×C47—21no—
289C2×C4×C47—22no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—22no—
302C2×C4×C47—42no—
303C2×C4×C47—44no—
304C2×C4×C47—42no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47#12011yescharacteristic
310C2×C4×C47#12011yescharacteristic
311C2×C4×C47#12011yescharacteristic
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C8×C47—22no—
316C8×C47—22no—
317C8×C47—41no—
318C8×C47—41no—
319C8×C47—41no—
320C8×C47—41no—
321#18649C4711yesmaximal, characteristic, direct product factor, Sylow
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47#45612yes—
328C22×C47C2×#12011yescharacteristic
329C4×C47—21no—
330C4×C47—22no—
331C4×C47—21no—
332C4×C47—21no—
333C4×C47—21no—
334C4×C47—41no—
335C4×C47—42no—
336C4×C47—41no—
337C4×C47—41no—
338C4×C47—42no—
339C4×C47—41no—
340C4×C47—41no—
341C4×C47—41no—
342C4×C47—81no—
343C4×C47—81no—
344C4×C47C2×#13511yescharacteristic
345C4×C47#57511yescharacteristic
346C4×C47#57711yescharacteristic
347C4×C47#57811yescharacteristic
348#3523C2×C4711yescharacteristic
349#3248C2×C4711yescharacteristic
350#3160C2×C4711yescharacteristic, complemented
351#3113C2×C4711yescharacteristic, complemented
352#1653C2×C4711yescharacteristic, complemented
353#1653C2×C4711yescharacteristic, complemented
354#1652C2×C4711yescharacteristic, complemented
355#1651C2×C4711yescharacteristic, complemented
356#1650C2×C4711yescharacteristic, complemented
357#1649C2×C4711yescharacteristic, complemented
358#1648C2×C4711yescharacteristic, complemented
359#1648C2×C4711yescharacteristic, complemented
360#1552C2×C4711yescharacteristic, complemented
361#1494C2×C4711yescharacteristic
362C2×Q8⋊C8C2×C4711yescharacteristic, complemented
363C2×C47—22no—
364C2×C47—81no—
365C2×C47#300211yescharacteristic
366C2×C47#301311yescharacteristic
367C2×C47C2×#45611yescharacteristic
368#557—21no—
369#557C22×C4711yescharacteristic
370#557C22×C4711yescharacteristic
371#556—21no—
372#556C22×C4711yescharacteristic
373#552—22no—
374#552—21no—
375D4×Q8—21no—
376D4×Q8C22×C4711yescharacteristic
377#541—22no—
378#541—21no—
379#533—21no—
380#533C22×C4711yescharacteristic
381#533C22×C4711yescharacteristic
382#529—21no—
383#529C22×C4711yescharacteristic
384#519—21no—
385C2×C4×Q8C22×C4711yescharacteristic
386#500C22×C4711yescharacteristic
387#500C22×C4711yescharacteristic
388#499—22no—
389#498C22×C4711yescharacteristic
390#498C22×C4711yescharacteristic
391#483—21no—
392#479—21no—
393#475C22×C4711yescharacteristic
394#475C22×C4711yescharacteristic
395#475C22×C4711yescharacteristic
396#474C22×C4711yescharacteristic
397#467—21no—
398#465—21no—
399#464—21no—
400#462C22×C4711yescharacteristic
401#462C22×C4711yescharacteristic
402#462C22×C4711yescharacteristic
403#461C22×C4711yescharacteristic
404#451—21no—
405#441—21no—
406#441—21no—
407#432C22×C4711yescharacteristic
408#427—22no—
409C2×C4⋊C8C22×C4711yescharacteristic
410C2×C4×C8C22×C4711yescharacteristic
411#332C22×C4711yescharacteristic
412#332C22×C4711yescharacteristic
413#332C22×C4711yescharacteristic
414#332C22×C4711yescharacteristic
415Q8⋊C8C22×C4711yescharacteristic
416Q8⋊C8C22×C4711yescharacteristic
417Q8⋊C8C22×C4711yescharacteristic
418Q8⋊C8C22×C4711yescharacteristic
419Q8⋊C8C22×C4711yescharacteristic
420Q8⋊C8C22×C4711yescharacteristic
421D4⋊C8C22×C4711yescharacteristic
422D4⋊C8C22×C4711yescharacteristic
423C47#1864911yescharacteristic, direct product factor, Sylow
424C22×Q8—21no—
425C22×Q8D4×C4711yescharacteristic
426C2×Q16—21no—
427C2×Q16—21no—
428C2×Q16—21no—
429C2×SD16—21no—
430C22×C8—21no—
431C22×C8—21no—
432C4⋊Q8—22no—
433C4⋊Q8—21no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8C23×C4711yescharacteristic
437C4⋊Q8C23×C4711yescharacteristic
438C4⋊Q8C23×C4711yescharacteristic
439C4⋊Q8C23×C4711yescharacteristic
440#126—22no—
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—22no—
450#125—22no—
451#125—21no—
452#125—21no—
453#125D4×C4711yescharacteristic
454#125D4×C4712yes—
455#124—21no—
456#124D4×C4711yescharacteristic
457#123—22no—
458#123—21no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8D4×C4711yescharacteristic
469#121D4×C4711yescharacteristic
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8D4×C4711yescharacteristic
484C4×Q8D4×C4711yescharacteristic
485C4×Q8C23×C4711yescharacteristic
486C4×Q8C23×C4711yescharacteristic
487C4×Q8C23×C4711yescharacteristic
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4C23×C4711yescharacteristic
492#117—22no—
493#117—22no—
494#117—22no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117D4×C4712yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C4711yescharacteristic
501C2×C42—21no—
502C2×C42C23×C4711yescharacteristic
503#107—22no—
504#107—22no—
505#107—21no—
506#106—22no—
507#106—22no—
508#106—21no—
509#106—21no—
510#106—21no—
511C4⋊C8—21no—
512C4⋊C8C23×C4711yescharacteristic
513C4⋊C8C23×C4711yescharacteristic
514C4⋊C8C23×C4711yescharacteristic
515C4⋊C8C23×C4711yescharacteristic
516#103—21no—
517#103—21no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#102—21no—
524C22⋊C8—21no—
525#97—21no—
526C4×C8—21no—
527C4×C8C23×C4711yescharacteristic
528C4×C8C23×C4711yescharacteristic
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—41no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8C2×D4×C4711yescharacteristic
540C2×Q8C2×D4×C4711yescharacteristic
541C2×Q8C2×D4×C4711yescharacteristic
542C2×D4—21no—
543C2×D4C2×D4×C4711yescharacteristic
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4C2×D4×C4711yescharacteristic
549C22×C4C2×D4×C4711yescharacteristic
550C22×C4C2×D4×C4711yescharacteristic
551Q16—42no—
552Q16—42no—
553Q16—81no—
554SD16—81no—
555C2×C8—24no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—81no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4C2×D4×C4711yescharacteristic
591C4⋊C4C2×D4×C4711yescharacteristic
592C4⋊C4C2×D4×C4711yescharacteristic
593C4⋊C4C2×D4×C4711yescharacteristic
594C4⋊C4C2×D4×C4712yes—
595C4⋊C4C2×D4×C4712yes—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—22no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—41no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—41no—
616C42C2×D4×C4711yescharacteristic
617C42C2×D4×C4711yescharacteristic
618C42C2×D4×C4711yescharacteristic
619C42C24×C4711yescharacteristic
620C23—21no—
621C23#120×C4711yescharacteristic
622Q8—21no—
623Q8—21no—
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—42no—
628Q8—44no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8#135×C4712yes—
638D4—21no—
639D4—21no—
640D4—42no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—42no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#120×C4711yescharacteristic
663C2×C4#120×C4711yescharacteristic
664C2×C4#120×C4711yescharacteristic
665C2×C4C22×D4×C4711yescharacteristic
666C2×C4C22×D4×C4711yescharacteristic
667C2×C4C22×D4×C4711yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—21no—
675C22—21no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C47×#45612yes—
680C22C2×#120×C4711yescharacteristic
681C4—21no—
682C4—22no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4C2×#135×C4711yescharacteristic
697C4C47×#57511yescharacteristic
698C4C47×#57711yescharacteristic
699C4C47×#57811yescharacteristic
700C2—22no—
701C2—81no—
702C2C47×#300211yescharacteristic
703C2C47×#301311yescharacteristic
704C2C2×C47×#45611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radical#121×C47D4
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
3. C47×#3160C2semidirect
4. C47×#3113C2semidirect
5. C47×#1653C2semidirect
6. C47×#1653C2semidirect
7. C47×#1652C2semidirect
8. C47×#1651C2semidirect
9. C47×#1650C2semidirect
10. C47×#1649C2semidirect
11. C47×#1648C2semidirect
12. C47×#1648C2semidirect
13. C47×#1552C2semidirect
15. C2×C47×Q8⋊C8C2semidirect
321. #18649C47direct (N × H)
350. #3160C2×C47semidirect
351. #3113C2×C47semidirect
352. #1653C2×C47semidirect
353. #1653C2×C47semidirect
354. #1652C2×C47semidirect
355. #1651C2×C47semidirect
356. #1650C2×C47semidirect
357. #1649C2×C47semidirect
358. #1648C2×C47semidirect
359. #1648C2×C47semidirect
360. #1552C2×C47semidirect
362. C2×Q8⋊C8C2×C47semidirect
423. C47#18649direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35232
C47×#32482
C47×#31602
C47×#31132
C47×#16532
C47×#16522
C47×#16512
C47×#16502
C47×#16492
C47×#16482
C47×#15522
C47×#14942
C2×C47×Q8⋊C82
#1864947