Finite Group Databasebeta

← C47×#18797 #26058495

Subgroups — C47×#18797 #26058495

Order 12032.

924 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C47C211yesmaximal, characteristic, complemented
2C47×#3210C211yesmaximal, characteristic, complemented
3C47×#3112C211yesmaximal, characteristic, complemented
4C47×#3106C211yesmaximal, characteristic
5C47×#1637C211yesmaximal, characteristic, complemented
6C47×#1636C211yesmaximal, characteristic, complemented
7C47×#1633C211yesmaximal, characteristic, complemented
8C47×#1632C211yesmaximal, characteristic, complemented
9C47×#1627C211yesmaximal, characteristic, complemented
10C47×#1626C211yesmaximal, characteristic, complemented
11C47×#1623C211yesmaximal, characteristic, complemented
12C47×#1622C211yesmaximal, characteristic, complemented
13C47×#1554C211yesmaximal, characteristic, complemented
14C47×#1488C211yesmaximal, characteristic, complemented
15C47×#1479C211yesmaximal, characteristic, complemented
16Q82×C47C2211yescharacteristic
17C47×#557—21no—
18C47×#557C2211yescharacteristic
19C47×#554—22no—
20C47×#554—21no—
21C47×#554—21no—
22C47×#554C2211yescharacteristic
23D4×Q8×C47—21no—
24D4×Q8×C47C2211yescharacteristic
25C47×#533—22no—
26C47×#533—21no—
27C47×#533—21no—
28C47×#533C2211yescharacteristic
29C47×#532C2211yescharacteristic
30C4×#41×C47—21no—
31C4×#41×C47C2211yescharacteristic
32C2×C4×Q8×C47—21no—
33C2×C4×Q8×C47C2211yescharacteristic
34C47×#494C2211yescharacteristic
35C47×#492C2211yescharacteristic
36C47×#487C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#482—21no—
39C47×#480—21no—
40C47×#477C2211yescharacteristic
41C47×#477C2211yescharacteristic
42C47×#477C2211yescharacteristic
43C47×#476C2211yescharacteristic
44C47×#464—22no—
45C47×#460C2211yescharacteristic
46C47×#460C2211yescharacteristic
47C47×#460C2211yescharacteristic
48C47×#459C2211yescharacteristic
49C47×#452—22no—
50C47×#449—21no—
51C47×#448—21no—
52C47×#440—21no—
53C47×#440—21no—
54C4×SD16×C47—21no—
55C4×D8×C47—21no—
56C47×#432C2211yescharacteristic
57C47×#431C2211yescharacteristic
58C47×#431C2211yescharacteristic
59C47×#333C2211yescharacteristic
60C47×#333C2211yescharacteristic
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
71C2×#41×C47—21no—
72C2×#41×C47D411yescharacteristic
73C22×Q8×C47—21no—
74C22×Q8×C47D411yescharacteristic
75C2×Q16×C47—22no—
76C2×SD16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—22no—
80C2×D8×C47—21no—
81C4⋊Q8×C47—22no—
82C4⋊Q8×C47—21no—
83C4⋊Q8×C47—22no—
84C4⋊Q8×C47—21no—
85C4⋊Q8×C47—21no—
86C4⋊Q8×C47—21no—
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89C4⋊Q8×C47C2311yescharacteristic
90#127×C47C2311yescharacteristic
91#125×C47—22no—
92#125×C47—22no—
93#125×C47—22no—
94#125×C47—21no—
95#125×C47—21no—
96#125×C47—21no—
97#124×C47—21no—
98C22⋊Q8×C47—22no—
99C22⋊Q8×C47—22no—
100C22⋊Q8×C47—22no—
101C22⋊Q8×C47—22no—
102C22⋊Q8×C47—22no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—22no—
105C22⋊Q8×C47—21no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—22no—
108C22⋊Q8×C47D412yes—
109#121×C47—21no—
110#121×C47—21no—
111C4×Q8×C47—22no—
112C4×Q8×C47—22no—
113C4×Q8×C47—22no—
114C4×Q8×C47—21no—
115C4×Q8×C47—21no—
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×C47D411yescharacteristic
124C4×Q8×C47D411yescharacteristic
125C4×Q8×C47C2311yescharacteristic
126C4×Q8×C47C2311yescharacteristic
127C4×Q8×C47C2311yescharacteristic
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C4×D4×C47—21no—
131C4×D4×C47—21no—
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
135C4×D4×C47—21no—
136C4×D4×C47D411yescharacteristic
137C4×D4×C47C2311yescharacteristic
138#117×C47—22no—
139#117×C47—21no—
140#117×C47—21no—
141#117×C47D411yescharacteristic
142C2×C4⋊C4×C47—22no—
143C2×C4⋊C4×C47—21no—
144C2×C4⋊C4×C47—21no—
145C2×C4⋊C4×C47D411yescharacteristic
146C2×C42×C47—22no—
147C2×C42×C47—21no—
148C2×C42×C47—21no—
149C2×C42×C47C2311yescharacteristic
150#107×C47—21no—
151#107×C47—21no—
152#107×C47—21no—
153#106×C47—21no—
154C4⋊C8×C47—21no—
155C4⋊C8×C47C2311yescharacteristic
156C4⋊C8×C47C2311yescharacteristic
157C4⋊C8×C47C2311yescharacteristic
158C4⋊C8×C47C2311yescharacteristic
159#103×C47—21no—
160#103×C47—21no—
161#103×C47—21no—
162#103×C47—22no—
163#102×C47—21no—
164#102×C47—22no—
165#102×C47—21no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169C22⋊C8×C47—21no—
170C22⋊C8×C47—21no—
171C22⋊C8×C47—21no—
172#97×C47—21no—
173C4×C8×C47—21no—
174C4×C8×C47C2311yescharacteristic
175C4×C8×C47C2311yescharacteristic
176#41×C47—22no—
177#41×C47—22no—
178#41×C47—82no—
179C2×Q8×C47—22no—
180C2×Q8×C47—22no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—21no—
185C2×Q8×C47—41no—
186C2×Q8×C47—42no—
187C2×Q8×C47—42no—
188C2×Q8×C47C2×D411yescharacteristic
189C2×Q8×C47C2×D411yescharacteristic
190C2×Q8×C47C2×D411yescharacteristic
191C2×Q8×C47C2×D412yes—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—41no—
197C2×D4×C47C2×D411yescharacteristic
198C22×C4×C47—21no—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—22no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—41no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209Q16×C47—82no—
210SD16×C47—42no—
211SD16×C47—42no—
212SD16×C47—42no—
213SD16×C47—82no—
214D8×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—22no—
226C4⋊C4×C47—22no—
227C4⋊C4×C47—22no—
228C4⋊C4×C47—22no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—22no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—22no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2×D412yes—
244C4⋊C4×C47C2×D411yescharacteristic
245C4⋊C4×C47C2×D411yescharacteristic
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C22⋊C4×C47—22no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—41no—
255C22⋊C4×C47—41no—
256C42×C47—22no—
257C42×C47—22no—
258C42×C47—21no—
259C42×C47—22no—
260C42×C47—21no—
261C42×C47—21no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—21no—
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2411yescharacteristic
270C23×C47—21no—
271C23×C47—41no—
272C23×C47#12011yescharacteristic
273Q8×C47—21no—
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—42no—
278Q8×C47—42no—
279Q8×C47—44no—
280Q8×C47—42no—
281Q8×C47—41no—
282Q8×C47—41no—
283Q8×C47—82no—
284Q8×C47#13512yes—
285Q8×C47#13712yes—
286D4×C47—24no—
287D4×C47—21no—
288D4×C47—42no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—82no—
294D4×C47#13712yes—
295C2×C4×C47—24no—
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—22no—
305C2×C4×C47—22no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—41no—
310C2×C4×C47—42no—
311C2×C4×C47—44no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—81no—
316C2×C4×C47—82no—
317C2×C4×C47—81no—
318C2×C4×C47—82no—
319C2×C4×C47#12011yescharacteristic
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C8×C47—41no—
326C8×C47—41no—
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331#18797C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—22no—
335C22×C47—21no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47C2×#12011yescharacteristic
342C4×C47—21no—
343C4×C47—22no—
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—42no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—81no—
356C4×C47C2×#13511yescharacteristic
357C4×C47C2×#13711yescharacteristic
358C4×C47C2×#13711yescharacteristic
359C4×C47#57511yescharacteristic
360Q8×#41C2×C4711yescharacteristic, complemented
361#3210C2×C4711yescharacteristic, complemented
362#3112C2×C4711yescharacteristic, complemented
363#3106C2×C4711yescharacteristic
364#1637C2×C4711yescharacteristic, complemented
365#1636C2×C4711yescharacteristic, complemented
366#1633C2×C4711yescharacteristic, complemented
367#1632C2×C4711yescharacteristic, complemented
368#1627C2×C4711yescharacteristic, complemented
369#1626C2×C4711yescharacteristic, complemented
370#1623C2×C4711yescharacteristic, complemented
371#1622C2×C4711yescharacteristic, complemented
372#1554C2×C4711yescharacteristic, complemented
373#1488C2×C4711yescharacteristic, complemented
374#1479C2×C4711yescharacteristic, complemented
375C2×C47—41no—
376C2×C47—42no—
377C2×C47—161no—
378C2×C47#300211yescharacteristic
379C2×C47#300411yescharacteristic
380C2×C47#302111yescharacteristic
381Q82C22×C4711yescharacteristic
382#557—21no—
383#557C22×C4711yescharacteristic
384#554—22no—
385#554—21no—
386#554—21no—
387#554C22×C4711yescharacteristic
388D4×Q8—21no—
389D4×Q8C22×C4711yescharacteristic
390#533—22no—
391#533—21no—
392#533—21no—
393#533C22×C4711yescharacteristic
394#532C22×C4711yescharacteristic
395C4×#41—21no—
396C4×#41C22×C4711yescharacteristic
397C2×C4×Q8—21no—
398C2×C4×Q8C22×C4711yescharacteristic
399#494C22×C4711yescharacteristic
400#492C22×C4711yescharacteristic
401#487C22×C4711yescharacteristic
402#486C22×C4711yescharacteristic
403#482—21no—
404#480—21no—
405#477C22×C4711yescharacteristic
406#477C22×C4711yescharacteristic
407#477C22×C4711yescharacteristic
408#476C22×C4711yescharacteristic
409#464—22no—
410#460C22×C4711yescharacteristic
411#460C22×C4711yescharacteristic
412#460C22×C4711yescharacteristic
413#459C22×C4711yescharacteristic
414#452—22no—
415#449—21no—
416#448—21no—
417#440—21no—
418#440—21no—
419C4×SD16—21no—
420C4×D8—21no—
421#432C22×C4711yescharacteristic
422#431C22×C4711yescharacteristic
423#431C22×C4711yescharacteristic
424#333C22×C4711yescharacteristic
425#333C22×C4711yescharacteristic
426#332C22×C4711yescharacteristic
427#332C22×C4711yescharacteristic
428Q8⋊C8C22×C4711yescharacteristic
429Q8⋊C8C22×C4711yescharacteristic
430Q8⋊C8C22×C4711yescharacteristic
431Q8⋊C8C22×C4711yescharacteristic
432Q8⋊C8C22×C4711yescharacteristic
433Q8⋊C8C22×C4711yescharacteristic
434D4⋊C8C22×C4711yescharacteristic
435D4⋊C8C22×C4711yescharacteristic
436C47#1879711yescharacteristic, direct product factor, Sylow
437C2×#41—21no—
438C2×#41D4×C4711yescharacteristic
439C22×Q8—21no—
440C22×Q8D4×C4711yescharacteristic
441C2×Q16—22no—
442C2×SD16—21no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×SD16—22no—
446C2×D8—21no—
447C4⋊Q8—22no—
448C4⋊Q8—21no—
449C4⋊Q8—22no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8C23×C4711yescharacteristic
454C4⋊Q8C23×C4711yescharacteristic
455C4⋊Q8C23×C4711yescharacteristic
456#127C23×C4711yescharacteristic
457#125—22no—
458#125—22no—
459#125—22no—
460#125—21no—
461#125—21no—
462#125—21no—
463#124—21no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8D4×C4712yes—
475#121—21no—
476#121—21no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8D4×C4711yescharacteristic
488C4×Q8D4×C4711yescharacteristic
489C4×Q8D4×C4711yescharacteristic
490C4×Q8D4×C4712yes—
491C4×Q8C23×C4711yescharacteristic
492C4×Q8C23×C4711yescharacteristic
493C4×Q8C23×C4711yescharacteristic
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4D4×C4711yescharacteristic
503C4×D4C23×C4711yescharacteristic
504#117—22no—
505#117—21no—
506#117—21no—
507#117D4×C4711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
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—21no—
519#106—21no—
520C4⋊C8—21no—
521C4⋊C8C23×C4711yescharacteristic
522C4⋊C8C23×C4711yescharacteristic
523C4⋊C8C23×C4711yescharacteristic
524C4⋊C8C23×C4711yescharacteristic
525#103—21no—
526#103—21no—
527#103—21no—
528#103—22no—
529#102—21no—
530#102—21no—
531#102—21no—
532#102—21no—
533#102—21no—
534#102—22no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538#97—21no—
539C4×C8—21no—
540C4×C8C23×C4711yescharacteristic
541C4×C8C23×C4711yescharacteristic
542#41—22no—
543#41—22no—
544#41—82no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8C2×D4×C4711yescharacteristic
555C2×Q8C2×D4×C4711yescharacteristic
556C2×Q8C2×D4×C4711yescharacteristic
557C2×Q8C2×D4×C4712yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4C2×D4×C4711yescharacteristic
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—41no—
572C22×C4C2×D4×C4711yescharacteristic
573C22×C4C2×D4×C4711yescharacteristic
574C22×C4C2×D4×C4711yescharacteristic
575Q16—82no—
576SD16—42no—
577SD16—42no—
578SD16—42no—
579SD16—82no—
580D8—42no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4C2×D4×C4712yes—
610C4⋊C4C2×D4×C4711yescharacteristic
611C4⋊C4C2×D4×C4711yescharacteristic
612C4⋊C4C2×D4×C4711yescharacteristic
613C4⋊C4C2×D4×C4711yescharacteristic
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—22no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42C2×D4×C4711yescharacteristic
633C42C2×D4×C4711yescharacteristic
634C42C2×D4×C4711yescharacteristic
635C42C24×C4711yescharacteristic
636C23—21no—
637C23—41no—
638C23#120×C4711yescharacteristic
639Q8—21no—
640Q8—21no—
641Q8—21no—
642Q8—21no—
643Q8—42no—
644Q8—42no—
645Q8—44no—
646Q8—42no—
647Q8—41no—
648Q8—41no—
649Q8—82no—
650Q8#135×C4712yes—
651Q8#137×C4712yes—
652D4—24no—
653D4—21no—
654D4—42no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—82no—
660D4#137×C4712yes—
661C2×C4—24no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—82no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4#120×C4711yescharacteristic
686C2×C4#120×C4711yescharacteristic
687C2×C4#120×C4711yescharacteristic
688C2×C4C22×D4×C4711yescharacteristic
689C2×C4C22×D4×C4711yescharacteristic
690C2×C4C22×D4×C4711yescharacteristic
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C8—41no—
696C8—41no—
697C22—21no—
698C22—21no—
699C22—22no—
700C22—21no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22C2×#120×C4711yescharacteristic
707C4—21no—
708C4—22no—
709C4—21no—
710C4—22no—
711C4—21no—
712C4—21no—
713C4—41no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—41no—
720C4—81no—
721C4C2×#135×C4711yescharacteristic
722C4C2×#137×C4711yescharacteristic
723C4C2×#137×C4711yescharacteristic
724C4C47×#57511yescharacteristic
725C2—41no—
726C2—42no—
727C2—161no—
728C2C47×#300211yescharacteristic
729C2C47×#300411yescharacteristic
730C2C47×#302111yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC47×#3106C2
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
1. Q8×#41×C47C2semidirect
2. C47×#3210C2semidirect
3. C47×#3112C2semidirect
5. C47×#1637C2semidirect
6. C47×#1636C2semidirect
7. C47×#1633C2semidirect
8. C47×#1632C2semidirect
9. C47×#1627C2semidirect
10. C47×#1626C2semidirect
11. C47×#1623C2semidirect
12. C47×#1622C2semidirect
13. C47×#1554C2semidirect
14. C47×#1488C2semidirect
15. C47×#1479C2semidirect
331. #18797C47direct (N × H)
360. Q8×#41C2×C47semidirect
361. #3210C2×C47semidirect
362. #3112C2×C47semidirect
364. #1637C2×C47semidirect
365. #1636C2×C47semidirect
366. #1633C2×C47semidirect
367. #1632C2×C47semidirect
368. #1627C2×C47semidirect
369. #1626C2×C47semidirect
370. #1623C2×C47semidirect
371. #1622C2×C47semidirect
372. #1554C2×C47semidirect
373. #1488C2×C47semidirect
374. #1479C2×C47semidirect
436. C47#18797direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×#41×C472
C47×#32102
C47×#31122
C47×#31062
C47×#16372
C47×#16362
C47×#16332
C47×#16322
C47×#16272
C47×#16262
C47×#16232
C47×#16222
C47×#15542
C47×#14882
C47×#14792
#1879747