Finite Group Databasebeta

← C47×#18560 #26058258

Subgroups — C47×#18560 #26058258

Order 12032.

986 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3475C211yesmaximal, characteristic, complemented
2C47×#3182C211yesmaximal, characteristic, complemented
3C47×#3115C211yesmaximal, characteristic, complemented
4C47×#3036C211yesmaximal, characteristic, complemented
5C47×#1650C211yesmaximal, characteristic, complemented
6C47×#1647C211yesmaximal, characteristic, complemented
7C47×#1646C211yesmaximal, characteristic, complemented
8C47×#1643C211yesmaximal, characteristic, complemented
9C47×#1628C211yesmaximal, characteristic, complemented
10C47×#1625C211yesmaximal, characteristic, complemented
11C47×#1624C211yesmaximal, characteristic, complemented
12C47×#1622C211yesmaximal, characteristic, complemented
13C47×#1559C211yesmaximal, characteristic, complemented
14C47×#1490C211yesmaximal, characteristic, complemented
15C47×#1489C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C47—21no—
17C47×#556C2211yescharacteristic
18C47×#555C2211yescharacteristic
19C47×#554C2211yescharacteristic
20C47×#553—21no—
21C47×#552—21no—
22C47×#552—21no—
23C47×#551—22no—
24C47×#547C2211yescharacteristic
25C47×#546—21no—
26C47×#533C2211yescharacteristic
27C47×#532C2211yescharacteristic
28C47×#529—22no—
29C47×#529—21no—
30C47×#525—21no—
31C4×#41×C47—21no—
32C4×#41×C47C2211yescharacteristic
33C2×C4×D4×C47C2211yescharacteristic
34C2×#117×C47—21no—
35C47×#500C2211yescharacteristic, complemented
36C47×#492C2211yescharacteristic, complemented
37C47×#487C2211yescharacteristic, complemented
38C47×#486C2211yescharacteristic, complemented
39C47×#482—21no—
40C47×#475C2211yescharacteristic, complemented
41C47×#474C2211yescharacteristic, complemented
42C47×#468—22no—
43C47×#463—21no—
44C47×#463—21no—
45C47×#461C2211yescharacteristic
46C47×#461C2211yescharacteristic
47C47×#460C2211yescharacteristic, complemented
48C47×#459C2211yescharacteristic
49C47×#459C2211yescharacteristic
50C47×#459C2211yescharacteristic, complemented
51C47×#449—21no—
52C47×#442—21no—
53C47×#440—21no—
54C47×#440—22no—
55C47×#432C2211yescharacteristic
56C47×#423C2211yescharacteristic
57C47×#417—21no—
58C4×M16×C47C2211yescharacteristic
59C47×#333C2211yescharacteristic, complemented
60C47×#333C2211yescharacteristic, complemented
61C47×#332C2211yescharacteristic, complemented
62C47×#332C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47D411yescharacteristic
74C22×D4×C47D411yescharacteristic
75C23×C4×C47—21no—
76AGL(1,ℤ/8)×C47—44no—
77C2×SD16×C47—21no—
78C2×SD16×C47—22no—
79C2×SD16×C47—21no—
80C2×SD16×C47—21no—
81C2×D8×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C4⋊Q8×C47C2311yescharacteristic
87C4⋊Q8×C47C2311yescharacteristic
88C4⋊Q8×C47C2311yescharacteristic
89#127×C47C2311yescharacteristic
90#126×C47—22no—
91#126×C47—22no—
92#126×C47—22no—
93#125×C47—22no—
94#125×C47—21no—
95#125×C47—21no—
96#124×C47—22no—
97#124×C47—21no—
98#124×C47—21no—
99#123×C47—22no—
100#123×C47—22no—
101#123×C47—22no—
102#123×C47—22no—
103C22⋊Q8×C47—21no—
104C22⋊Q8×C47—21no—
105C22⋊Q8×C47—22no—
106C22⋊Q8×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47D412yes—
109#121×C47—22no—
110#121×C47—21no—
111#121×C47—21no—
112#121×C47—21no—
113#121×C47—21no—
114#121×C47—21no—
115#120×C47—22no—
116C4×Q8×C47—21no—
117C4×Q8×C47—21no—
118C4×Q8×C47D411yescharacteristic
119C4×Q8×C47D412yes—
120C4×Q8×C47C2311yescharacteristic
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123C4×D4×C47—22no—
124C4×D4×C47—21no—
125C4×D4×C47—21no—
126C4×D4×C47—21no—
127C4×D4×C47—21no—
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47D411yescharacteristic
132C4×D4×C47D411yescharacteristic
133C4×D4×C47D411yescharacteristic
134C4×D4×C47C2311yescharacteristic
135C4×D4×C47C2311yescharacteristic
136C4×D4×C47C2311yescharacteristic
137#117×C47—22no—
138#117×C47—22no—
139#117×C47—22no—
140#117×C47—21no—
141#117×C47—21no—
142#117×C47—21no—
143#117×C47—21no—
144#117×C47—21no—
145#117×C47D411yescharacteristic
146C2×C4⋊C4×C47—21no—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47D411yescharacteristic
149C2×C22⋊C4×C47—22no—
150C2×C22⋊C4×C47—21no—
151C2×C42×C47—22no—
152C2×C42×C47—21no—
153C2×C42×C47C2311yescharacteristic
154#107×C47—22no—
155#107×C47—21no—
156#106×C47—21no—
157C4⋊C8×C47—21no—
158C4⋊C8×C47C2311yescharacteristic
159C4⋊C8×C47C2311yescharacteristic
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162#103×C47—21no—
163#103×C47—22no—
164#103×C47—21no—
165#103×C47—21no—
166#102×C47—21no—
167#102×C47—21no—
168#102×C47—21no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—22no—
172C22⋊C8×C47—21no—
173#97×C47—21no—
174#97×C47—21no—
175C4×C8×C47C2311yescharacteristic
176C4×C8×C47C2311yescharacteristic
177C24×C47—21no—
178#41×C47—41no—
179#41×C47—41no—
180#41×C47—42no—
181#41×C47—42no—
182#41×C47—42no—
183#41×C47—42no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47C2×D411yescharacteristic
187C2×Q8×C47C2×D412yes—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—41no—
197C2×D4×C47—41no—
198C2×D4×C47C2×D411yescharacteristic
199C2×D4×C47C2×D411yescharacteristic
200C2×D4×C47C2×D411yescharacteristic
201C22×C4×C47—22no—
202C22×C4×C47—21no—
203C22×C4×C47—22no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—42no—
212C22×C4×C47—42no—
213C22×C4×C47—41no—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217SD16×C47—44no—
218SD16×C47—42no—
219SD16×C47—42no—
220SD16×C47—42no—
221D8×C47—42no—
222D8×C47—42no—
223D8×C47—42no—
224M16×C47—42no—
225M16×C47—42no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—22no—
234C4⋊C4×C47—22no—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—22no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47C2×D411yescharacteristic
247C4⋊C4×C47C2×D411yescharacteristic
248C4⋊C4×C47C2×D411yescharacteristic
249C4⋊C4×C47C2×D411yescharacteristic
250C4⋊C4×C47C2×D412yes—
251C22⋊C4×C47—22no—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—21no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—41no—
266C22⋊C4×C47—41no—
267C42×C47—22no—
268C42×C47—22no—
269C42×C47—21no—
270C42×C47—22no—
271C42×C47—21no—
272C42×C47—21no—
273C42×C47C2×D411yescharacteristic
274C42×C47C2×D411yescharacteristic
275C42×C47C2×D411yescharacteristic
276C42×C47C2411yescharacteristic
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47—41no—
283C23×C47—81no—
284C23×C47#12011yescharacteristic
285Q8×C47—21no—
286Q8×C47—21no—
287Q8×C47—42no—
288Q8×C47—41no—
289Q8×C47—41no—
290Q8×C47—41no—
291Q8×C47—41no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—42no—
300D4×C47—44no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—82no—
306D4×C47—82no—
307D4×C47AGL(1,ℤ/8)12yes—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—21no—
319C2×C4×C47—41no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—44no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—81no—
333C2×C4×C47—82no—
334C2×C4×C47—82no—
335C2×C4×C47#12011yescharacteristic
336C2×C4×C47#12011yescharacteristic
337C2×C4×C47#12011yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C8×C47—22no—
342C8×C47—41no—
343C8×C47—41no—
344C8×C47—41no—
345C8×C47—41no—
346C8×C47—41no—
347#18560C4711yesmaximal, characteristic, direct product factor, Sylow
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—22no—
351C22×C47—21no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—84no—
361C22×C47—81no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47C2×#12011yescharacteristic
365C4×C47—21no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—41no—
370C4×C47—41no—
371C4×C47—41no—
372C4×C47—41no—
373C4×C47—42no—
374C4×C47—41no—
375C4×C47—42no—
376C4×C47—81no—
377C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
378C4×C47#57511yescharacteristic
379C4×C47#57511yescharacteristic
380C4×C47#57511yescharacteristic
381#3475C2×C4711yescharacteristic, complemented
382#3182C2×C4711yescharacteristic, complemented
383#3115C2×C4711yescharacteristic, complemented
384#3036C2×C4711yescharacteristic, complemented
385#1650C2×C4711yescharacteristic, complemented
386#1647C2×C4711yescharacteristic, complemented
387#1646C2×C4711yescharacteristic, complemented
388#1643C2×C4711yescharacteristic, complemented
389#1628C2×C4711yescharacteristic, complemented
390#1625C2×C4711yescharacteristic, complemented
391#1624C2×C4711yescharacteristic, complemented
392#1622C2×C4711yescharacteristic, complemented
393#1559C2×C4711yescharacteristic, complemented
394#1490C2×C4711yescharacteristic, complemented
395#1489C2×C4711yescharacteristic, complemented
396C2×C47—41no—
397C2×C47—42no—
398C2×C47—81no—
399C2×C47—81no—
400C2×C47—161no—
401C2×C47#300511yescharacteristic
402C2×C47#300611yescharacteristic
403C2×C47#301811yescharacteristic
404C2×AGL(1,ℤ/8)—21no—
405#556C22×C4711yescharacteristic
406#555C22×C4711yescharacteristic
407#554C22×C4711yescharacteristic
408#553—21no—
409#552—21no—
410#552—21no—
411#551—22no—
412#547C22×C4711yescharacteristic
413#546—21no—
414#533C22×C4711yescharacteristic
415#532C22×C4711yescharacteristic
416#529—22no—
417#529—21no—
418#525—21no—
419C4×#41—21no—
420C4×#41C22×C4711yescharacteristic
421C2×C4×D4C22×C4711yescharacteristic
422C2×#117—21no—
423#500C22×C4711yescharacteristic, complemented
424#492C22×C4711yescharacteristic, complemented
425#487C22×C4711yescharacteristic, complemented
426#486C22×C4711yescharacteristic, complemented
427#482—21no—
428#475C22×C4711yescharacteristic, complemented
429#474C22×C4711yescharacteristic, complemented
430#468—22no—
431#463—21no—
432#463—21no—
433#461C22×C4711yescharacteristic
434#461C22×C4711yescharacteristic
435#460C22×C4711yescharacteristic, complemented
436#459C22×C4711yescharacteristic
437#459C22×C4711yescharacteristic
438#459C22×C4711yescharacteristic, complemented
439#449—21no—
440#442—21no—
441#440—21no—
442#440—22no—
443#432C22×C4711yescharacteristic
444#423C22×C4711yescharacteristic
445#417—21no—
446C4×M16C22×C4711yescharacteristic
447#333C22×C4711yescharacteristic, complemented
448#333C22×C4711yescharacteristic, complemented
449#332C22×C4711yescharacteristic, complemented
450#332C22×C4711yescharacteristic, complemented
451Q8⋊C8C22×C4711yescharacteristic, complemented
452Q8⋊C8C22×C4711yescharacteristic, complemented
453D4⋊C8C22×C4711yescharacteristic
454D4⋊C8C22×C4711yescharacteristic
455D4⋊C8C22×C4711yescharacteristic
456D4⋊C8C22×C4711yescharacteristic
457D4⋊C8C22×C4711yescharacteristic, complemented
458D4⋊C8C22×C4711yescharacteristic, complemented
459C47#1856011yescharacteristic, direct product factor, Sylow
460C2×#41—21no—
461C2×#41—21no—
462C2×#41D4×C4711yescharacteristic
463C22×D4D4×C4711yescharacteristic
464C23×C4—21no—
465AGL(1,ℤ/8)—44no—
466C2×SD16—21no—
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×D8—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×M16—21no—
474C2×M16—21no—
475C4⋊Q8C23×C4711yescharacteristic
476C4⋊Q8C23×C4711yescharacteristic
477C4⋊Q8C23×C4711yescharacteristic
478#127C23×C4711yescharacteristic
479#126—22no—
480#126—22no—
481#126—22no—
482#125—22no—
483#125—21no—
484#125—21no—
485#124—22no—
486#124—21no—
487#124—21no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4712yes—
498#121—22no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#120—22no—
505C4×Q8—21no—
506C4×Q8—21no—
507C4×Q8D4×C4711yescharacteristic
508C4×Q8D4×C4712yes—
509C4×Q8C23×C4711yescharacteristic
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4D4×C4711yescharacteristic
521C4×D4D4×C4711yescharacteristic
522C4×D4D4×C4711yescharacteristic
523C4×D4C23×C4711yescharacteristic
524C4×D4C23×C4711yescharacteristic
525C4×D4C23×C4711yescharacteristic
526#117—22no—
527#117—22no—
528#117—22no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533#117—21no—
534#117D4×C4711yescharacteristic
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4D4×C4711yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—21no—
540C2×C42—22no—
541C2×C42—21no—
542C2×C42C23×C4711yescharacteristic
543#107—22no—
544#107—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8C23×C4711yescharacteristic
548C4⋊C8C23×C4711yescharacteristic
549C4⋊C8C23×C4711yescharacteristic
550C4⋊C8C23×C4711yescharacteristic
551#103—21no—
552#103—22no—
553#103—21no—
554#103—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102—22no—
560#102—21no—
561C22⋊C8—21no—
562#97—21no—
563#97—21no—
564C4×C8C23×C4711yescharacteristic
565C4×C8C23×C4711yescharacteristic
566C24—21no—
567#41—41no—
568#41—41no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C2×D4×C4711yescharacteristic
576C2×Q8C2×D4×C4712yes—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4C2×D4×C4711yescharacteristic
588C2×D4C2×D4×C4711yescharacteristic
589C2×D4C2×D4×C4711yescharacteristic
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—41no—
603C22×C4C2×D4×C4711yescharacteristic
604C22×C4C2×D4×C4711yescharacteristic
605C22×C4C2×D4×C4711yescharacteristic
606SD16—44no—
607SD16—42no—
608SD16—42no—
609SD16—42no—
610D8—42no—
611D8—42no—
612D8—42no—
613M16—42no—
614M16—42no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D4×C4711yescharacteristic
636C4⋊C4C2×D4×C4711yescharacteristic
637C4⋊C4C2×D4×C4711yescharacteristic
638C4⋊C4C2×D4×C4711yescharacteristic
639C4⋊C4C2×D4×C4712yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—22no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C22⋊C4—41no—
656C42—22no—
657C42—22no—
658C42—21no—
659C42—22no—
660C42—21no—
661C42—21no—
662C42C2×D4×C4711yescharacteristic
663C42C2×D4×C4711yescharacteristic
664C42C2×D4×C4711yescharacteristic
665C42C24×C4711yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—81no—
673C23#120×C4711yescharacteristic
674Q8—21no—
675Q8—21no—
676Q8—42no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—82no—
695D4—82no—
696D4AGL(1,ℤ/8)×C4712yes—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—81no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4#120×C4711yescharacteristic
725C2×C4#120×C4711yescharacteristic
726C2×C4#120×C4711yescharacteristic
727C2×C4C22×D4×C4711yescharacteristic
728C2×C4C22×D4×C4711yescharacteristic
729C2×C4C22×D4×C4711yescharacteristic
730C8—22no—
731C8—41no—
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—84no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22C2×#120×C4711yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—42no—
762C4—41no—
763C4—42no—
764C4—81no—
765C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
766C4C47×#57511yescharacteristic
767C4C47×#57511yescharacteristic
768C4C47×#57511yescharacteristic
769C2—41no—
770C2—42no—
771C2—81no—
772C2—81no—
773C2—161no—
774C2C47×#300511yescharacteristic
775C2C47×#300611yescharacteristic
776C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
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. C47×#3475C2semidirect
2. C47×#3182C2semidirect
3. C47×#3115C2semidirect
4. C47×#3036C2semidirect
5. C47×#1650C2semidirect
6. C47×#1647C2semidirect
7. C47×#1646C2semidirect
8. C47×#1643C2semidirect
9. C47×#1628C2semidirect
10. C47×#1625C2semidirect
11. C47×#1624C2semidirect
12. C47×#1622C2semidirect
13. C47×#1559C2semidirect
14. C47×#1490C2semidirect
15. C47×#1489C2semidirect
35. C47×#500C22semidirect
36. C47×#492C22semidirect
37. C47×#487C22semidirect
38. C47×#486C22semidirect
40. C47×#475C22semidirect
41. C47×#474C22semidirect
47. C47×#460C22semidirect
50. C47×#459C22semidirect
59. C47×#333C22semidirect
60. C47×#333C22semidirect
61. C47×#332C22semidirect
62. C47×#332C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
347. #18560C47direct (N × H)
381. #3475C2×C47semidirect
382. #3182C2×C47semidirect
383. #3115C2×C47semidirect
384. #3036C2×C47semidirect
385. #1650C2×C47semidirect
386. #1647C2×C47semidirect
387. #1646C2×C47semidirect
388. #1643C2×C47semidirect
389. #1628C2×C47semidirect
390. #1625C2×C47semidirect
391. #1624C2×C47semidirect
392. #1622C2×C47semidirect
393. #1559C2×C47semidirect
394. #1490C2×C47semidirect
395. #1489C2×C47semidirect
423. #500C22×C47semidirect
424. #492C22×C47semidirect
425. #487C22×C47semidirect
426. #486C22×C47semidirect
428. #475C22×C47semidirect
429. #474C22×C47semidirect
435. #460C22×C47semidirect
438. #459C22×C47semidirect
447. #333C22×C47semidirect
448. #333C22×C47semidirect
449. #332C22×C47semidirect
450. #332C22×C47semidirect
451. Q8⋊C8C22×C47semidirect
452. Q8⋊C8C22×C47semidirect
457. D4⋊C8C22×C47semidirect
458. D4⋊C8C22×C47semidirect
459. C47#18560direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34752
C47×#31822
C47×#31152
C47×#30362
C47×#16502
C47×#16472
C47×#16462
C47×#16432
C47×#16282
C47×#16252
C47×#16242
C47×#16222
C47×#15592
C47×#14902
C47×#14892
#1856047