Finite Group Databasebeta

← C47×#18606 #26058304

Subgroups — C47×#18606 #26058304

Order 12032.

984 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3517C211yesmaximal, characteristic, complemented
2C47×#3251C211yesmaximal, characteristic, complemented
3C47×#3184C211yesmaximal, characteristic, complemented
4C47×#3035C211yesmaximal, characteristic, complemented
5C47×#1654C211yesmaximal, characteristic, complemented
6C47×#1653C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1641C211yesmaximal, characteristic, complemented
9C47×#1626C211yesmaximal, characteristic, complemented
10C47×#1625C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1621C211yesmaximal, characteristic, complemented
13C47×#1547C211yesmaximal, characteristic, complemented
14C47×#1489C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C2×#135×C47—21no—
17C47×#557C2211yescharacteristic
18C47×#553—22no—
19C47×#553—21no—
20C47×#550—21no—
21C47×#550—21no—
22C47×#550C2211yescharacteristic
23C47×#550C2211yescharacteristic
24C47×#547—21no—
25C47×#547C2211yescharacteristic
26C47×#540—22no—
27C47×#540—21no—
28C47×#532—21no—
29C47×#532C2211yescharacteristic
30C47×#532C2211yescharacteristic
31C47×#529—21no—
32C47×#529C2211yescharacteristic
33C47×#520—21no—
34C4×#41×C47C2211yescharacteristic
35C47×#498C2211yescharacteristic
36C47×#493C2211yescharacteristic
37C47×#486C2211yescharacteristic
38C47×#486C2211yescharacteristic
39C47×#478—21no—
40C47×#475C2211yescharacteristic
41C47×#474C2211yescharacteristic
42C47×#469—22no—
43C47×#469—21no—
44C47×#468—21no—
45C47×#464—21no—
46C47×#463—21no—
47C47×#463—21no—
48C47×#462C2211yescharacteristic
49C47×#461C2211yescharacteristic
50C47×#460C2211yescharacteristic
51C47×#460C2211yescharacteristic
52C47×#459C2211yescharacteristic
53C47×#459C2211yescharacteristic
54C47×#442—22no—
55C47×#423C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C47×#416—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×D4⋊C8C2211yescharacteristic
68C47×D4⋊C8C2211yescharacteristic
69C47×D4⋊C8C2211yescharacteristic
70C47×D4⋊C8C2211yescharacteristic
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47D411yescharacteristic
77#135×C47—44no—
78C2×Q16×C47—21no—
79C2×SD16×C47—21no—
80C2×SD16×C47—21no—
81C2×SD16×C47—21no—
82C2×D8×C47—21no—
83C2×D8×C47—22no—
84C2×D8×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C22×C8×C47—21no—
88C4⋊Q8×C47—21no—
89C4⋊Q8×C47C2311yescharacteristic
90C4⋊Q8×C47C2311yescharacteristic
91#127×C47—22no—
92#127×C47—21no—
93#127×C47—21no—
94#127×C47C2311yescharacteristic
95#127×C47C2311yescharacteristic
96#126×C47—22no—
97#126×C47—21no—
98#125×C47—22no—
99#125×C47—21no—
100#125×C47D411yescharacteristic
101#124×C47—21no—
102#124×C47—21no—
103#124×C47D411yescharacteristic
104#123×C47—22no—
105#123×C47—22no—
106#123×C47—22no—
107#123×C47—21no—
108#123×C47—22no—
109C22⋊Q8×C47—21no—
110C22⋊Q8×C47D411yescharacteristic
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—22no—
115#121×C47—22no—
116#121×C47—21no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47D411yescharacteristic
125#121×C47D412yes—
126C4×Q8×C47—21no—
127C4×Q8×C47—21no—
128C4×Q8×C47D411yescharacteristic
129C4×Q8×C47C2311yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×D4×C47—22no—
132C4×D4×C47—22no—
133C4×D4×C47—22no—
134C4×D4×C47—22no—
135C4×D4×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47—21no—
139C4×D4×C47—21no—
140C4×D4×C47—21no—
141C4×D4×C47—21no—
142C4×D4×C47—21no—
143C4×D4×C47D411yescharacteristic
144C4×D4×C47D412yes—
145C4×D4×C47C2311yescharacteristic
146C4×D4×C47C2311yescharacteristic
147#117×C47—22no—
148#117×C47—21no—
149#117×C47—21no—
150#117×C47D411yescharacteristic
151C2×C4⋊C4×C47—22no—
152C2×C4⋊C4×C47—21no—
153C2×C42×C47—21no—
154C2×C42×C47C2311yescharacteristic
155#107×C47—21no—
156#106×C47—21no—
157#106×C47—22no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47—21no—
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163C4⋊C8×C47C2311yescharacteristic
164#103×C47—21no—
165#103×C47—21no—
166#103×C47—21no—
167#102×C47—21no—
168#102×C47—22no—
169#102×C47—21no—
170#102×C47—21no—
171#102×C47—21no—
172#102×C47—21no—
173#102×C47—22no—
174#97×C47—21no—
175C4×C8×C47C2311yescharacteristic
176C4×C8×C47C2311yescharacteristic
177#41×C47—22no—
178#41×C47—41no—
179#41×C47—42no—
180#41×C47—42no—
181#41×C47—42no—
182#41×C47—42no—
183#41×C47—81no—
184#41×C47—81no—
185#41×C47—81no—
186#41×C47—81no—
187#41×C47—81no—
188#41×C47—81no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47C2×D411yescharacteristic
192C2×Q8×C47C2×D411yescharacteristic
193C2×D4×C47—22no—
194C2×D4×C47—21no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—21no—
200C2×D4×C47—22no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—41no—
207C2×D4×C47C2×D411yescharacteristic
208C2×D4×C47C2×D411yescharacteristic
209C2×D4×C47C2×D412yes—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—22no—
218C22×C4×C47—41no—
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222Q16×C47—42no—
223SD16×C47—42no—
224SD16×C47—42no—
225SD16×C47—81no—
226D8×C47—44no—
227D8×C47—42no—
228D8×C47—81no—
229M16×C47—42no—
230M16×C47—81no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—42no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—22no—
240C4⋊C4×C47—22no—
241C4⋊C4×C47—22no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2×D411yescharacteristic
252C4⋊C4×C47C2×D411yescharacteristic
253C4⋊C4×C47C2×D412yes—
254C4⋊C4×C47C2×D411yescharacteristic
255C4⋊C4×C47C2×D411yescharacteristic
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—22no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—22no—
267C22⋊C4×C47—21no—
268C22⋊C4×C47—21no—
269C22⋊C4×C47—41no—
270C22⋊C4×C47—41no—
271C42×C47—22no—
272C42×C47—21no—
273C42×C47—21no—
274C42×C47—21no—
275C42×C47—21no—
276C42×C47C2×D411yescharacteristic
277C42×C47C2×D411yescharacteristic
278C42×C47C2×D411yescharacteristic
279C42×C47C2411yescharacteristic
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—22no—
283C23×C47—41no—
284C23×C47#12011yescharacteristic
285Q8×C47—21no—
286Q8×C47—21no—
287Q8×C47—21no—
288Q8×C47—41no—
289Q8×C47—41no—
290Q8×C47—41no—
291Q8×C47—41no—
292Q8×C47AGL(1,ℤ/8)12yes—
293D4×C47—21no—
294D4×C47—21no—
295D4×C47—21no—
296D4×C47—21no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—44no—
300D4×C47—42no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—41no—
304D4×C47—41no—
305D4×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—81no—
310D4×C47—82no—
311D4×C47—82no—
312D4×C47—82no—
313D4×C47—82no—
314D4×C47—82no—
315D4×C47—82no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—21no—
327C2×C4×C47—41no—
328C2×C4×C47—42no—
329C2×C4×C47—44no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—81no—
336C2×C4×C47—82no—
337C2×C4×C47—82no—
338C2×C4×C47—82no—
339C2×C4×C47—82no—
340C2×C4×C47#12011yescharacteristic
341C2×C4×C47#12011yescharacteristic
342C2×C4×C47#12011yescharacteristic
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C8×C47—22no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350C8×C47—41no—
351C8×C47—41no—
352#18606C4711yesmaximal, characteristic, direct product factor, Sylow
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—41no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—41no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47C2×#12011yescharacteristic
369C4×C47—21no—
370C4×C47—22no—
371C4×C47—21no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—41no—
377C4×C47—42no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—81no—
381C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
382C4×C47#57511yescharacteristic
383C4×C47#57611yescharacteristic
384C4×C47#57711yescharacteristic
385#3517C2×C4711yescharacteristic, complemented
386#3251C2×C4711yescharacteristic, complemented
387#3184C2×C4711yescharacteristic, complemented
388#3035C2×C4711yescharacteristic, complemented
389#1654C2×C4711yescharacteristic, complemented
390#1653C2×C4711yescharacteristic, complemented
391#1642C2×C4711yescharacteristic, complemented
392#1641C2×C4711yescharacteristic, complemented
393#1626C2×C4711yescharacteristic, complemented
394#1625C2×C4711yescharacteristic, complemented
395#1621C2×C4711yescharacteristic, complemented
396#1621C2×C4711yescharacteristic, complemented
397#1547C2×C4711yescharacteristic, complemented
398#1489C2×C4711yescharacteristic, complemented
399#1483C2×C4711yescharacteristic, complemented
400C2×C47—41no—
401C2×C47—81no—
402C2×C47—81no—
403C2×C47—82no—
404C2×C47—161no—
405C2×C47#300611yescharacteristic
406C2×C47#301211yescharacteristic
407C2×C47#301811yescharacteristic
408C2×#135—21no—
409#557C22×C4711yescharacteristic
410#553—22no—
411#553—21no—
412#550—21no—
413#550—21no—
414#550C22×C4711yescharacteristic
415#550C22×C4711yescharacteristic
416#547—21no—
417#547C22×C4711yescharacteristic
418#540—22no—
419#540—21no—
420#532—21no—
421#532C22×C4711yescharacteristic
422#532C22×C4711yescharacteristic
423#529—21no—
424#529C22×C4711yescharacteristic
425#520—21no—
426C4×#41C22×C4711yescharacteristic
427#498C22×C4711yescharacteristic
428#493C22×C4711yescharacteristic
429#486C22×C4711yescharacteristic
430#486C22×C4711yescharacteristic
431#478—21no—
432#475C22×C4711yescharacteristic
433#474C22×C4711yescharacteristic
434#469—22no—
435#469—21no—
436#468—21no—
437#464—21no—
438#463—21no—
439#463—21no—
440#462C22×C4711yescharacteristic
441#461C22×C4711yescharacteristic
442#460C22×C4711yescharacteristic
443#460C22×C4711yescharacteristic
444#459C22×C4711yescharacteristic
445#459C22×C4711yescharacteristic
446#442—22no—
447#423C22×C4711yescharacteristic
448C2×C4⋊C8C22×C4711yescharacteristic
449#416—21no—
450C4×M16C22×C4711yescharacteristic
451#332C22×C4711yescharacteristic
452#332C22×C4711yescharacteristic
453#331C22×C4711yescharacteristic
454#331C22×C4711yescharacteristic
455Q8⋊C8C22×C4711yescharacteristic
456Q8⋊C8C22×C4711yescharacteristic
457Q8⋊C8C22×C4711yescharacteristic
458Q8⋊C8C22×C4711yescharacteristic
459D4⋊C8C22×C4711yescharacteristic
460D4⋊C8C22×C4711yescharacteristic
461D4⋊C8C22×C4711yescharacteristic
462D4⋊C8C22×C4711yescharacteristic
463C47#1860611yescharacteristic, direct product factor, Sylow
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41D4×C4711yescharacteristic
470#135—44no—
471C2×Q16—21no—
472C2×SD16—21no—
473C2×SD16—21no—
474C2×SD16—21no—
475C2×D8—21no—
476C2×D8—22no—
477C2×D8—21no—
478C2×M16—21no—
479C2×M16—21no—
480C22×C8—21no—
481C4⋊Q8—21no—
482C4⋊Q8C23×C4711yescharacteristic
483C4⋊Q8C23×C4711yescharacteristic
484#127—22no—
485#127—21no—
486#127—21no—
487#127C23×C4711yescharacteristic
488#127C23×C4711yescharacteristic
489#126—22no—
490#126—21no—
491#125—22no—
492#125—21no—
493#125D4×C4711yescharacteristic
494#124—21no—
495#124—21no—
496#124D4×C4711yescharacteristic
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—22no—
502C22⋊Q8—21no—
503C22⋊Q8D4×C4711yescharacteristic
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121D4×C4711yescharacteristic
518#121D4×C4712yes—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8D4×C4711yescharacteristic
522C4×Q8C23×C4711yescharacteristic
523C4×Q8C23×C4711yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4D4×C4711yescharacteristic
537C4×D4D4×C4712yes—
538C4×D4C23×C4711yescharacteristic
539C4×D4C23×C4711yescharacteristic
540#117—22no—
541#117—21no—
542#117—21no—
543#117D4×C4711yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C42—21no—
547C2×C42C23×C4711yescharacteristic
548#107—21no—
549#106—22no—
550#106—21no—
551C4⋊C8—21no—
552C4⋊C8—21no—
553C4⋊C8C23×C4711yescharacteristic
554C4⋊C8C23×C4711yescharacteristic
555C4⋊C8C23×C4711yescharacteristic
556C4⋊C8C23×C4711yescharacteristic
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—22no—
565#102—21no—
566#102—21no—
567#97—21no—
568C4×C8C23×C4711yescharacteristic
569C4×C8C23×C4711yescharacteristic
570#41—22no—
571#41—41no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576#41—81no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C4711yescharacteristic
585C2×Q8C2×D4×C4711yescharacteristic
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—41no—
600C2×D4C2×D4×C4711yescharacteristic
601C2×D4C2×D4×C4711yescharacteristic
602C2×D4C2×D4×C4712yes—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—41no—
612C22×C4C2×D4×C4711yescharacteristic
613C22×C4C2×D4×C4711yescharacteristic
614C22×C4C2×D4×C4711yescharacteristic
615Q16—42no—
616SD16—42no—
617SD16—42no—
618SD16—81no—
619D8—44no—
620D8—42no—
621D8—81no—
622M16—42no—
623M16—81no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—42no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4C2×D4×C4711yescharacteristic
645C4⋊C4C2×D4×C4711yescharacteristic
646C4⋊C4C2×D4×C4712yes—
647C4⋊C4C2×D4×C4711yescharacteristic
648C4⋊C4C2×D4×C4711yescharacteristic
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—22no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C42—22no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42C2×D4×C4711yescharacteristic
670C42C2×D4×C4711yescharacteristic
671C42C2×D4×C4711yescharacteristic
672C42C24×C4711yescharacteristic
673C23—21no—
674C23—21no—
675C23—22no—
676C23—41no—
677C23#120×C4711yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8AGL(1,ℤ/8)×C4712yes—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—42no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—81no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C4711yescharacteristic
734C2×C4#120×C4711yescharacteristic
735C2×C4#120×C4711yescharacteristic
736C2×C4C22×D4×C4711yescharacteristic
737C2×C4C22×D4×C4711yescharacteristic
738C2×C4C22×D4×C4711yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22C2×#120×C4711yescharacteristic
761C4—21no—
762C4—22no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
774C4C47×#57511yescharacteristic
775C4C47×#57611yescharacteristic
776C4C47×#57711yescharacteristic
777C2—41no—
778C2—81no—
779C2—81no—
780C2—82no—
781C2—161no—
782C2C47×#300611yescharacteristic
783C2C47×#301211yescharacteristic
784C2C47×#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×#3517C2semidirect
2. C47×#3251C2semidirect
3. C47×#3184C2semidirect
4. C47×#3035C2semidirect
5. C47×#1654C2semidirect
6. C47×#1653C2semidirect
7. C47×#1642C2semidirect
8. C47×#1641C2semidirect
9. C47×#1626C2semidirect
10. C47×#1625C2semidirect
11. C47×#1621C2semidirect
12. C47×#1621C2semidirect
13. C47×#1547C2semidirect
14. C47×#1489C2semidirect
15. C47×#1483C2semidirect
352. #18606C47direct (N × H)
385. #3517C2×C47semidirect
386. #3251C2×C47semidirect
387. #3184C2×C47semidirect
388. #3035C2×C47semidirect
389. #1654C2×C47semidirect
390. #1653C2×C47semidirect
391. #1642C2×C47semidirect
392. #1641C2×C47semidirect
393. #1626C2×C47semidirect
394. #1625C2×C47semidirect
395. #1621C2×C47semidirect
396. #1621C2×C47semidirect
397. #1547C2×C47semidirect
398. #1489C2×C47semidirect
399. #1483C2×C47semidirect
463. C47#18606direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35172
C47×#32512
C47×#31842
C47×#30352
C47×#16542
C47×#16532
C47×#16422
C47×#16412
C47×#16262
C47×#16252
C47×#16212
C47×#15472
C47×#14892
C47×#14832
#1860647