Finite Group Databasebeta

← C47×#18810 #26058508

Subgroups — C47×#18810 #26058508

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3519C211yesmaximal, characteristic, complemented
2C47×#3251C211yesmaximal, characteristic, complemented
3C47×#3207C211yesmaximal, characteristic, complemented
4C47×#3036C211yesmaximal, characteristic, complemented
5C47×#1646C211yesmaximal, characteristic, complemented
6C47×#1643C211yesmaximal, characteristic, complemented
7C47×#1642C211yesmaximal, characteristic, complemented
8C47×#1639C211yesmaximal, characteristic, complemented
9C47×#1624C211yesmaximal, characteristic, complemented
10C47×#1622C211yesmaximal, characteristic, complemented
11C47×#1621C211yesmaximal, characteristic, complemented
12C47×#1619C211yesmaximal, characteristic, complemented
13C47×#1560C211yesmaximal, characteristic, complemented
14C47×#1495C211yesmaximal, characteristic, complemented
15C47×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C47—21no—
17C47×#555C2211yescharacteristic
18C47×#554C2211yescharacteristic
19C47×#553—21no—
20C47×#553—21no—
21C47×#550C2211yescharacteristic
22C47×#546—22no—
23C47×#546—21no—
24D42×C47—21no—
25D42×C47C2211yescharacteristic
26C47×#540—21no—
27C47×#538—22no—
28C47×#532C2211yescharacteristic
29C47×#532C2211yescharacteristic, complemented
30C47×#529C2211yescharacteristic
31C47×#525—21no—
32C2×#121×C47—21no—
33C47×#518—21no—
34C2×C4×D4×C47C2211yescharacteristic
35C47×#493C2211yescharacteristic, complemented
36C47×#492C2211yescharacteristic, complemented
37C47×#487C2211yescharacteristic, complemented
38C47×#486C2211yescharacteristic, complemented
39C47×#478—21no—
40C47×#475C2211yescharacteristic, complemented
41C47×#474C2211yescharacteristic, complemented
42C47×#469—21no—
43C47×#468—21no—
44C47×#463—22no—
45C47×#463—21no—
46C47×#463—21no—
47C47×#463—21no—
48C47×#461C2211yescharacteristic
49C47×#461C2211yescharacteristic, complemented
50C47×#460C2211yescharacteristic, complemented
51C47×#459C2211yescharacteristic
52C47×#459C2211yescharacteristic, complemented
53C47×#459C2211yescharacteristic, complemented
54C47×#449—22no—
55C47×#431C2211yescharacteristic, complemented
56C47×#423C2211yescharacteristic, complemented
57C47×#423C2211yescharacteristic, complemented
58C47×#417—21no—
59C47×#333C2211yescharacteristic, complemented
60C47×#333C2211yescharacteristic, complemented
61C47×#331C2211yescharacteristic, complemented
62C47×#331C2211yescharacteristic, complemented
63C47×Q8⋊C8C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C47×D4⋊C8C2211yescharacteristic, complemented
68C47×D4⋊C8C2211yescharacteristic, complemented
69C47×D4⋊C8C2211yescharacteristic, complemented
70C47×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47D412yes—
74C22×D4×C47—22no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47D411yescharacteristic
78C23×C4×C47—21no—
79AGL(1,ℤ/8)×C47—44no—
80C2×SD16×C47—21no—
81C2×SD16×C47—21no—
82C2×SD16×C47—22no—
83C2×SD16×C47—21no—
84C2×D8×C47—21no—
85C2×D8×C47—21no—
86C2×D8×C47—22no—
87C2×D8×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C4⋊Q8×C47C2311yescharacteristic
91C4⋊Q8×C47C2311yescharacteristic
92#127×C47—21no—
93#127×C47C2311yescharacteristic
94#127×C47C2311yescharacteristic
95#126×C47—22no—
96#126×C47—21no—
97#125×C47—21no—
98#125×C47D411yescharacteristic
99#124×C47—22no—
100#124×C47—21no—
101#124×C47D411yescharacteristic
102#124×C47D412yes—
103#123×C47—22no—
104#123×C47—22no—
105#123×C47—22no—
106#123×C47—21no—
107C22⋊Q8×C47—21no—
108C22⋊Q8×C47—22no—
109C22⋊Q8×C47D411yescharacteristic
110#121×C47—22no—
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—22no—
114#121×C47—21no—
115#121×C47—22no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47—21no—
119#121×C47—21no—
120#121×C47—21no—
121#121×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47D411yescharacteristic
125#120×C47—22no—
126#120×C47—22no—
127#120×C47—22no—
128C4×Q8×C47C2311yescharacteristic
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47—22no—
132C4×D4×C47—21no—
133C4×D4×C47—21no—
134C4×D4×C47—21no—
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×C47D411yescharacteristic
142C4×D4×C47D411yescharacteristic
143C4×D4×C47C2311yescharacteristic
144C4×D4×C47C2311yescharacteristic
145C4×D4×C47C2311yescharacteristic
146#117×C47—21no—
147#117×C47—21no—
148#117×C47—21no—
149C2×C4⋊C4×C47—21no—
150C2×C4⋊C4×C47D411yescharacteristic
151C2×C22⋊C4×C47—22no—
152C2×C22⋊C4×C47—22no—
153C2×C22⋊C4×C47—21no—
154C2×C42×C47C2311yescharacteristic
155#107×C47—21no—
156#106×C47—21no—
157C4⋊C8×C47—21no—
158C4⋊C8×C47—21no—
159C4⋊C8×C47—21no—
160C4⋊C8×C47C2311yescharacteristic
161C4⋊C8×C47C2311yescharacteristic
162C4⋊C8×C47C2311yescharacteristic
163C4⋊C8×C47C2311yescharacteristic
164#103×C47—22no—
165#103×C47—21no—
166#103×C47—21no—
167#103×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—21no—
174C22⋊C8×C47—21no—
175C4×C8×C47C2311yescharacteristic
176C4×C8×C47C2311yescharacteristic
177C24×C47—22no—
178C24×C47—21no—
179#41×C47—42no—
180#41×C47—42no—
181#41×C47—81no—
182#41×C47—81no—
183#41×C47—82no—
184C2×Q8×C47—21no—
185C2×Q8×C47C2×D411yescharacteristic
186C2×Q8×C47C2×D412yes—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—21no—
191C2×D4×C47—22no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—22no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—41no—
202C2×D4×C47—42no—
203C2×D4×C47—42no—
204C2×D4×C47—41no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47—84no—
208C2×D4×C47C2×D411yescharacteristic
209C2×D4×C47C2×D411yescharacteristic
210C2×D4×C47C2×D411yescharacteristic
211C2×D4×C47C2×D412yes—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—22no—
220C22×C4×C47—21no—
221C22×C4×C47—41no—
222C22×C4×C47—81no—
223C22×C4×C47—81no—
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227SD16×C47—42no—
228SD16×C47—42no—
229SD16×C47—81no—
230SD16×C47—82no—
231D8×C47—42no—
232D8×C47—42no—
233D8×C47—81no—
234D8×C47—82no—
235M16×C47—42no—
236M16×C47—81no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C4⋊C4×C47—22no—
244C4⋊C4×C47—22no—
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×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47C2×D411yescharacteristic
255C4⋊C4×C47C2×D411yescharacteristic
256C4⋊C4×C47C2×D411yescharacteristic
257C4⋊C4×C47C2×D411yescharacteristic
258C22⋊C4×C47—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C22⋊C4×C47—21no—
266C22⋊C4×C47—21no—
267C22⋊C4×C47—22no—
268C22⋊C4×C47—21no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—22no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—21no—
273C22⋊C4×C47—21no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—41no—
276C42×C47—22no—
277C42×C47—21no—
278C42×C47C2×D411yescharacteristic
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2411yescharacteristic
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—22no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—44no—
289C23×C47—41no—
290C23×C47—81no—
291C23×C47—82no—
292C23×C47—82no—
293C23×C47#12011yescharacteristic
294Q8×C47—21no—
295Q8×C47—21no—
296Q8×C47—42no—
297Q8×C47—41no—
298Q8×C47—41no—
299D4×C47—21no—
300D4×C47—21no—
301D4×C47—21no—
302D4×C47—21no—
303D4×C47—21no—
304D4×C47—42no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—44no—
308D4×C47—42no—
309D4×C47—44no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—82no—
319D4×C47—82no—
320D4×C47—82no—
321D4×C47—82no—
322D4×C47—82no—
323D4×C47AGL(1,ℤ/8)12yes—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—22no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—81no—
343C2×C4×C47—81no—
344C2×C4×C47—82no—
345C2×C4×C47—82no—
346C2×C4×C47—81no—
347C2×C4×C47—82no—
348C2×C4×C47—82no—
349C2×C4×C47#12011yescharacteristic
350C2×C4×C47#12011yescharacteristic
351C2×C4×C47#12011yescharacteristic
352C2×C4×C47C22×D411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C8×C47—41no—
356C8×C47—41no—
357C8×C47—41no—
358C8×C47—41no—
359C8×C47—41no—
360C8×C47—41no—
361#18810C4711yesmaximal, characteristic, direct product factor, Sylow
362C22×C47—21no—
363C22×C47—22no—
364C22×C47—21no—
365C22×C47—21no—
366C22×C47—41no—
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—42no—
371C22×C47—41no—
372C22×C47—42no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—84no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—164no—
382C22×C47C2×#12011yescharacteristic
383C4×C47—21no—
384C4×C47—21no—
385C4×C47—21no—
386C4×C47—21no—
387C4×C47—41no—
388C4×C47—41no—
389C4×C47—41no—
390C4×C47—41no—
391C4×C47—41no—
392C4×C47—42no—
393C4×C47—81no—
394C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
395C4×C47#57511yescharacteristic
396C4×C47#57611yescharacteristic
397C4×C47#57711yescharacteristic
398#3519C2×C4711yescharacteristic, complemented
399#3251C2×C4711yescharacteristic, complemented
400#3207C2×C4711yescharacteristic, complemented
401#3036C2×C4711yescharacteristic, complemented
402#1646C2×C4711yescharacteristic, complemented
403#1643C2×C4711yescharacteristic, complemented
404#1642C2×C4711yescharacteristic, complemented
405#1639C2×C4711yescharacteristic, complemented
406#1624C2×C4711yescharacteristic, complemented
407#1622C2×C4711yescharacteristic, complemented
408#1621C2×C4711yescharacteristic, complemented
409#1619C2×C4711yescharacteristic, complemented
410#1560C2×C4711yescharacteristic, complemented
411#1495C2×C4711yescharacteristic, complemented
412#1486C2×C4711yescharacteristic, complemented
413C2×C47—41no—
414C2×C47—42no—
415C2×C47—81no—
416C2×C47—82no—
417C2×C47—81no—
418C2×C47—161no—
419C2×C47#300611yescharacteristic
420C2×C47#301211yescharacteristic
421C2×C47#301911yescharacteristic
422C2×AGL(1,ℤ/8)—21no—
423#555C22×C4711yescharacteristic
424#554C22×C4711yescharacteristic
425#553—21no—
426#553—21no—
427#550C22×C4711yescharacteristic
428#546—22no—
429#546—21no—
430D42—21no—
431D42C22×C4711yescharacteristic
432#540—21no—
433#538—22no—
434#532C22×C4711yescharacteristic
435#532C22×C4711yescharacteristic, complemented
436#529C22×C4711yescharacteristic
437#525—21no—
438C2×#121—21no—
439#518—21no—
440C2×C4×D4C22×C4711yescharacteristic
441#493C22×C4711yescharacteristic, complemented
442#492C22×C4711yescharacteristic, complemented
443#487C22×C4711yescharacteristic, complemented
444#486C22×C4711yescharacteristic, complemented
445#478—21no—
446#475C22×C4711yescharacteristic, complemented
447#474C22×C4711yescharacteristic, complemented
448#469—21no—
449#468—21no—
450#463—22no—
451#463—21no—
452#463—21no—
453#463—21no—
454#461C22×C4711yescharacteristic
455#461C22×C4711yescharacteristic, complemented
456#460C22×C4711yescharacteristic, complemented
457#459C22×C4711yescharacteristic
458#459C22×C4711yescharacteristic, complemented
459#459C22×C4711yescharacteristic, complemented
460#449—22no—
461#431C22×C4711yescharacteristic, complemented
462#423C22×C4711yescharacteristic, complemented
463#423C22×C4711yescharacteristic, complemented
464#417—21no—
465#333C22×C4711yescharacteristic, complemented
466#333C22×C4711yescharacteristic, complemented
467#331C22×C4711yescharacteristic, complemented
468#331C22×C4711yescharacteristic, complemented
469Q8⋊C8C22×C4711yescharacteristic, complemented
470Q8⋊C8C22×C4711yescharacteristic, complemented
471D4⋊C8C22×C4711yescharacteristic
472D4⋊C8C22×C4711yescharacteristic
473D4⋊C8C22×C4711yescharacteristic, complemented
474D4⋊C8C22×C4711yescharacteristic, complemented
475D4⋊C8C22×C4711yescharacteristic, complemented
476D4⋊C8C22×C4711yescharacteristic, complemented
477C47#1881011yescharacteristic, direct product factor, Sylow
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C4712yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C4711yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C4711yescharacteristic
498C4⋊Q8C23×C4711yescharacteristic
499#127—21no—
500#127C23×C4711yescharacteristic
501#127C23×C4711yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C4711yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C4711yescharacteristic
509#124D4×C4712yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C4711yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C4711yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C4711yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C4711yescharacteristic
549C4×D4D4×C4711yescharacteristic
550C4×D4C23×C4711yescharacteristic
551C4×D4C23×C4711yescharacteristic
552C4×D4C23×C4711yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C4711yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C4711yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C4711yescharacteristic
568C4⋊C8C23×C4711yescharacteristic
569C4⋊C8C23×C4711yescharacteristic
570C4⋊C8C23×C4711yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C4711yescharacteristic
583C4×C8C23×C4711yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C4711yescharacteristic
593C2×Q8C2×D4×C4712yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C4711yescharacteristic
616C2×D4C2×D4×C4711yescharacteristic
617C2×D4C2×D4×C4711yescharacteristic
618C2×D4C2×D4×C4712yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C4711yescharacteristic
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C2×D4×C4711yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C4711yescharacteristic
662C4⋊C4C2×D4×C4711yescharacteristic
663C4⋊C4C2×D4×C4711yescharacteristic
664C4⋊C4C2×D4×C4711yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C4711yescharacteristic
686C42C2×D4×C4711yescharacteristic
687C42C2×D4×C4711yescharacteristic
688C42C24×C4711yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C4711yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C4712yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C4711yescharacteristic
757C2×C4#120×C4711yescharacteristic
758C2×C4#120×C4711yescharacteristic
759C2×C4C22×D4×C4711yescharacteristic
760C2×C4C22×D4×C4711yescharacteristic
761C2×C4C22×D4×C4711yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C4711yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
801C4C47×#57511yescharacteristic
802C4C47×#57611yescharacteristic
803C4C47×#57711yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C47×#300611yescharacteristic
811C2C47×#301211yescharacteristic
812C2C47×#301911yescharacteristic
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×#3519C2semidirect
2. C47×#3251C2semidirect
3. C47×#3207C2semidirect
4. C47×#3036C2semidirect
5. C47×#1646C2semidirect
6. C47×#1643C2semidirect
7. C47×#1642C2semidirect
8. C47×#1639C2semidirect
9. C47×#1624C2semidirect
10. C47×#1622C2semidirect
11. C47×#1621C2semidirect
12. C47×#1619C2semidirect
13. C47×#1560C2semidirect
14. C47×#1495C2semidirect
15. C47×#1486C2semidirect
29. C47×#532C22semidirect
35. C47×#493C22semidirect
36. C47×#492C22semidirect
37. C47×#487C22semidirect
38. C47×#486C22semidirect
40. C47×#475C22semidirect
41. C47×#474C22semidirect
49. C47×#461C22semidirect
50. C47×#460C22semidirect
52. C47×#459C22semidirect
53. C47×#459C22semidirect
55. C47×#431C22semidirect
56. C47×#423C22semidirect
57. C47×#423C22semidirect
59. C47×#333C22semidirect
60. C47×#333C22semidirect
61. C47×#331C22semidirect
62. C47×#331C22semidirect
63. C47×Q8⋊C8C22semidirect
64. C47×Q8⋊C8C22semidirect
67. C47×D4⋊C8C22semidirect
68. C47×D4⋊C8C22semidirect
69. C47×D4⋊C8C22semidirect
70. C47×D4⋊C8C22semidirect
361. #18810C47direct (N × H)
398. #3519C2×C47semidirect
399. #3251C2×C47semidirect
400. #3207C2×C47semidirect
401. #3036C2×C47semidirect
402. #1646C2×C47semidirect
403. #1643C2×C47semidirect
404. #1642C2×C47semidirect
405. #1639C2×C47semidirect
406. #1624C2×C47semidirect
407. #1622C2×C47semidirect
408. #1621C2×C47semidirect
409. #1619C2×C47semidirect
410. #1560C2×C47semidirect
411. #1495C2×C47semidirect
412. #1486C2×C47semidirect
435. #532C22×C47semidirect
441. #493C22×C47semidirect
442. #492C22×C47semidirect
443. #487C22×C47semidirect
444. #486C22×C47semidirect
446. #475C22×C47semidirect
447. #474C22×C47semidirect
455. #461C22×C47semidirect
456. #460C22×C47semidirect
458. #459C22×C47semidirect
459. #459C22×C47semidirect
461. #431C22×C47semidirect
462. #423C22×C47semidirect
463. #423C22×C47semidirect
465. #333C22×C47semidirect
466. #333C22×C47semidirect
467. #331C22×C47semidirect
468. #331C22×C47semidirect
469. Q8⋊C8C22×C47semidirect
470. Q8⋊C8C22×C47semidirect
473. D4⋊C8C22×C47semidirect
474. D4⋊C8C22×C47semidirect
475. D4⋊C8C22×C47semidirect
476. D4⋊C8C22×C47semidirect
477. C47#18810direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35192
C47×#32512
C47×#32072
C47×#30362
C47×#16462
C47×#16432
C47×#16422
C47×#16392
C47×#16242
C47×#16222
C47×#16212
C47×#16192
C47×#15602
C47×#14952
C47×#14862
#1881047