Finite Group Databasebeta

← C47×#18228 #26057926

Subgroups — C47×#18228 #26057926

Order 12032.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3537C211yesmaximal, characteristic, complemented
2C47×#3006C211yesmaximal, characteristic, complemented
3C47×#3002C211yesmaximal, characteristic, complemented
4C47×#2615C211yesmaximal, characteristic, complemented
5C47×#1606C212yesmaximal, complemented
6C47×#1601C212yesmaximal, complemented
7C47×#1600C212yesmaximal, complemented
8C47×#1595C212yesmaximal, complemented
9C47×#1519C211yesmaximal, characteristic, complemented
10C47×#1513C211yesmaximal, characteristic, complemented
11C47×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C47C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C47—21no—
14C2×#135×C47—21no—
15C47×#560—22no—
16C47×#553—21no—
17C47×#553—21no—
18D42×C47—22no—
19D42×C47—21no—
20D42×C47—21no—
21C47×#540—21no—
22C47×#538—21no—
23C47×#538C2212yes—
24C47×#535—21no—
25C47×#534—21no—
26C47×#534C2212yes—
27C47×#525C2211yescharacteristic
28C2×#121×C47—21no—
29C2×#121×C47C2211yescharacteristic
30C2×#121×C47C2211yescharacteristic
31C47×#452—21no—
32C47×#451C2211yescharacteristic, complemented
33C47×#450C2211yescharacteristic, complemented
34C47×#449—21no—
35C47×#449—22no—
36C47×#448C2211yescharacteristic, complemented
37C47×#448C2212yescomplemented
38C47×#447C2211yescharacteristic, complemented
39C47×#447C2212yescomplemented
40C47×#417—21no—
41C47×#416—21no—
42C47×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C47C2211yescharacteristic, complemented
44C47×#393C2212yescomplemented
45C47×#392—22no—
46C47×#392C2212yescomplemented
47C47×#380—21no—
48C47×#380C2211yescharacteristic, complemented
49C47×#328C2212yescomplemented
50C47×#327C2212yescomplemented
51C47×#327C2212yescomplemented
52C47×#327C2212yescomplemented
53C47×#323C2212yescomplemented
54C47×#323C2212yescomplemented
55C2×#41×C47—21no—
56C2×#41×C47—21no—
57C2×#41×C47—21no—
58C2×#41×C47—21no—
59C2×#41×C47—44no—
60C2×#41×C47D411yescharacteristic, complemented
61C22×Q8×C47C2311yescharacteristic
62C22×D4×C47—22no—
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—22no—
68C22×D4×C47D411yescharacteristic
69C22×D4×C47D412yes—
70C22×D4×C47D411yescharacteristic, complemented
71C22×D4×C47C2311yescharacteristic
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74AGL(1,ℤ/8)×C47—44no—
75#135×C47—44no—
76C2×Q16×C47—21no—
77C2×SD16×C47—21no—
78C2×SD16×C47—21no—
79C2×SD16×C47—22no—
80C2×D8×C47—21no—
81C2×D8×C47—22no—
82C2×M16×C47—21no—
83C22×C8×C47—21no—
84#127×C47—22no—
85#127×C47—21no—
86#126×C47—22no—
87#126×C47—22no—
88#125×C47—21no—
89#124×C47—22no—
90#123×C47—22no—
91#123×C47—21no—
92#123×C47—22no—
93#123×C47—22no—
94#123×C47—22no—
95C22⋊Q8×C47D411yescharacteristic, complemented
96C22⋊Q8×C47C2311yescharacteristic
97#121×C47—22no—
98#121×C47—21no—
99#121×C47—21no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—22no—
104#121×C47—21no—
105#121×C47—21no—
106#121×C47—21no—
107#121×C47—21no—
108#121×C47—21no—
109#121×C47—21no—
110#121×C47—22no—
111#121×C47—44no—
112#121×C47D412yescomplemented
113#121×C47D411yescharacteristic, complemented
114#121×C47C2312yes—
115#121×C47C2311yescharacteristic
116#120×C47—22no—
117#120×C47—22no—
118#120×C47—22no—
119#120×C47—21no—
120#120×C47—22no—
121#120×C47—22no—
122#120×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—22no—
129#117×C47—21no—
130#117×C47D411yescharacteristic, complemented
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47D411yescharacteristic
133C2×C4⋊C4×C47D411yescharacteristic, complemented
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—22no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47C2312yes—
139#103×C47—21no—
140#103×C47—22no—
141#103×C47—21no—
142#102×C47—21no—
143#102×C47—22no—
144#102×C47—21no—
145C22⋊C8×C47—21no—
146C22⋊C8×C47—21no—
147C22⋊C8×C47C2311yescharacteristic
148C22⋊C8×C47C2311yescharacteristic
149C22⋊C8×C47C2312yes—
150#95×C47—22no—
151#95×C47C2312yes—
152C24×C47—22no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47C2×D412yes—
156C24×C47C2×D411yescharacteristic
157#41×C47—24no—
158#41×C47—24no—
159#41×C47—42no—
160#41×C47—42no—
161#41×C47—42no—
162#41×C47—42no—
163#41×C47—42no—
164#41×C47—42no—
165#41×C47—42no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47—42no—
169C2×Q8×C47C2×D411yescharacteristic
170C2×D4×C47—22no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—22no—
174C2×D4×C47—22no—
175C2×D4×C47—22no—
176C2×D4×C47—22no—
177C2×D4×C47—22no—
178C2×D4×C47—22no—
179C2×D4×C47—21no—
180C2×D4×C47—22no—
181C2×D4×C47—22no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—41no—
193C2×D4×C47—41no—
194C2×D4×C47—44no—
195C2×D4×C47—82no—
196C2×D4×C47—82no—
197C2×D4×C47—82no—
198C2×D4×C47—82no—
199C2×D4×C47—81no—
200C2×D4×C47—81no—
201C2×D4×C47—82no—
202C2×D4×C47—82no—
203C2×D4×C47—84no—
204C2×D4×C47C2×D411yescharacteristic
205C2×D4×C47C2×D412yes—
206C22×C4×C47—24no—
207C22×C4×C47—21no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—22no—
213C22×C4×C47—42no—
214C22×C4×C47—42no—
215C22×C4×C47—41no—
216C22×C4×C47—41no—
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D412yes—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224Q16×C47—42no—
225SD16×C47—42no—
226SD16×C47—42no—
227SD16×C47—44no—
228D8×C47—42no—
229D8×C47—44no—
230M16×C47—42no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—22no—
234C2×C8×C47—42no—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—22no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—42no—
243C4⋊C4×C47C2×D412yes—
244C4⋊C4×C47C2×D411yescharacteristic
245C4⋊C4×C47C2×D411yescharacteristic
246C22⋊C4×C47—22no—
247C22⋊C4×C47—22no—
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—22no—
255C22⋊C4×C47—21no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—44no—
261C22⋊C4×C47—81no—
262C22⋊C4×C47—82no—
263C42×C47—22no—
264C42×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—21no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—81no—
285C23×C47—81no—
286C23×C47—82no—
287C23×C47—82no—
288C23×C47—82no—
289C23×C47#12011yescharacteristic
290C23×C47#12011yescharacteristic
291C23×C47C22×D411yescharacteristic
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—41no—
295Q8×C47—41no—
296Q8×C47—41no—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47—42no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—44no—
304D4×C47—42no—
305D4×C47—44no—
306D4×C47—44no—
307D4×C47—42no—
308D4×C47—41no—
309D4×C47—42no—
310D4×C47—41no—
311D4×C47—42no—
312D4×C47—42no—
313D4×C47—81no—
314D4×C47—82no—
315D4×C47—82no—
316D4×C47—81no—
317D4×C47—82no—
318D4×C47—82no—
319D4×C47—82no—
320D4×C47—82no—
321D4×C47—82no—
322D4×C47—88no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—21no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—44no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—44no—
339C2×C4×C47—42no—
340C2×C4×C47—42no—
341C2×C4×C47—42no—
342C2×C4×C47—42no—
343C2×C4×C47—42no—
344C2×C4×C47—81no—
345C2×C4×C47—82no—
346C2×C4×C47—82no—
347C2×C4×C47#12011yescharacteristic
348C2×C4×C47#12011yescharacteristic
349C2×C4×C47C22×D411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C8×C47—41no—
352C8×C47—41no—
353C8×C47—42no—
354#18228C4711yesmaximal, characteristic, direct product factor, Sylow
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—41no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—41no—
371C22×C47—42no—
372C22×C47—41no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—82no—
378C22×C47—82no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—162no—
384C22×C47—164no—
385C22×C47C2×#12011yescharacteristic
386C22×C47#57611yescharacteristic
387C22×C47#57711yescharacteristic
388C4×C47—21no—
389C4×C47—21no—
390C4×C47—21no—
391C4×C47—42no—
392C4×C47—41no—
393C4×C47—42no—
394C4×C47—41no—
395C4×C47—42no—
396C4×C47—41no—
397C4×C47—82no—
398C4×C47B(4,𝔽2)12yes—
399#3537C2×C4711yescharacteristic, complemented
400#3006C2×C4711yescharacteristic, complemented
401#3002C2×C4711yescharacteristic, complemented
402#2615C2×C4711yescharacteristic, complemented
403#1606C2×C4712yescomplemented
404#1601C2×C4712yescomplemented
405#1600C2×C4712yescomplemented
406#1595C2×C4712yescomplemented
407#1519C2×C4711yescharacteristic, complemented
408#1513C2×C4711yescharacteristic, complemented
409#1471C2×C4711yescharacteristic, complemented
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—41no—
413C2×C47—41no—
414C2×C47—82no—
415C2×C47—82no—
416C2×C47—82no—
417C2×C47—81no—
418C2×C47#301211yescharacteristic
419C2×C47#301911yescharacteristic
420C2×C47C2×B(4,𝔽2)11yescharacteristic
421C22×#41C22×C4711yescharacteristic, complemented
422C2×AGL(1,ℤ/8)—21no—
423C2×#135—21no—
424#560—22no—
425#553—21no—
426#553—21no—
427D42—22no—
428D42—21no—
429D42—21no—
430#540—21no—
431#538—21no—
432#538C22×C4712yes—
433#535—21no—
434#534—21no—
435#534C22×C4712yes—
436#525C22×C4711yescharacteristic
437C2×#121—21no—
438C2×#121C22×C4711yescharacteristic
439C2×#121C22×C4711yescharacteristic
440#452—21no—
441#451C22×C4711yescharacteristic, complemented
442#450C22×C4711yescharacteristic, complemented
443#449—21no—
444#449—22no—
445#448C22×C4711yescharacteristic, complemented
446#448C22×C4712yescomplemented
447#447C22×C4711yescharacteristic, complemented
448#447C22×C4712yescomplemented
449#417—21no—
450#416—21no—
451#407C22×C4711yescharacteristic, complemented
452C2×C22⋊C8C22×C4711yescharacteristic, complemented
453#393C22×C4712yescomplemented
454#392—22no—
455#392C22×C4712yescomplemented
456#380—21no—
457#380C22×C4711yescharacteristic, complemented
458#328C22×C4712yescomplemented
459#327C22×C4712yescomplemented
460#327C22×C4712yescomplemented
461#327C22×C4712yescomplemented
462#323C22×C4712yescomplemented
463#323C22×C4712yescomplemented
464C47#1822811yescharacteristic, direct product factor, Sylow
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C4711yescharacteristic, complemented
471C22×Q8C23×C4711yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C4711yescharacteristic
479C22×D4D4×C4712yes—
480C22×D4D4×C4711yescharacteristic, complemented
481C22×D4C23×C4711yescharacteristic
482C23×C4—21no—
483C23×C4C23×C4711yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C4711yescharacteristic, complemented
506C22⋊Q8C23×C4711yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C4712yescomplemented
523#121D4×C4711yescharacteristic, complemented
524#121C23×C4712yes—
525#121C23×C4711yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C4711yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C4711yescharacteristic
543C2×C4⋊C4D4×C4711yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C4712yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C4711yescharacteristic
558C22⋊C8C23×C4711yescharacteristic
559C22⋊C8C23×C4712yes—
560#95—22no—
561#95C23×C4712yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C4712yes—
566C24C2×D4×C4711yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C4711yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C4711yescharacteristic
615C2×D4C2×D4×C4712yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C4711yescharacteristic
628C22×C4C2×D4×C4711yescharacteristic
629C22×C4C2×D4×C4711yescharacteristic
630C22×C4C2×D4×C4712yes—
631C22×C4C2×D4×C4711yescharacteristic
632C22×C4C2×D4×C4711yescharacteristic
633C22×C4C24×C4711yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C4712yes—
654C4⋊C4C2×D4×C4711yescharacteristic
655C4⋊C4C2×D4×C4711yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C4711yescharacteristic
700C23#120×C4711yescharacteristic
701C23C22×D4×C4711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C4711yescharacteristic
758C2×C4#120×C4711yescharacteristic
759C2×C4C22×D4×C4711yescharacteristic
760C2×C4C22×D4×C4711yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C4711yescharacteristic
795C22C47×#57611yescharacteristic
796C22C47×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C47×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C47×#301211yescharacteristic
817C2C47×#301911yescharacteristic
818C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C47×#3537C2semidirect
2. C47×#3006C2semidirect
3. C47×#3002C2semidirect
4. C47×#2615C2semidirect
5. C47×#1606C2semidirect
6. C47×#1601C2semidirect
7. C47×#1600C2semidirect
8. C47×#1595C2semidirect
9. C47×#1519C2semidirect
10. C47×#1513C2semidirect
11. C47×#1471C2semidirect
12. C22×#41×C47C22semidirect
32. C47×#451C22semidirect
33. C47×#450C22semidirect
36. C47×#448C22semidirect
37. C47×#448C22semidirect
38. C47×#447C22semidirect
39. C47×#447C22semidirect
42. C47×#407C22semidirect
43. C2×C22⋊C8×C47C22semidirect
44. C47×#393C22semidirect
46. C47×#392C22semidirect
48. C47×#380C22semidirect
49. C47×#328C22semidirect
50. C47×#327C22semidirect
51. C47×#327C22semidirect
52. C47×#327C22semidirect
53. C47×#323C22semidirect
54. C47×#323C22semidirect
60. C2×#41×C47D4semidirect
70. C22×D4×C47D4semidirect
95. C22⋊Q8×C47D4semidirect
112. #121×C47D4semidirect
113. #121×C47D4semidirect
130. #117×C47D4semidirect
133. C2×C4⋊C4×C47D4semidirect
354. #18228C47direct (N × H)
399. #3537C2×C47semidirect
400. #3006C2×C47semidirect
401. #3002C2×C47semidirect
402. #2615C2×C47semidirect
403. #1606C2×C47semidirect
404. #1601C2×C47semidirect
405. #1600C2×C47semidirect
406. #1595C2×C47semidirect
407. #1519C2×C47semidirect
408. #1513C2×C47semidirect
409. #1471C2×C47semidirect
421. C22×#41C22×C47semidirect
441. #451C22×C47semidirect
442. #450C22×C47semidirect
445. #448C22×C47semidirect
446. #448C22×C47semidirect
447. #447C22×C47semidirect
448. #447C22×C47semidirect
451. #407C22×C47semidirect
452. C2×C22⋊C8C22×C47semidirect
453. #393C22×C47semidirect
455. #392C22×C47semidirect
457. #380C22×C47semidirect
458. #328C22×C47semidirect
459. #327C22×C47semidirect
460. #327C22×C47semidirect
461. #327C22×C47semidirect
462. #323C22×C47semidirect
463. #323C22×C47semidirect
464. C47#18228direct (N × H)
470. C2×#41D4×C47semidirect
480. C22×D4D4×C47semidirect
505. C22⋊Q8D4×C47semidirect
522. #121D4×C47semidirect
523. #121D4×C47semidirect
540. #117D4×C47semidirect
543. C2×C4⋊C4D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35372
C47×#30062
C47×#30022
C47×#26152
C47×#16062
C47×#16012
C47×#16002
C47×#15952
C47×#15192
C47×#15132
C47×#14712
#1822847