Finite Group Databasebeta

← C47×#25409 #26065107

Subgroups — C47×#25409 #26065107

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3153C211yesmaximal, characteristic
2C2×C47×#473C211yesmaximal, characteristic, complemented
3C2×C47×#471C211yesmaximal, characteristic, complemented
4C47×#3037C211yesmaximal, characteristic, complemented
5C2×C47×#464C211yesmaximal, characteristic, complemented
6C47×#2935C211yesmaximal, characteristic, complemented
7C47×#2052C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2020C211yesmaximal, characteristic, complemented
10C47×#2019C211yesmaximal, characteristic, complemented
11C47×#1967C211yesmaximal, characteristic, complemented
12C47×#1950C211yesmaximal, characteristic, complemented
13C47×#1908C211yesmaximal, characteristic, complemented
14C47×#1907C211yesmaximal, characteristic, complemented
15C4×#101×C47C211yesmaximal, characteristic, complemented
16C2×#137×C47C2211yescharacteristic
17C2×#137×C47C2211yescharacteristic
18C2×#137×C47C2211yescharacteristic
19C2×#137×C47C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
22C22×Q16×C47C2211yescharacteristic
23C22×SD16×C47C2211yescharacteristic
24C2×#131×C47C2211yescharacteristic
25C2×#131×C47C2211yescharacteristic
26C47×#532C2211yescharacteristic
27C2×#124×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C47×#497—21no—
30C47×#496—21no—
31C47×#495—21no—
32C47×#495—21no—
33C47×#473—24no—
34C47×#471—24no—
35C47×#464—21no—
36C47×#464—21no—
37C47×#464—21no—
38C47×#464—21no—
39C47×#464—21no—
40C47×#464—21no—
41C47×#462—21no—
42C47×#460—21no—
43C47×#436—21no—
44C47×#435—21no—
45C47×#435—21no—
46C8×D4×C47—21no—
47C2×#108×C47C2211yescharacteristic
48C2×#108×C47C2211yescharacteristic
49C47×#423C2211yescharacteristic
50C2×C4⋊C8×C47C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C47×#417C2211yescharacteristic
53C2×#103×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#101×C47C2211yescharacteristic
56C2×#101×C47C2211yescharacteristic
57C2×#101×C47C2211yescharacteristic
58C2×#101×C47C2211yescharacteristic
59C2×#100×C47C2211yescharacteristic
60C2×#100×C47C2211yescharacteristic
61C47×#408C2211yescharacteristic
62C47×#408C2211yescharacteristic
63C4×M16×C47C2211yescharacteristic
64C4×M16×C47C2211yescharacteristic
65C47×#343C2211yescharacteristic
66C47×#343C2211yescharacteristic
67C47×#341C2211yescharacteristic
68C47×#341C2211yescharacteristic
69C2×#41×C47C2311yescharacteristic
70C2×#41×C47C2311yescharacteristic
71C22×Q8×C47C2311yescharacteristic
72C22×Q8×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74#137×C47—22no—
75#137×C47—22no—
76#137×C47—22no—
77#137×C47—22no—
78#137×C47—41no—
79#137×C47—41no—
80#137×C47—41no—
81#137×C47—41no—
82AGL(1,ℤ/8)×C47—22no—
83AGL(1,ℤ/8)×C47—22no—
84AGL(1,ℤ/8)×C47—41no—
85AGL(1,ℤ/8)×C47—41no—
86C2×Q16×C47—21no—
87C2×Q16×C47—21no—
88C2×Q16×C47—22no—
89C2×Q16×C47—21no—
90C2×Q16×C47—21no—
91C2×Q16×C47—21no—
92C2×Q16×C47—21no—
93C2×Q16×C47—41no—
94C2×SD16×C47—22no—
95C2×SD16×C47—21no—
96C2×SD16×C47—21no—
97C2×SD16×C47—21no—
98C2×SD16×C47—21no—
99C2×SD16×C47—21no—
100C2×SD16×C47—21no—
101C2×SD16×C47—21no—
102C2×SD16×C47—21no—
103C2×SD16×C47—41no—
104C2×D8×C47—21no—
105C2×D8×C47—21no—
106#131×C47—22no—
107#131×C47—22no—
108#131×C47—41no—
109#131×C47—41no—
110C2×M16×C47—21no—
111C2×M16×C47—21no—
112C2×M16×C47C2311yescharacteristic
113C2×M16×C47C2311yescharacteristic
114C2×M16×C47C2311yescharacteristic
115C2×M16×C47C2311yescharacteristic
116C2×M16×C47C2311yescharacteristic
117C2×M16×C47C2311yescharacteristic
118C22×C8×C47—21no—
119C22×C8×C47—21no—
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122C4⋊Q8×C47D411yescharacteristic
123#127×C47D411yescharacteristic
124#124×C47—21no—
125#124×C47—21no—
126#124×C47—21no—
127#124×C47—21no—
128#124×C47D411yescharacteristic
129#124×C47D411yescharacteristic
130#121×C47—21no—
131#121×C47—21no—
132C4×Q8×C47—21no—
133C4×Q8×C47—21no—
134C4×Q8×C47—21no—
135C4×Q8×C47—21no—
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C42×C47—21no—
143C2×C42×C47C2311yescharacteristic
144#108×C47—22no—
145#108×C47—22no—
146C4⋊C8×C47—21no—
147C4⋊C8×C47—21no—
148C4⋊C8×C47D411yescharacteristic
149C4⋊C8×C47D411yescharacteristic
150C4⋊C8×C47D411yescharacteristic
151C4⋊C8×C47D411yescharacteristic
152#103×C47—21no—
153#103×C47—21no—
154#103×C47—21no—
155#103×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#101×C47—22no—
161#101×C47—22no—
162#101×C47—41no—
163#101×C47D414yescomplemented
164#100×C47—22no—
165#100×C47—41no—
166C22⋊C8×C47—21no—
167C22⋊C8×C47—21no—
168C22⋊C8×C47—21no—
169C22⋊C8×C47—21no—
170#97×C47—21no—
171#97×C47—21no—
172C4×C8×C47—21no—
173C4×C8×C47—21no—
174C24×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—21no—
193C2×Q8×C47—21no—
194C2×Q8×C47C2×D411yescharacteristic
195C2×Q8×C47C2×D411yescharacteristic
196C2×Q8×C47C2×D412yes—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47C2×D411yescharacteristic
208C2×D4×C47C2×D411yescharacteristic
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47#4111yescharacteristic
215C22×C4×C47#4111yescharacteristic
216C22×C4×C47C2411yescharacteristic
217Q16×C47—42no—
218Q16×C47—42no—
219Q16×C47—42no—
220Q16×C47—42no—
221Q16×C47—42no—
222Q16×C47—42no—
223SD16×C47—42no—
224SD16×C47—42no—
225SD16×C47—42no—
226SD16×C47—42no—
227SD16×C47—42no—
228SD16×C47—42no—
229SD16×C47—42no—
230SD16×C47—42no—
231D8×C47—42no—
232D8×C47—42no—
233M16×C47—21no—
234M16×C47—21no—
235M16×C47—21no—
236M16×C47—21no—
237M16×C47—21no—
238M16×C47—21no—
239M16×C47—21no—
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—42no—
243M16×C47—42no—
244M16×C47C2×D412yes—
245M16×C47C2×D412yes—
246M16×C47#4112yes—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—42no—
258C2×C8×C47—42no—
259C2×C8×C47C2×D411yescharacteristic
260C2×C8×C47C2×D411yescharacteristic
261C2×C8×C47C2×D411yescharacteristic
262C2×C8×C47C2×D411yescharacteristic
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—41no—
268C4⋊C4×C47—41no—
269C22⋊C4×C47—21no—
270C22⋊C4×C47—21no—
271C22⋊C4×C47—21no—
272C22⋊C4×C47—21no—
273C22⋊C4×C47—41no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—41no—
276C22⋊C4×C47—41no—
277C42×C47—41no—
278C42×C47—41no—
279C42×C47C2×D411yescharacteristic
280C42×C47C2×D411yescharacteristic
281C42×C47C2×D411yescharacteristic
282C42×C47C2×D411yescharacteristic
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—81no—
289C23×C47—81no—
290C23×C47C2×#4111yescharacteristic
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—21no—
294Q8×C47—21no—
295Q8×C47—21no—
296Q8×C47—21no—
297Q8×C47—41no—
298Q8×C47—41no—
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47—41no—
302Q8×C47—41no—
303D4×C47—21no—
304D4×C47—21no—
305D4×C47—21no—
306D4×C47—21no—
307D4×C47—42no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—81no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—22no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
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#12111yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C2×C4×C47H(5,𝔽2)11yescharacteristic
342C2×C4×C47H(5,𝔽2)11yescharacteristic
343C8×C47—21no—
344C8×C47—21no—
345C8×C47—21no—
346C8×C47—21no—
347C8×C47—22no—
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—41no—
351C8×C47—41no—
352C8×C47—41no—
353#25409C4711yesmaximal, characteristic, direct product factor, Sylow
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—81no—
363C22×C47—81no—
364C22×C47—81no—
365C22×C47—161no—
366C22×C47—161no—
367C22×C47C2×#12111yescharacteristic
368C22×C47#53211yescharacteristic
369C22×C47#54011yescharacteristic
370C4×C47—21no—
371C4×C47—21no—
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—41no—
375C4×C47—41no—
376C4×C47—42no—
377C4×C47—81no—
378C4×C47—81no—
379C4×C47D4211yescharacteristic
380C4×C47D4211yescharacteristic
381C4×C47#54611yescharacteristic
382C4×C47#55011yescharacteristic
383#3153C2×C4711yescharacteristic
384C2×#473C2×C4711yescharacteristic, complemented
385C2×#471C2×C4711yescharacteristic, complemented
386#3037C2×C4711yescharacteristic, complemented
387C2×#464C2×C4711yescharacteristic, complemented
388#2935C2×C4711yescharacteristic, complemented
389#2052C2×C4711yescharacteristic, complemented
390#2051C2×C4711yescharacteristic, complemented
391#2020C2×C4711yescharacteristic, complemented
392#2019C2×C4711yescharacteristic, complemented
393#1967C2×C4711yescharacteristic, complemented
394#1950C2×C4711yescharacteristic, complemented
395#1908C2×C4711yescharacteristic, complemented
396#1907C2×C4711yescharacteristic, complemented
397C4×#101C2×C4711yescharacteristic, complemented
398C2×C47—21no—
399C2×C47—21no—
400C2×C47—81no—
401C2×C47—81no—
402C2×C47—161no—
403C2×C47#242811yescharacteristic
404C2×C47#306711yescharacteristic
405C2×C47#306911yescharacteristic
406C2×#137C22×C4711yescharacteristic
407C2×#137C22×C4711yescharacteristic
408C2×#137C22×C4711yescharacteristic
409C2×#137C22×C4711yescharacteristic
410C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
411C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
412C22×Q16C22×C4711yescharacteristic
413C22×SD16C22×C4711yescharacteristic
414C2×#131C22×C4711yescharacteristic
415C2×#131C22×C4711yescharacteristic
416#532C22×C4711yescharacteristic
417C2×#124C22×C4711yescharacteristic
418C2×C4×Q8C22×C4711yescharacteristic
419#497—21no—
420#496—21no—
421#495—21no—
422#495—21no—
423#473—24no—
424#471—24no—
425#464—21no—
426#464—21no—
427#464—21no—
428#464—21no—
429#464—21no—
430#464—21no—
431#462—21no—
432#460—21no—
433#436—21no—
434#435—21no—
435#435—21no—
436C8×D4—21no—
437C2×#108C22×C4711yescharacteristic
438C2×#108C22×C4711yescharacteristic
439#423C22×C4711yescharacteristic
440C2×C4⋊C8C22×C4711yescharacteristic
441#417C22×C4711yescharacteristic
442#417C22×C4711yescharacteristic
443C2×#103C22×C4711yescharacteristic
444C2×#102C22×C4711yescharacteristic
445C2×#101C22×C4711yescharacteristic
446C2×#101C22×C4711yescharacteristic
447C2×#101C22×C4711yescharacteristic
448C2×#101C22×C4711yescharacteristic
449C2×#100C22×C4711yescharacteristic
450C2×#100C22×C4711yescharacteristic
451#408C22×C4711yescharacteristic
452#408C22×C4711yescharacteristic
453C4×M16C22×C4711yescharacteristic
454C4×M16C22×C4711yescharacteristic
455#343C22×C4711yescharacteristic
456#343C22×C4711yescharacteristic
457#341C22×C4711yescharacteristic
458#341C22×C4711yescharacteristic
459C47#2540911yescharacteristic, direct product factor, Sylow
460C2×#41C23×C4711yescharacteristic
461C2×#41C23×C4711yescharacteristic
462C22×Q8C23×C4711yescharacteristic
463C22×Q8C23×C4711yescharacteristic
464C22×D4C23×C4711yescharacteristic
465#137—22no—
466#137—22no—
467#137—22no—
468#137—22no—
469#137—41no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—41no—
476AGL(1,ℤ/8)—41no—
477C2×Q16—22no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—21no—
484C2×Q16—41no—
485C2×SD16—22no—
486C2×SD16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—41no—
495C2×D8—21no—
496C2×D8—21no—
497#131—22no—
498#131—22no—
499#131—41no—
500#131—41no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16C23×C4711yescharacteristic
504C2×M16C23×C4711yescharacteristic
505C2×M16C23×C4711yescharacteristic
506C2×M16C23×C4711yescharacteristic
507C2×M16C23×C4711yescharacteristic
508C2×M16C23×C4711yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8C23×C4711yescharacteristic
512C22×C8C23×C4711yescharacteristic
513C4⋊Q8D4×C4711yescharacteristic
514#127D4×C4711yescharacteristic
515#124—21no—
516#124—21no—
517#124—21no—
518#124—21no—
519#124D4×C4711yescharacteristic
520#124D4×C4711yescharacteristic
521#121—21no—
522#121—21no—
523C4×Q8—21no—
524C4×Q8—21no—
525C4×Q8—21no—
526C4×Q8—21no—
527C4×D4—21no—
528C4×D4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C4711yescharacteristic
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C42—21no—
534C2×C42C23×C4711yescharacteristic
535#108—22no—
536#108—22no—
537C4⋊C8—21no—
538C4⋊C8—21no—
539C4⋊C8D4×C4711yescharacteristic
540C4⋊C8D4×C4711yescharacteristic
541C4⋊C8D4×C4711yescharacteristic
542C4⋊C8D4×C4711yescharacteristic
543#103—21no—
544#103—21no—
545#103—21no—
546#103—21no—
547#102—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#101—22no—
552#101—22no—
553#101—41no—
554#101D4×C4714yescomplemented
555#100—22no—
556#100—41no—
557C22⋊C8—21no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561#97—21no—
562#97—21no—
563C4×C8—21no—
564C4×C8—21no—
565C24—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C4712yes—
586C2×Q8C2×D4×C4711yescharacteristic
587C2×Q8C2×D4×C4711yescharacteristic
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4C2×D4×C4711yescharacteristic
599C2×D4C2×D4×C4711yescharacteristic
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4#41×C4711yescharacteristic
606C22×C4#41×C4711yescharacteristic
607C22×C4C24×C4711yescharacteristic
608Q16—42no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612Q16—42no—
613Q16—42no—
614SD16—42no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622D8—42no—
623D8—42no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—42no—
634M16—42no—
635M16C2×D4×C4712yes—
636M16C2×D4×C4712yes—
637M16#41×C4712yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8C2×D4×C4711yescharacteristic
651C2×C8C2×D4×C4711yescharacteristic
652C2×C8C2×D4×C4711yescharacteristic
653C2×C8C2×D4×C4711yescharacteristic
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C42—41no—
669C42—41no—
670C42C2×D4×C4711yescharacteristic
671C42C2×D4×C4711yescharacteristic
672C42C2×D4×C4711yescharacteristic
673C42C2×D4×C4711yescharacteristic
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—81no—
680C23—81no—
681C23C2×#41×C4711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—42no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—81no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—81no—
724C2×C4#121×C4711yescharacteristic
725C2×C4#121×C4711yescharacteristic
726C2×C4#121×C4711yescharacteristic
727C2×C4#121×C4711yescharacteristic
728C2×C4C22×D4×C4711yescharacteristic
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C22×D4×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4H(5,𝔽2)×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—22no—
739C8—22no—
740C8—22no—
741C8—41no—
742C8—41no—
743C8—41no—
744C22—21no—
745C22—21no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—161no—
756C22—161no—
757C22C2×#121×C4711yescharacteristic
758C22C47×#53211yescharacteristic
759C22C47×#54011yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4D42×C4711yescharacteristic
770C4D42×C4711yescharacteristic
771C4C47×#54611yescharacteristic
772C4C47×#55011yescharacteristic
773C2—21no—
774C2—21no—
775C2—81no—
776C2—81no—
777C2—161no—
778C2C47×#242811yescharacteristic
779C2C47×#306711yescharacteristic
780C2C47×#306911yescharacteristic
subgroupG/H
center, socleC22×C47C2×#121
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#3153C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#473C2semidirect
3. C2×C47×#471C2semidirect
4. C47×#3037C2semidirect
5. C2×C47×#464C2semidirect
6. C47×#2935C2semidirect
7. C47×#2052C2semidirect
8. C47×#2051C2semidirect
9. C47×#2020C2semidirect
10. C47×#2019C2semidirect
11. C47×#1967C2semidirect
12. C47×#1950C2semidirect
13. C47×#1908C2semidirect
14. C47×#1907C2semidirect
15. C4×#101×C47C2semidirect
163. #101×C47D4semidirect
353. #25409C47direct (N × H)
384. C2×#473C2×C47semidirect
385. C2×#471C2×C47semidirect
386. #3037C2×C47semidirect
387. C2×#464C2×C47semidirect
388. #2935C2×C47semidirect
389. #2052C2×C47semidirect
390. #2051C2×C47semidirect
391. #2020C2×C47semidirect
392. #2019C2×C47semidirect
393. #1967C2×C47semidirect
394. #1950C2×C47semidirect
395. #1908C2×C47semidirect
396. #1907C2×C47semidirect
397. C4×#101C2×C47semidirect
459. C47#25409direct (N × H)
554. #101D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31532
C2×C47×#4732
C2×C47×#4712
C47×#30372
C2×C47×#4642
C47×#29352
C47×#20522
C47×#20512
C47×#20202
C47×#20192
C47×#19672
C47×#19502
C47×#19082
C47×#19072
C4×#101×C472
#2540947