Finite Group Databasebeta

← C47×#25188 #26064886

Subgroups — C47×#25188 #26064886

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3062C211yesmaximal, characteristic, complemented
2C47×#3045C211yesmaximal, characteristic, complemented
3C2×C47×#453C211yesmaximal, characteristic, complemented
4C47×#3012C211yesmaximal, characteristic, complemented
5C2×C47×#443C211yesmaximal, characteristic, complemented
6C47×#2897C211yesmaximal, characteristic, complemented
7C47×#2063C211yesmaximal, characteristic, complemented
8C47×#2051C211yesmaximal, characteristic, complemented
9C47×#2039C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1957C211yesmaximal, characteristic, complemented
12C47×#1937C211yesmaximal, characteristic, complemented
13C47×#1907C211yesmaximal, characteristic, complemented
14C47×#1907C211yesmaximal, characteristic, complemented
15C47×#1859C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
20C2×#135×C47C2211yescharacteristic
21C2×#131×C47C2211yescharacteristic
22C2×#131×C47C2211yescharacteristic, complemented
23C47×#537C2211yescharacteristic
24C47×#535C2211yescharacteristic, complemented
25C2×#127×C47C2211yescharacteristic
26C47×#520C2211yescharacteristic
27C47×#469—21no—
28C47×#468—21no—
29C47×#466—21no—
30C47×#465—21no—
31C47×#464—21no—
32C47×#463—21no—
33C47×#460—21no—
34C47×#459—21no—
35C47×#453—24no—
36C47×#452—21no—
37C47×#450—21no—
38C47×#449—21no—
39C47×#447—21no—
40C47×#443—24no—
41C2×#108×C47C2211yescharacteristic, complemented
42C47×#428C2211yescharacteristic, complemented
43C47×#424C2211yescharacteristic, complemented
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic, complemented
47C47×#418—21no—
48C47×#418C2211yescharacteristic
49C47×#417—21no—
50C47×#417C2211yescharacteristic
51C47×#417C2211yescharacteristic
52C47×#417C2211yescharacteristic, complemented
53C47×#416—21no—
54C47×#416C2211yescharacteristic
55C2×#102×C47—21no—
56C2×#102×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic, complemented
59C2×#102×C47C2211yescharacteristic, complemented
60C2×#100×C47C2211yescharacteristic
61C2×#100×C47C2211yescharacteristic, complemented
62C47×#408C2211yescharacteristic
63C2×C4×C8×C47C2211yescharacteristic, complemented
64C47×#384C2211yescharacteristic, complemented
65C47×#343C2211yescharacteristic, complemented
66C47×#343C2211yescharacteristic, complemented
67C47×#341C2211yescharacteristic, complemented
68C47×#339C2211yescharacteristic, complemented
69H(5,𝔽2)×C47—22no—
70H(5,𝔽2)×C47—22no—
71H(5,𝔽2)×C47—22no—
72H(5,𝔽2)×C47—41no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47C2311yescharacteristic
76C2×#41×C47C2311yescharacteristic
77C2×#41×C47C2311yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—41no—
81C22×D4×C47—41no—
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84AGL(1,ℤ/8)×C47—22no—
85AGL(1,ℤ/8)×C47—22no—
86AGL(1,ℤ/8)×C47—22no—
87AGL(1,ℤ/8)×C47—22no—
88AGL(1,ℤ/8)×C47—41no—
89AGL(1,ℤ/8)×C47—41no—
90#135×C47—22no—
91#135×C47—22no—
92C2×Q16×C47D411yescharacteristic, complemented
93C2×SD16×C47—21no—
94C2×SD16×C47—21no—
95C2×SD16×C47—21no—
96C2×SD16×C47D411yescharacteristic, complemented
97C2×SD16×C47D411yescharacteristic, complemented
98C2×D8×C47—21no—
99C2×D8×C47—21no—
100C2×D8×C47—21no—
101C2×D8×C47D411yescharacteristic, complemented
102#131×C47—22no—
103#131×C47—22no—
104#131×C47—41no—
105#131×C47—41no—
106C2×M16×C47—21no—
107C2×M16×C47—21no—
108C2×M16×C47C2311yescharacteristic
109C2×M16×C47C2311yescharacteristic
110C2×M16×C47C2311yescharacteristic
111C2×M16×C47C2311yescharacteristic
112C22×C8×C47—21no—
113C22×C8×C47—21no—
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116#127×C47—21no—
117#127×C47—22no—
118#127×C47—22no—
119#124×C47—21no—
120C22⋊Q8×C47—21no—
121C22⋊Q8×C47—21no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#121×C47—41no—
127#120×C47—41no—
128C4×Q8×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—41no—
131#117×C47—21no—
132#117×C47C2311yescharacteristic
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—41no—
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138#108×C47—22no—
139#107×C47—21no—
140#106×C47—21no—
141C4⋊C8×C47—21no—
142C4⋊C8×C47—21no—
143#104×C47—22no—
144#104×C47—22no—
145#104×C47D414yescomplemented
146#103×C47—21no—
147#103×C47—21no—
148#103×C47—21no—
149#103×C47D411yescharacteristic, complemented
150#103×C47D411yescharacteristic, complemented
151#102×C47—21no—
152#102×C47—21no—
153#102×C47—21no—
154#102×C47—21no—
155#102×C47—21no—
156#102×C47—21no—
157#102×C47—21no—
158#102×C47—21no—
159#102×C47—21no—
160#102×C47—21no—
161#102×C47—21no—
162#102×C47—21no—
163#102×C47—21no—
164#102×C47D411yescharacteristic, complemented
165#102×C47D411yescharacteristic, complemented
166#100×C47—22no—
167#100×C47—41no—
168C22⋊C8×C47—21no—
169C22⋊C8×C47—21no—
170C4×C8×C47—22no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—41no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—24no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—42no—
186#41×C47—42no—
187#41×C47—42no—
188#41×C47C2×D412yes—
189#41×C47#4112yes—
190C2×Q8×C47C2×D411yescharacteristic
191C2×Q8×C47C2×D411yescharacteristic
192C2×Q8×C47C2×D411yescharacteristic
193C2×D4×C47—21no—
194C2×D4×C47—24no—
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—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—42no—
209C2×D4×C47—41no—
210C2×D4×C47—41no—
211C2×D4×C47—44no—
212C2×D4×C47—41no—
213C2×D4×C47—41no—
214C2×D4×C47—42no—
215C2×D4×C47—44no—
216C2×D4×C47—44no—
217C2×D4×C47—42no—
218C2×D4×C47—41no—
219C2×D4×C47—82no—
220C2×D4×C47—82no—
221C2×D4×C47C2×D411yescharacteristic
222C2×D4×C47C2×D411yescharacteristic
223C2×D4×C47C2×D411yescharacteristic
224C2×D4×C47#4112yes—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—41no—
232C22×C4×C47—41no—
233C22×C4×C47C2411yescharacteristic
234Q16×C47—22no—
235SD16×C47—22no—
236SD16×C47—22no—
237SD16×C47—42no—
238SD16×C47—42no—
239SD16×C47—42no—
240D8×C47—22no—
241D8×C47—42no—
242D8×C47—42no—
243D8×C47—42no—
244M16×C47—21no—
245M16×C47—21no—
246M16×C47—21no—
247M16×C47—21no—
248M16×C47—21no—
249M16×C47—21no—
250M16×C47—21no—
251M16×C47—42no—
252M16×C47—42no—
253M16×C47C2×D412yes—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—42no—
263C2×C8×C47—42no—
264C2×C8×C47C2×D411yescharacteristic
265C2×C8×C47C2×D411yescharacteristic
266C2×C8×C47C2×D411yescharacteristic
267C2×C8×C47C2×D411yescharacteristic
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—41no—
273C4⋊C4×C47—41no—
274C4⋊C4×C47—82no—
275C4⋊C4×C47C2×D411yescharacteristic
276C4⋊C4×C47C2×D411yescharacteristic
277C22⋊C4×C47—21no—
278C22⋊C4×C47—41no—
279C22⋊C4×C47—41no—
280C22⋊C4×C47—41no—
281C22⋊C4×C47—41no—
282C22⋊C4×C47—41no—
283C42×C47—21no—
284C42×C47—21no—
285C42×C47—41no—
286C42×C47C2×D412yes—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—22no—
291C23×C47—44no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—81no—
298C23×C47—81no—
299C23×C47—81no—
300C23×C47—81no—
301C23×C47—161no—
302C23×C47—161no—
303C23×C47H(5,𝔽2)11yescharacteristic
304Q8×C47—21no—
305Q8×C47—21no—
306Q8×C47—21no—
307Q8×C47—21no—
308Q8×C47—21no—
309Q8×C47#12112yes—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—21no—
313D4×C47—21no—
314D4×C47—22no—
315D4×C47—21no—
316D4×C47—21no—
317D4×C47—21no—
318D4×C47—22no—
319D4×C47—44no—
320D4×C47—44no—
321D4×C47—41no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47—41no—
328D4×C47—41no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—88no—
332D4×C47—161no—
333D4×C47—161no—
334D4×C47—161no—
335D4×C47#12112yes—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—21no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—44no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—81no—
354C2×C4×C47—81no—
355C2×C4×C47—161no—
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C8×C47—21no—
363C8×C47—21no—
364C8×C47—21no—
365C8×C47—21no—
366C8×C47—22no—
367C8×C47—41no—
368C8×C47—41no—
369C8×C47—41no—
370#25188C4711yesmaximal, characteristic, direct product factor, Sylow
371C22×C47—21no—
372C22×C47—21no—
373C22×C47—22no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—42no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—82no—
384C22×C47—82no—
385C22×C47—81no—
386C22×C47—81no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—161no—
391C22×C47—161no—
392C22×C47—164no—
393C22×C47#53811yescharacteristic
394C22×C47D4211yescharacteristic
395C22×C47#54611yescharacteristic
396C4×C47—24no—
397C4×C47—22no—
398C4×C47—41no—
399C4×C47—41no—
400C4×C47—41no—
401C4×C47—41no—
402C4×C47—81no—
403C4×C47—81no—
404C4×C47C2×#12111yescharacteristic
405C4×C47#52511yescharacteristic
406C4×C47D4211yescharacteristic
407C4×C47#54611yescharacteristic
408#3062C2×C4711yescharacteristic, complemented
409#3045C2×C4711yescharacteristic, complemented
410C2×#453C2×C4711yescharacteristic, complemented
411#3012C2×C4711yescharacteristic, complemented
412C2×#443C2×C4711yescharacteristic, complemented
413#2897C2×C4711yescharacteristic, complemented
414#2063C2×C4711yescharacteristic, complemented
415#2051C2×C4711yescharacteristic, complemented
416#2039C2×C4711yescharacteristic, complemented
417#2002C2×C4711yescharacteristic, complemented
418#1957C2×C4711yescharacteristic, complemented
419#1937C2×C4711yescharacteristic, complemented
420#1907C2×C4711yescharacteristic, complemented
421#1907C2×C4711yescharacteristic, complemented
422#1859C2×C4711yescharacteristic, complemented
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—42no—
426C2×C47—81no—
427C2×C47—81no—
428C2×C47—82no—
429C2×C47—161no—
430C2×C47#242411yescharacteristic
431C2×C47#329111yescharacteristic
432C2×C47#329211yescharacteristic
433C2×H(5,𝔽2)C22×C4711yescharacteristic
434C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
435C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
436C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
437C2×#135C22×C4711yescharacteristic
438C2×#131C22×C4711yescharacteristic
439C2×#131C22×C4711yescharacteristic, complemented
440#537C22×C4711yescharacteristic
441#535C22×C4711yescharacteristic, complemented
442C2×#127C22×C4711yescharacteristic
443#520C22×C4711yescharacteristic
444#469—21no—
445#468—21no—
446#466—21no—
447#465—21no—
448#464—21no—
449#463—21no—
450#460—21no—
451#459—21no—
452#453—24no—
453#452—21no—
454#450—21no—
455#449—21no—
456#447—21no—
457#443—24no—
458C2×#108C22×C4711yescharacteristic, complemented
459#428C22×C4711yescharacteristic, complemented
460#424C22×C4711yescharacteristic, complemented
461C2×#104C22×C4711yescharacteristic
462C2×#104C22×C4711yescharacteristic
463C2×#104C22×C4711yescharacteristic, complemented
464#418—21no—
465#418C22×C4711yescharacteristic
466#417—21no—
467#417C22×C4711yescharacteristic
468#417C22×C4711yescharacteristic
469#417C22×C4711yescharacteristic, complemented
470#416—21no—
471#416C22×C4711yescharacteristic
472C2×#102—21no—
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic, complemented
476C2×#102C22×C4711yescharacteristic, complemented
477C2×#100C22×C4711yescharacteristic
478C2×#100C22×C4711yescharacteristic, complemented
479#408C22×C4711yescharacteristic
480C2×C4×C8C22×C4711yescharacteristic, complemented
481#384C22×C4711yescharacteristic, complemented
482#343C22×C4711yescharacteristic, complemented
483#343C22×C4711yescharacteristic, complemented
484#341C22×C4711yescharacteristic, complemented
485#339C22×C4711yescharacteristic, complemented
486C47#2518811yescharacteristic, direct product factor, Sylow
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C4711yescharacteristic
494C2×#41C23×C4711yescharacteristic
495C2×#41C23×C4711yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C4711yescharacteristic
501C22×D4C23×C4711yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C4711yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C4711yescharacteristic, complemented
515C2×SD16D4×C4711yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C4711yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C4711yescharacteristic
527C2×M16C23×C4711yescharacteristic
528C2×M16C23×C4711yescharacteristic
529C2×M16C23×C4711yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C4711yescharacteristic
533C22×C8C23×C4711yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C4711yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C4711yescharacteristic
554C2×C4⋊C4C23×C4711yescharacteristic
555C2×C42C23×C4711yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C4714yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C4711yescharacteristic, complemented
568#103D4×C4711yescharacteristic, complemented
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102D4×C4711yescharacteristic, complemented
583#102D4×C4711yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C4712yes—
607#41#41×C4712yes—
608C2×Q8C2×D4×C4711yescharacteristic
609C2×Q8C2×D4×C4711yescharacteristic
610C2×Q8C2×D4×C4711yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C4711yescharacteristic
640C2×D4C2×D4×C4711yescharacteristic
641C2×D4C2×D4×C4711yescharacteristic
642C2×D4#41×C4712yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C4711yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C4712yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C4711yescharacteristic
683C2×C8C2×D4×C4711yescharacteristic
684C2×C8C2×D4×C4711yescharacteristic
685C2×C8C2×D4×C4711yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C4711yescharacteristic
694C4⋊C4C2×D4×C4711yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C4712yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C4711yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C4712yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C4712yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C4711yescharacteristic
775C2×C4C22×D4×C4711yescharacteristic
776C2×C4C22×D4×C4711yescharacteristic
777C2×C4C2×#41×C4711yescharacteristic
778C2×C4C2×#41×C4711yescharacteristic
779C2×C4H(5,𝔽2)×C4711yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22C47×#53811yescharacteristic
811C22D42×C4711yescharacteristic
812C22C47×#54611yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C4711yescharacteristic
822C4C47×#52511yescharacteristic
823C4D42×C4711yescharacteristic
824C4C47×#54611yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2C47×#242411yescharacteristic
833C2C47×#329111yescharacteristic
834C2C47×#329211yescharacteristic
subgroupG/H
center, socleC22×C47D42
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3062C2semidirect
2. C47×#3045C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3012C2semidirect
5. C2×C47×#443C2semidirect
6. C47×#2897C2semidirect
7. C47×#2063C2semidirect
8. C47×#2051C2semidirect
9. C47×#2039C2semidirect
10. C47×#2002C2semidirect
11. C47×#1957C2semidirect
12. C47×#1937C2semidirect
13. C47×#1907C2semidirect
14. C47×#1907C2semidirect
15. C47×#1859C2semidirect
22. C2×#131×C47C22semidirect
24. C47×#535C22semidirect
41. C2×#108×C47C22semidirect
42. C47×#428C22semidirect
43. C47×#424C22semidirect
46. C2×#104×C47C22semidirect
52. C47×#417C22semidirect
58. C2×#102×C47C22semidirect
59. C2×#102×C47C22semidirect
61. C2×#100×C47C22semidirect
63. C2×C4×C8×C47C22semidirect
64. C47×#384C22semidirect
65. C47×#343C22semidirect
66. C47×#343C22semidirect
67. C47×#341C22semidirect
68. C47×#339C22semidirect
92. C2×Q16×C47D4semidirect
96. C2×SD16×C47D4semidirect
97. C2×SD16×C47D4semidirect
101. C2×D8×C47D4semidirect
145. #104×C47D4semidirect
149. #103×C47D4semidirect
150. #103×C47D4semidirect
164. #102×C47D4semidirect
165. #102×C47D4semidirect
370. #25188C47direct (N × H)
408. #3062C2×C47semidirect
409. #3045C2×C47semidirect
410. C2×#453C2×C47semidirect
411. #3012C2×C47semidirect
412. C2×#443C2×C47semidirect
413. #2897C2×C47semidirect
414. #2063C2×C47semidirect
415. #2051C2×C47semidirect
416. #2039C2×C47semidirect
417. #2002C2×C47semidirect
418. #1957C2×C47semidirect
419. #1937C2×C47semidirect
420. #1907C2×C47semidirect
421. #1907C2×C47semidirect
422. #1859C2×C47semidirect
439. C2×#131C22×C47semidirect
441. #535C22×C47semidirect
458. C2×#108C22×C47semidirect
459. #428C22×C47semidirect
460. #424C22×C47semidirect
463. C2×#104C22×C47semidirect
469. #417C22×C47semidirect
475. C2×#102C22×C47semidirect
476. C2×#102C22×C47semidirect
478. C2×#100C22×C47semidirect
480. C2×C4×C8C22×C47semidirect
481. #384C22×C47semidirect
482. #343C22×C47semidirect
483. #343C22×C47semidirect
484. #341C22×C47semidirect
485. #339C22×C47semidirect
486. C47#25188direct (N × H)
510. C2×Q16D4×C47semidirect
514. C2×SD16D4×C47semidirect
515. C2×SD16D4×C47semidirect
519. C2×D8D4×C47semidirect
563. #104D4×C47semidirect
567. #103D4×C47semidirect
568. #103D4×C47semidirect
582. #102D4×C47semidirect
583. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#30622
C47×#30452
C2×C47×#4532
C47×#30122
C2×C47×#4432
C47×#28972
C47×#20632
C47×#20512
C47×#20392
C47×#20022
C47×#19572
C47×#19372
C47×#19072
C47×#18592
#2518847