Finite Group Databasebeta

← C47×#33551 #26073249

Subgroups — C47×#33551 #26073249

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3532C211yesmaximal, characteristic, complemented
2C47×#3026C211yesmaximal, characteristic, complemented
3C2×C47×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C47×#3019C211yesmaximal, characteristic, complemented
5C47×#2200C212yesmaximal, complemented
6C47×#2199C212yesmaximal, complemented
7C47×#2197C212yesmaximal, complemented
8C47×#2196C212yesmaximal, complemented
9C47×#2127C211yesmaximal, characteristic, complemented
10C47×#2121C211yesmaximal, characteristic, complemented
11C2×C47×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C47C2211yescharacteristic, complemented
13C47×#575—21no—
14C47×H(3,𝔽4)C2211yescharacteristic, complemented
15C47×#560—21no—
16C47×#560C2211yescharacteristic, complemented
17C47×#551—21no—
18C47×#551C2211yescharacteristic, complemented
19C47×#546—21no—
20C47×#546—21no—
21C47×#546—21no—
22D42×C47—21no—
23D42×C47C2211yescharacteristic, complemented
24C47×#538—21no—
25C47×#538—21no—
26C47×#538—21no—
27C47×#535—21no—
28C47×#535C2211yescharacteristic
29C47×#534—21no—
30C47×#534—21no—
31C47×#534C2211yescharacteristic
32C2×#120×C47—21no—
33C2×#120×C47—21no—
34C2×#120×C47C2211yescharacteristic
35C47×#458—21no—
36C47×#458C2212yescomplemented
37C47×B(4,𝔽2)—21no—
38C47×B(4,𝔽2)—21no—
39C47×B(4,𝔽2)—21no—
40C47×B(4,𝔽2)C2212yes—
41C47×B(4,𝔽2)C2212yescomplemented
42C47×B(4,𝔽2)C2212yescomplemented
43C47×#455—21no—
44C47×#455C2212yescomplemented
45C47×#453—21no—
46C47×#453C2212yescomplemented
47C47×#421—21no—
48C2×#100×C47C2211yescharacteristic, complemented
49C2×#99×C47—21no—
50C2×#99×C47—21no—
51C2×#99×C47C2211yescharacteristic, complemented
52C2×#99×C47C2211yescharacteristic, complemented
53C47×#354C2212yescomplemented
54C47×#353C2212yescomplemented
55C47×#352C2212yescomplemented
56C47×AΣL(1,𝔽16)C2212yescomplemented
57C47×AΣL(1,𝔽16)C2212yescomplemented
58C47×AΣL(1,𝔽16)C2212yescomplemented
59C25×C47D411yescharacteristic, complemented
60H(5,𝔽2)×C47—21no—
61H(5,𝔽2)×C47—21no—
62H(5,𝔽2)×C47—21no—
63H(5,𝔽2)×C47—42no—
64H(5,𝔽2)×C47C2312yes—
65C2×#41×C47—21no—
66C2×#41×C47—21no—
67C2×#41×C47—41no—
68C2×#41×C47D411yescharacteristic, complemented
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—41no—
77C22×D4×C47—41no—
78C22×D4×C47D411yescharacteristic, complemented
79C22×D4×C47C2311yescharacteristic
80#137×C47—22no—
81#137×C47—41no—
82AGL(1,ℤ/8)×C47—22no—
83AGL(1,ℤ/8)×C47—41no—
84#135×C47—42no—
85C2×M16×C47—21no—
86#127×C47—21no—
87#127×C47D411yescharacteristic, complemented
88#127×C47C2311yescharacteristic
89#126×C47—21no—
90#126×C47—21no—
91#126×C47—21no—
92#126×C47—21no—
93#124×C47—21no—
94#124×C47—21no—
95#124×C47—21no—
96#124×C47—21no—
97#124×C47—21no—
98#124×C47D411yescharacteristic, complemented
99#124×C47C2311yescharacteristic
100#123×C47—21no—
101#123×C47—21no—
102#123×C47—21no—
103#123×C47—21no—
104#123×C47—21no—
105#123×C47—21no—
106#123×C47—21no—
107#123×C47—21no—
108#123×C47—22no—
109#123×C47—41no—
110#123×C47D411yescharacteristic, complemented
111#123×C47C2311yescharacteristic
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115#121×C47—21no—
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×C47—21no—
125#121×C47—21no—
126#121×C47—21no—
127#121×C47—21no—
128#121×C47—21no—
129#121×C47—21no—
130#121×C47—42no—
131#120×C47—21no—
132#120×C47—21no—
133#120×C47—21no—
134#120×C47—21no—
135#120×C47—21no—
136#120×C47—21no—
137#120×C47—21no—
138#120×C47—21no—
139#120×C47—21no—
140#120×C47—21no—
141#120×C47—21no—
142#120×C47—21no—
143#120×C47—21no—
144#120×C47—21no—
145#120×C47—22no—
146#120×C47—22no—
147#120×C47—22no—
148#120×C47—42no—
149#120×C47—41no—
150#120×C47D411yescharacteristic, complemented
151#120×C47D411yescharacteristic, complemented
152#120×C47D411yescharacteristic, complemented
153#120×C47C2311yescharacteristic
154#120×C47C2311yescharacteristic
155#120×C47C2311yescharacteristic
156C4×D4×C47—21no—
157C4×D4×C47—21no—
158C4×D4×C47—21no—
159C4×D4×C47—21no—
160C4×D4×C47—21no—
161C4×D4×C47—21no—
162#117×C47—21no—
163#117×C47D411yescharacteristic, complemented
164C2×C22⋊C4×C47—21no—
165C2×C22⋊C4×C47—21no—
166C2×C22⋊C4×C47—21no—
167C2×C22⋊C4×C47—21no—
168C2×C22⋊C4×C47—21no—
169C2×C22⋊C4×C47—21no—
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—41no—
172C2×C22⋊C4×C47D411yescharacteristic, complemented
173C2×C22⋊C4×C47D411yescharacteristic, complemented
174#104×C47—22no—
175#104×C47—22no—
176#100×C47—21no—
177#100×C47C2312yes—
178#99×C47—21no—
179#99×C47—21no—
180#99×C47—22no—
181#99×C47—22no—
182#99×C47—22no—
183#99×C47—22no—
184#99×C47C2312yes—
185#99×C47C2312yes—
186C24×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—21no—
190C24×C47—21no—
191C24×C47—41no—
192C24×C47—41no—
193C24×C47—82no—
194C24×C47C2×D411yescharacteristic
195C24×C47C2×D411yescharacteristic
196C24×C47C2×D411yescharacteristic
197C24×C47C2×D411yescharacteristic
198C24×C47C2×D411yescharacteristic, complemented
199#41×C47—22no—
200#41×C47—22no—
201#41×C47—42no—
202#41×C47—41no—
203#41×C47—42no—
204#41×C47—42no—
205#41×C47—41no—
206#41×C47—41no—
207#41×C47—42no—
208#41×C47—41no—
209#41×C47—82no—
210C2×Q8×C47—21no—
211C2×Q8×C47—21no—
212C2×Q8×C47C2×D411yescharacteristic, complemented
213C2×D4×C47—21no—
214C2×D4×C47—21no—
215C2×D4×C47—21no—
216C2×D4×C47—22no—
217C2×D4×C47—22no—
218C2×D4×C47—21no—
219C2×D4×C47—21no—
220C2×D4×C47—21no—
221C2×D4×C47—21no—
222C2×D4×C47—22no—
223C2×D4×C47—22no—
224C2×D4×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—21no—
227C2×D4×C47—21no—
228C2×D4×C47—21no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—21no—
235C2×D4×C47—21no—
236C2×D4×C47—21no—
237C2×D4×C47—21no—
238C2×D4×C47—41no—
239C2×D4×C47—41no—
240C2×D4×C47—42no—
241C2×D4×C47—42no—
242C2×D4×C47—41no—
243C2×D4×C47—41no—
244C2×D4×C47—41no—
245C2×D4×C47—41no—
246C2×D4×C47—42no—
247C2×D4×C47—42no—
248C2×D4×C47—41no—
249C2×D4×C47—41no—
250C2×D4×C47—41no—
251C2×D4×C47—41no—
252C2×D4×C47—41no—
253C2×D4×C47—42no—
254C2×D4×C47—42no—
255C2×D4×C47—42no—
256C2×D4×C47—82no—
257C2×D4×C47—82no—
258C2×D4×C47—82no—
259C2×D4×C47—82no—
260C2×D4×C47—81no—
261C2×D4×C47—81no—
262C2×D4×C47—84no—
263C2×D4×C47C2×D411yescharacteristic
264C2×D4×C47C2×D411yescharacteristic
265C2×D4×C47C2×D411yescharacteristic
266C2×D4×C47C2×D411yescharacteristic, complemented
267C2×D4×C47C2411yescharacteristic
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—21no—
271C22×C4×C47—21no—
272C22×C4×C47—21no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—21no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—41no—
279C22×C4×C47—41no—
280C22×C4×C47—41no—
281C22×C4×C47C2×D411yescharacteristic
282C22×C4×C47C2×D411yescharacteristic, complemented
283Q16×C47—42no—
284SD16×C47—42no—
285SD16×C47—42no—
286D8×C47—42no—
287M16×C47—22no—
288M16×C47—41no—
289C2×C8×C47—41no—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—21no—
293C4⋊C4×C47—21no—
294C4⋊C4×C47—21no—
295C4⋊C4×C47—21no—
296C4⋊C4×C47—21no—
297C4⋊C4×C47—21no—
298C4⋊C4×C47—21no—
299C4⋊C4×C47—42no—
300C22⋊C4×C47—21no—
301C22⋊C4×C47—21no—
302C22⋊C4×C47—21no—
303C22⋊C4×C47—21no—
304C22⋊C4×C47—21no—
305C22⋊C4×C47—21no—
306C22⋊C4×C47—21no—
307C22⋊C4×C47—21no—
308C22⋊C4×C47—21no—
309C22⋊C4×C47—21no—
310C22⋊C4×C47—21no—
311C22⋊C4×C47—21no—
312C22⋊C4×C47—21no—
313C22⋊C4×C47—21no—
314C22⋊C4×C47—21no—
315C22⋊C4×C47—21no—
316C22⋊C4×C47—21no—
317C22⋊C4×C47—21no—
318C22⋊C4×C47—21no—
319C22⋊C4×C47—21no—
320C22⋊C4×C47—21no—
321C22⋊C4×C47—21no—
322C22⋊C4×C47—21no—
323C22⋊C4×C47—21no—
324C22⋊C4×C47—21no—
325C22⋊C4×C47—22no—
326C22⋊C4×C47—22no—
327C22⋊C4×C47—42no—
328C22⋊C4×C47—42no—
329C22⋊C4×C47—42no—
330C22⋊C4×C47—41no—
331C22⋊C4×C47—41no—
332C22⋊C4×C47—42no—
333C22⋊C4×C47C2×D411yescharacteristic
334C22⋊C4×C47C2×D411yescharacteristic
335C22⋊C4×C47C2×D411yescharacteristic, complemented
336C22⋊C4×C47C2×D411yescharacteristic, complemented
337C42×C47—21no—
338C42×C47—21no—
339C42×C47C2×D411yescharacteristic, complemented
340C42×C47C2×D411yescharacteristic, complemented
341C23×C47—21no—
342C23×C47—21no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—21no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—21no—
349C23×C47—21no—
350C23×C47—21no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—42no—
354C23×C47—42no—
355C23×C47—42no—
356C23×C47—41no—
357C23×C47—41no—
358C23×C47—42no—
359C23×C47—41no—
360C23×C47—44no—
361C23×C47—41no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—81no—
365C23×C47—81no—
366C23×C47—81no—
367C23×C47—81no—
368C23×C47—81no—
369C23×C47—81no—
370C23×C47—81no—
371C23×C47—81no—
372C23×C47—81no—
373C23×C47—82no—
374C23×C47—82no—
375C23×C47—82no—
376C23×C47—82no—
377C23×C47—161no—
378C23×C47#12011yescharacteristic
379C23×C47#12011yescharacteristic
380C23×C47#12011yescharacteristic
381C23×C47C22×D411yescharacteristic
382C23×C47C22×D411yescharacteristic
383Q8×C47—22no—
384Q8×C47—41no—
385Q8×C47—41no—
386Q8×C47—81no—
387D4×C47—22no—
388D4×C47—41no—
389D4×C47—41no—
390D4×C47—41no—
391D4×C47—41no—
392D4×C47—41no—
393D4×C47—41no—
394D4×C47—42no—
395D4×C47—42no—
396D4×C47—42no—
397D4×C47—42no—
398D4×C47—42no—
399D4×C47—42no—
400D4×C47—42no—
401D4×C47—42no—
402D4×C47—42no—
403D4×C47—42no—
404D4×C47—41no—
405D4×C47—41no—
406D4×C47—41no—
407D4×C47—41no—
408D4×C47—81no—
409D4×C47—81no—
410D4×C47—81no—
411D4×C47—81no—
412D4×C47—81no—
413D4×C47—81no—
414D4×C47—81no—
415D4×C47—81no—
416D4×C47—81no—
417D4×C47—81no—
418D4×C47—81no—
419D4×C47—81no—
420D4×C47—81no—
421D4×C47—81no—
422D4×C47—84no—
423D4×C47—84no—
424D4×C47—162no—
425C2×C4×C47—21no—
426C2×C4×C47—21no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—21no—
430C2×C4×C47—21no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—21no—
434C2×C4×C47—21no—
435C2×C4×C47—21no—
436C2×C4×C47—21no—
437C2×C4×C47—42no—
438C2×C4×C47—42no—
439C2×C4×C47—41no—
440C2×C4×C47—41no—
441C2×C4×C47—42no—
442C2×C4×C47—41no—
443C2×C4×C47—41no—
444C2×C4×C47—42no—
445C2×C4×C47—42no—
446C2×C4×C47—81no—
447C2×C4×C47—81no—
448C2×C4×C47—81no—
449C2×C4×C47—81no—
450C2×C4×C47—81no—
451C2×C4×C47—81no—
452C2×C4×C47—81no—
453C2×C4×C47—82no—
454C2×C4×C47—161no—
455C2×C4×C47#12011yescharacteristic
456C2×C4×C47C22×D411yescharacteristic
457C8×C47—42no—
458#33551C4711yesmaximal, characteristic, direct product factor, Sylow
459C22×C47—22no—
460C22×C47—21no—
461C22×C47—21no—
462C22×C47—21no—
463C22×C47—21no—
464C22×C47—41no—
465C22×C47—41no—
466C22×C47—41no—
467C22×C47—41no—
468C22×C47—41no—
469C22×C47—41no—
470C22×C47—42no—
471C22×C47—41no—
472C22×C47—41no—
473C22×C47—41no—
474C22×C47—41no—
475C22×C47—41no—
476C22×C47—41no—
477C22×C47—42no—
478C22×C47—41no—
479C22×C47—42no—
480C22×C47—42no—
481C22×C47—41no—
482C22×C47—41no—
483C22×C47—41no—
484C22×C47—81no—
485C22×C47—81no—
486C22×C47—81no—
487C22×C47—82no—
488C22×C47—82no—
489C22×C47—82no—
490C22×C47—81no—
491C22×C47—84no—
492C22×C47—82no—
493C22×C47—82no—
494C22×C47—82no—
495C22×C47—81no—
496C22×C47—162no—
497C22×C47—161no—
498C22×C47—161no—
499C22×C47B(4,𝔽2)11yescharacteristic
500C22×C47B(4,𝔽2)11yescharacteristic
501C22×C47C2×#12011yescharacteristic
502C4×C47—21no—
503C4×C47—21no—
504C4×C47—41no—
505C4×C47—41no—
506C4×C47—41no—
507C4×C47—41no—
508C4×C47—41no—
509C4×C47—41no—
510C4×C47—42no—
511C4×C47—41no—
512C4×C47—41no—
513C4×C47—82no—
514C4×C47—82no—
515#3532C2×C4711yescharacteristic, complemented
516#3026C2×C4711yescharacteristic, complemented
517C2×B(4,𝔽2)C2×C4711yescharacteristic, complemented
518#3019C2×C4711yescharacteristic, complemented
519#2200C2×C4712yescomplemented
520#2199C2×C4712yescomplemented
521#2197C2×C4712yescomplemented
522#2196C2×C4712yescomplemented
523#2127C2×C4711yescharacteristic, complemented
524#2121C2×C4711yescharacteristic, complemented
525C2×AΣL(1,𝔽16)C2×C4711yescharacteristic, complemented
526C2×C47—21no—
527C2×C47—21no—
528C2×C47—21no—
529C2×C47—41no—
530C2×C47—41no—
531C2×C47—42no—
532C2×C47—41no—
533C2×C47—41no—
534C2×C47—81no—
535C2×C47—81no—
536C2×C47—81no—
537C2×C47—82no—
538C2×C47C2×B(4,𝔽2)11yescharacteristic
539C2×H(5,𝔽2)C22×C4711yescharacteristic, complemented
540#575—21no—
541H(3,𝔽4)C22×C4711yescharacteristic, complemented
542#560—21no—
543#560C22×C4711yescharacteristic, complemented
544#551—21no—
545#551C22×C4711yescharacteristic, complemented
546#546—21no—
547#546—21no—
548#546—21no—
549D42—21no—
550D42C22×C4711yescharacteristic, complemented
551#538—21no—
552#538—21no—
553#538—21no—
554#535—21no—
555#535C22×C4711yescharacteristic
556#534—21no—
557#534—21no—
558#534C22×C4711yescharacteristic
559C2×#120—21no—
560C2×#120—21no—
561C2×#120C22×C4711yescharacteristic
562#458—21no—
563#458C22×C4712yescomplemented
564B(4,𝔽2)—21no—
565B(4,𝔽2)—21no—
566B(4,𝔽2)—21no—
567B(4,𝔽2)C22×C4712yes—
568B(4,𝔽2)C22×C4712yescomplemented
569B(4,𝔽2)C22×C4712yescomplemented
570#455—21no—
571#455C22×C4712yescomplemented
572#453—21no—
573#453C22×C4712yescomplemented
574#421—21no—
575C2×#100C22×C4711yescharacteristic, complemented
576C2×#99—21no—
577C2×#99—21no—
578C2×#99C22×C4711yescharacteristic, complemented
579C2×#99C22×C4711yescharacteristic, complemented
580#354C22×C4712yescomplemented
581#353C22×C4712yescomplemented
582#352C22×C4712yescomplemented
583AΣL(1,𝔽16)C22×C4712yescomplemented
584AΣL(1,𝔽16)C22×C4712yescomplemented
585AΣL(1,𝔽16)C22×C4712yescomplemented
586C47#3355111yescharacteristic, direct product factor, Sylow
587C25D4×C4711yescharacteristic, complemented
588H(5,𝔽2)—21no—
589H(5,𝔽2)—21no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—42no—
592H(5,𝔽2)C23×C4712yes—
593C2×#41—21no—
594C2×#41—21no—
595C2×#41—41no—
596C2×#41D4×C4711yescharacteristic, complemented
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—21no—
602C22×D4—21no—
603C22×D4—21no—
604C22×D4—41no—
605C22×D4—41no—
606C22×D4D4×C4711yescharacteristic, complemented
607C22×D4C23×C4711yescharacteristic
608#137—22no—
609#137—41no—
610AGL(1,ℤ/8)—22no—
611AGL(1,ℤ/8)—41no—
612#135—42no—
613C2×M16—21no—
614#127—21no—
615#127D4×C4711yescharacteristic, complemented
616#127C23×C4711yescharacteristic
617#126—21no—
618#126—21no—
619#126—21no—
620#126—21no—
621#124—21no—
622#124—21no—
623#124—21no—
624#124—21no—
625#124—21no—
626#124D4×C4711yescharacteristic, complemented
627#124C23×C4711yescharacteristic
628#123—21no—
629#123—21no—
630#123—21no—
631#123—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—22no—
637#123—41no—
638#123D4×C4711yescharacteristic, complemented
639#123C23×C4711yescharacteristic
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121—21no—
648#121—21no—
649#121—21no—
650#121—21no—
651#121—21no—
652#121—21no—
653#121—21no—
654#121—21no—
655#121—21no—
656#121—21no—
657#121—21no—
658#121—42no—
659#120—21no—
660#120—21no—
661#120—21no—
662#120—21no—
663#120—21no—
664#120—21no—
665#120—21no—
666#120—21no—
667#120—21no—
668#120—21no—
669#120—21no—
670#120—21no—
671#120—21no—
672#120—21no—
673#120—22no—
674#120—22no—
675#120—22no—
676#120—42no—
677#120—41no—
678#120D4×C4711yescharacteristic, complemented
679#120D4×C4711yescharacteristic, complemented
680#120D4×C4711yescharacteristic, complemented
681#120C23×C4711yescharacteristic
682#120C23×C4711yescharacteristic
683#120C23×C4711yescharacteristic
684C4×D4—21no—
685C4×D4—21no—
686C4×D4—21no—
687C4×D4—21no—
688C4×D4—21no—
689C4×D4—21no—
690#117—21no—
691#117D4×C4711yescharacteristic, complemented
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4D4×C4711yescharacteristic, complemented
701C2×C22⋊C4D4×C4711yescharacteristic, complemented
702#104—22no—
703#104—22no—
704#100—21no—
705#100C23×C4712yes—
706#99—21no—
707#99—21no—
708#99—22no—
709#99—22no—
710#99—22no—
711#99—22no—
712#99C23×C4712yes—
713#99C23×C4712yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—41no—
720C24—41no—
721C24—82no—
722C24C2×D4×C4711yescharacteristic
723C24C2×D4×C4711yescharacteristic
724C24C2×D4×C4711yescharacteristic
725C24C2×D4×C4711yescharacteristic
726C24C2×D4×C4711yescharacteristic, complemented
727#41—22no—
728#41—22no—
729#41—42no—
730#41—41no—
731#41—42no—
732#41—42no—
733#41—41no—
734#41—41no—
735#41—42no—
736#41—41no—
737#41—82no—
738C2×Q8—21no—
739C2×Q8—21no—
740C2×Q8C2×D4×C4711yescharacteristic, complemented
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—22no—
750C2×D4—22no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—42no—
769C2×D4—42no—
770C2×D4—41no—
771C2×D4—41no—
772C2×D4—41no—
773C2×D4—41no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—82no—
787C2×D4—82no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—84no—
791C2×D4C2×D4×C4711yescharacteristic
792C2×D4C2×D4×C4711yescharacteristic
793C2×D4C2×D4×C4711yescharacteristic
794C2×D4C2×D4×C4711yescharacteristic, complemented
795C2×D4C24×C4711yescharacteristic
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4C2×D4×C4711yescharacteristic
810C22×C4C2×D4×C4711yescharacteristic, complemented
811Q16—42no—
812SD16—42no—
813SD16—42no—
814D8—42no—
815M16—22no—
816M16—41no—
817C2×C8—41no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—42no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—21no—
835C22⋊C4—21no—
836C22⋊C4—21no—
837C22⋊C4—21no—
838C22⋊C4—21no—
839C22⋊C4—21no—
840C22⋊C4—21no—
841C22⋊C4—21no—
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—41no—
859C22⋊C4—41no—
860C22⋊C4—42no—
861C22⋊C4C2×D4×C4711yescharacteristic
862C22⋊C4C2×D4×C4711yescharacteristic
863C22⋊C4C2×D4×C4711yescharacteristic, complemented
864C22⋊C4C2×D4×C4711yescharacteristic, complemented
865C42—21no—
866C42—21no—
867C42C2×D4×C4711yescharacteristic, complemented
868C42C2×D4×C4711yescharacteristic, complemented
869C23—21no—
870C23—21no—
871C23—21no—
872C23—21no—
873C23—21no—
874C23—22no—
875C23—22no—
876C23—21no—
877C23—21no—
878C23—21no—
879C23—41no—
880C23—41no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—41no—
885C23—41no—
886C23—42no—
887C23—41no—
888C23—44no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—81no—
893C23—81no—
894C23—81no—
895C23—81no—
896C23—81no—
897C23—81no—
898C23—81no—
899C23—81no—
900C23—81no—
901C23—82no—
902C23—82no—
903C23—82no—
904C23—82no—
905C23—161no—
906C23#120×C4711yescharacteristic
907C23#120×C4711yescharacteristic
908C23#120×C4711yescharacteristic
909C23C22×D4×C4711yescharacteristic
910C23C22×D4×C4711yescharacteristic
911Q8—22no—
912Q8—41no—
913Q8—41no—
914Q8—81no—
915D4—22no—
916D4—41no—
917D4—41no—
918D4—41no—
919D4—41no—
920D4—41no—
921D4—41no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—42no—
936D4—81no—
937D4—81no—
938D4—81no—
939D4—81no—
940D4—81no—
941D4—81no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—84no—
951D4—84no—
952D4—162no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—82no—
982C2×C4—161no—
983C2×C4#120×C4711yescharacteristic
984C2×C4C22×D4×C4711yescharacteristic
985C8—42no—
986C22—22no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—42no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—41no—
1004C22—42no—
1005C22—41no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—81no—
1012C22—81no—
1013C22—81no—
1014C22—82no—
1015C22—82no—
1016C22—82no—
1017C22—81no—
1018C22—84no—
1019C22—82no—
1020C22—82no—
1021C22—82no—
1022C22—81no—
1023C22—162no—
1024C22—161no—
1025C22—161no—
1026C22C47×B(4,𝔽2)11yescharacteristic
1027C22C47×B(4,𝔽2)11yescharacteristic
1028C22C2×#120×C4711yescharacteristic
1029C4—21no—
1030C4—21no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—42no—
1038C4—41no—
1039C4—41no—
1040C4—82no—
1041C4—82no—
1042C2—21no—
1043C2—21no—
1044C2—21no—
1045C2—41no—
1046C2—41no—
1047C2—42no—
1048C2—41no—
1049C2—41no—
1050C2—81no—
1051C2—81no—
1052C2—81no—
1053C2—82no—
1054C2C2×C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C47C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C47
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C23×C47 ◁ C22×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3532C2semidirect
2. C47×#3026C2semidirect
3. C2×C47×B(4,𝔽2)C2semidirect
4. C47×#3019C2semidirect
5. C47×#2200C2semidirect
6. C47×#2199C2semidirect
7. C47×#2197C2semidirect
8. C47×#2196C2semidirect
9. C47×#2127C2semidirect
10. C47×#2121C2semidirect
11. C2×C47×AΣL(1,𝔽16)C2semidirect
12. C2×H(5,𝔽2)×C47C22semidirect
14. C47×H(3,𝔽4)C22semidirect
16. C47×#560C22semidirect
18. C47×#551C22semidirect
23. D42×C47C22semidirect
36. C47×#458C22semidirect
41. C47×B(4,𝔽2)C22semidirect
42. C47×B(4,𝔽2)C22semidirect
44. C47×#455C22semidirect
46. C47×#453C22semidirect
48. C2×#100×C47C22semidirect
51. C2×#99×C47C22semidirect
52. C2×#99×C47C22semidirect
53. C47×#354C22semidirect
54. C47×#353C22semidirect
55. C47×#352C22semidirect
56. C47×AΣL(1,𝔽16)C22semidirect
57. C47×AΣL(1,𝔽16)C22semidirect
58. C47×AΣL(1,𝔽16)C22semidirect
59. C25×C47D4semidirect
68. C2×#41×C47D4semidirect
78. C22×D4×C47D4semidirect
87. #127×C47D4semidirect
98. #124×C47D4semidirect
110. #123×C47D4semidirect
150. #120×C47D4semidirect
151. #120×C47D4semidirect
152. #120×C47D4semidirect
163. #117×C47D4semidirect
172. C2×C22⋊C4×C47D4semidirect
173. C2×C22⋊C4×C47D4semidirect
198. C24×C47C2×D4semidirect
212. C2×Q8×C47C2×D4semidirect
266. C2×D4×C47C2×D4semidirect
282. C22×C4×C47C2×D4semidirect
335. C22⋊C4×C47C2×D4semidirect
336. C22⋊C4×C47C2×D4semidirect
339. C42×C47C2×D4semidirect
340. C42×C47C2×D4semidirect
458. #33551C47direct (N × H)
515. #3532C2×C47semidirect
516. #3026C2×C47semidirect
517. C2×B(4,𝔽2)C2×C47semidirect
518. #3019C2×C47semidirect
519. #2200C2×C47semidirect
520. #2199C2×C47semidirect
521. #2197C2×C47semidirect
522. #2196C2×C47semidirect
523. #2127C2×C47semidirect
524. #2121C2×C47semidirect
525. C2×AΣL(1,𝔽16)C2×C47semidirect
539. C2×H(5,𝔽2)C22×C47semidirect
541. H(3,𝔽4)C22×C47semidirect
543. #560C22×C47semidirect
545. #551C22×C47semidirect
550. D42C22×C47semidirect
563. #458C22×C47semidirect
568. B(4,𝔽2)C22×C47semidirect
569. B(4,𝔽2)C22×C47semidirect
571. #455C22×C47semidirect
573. #453C22×C47semidirect
575. C2×#100C22×C47semidirect
578. C2×#99C22×C47semidirect
579. C2×#99C22×C47semidirect
580. #354C22×C47semidirect
581. #353C22×C47semidirect
582. #352C22×C47semidirect
583. AΣL(1,𝔽16)C22×C47semidirect
584. AΣL(1,𝔽16)C22×C47semidirect
585. AΣL(1,𝔽16)C22×C47semidirect
586. C47#33551direct (N × H)
587. C25D4×C47semidirect
596. C2×#41D4×C47semidirect
606. C22×D4D4×C47semidirect
615. #127D4×C47semidirect
626. #124D4×C47semidirect
638. #123D4×C47semidirect
678. #120D4×C47semidirect
679. #120D4×C47semidirect
680. #120D4×C47semidirect
691. #117D4×C47semidirect
700. C2×C22⋊C4D4×C47semidirect
701. C2×C22⋊C4D4×C47semidirect
726. C24C2×D4×C47semidirect
740. C2×Q8C2×D4×C47semidirect
794. C2×D4C2×D4×C47semidirect
810. C22×C4C2×D4×C47semidirect
863. C22⋊C4C2×D4×C47semidirect
864. C22⋊C4C2×D4×C47semidirect
867. C42C2×D4×C47semidirect
868. C42C2×D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#35322
C47×#30262
C2×C47×B(4,𝔽2)2
C47×#30192
C47×#22002
C47×#21992
C47×#21972
C47×#21962
C47×#21272
C47×#21212
C2×C47×AΣL(1,𝔽16)2
#3355147