Finite Group Databasebeta

← C47×#23889 #26063587

Subgroups — C47×#23889 #26063587

Order 12032.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#578C211yesmaximal, characteristic, complemented
2C2×C47×#577C211yesmaximal, characteristic, complemented
3C2×C47×#454C211yesmaximal, characteristic, complemented
4C2×C47×#455C211yesmaximal, characteristic, complemented
5C47×#3013C211yesmaximal, characteristic, complemented
6C47×#3012C211yesmaximal, characteristic, complemented
7C47×#2020C211yesmaximal, characteristic, complemented
8C47×#2019C211yesmaximal, characteristic, complemented
9C47×#2015C211yesmaximal, characteristic, complemented
10C47×#2007C211yesmaximal, characteristic, complemented
11C47×#1908C211yesmaximal, characteristic, complemented
12C47×#1907C211yesmaximal, characteristic, complemented
13C47×#1876C211yesmaximal, characteristic, complemented
14C47×#1876C211yesmaximal, characteristic, complemented
15C47×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C47C2211yescharacteristic
17C2×2−1+4×C47C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C47C2211yescharacteristic
19C47×#578—24no—
20C47×#578—24no—
21C47×#577—24no—
22C47×#577—24no—
23C2×#137×C47—21no—
24C2×#137×C47—21no—
25C2×#137×C47—21no—
26C2×#137×C47C2211yescharacteristic
27C2×#137×C47C2211yescharacteristic
28C2×#137×C47C2211yescharacteristic
29C2×#137×C47C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C47—21no—
31C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
33C2×#135×C47—21no—
34C2×#135×C47—21no—
35C2×#135×C47C2211yescharacteristic
36C2×#135×C47C2211yescharacteristic
37C22×Q16×C47—21no—
38C22×Q16×C47C2211yescharacteristic, complemented
39C22×SD16×C47—21no—
40C22×SD16×C47C2211yescharacteristic
41C2×#131×C47C2211yescharacteristic
42C2×#131×C47C2211yescharacteristic, complemented
43C47×#537C2211yescharacteristic
44C2×#124×C47C2211yescharacteristic
45C47×#455—24no—
46C47×#454—24no—
47C47×#452—21no—
48C47×#452—21no—
49C47×#451—21no—
50C47×#450—21no—
51C47×#449—21no—
52C47×#449—21no—
53C47×#448—21no—
54C47×#447—21no—
55C2×#104×C47C2211yescharacteristic
56C2×#104×C47C2211yescharacteristic
57C2×#104×C47C2211yescharacteristic, complemented
58C2×#104×C47C2211yescharacteristic, complemented
59C47×#417C2211yescharacteristic
60C47×#417C2211yescharacteristic, complemented
61C2×#103×C47C2211yescharacteristic, complemented
62C2×#102×C47C2211yescharacteristic
63C2×#101×C47C2211yescharacteristic, complemented
64C2×#101×C47C2211yescharacteristic, complemented
65C2×#100×C47C2211yescharacteristic
66C47×#408C2211yescharacteristic
67C47×#408C2211yescharacteristic, complemented
68C47×#391C2211yescharacteristic, complemented
69C47×#343C2211yescharacteristic, complemented
70C47×#341C2211yescharacteristic, complemented
71C47×#341C2211yescharacteristic, complemented
72C47×#336C2211yescharacteristic, complemented
732−1+4×C47—22no—
742−1+4×C47—22no—
752−1+4×C47—22no—
762−1+4×C47—22no—
772−1+4×C47—22no—
782−1+4×C47—41no—
792−1+4×C47—41no—
802−1+4×C47D414yescomplemented
81H(5,𝔽2)×C47—22no—
82H(5,𝔽2)×C47—22no—
83H(5,𝔽2)×C47—22no—
84H(5,𝔽2)×C47—41no—
85C2×#41×C47—21no—
86C2×#41×C47—21no—
87C2×#41×C47—21no—
88C2×#41×C47—21no—
89C2×#41×C47—21no—
90C2×#41×C47—21no—
91C2×#41×C47—41no—
92C2×#41×C47—41no—
93C2×#41×C47C2311yescharacteristic
94C2×#41×C47C2311yescharacteristic
95C2×#41×C47C2311yescharacteristic
96C2×#41×C47C2311yescharacteristic
97C22×Q8×C47—21no—
98C22×Q8×C47—21no—
99C22×Q8×C47—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47C2311yescharacteristic
102C22×Q8×C47C2311yescharacteristic
103C22×D4×C47—21no—
104C22×D4×C47—21no—
105C22×D4×C47—41no—
106C22×D4×C47C2311yescharacteristic
107#137×C47—28no—
108#137×C47—28no—
109#137×C47—28no—
110#137×C47—22no—
111#137×C47—22no—
112#137×C47—22no—
113#137×C47—22no—
114#137×C47—22no—
115#137×C47—22no—
116#137×C47—41no—
117#137×C47D414yescomplemented
118AGL(1,ℤ/8)×C47—28no—
119AGL(1,ℤ/8)×C47—22no—
120AGL(1,ℤ/8)×C47—22no—
121AGL(1,ℤ/8)×C47—41no—
122AGL(1,ℤ/8)×C47D414yescomplemented
123#135×C47—28no—
124#135×C47—28no—
125#135×C47—22no—
126#135×C47—22no—
127#135×C47—22no—
128#135×C47—22no—
129C2×Q16×C47—28no—
130C2×Q16×C47—21no—
131C2×Q16×C47—21no—
132C2×Q16×C47—22no—
133C2×Q16×C47—22no—
134C2×Q16×C47—21no—
135C2×Q16×C47—21no—
136C2×Q16×C47—21no—
137C2×Q16×C47—21no—
138C2×Q16×C47D411yescharacteristic
139C2×Q16×C47D411yescharacteristic
140C2×SD16×C47—28no—
141C2×SD16×C47—21no—
142C2×SD16×C47—22no—
143C2×SD16×C47—21no—
144C2×SD16×C47—22no—
145C2×SD16×C47—21no—
146C2×SD16×C47—21no—
147C2×SD16×C47—21no—
148C2×SD16×C47—21no—
149C2×SD16×C47—21no—
150C2×SD16×C47—21no—
151C2×SD16×C47D411yescharacteristic
152C2×SD16×C47D411yescharacteristic
153C2×SD16×C47D411yescharacteristic
154C2×SD16×C47D411yescharacteristic
155C2×D8×C47—21no—
156C2×D8×C47—21no—
157C2×D8×C47D411yescharacteristic
158C2×D8×C47D411yescharacteristic
159#131×C47—22no—
160#131×C47—22no—
161#131×C47—22no—
162#131×C47—22no—
163C2×M16×C47—21no—
164C2×M16×C47—21no—
165C2×M16×C47C2311yescharacteristic
166C2×M16×C47C2311yescharacteristic
167C2×M16×C47C2311yescharacteristic
168C2×M16×C47C2311yescharacteristic
169C22×C8×C47—21no—
170C22×C8×C47—21no—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173#124×C47—22no—
174#124×C47—22no—
175C22⋊Q8×C47—21no—
176C22⋊Q8×C47—21no—
177#121×C47—21no—
178#121×C47—21no—
179#121×C47—41no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—41no—
182C2×C42×C47C2311yescharacteristic
183#104×C47—22no—
184#104×C47—22no—
185#104×C47—22no—
186#104×C47—22no—
187#103×C47—21no—
188#103×C47—21no—
189#103×C47—21no—
190#103×C47—21no—
191#102×C47—21no—
192#102×C47—21no—
193#102×C47—21no—
194#102×C47—21no—
195#101×C47—22no—
196#101×C47—41no—
197#100×C47—22no—
198C22⋊C8×C47—21no—
199C22⋊C8×C47—21no—
200C22⋊C8×C47—21no—
201C22⋊C8×C47—21no—
202#95×C47—41no—
203C24×C47—21no—
204C24×C47—41no—
205#41×C47—21no—
206#41×C47—21no—
207#41×C47—21no—
208#41×C47—21no—
209#41×C47—24no—
210#41×C47—24no—
211#41×C47—24no—
212#41×C47—24no—
213#41×C47—21no—
214#41×C47—21no—
215#41×C47—21no—
216#41×C47—21no—
217#41×C47—21no—
218#41×C47—21no—
219#41×C47—21no—
220#41×C47—21no—
221#41×C47—44no—
222#41×C47—42no—
223#41×C47—42no—
224#41×C47—42no—
225#41×C47—44no—
226#41×C47—42no—
227#41×C47—44no—
228#41×C47—42no—
229#41×C47—42no—
230#41×C47—44no—
231#41×C47—42no—
232#41×C47—42no—
233#41×C47C2×D412yes—
234#41×C47C2×D412yes—
235#41×C47C2×D412yes—
236#41×C47C2×D412yes—
237C2×Q8×C47—21no—
238C2×Q8×C47—21no—
239C2×Q8×C47—24no—
240C2×Q8×C47—24no—
241C2×Q8×C47—24no—
242C2×Q8×C47—21no—
243C2×Q8×C47—21no—
244C2×Q8×C47—21no—
245C2×Q8×C47—21no—
246C2×Q8×C47—21no—
247C2×Q8×C47—21no—
248C2×Q8×C47—21no—
249C2×Q8×C47—21no—
250C2×Q8×C47—41no—
251C2×Q8×C47—41no—
252C2×Q8×C47—42no—
253C2×Q8×C47—42no—
254C2×Q8×C47—42no—
255C2×Q8×C47—42no—
256C2×Q8×C47—42no—
257C2×Q8×C47C2×D411yescharacteristic
258C2×Q8×C47C2×D411yescharacteristic
259C2×Q8×C47C2×D412yes—
260C2×Q8×C47C2×D412yes—
261C2×Q8×C47C2×D411yescharacteristic
262C2×Q8×C47C2×D411yescharacteristic
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—24no—
266C2×D4×C47—21no—
267C2×D4×C47—21no—
268C2×D4×C47—21no—
269C2×D4×C47—21no—
270C2×D4×C47—21no—
271C2×D4×C47—21no—
272C2×D4×C47—21no—
273C2×D4×C47—42no—
274C2×D4×C47—41no—
275C2×D4×C47—41no—
276C2×D4×C47—42no—
277C2×D4×C47—44no—
278C2×D4×C47—44no—
279C2×D4×C47—41no—
280C2×D4×C47—41no—
281C2×D4×C47—42no—
282C2×D4×C47—41no—
283C2×D4×C47C2×D411yescharacteristic
284C2×D4×C47C2×D411yescharacteristic
285C2×D4×C47C2×D412yes—
286C2×D4×C47C2×D411yescharacteristic
287C2×D4×C47C2×D411yescharacteristic
288C22×C4×C47—21no—
289C22×C4×C47—21no—
290C22×C4×C47—21no—
291C22×C4×C47—21no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—21no—
295C22×C4×C47—21no—
296C22×C4×C47—41no—
297C22×C4×C47—41no—
298C22×C4×C47—41no—
299C22×C4×C47—41no—
300C22×C4×C47—41no—
301C22×C4×C47C2411yescharacteristic
302Q16×C47—24no—
303Q16×C47—24no—
304Q16×C47—24no—
305Q16×C47—24no—
306Q16×C47—22no—
307Q16×C47—24no—
308Q16×C47—22no—
309Q16×C47—42no—
310SD16×C47—24no—
311SD16×C47—24no—
312SD16×C47—24no—
313SD16×C47—24no—
314SD16×C47—22no—
315SD16×C47—24no—
316SD16×C47—22no—
317SD16×C47—24no—
318SD16×C47—22no—
319SD16×C47—22no—
320SD16×C47—42no—
321SD16×C47—42no—
322D8×C47—24no—
323D8×C47—22no—
324D8×C47—22no—
325D8×C47—42no—
326M16×C47—24no—
327M16×C47—24no—
328M16×C47—21no—
329M16×C47—21no—
330M16×C47—21no—
331M16×C47—21no—
332M16×C47—21no—
333M16×C47—21no—
334M16×C47C2×D412yes—
335M16×C47C2×D412yes—
336C2×C8×C47—24no—
337C2×C8×C47—24no—
338C2×C8×C47—21no—
339C2×C8×C47—21no—
340C2×C8×C47—21no—
341C2×C8×C47—21no—
342C2×C8×C47—21no—
343C2×C8×C47—21no—
344C2×C8×C47—21no—
345C2×C8×C47—21no—
346C2×C8×C47C2×D411yescharacteristic
347C2×C8×C47C2×D411yescharacteristic
348C2×C8×C47C2×D411yescharacteristic
349C2×C8×C47C2×D411yescharacteristic
350C4⋊C4×C47—21no—
351C4⋊C4×C47—21no—
352C4⋊C4×C47—41no—
353C22⋊C4×C47—44no—
354C22⋊C4×C47—41no—
355C22⋊C4×C47—41no—
356C42×C47—21no—
357C42×C47—21no—
358C23×C47—21no—
359C23×C47—21no—
360C23×C47—21no—
361C23×C47—21no—
362C23×C47—22no—
363C23×C47—44no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—81no—
367C23×C47—81no—
368C23×C47—161no—
369C23×C47—161no—
370C23×C47H(5,𝔽2)11yescharacteristic
371Q8×C47—21no—
372Q8×C47—21no—
373Q8×C47—22no—
374Q8×C47—22no—
375Q8×C47—22no—
376Q8×C47—21no—
377Q8×C47—21no—
378Q8×C47—21no—
379Q8×C47—22no—
380Q8×C47—21no—
381Q8×C47—44no—
382Q8×C47—44no—
383Q8×C47—41no—
384Q8×C47—41no—
385Q8×C47—41no—
386Q8×C47—41no—
387Q8×C47#12012yes—
388Q8×C47#12012yes—
389D4×C47—22no—
390D4×C47—22no—
391D4×C47—22no—
392D4×C47—22no—
393D4×C47—22no—
394D4×C47—21no—
395D4×C47—21no—
396D4×C47—21no—
397D4×C47—21no—
398D4×C47—21no—
399D4×C47—22no—
400D4×C47—21no—
401D4×C47—44no—
402D4×C47—44no—
403D4×C47—44no—
404D4×C47—44no—
405D4×C47—41no—
406D4×C47—41no—
407D4×C47—41no—
408D4×C47—41no—
409D4×C47—41no—
410D4×C47—41no—
411D4×C47—161no—
412D4×C47#12012yes—
413D4×C47#12012yes—
414C2×C4×C47—21no—
415C2×C4×C47—21no—
416C2×C4×C47—22no—
417C2×C4×C47—22no—
418C2×C4×C47—22no—
419C2×C4×C47—22no—
420C2×C4×C47—22no—
421C2×C4×C47—22no—
422C2×C4×C47—21no—
423C2×C4×C47—21no—
424C2×C4×C47—44no—
425C2×C4×C47—44no—
426C2×C4×C47—44no—
427C2×C4×C47—44no—
428C2×C4×C47—44no—
429C2×C4×C47—41no—
430C2×C4×C47—41no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—41no—
435C2×C4×C47—41no—
436C2×C4×C47—41no—
437C2×C4×C47—41no—
438C2×C4×C47—41no—
439C2×C4×C47—41no—
440C2×C4×C47—41no—
441C2×C4×C47—81no—
442C2×C4×C47C22×D411yescharacteristic
443C2×C4×C47C22×D411yescharacteristic
444C2×C4×C47C22×D411yescharacteristic
445C2×C4×C47C22×D411yescharacteristic
446C2×C4×C47C22×D411yescharacteristic
447C2×C4×C47H(5,𝔽2)11yescharacteristic
448C8×C47—21no—
449C8×C47—21no—
450C8×C47—22no—
451C8×C47—22no—
452C8×C47—21no—
453C8×C47—21no—
454C8×C47—41no—
455C8×C47—41no—
456#23889C4711yesmaximal, characteristic, direct product factor, Sylow
457C22×C47—21no—
458C22×C47—21no—
459C22×C47—22no—
460C22×C47—22no—
461C22×C47—41no—
462C22×C47—41no—
463C22×C47—41no—
464C22×C47—41no—
465C22×C47—41no—
466C22×C47—41no—
467C22×C47—42no—
468C22×C47—41no—
469C22×C47—41no—
470C22×C47—41no—
471C22×C47—41no—
472C22×C47—82no—
473C22×C47—81no—
474C22×C47—81no—
475C22×C47—161no—
476C22×C47—164no—
477C22×C47#53411yescharacteristic
478C22×C47D4211yescharacteristic
479C22×C47D4211yescharacteristic
480C4×C47—22no—
481C4×C47—22no—
482C4×C47—41no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—41no—
486C4×C47—81no—
487C4×C47—81no—
488C4×C47C2×#12011yescharacteristic
489C4×C47C2×#12011yescharacteristic
490C4×C47D4211yescharacteristic
491C4×C47D4211yescharacteristic
492C2×#578C2×C4711yescharacteristic, complemented
493C2×#577C2×C4711yescharacteristic, complemented
494C2×#454C2×C4711yescharacteristic, complemented
495C2×#455C2×C4711yescharacteristic, complemented
496#3013C2×C4711yescharacteristic, complemented
497#3012C2×C4711yescharacteristic, complemented
498#2020C2×C4711yescharacteristic, complemented
499#2019C2×C4711yescharacteristic, complemented
500#2015C2×C4711yescharacteristic, complemented
501#2007C2×C4711yescharacteristic, complemented
502#1908C2×C4711yescharacteristic, complemented
503#1907C2×C4711yescharacteristic, complemented
504#1876C2×C4711yescharacteristic, complemented
505#1876C2×C4711yescharacteristic, complemented
506#1793C2×C4711yescharacteristic, complemented
507C2×C47—21no—
508C2×C47—21no—
509C2×C47—42no—
510C2×C47—42no—
511C2×C47—81no—
512C2×C47—81no—
513C2×C47—82no—
514C2×C47#240311yescharacteristic
515C2×C47#328911yescharacteristic
516C2×C47#329011yescharacteristic
517C2×2−1+4C22×C4711yescharacteristic
518C2×2−1+4C22×C4711yescharacteristic, complemented
519C2×H(5,𝔽2)C22×C4711yescharacteristic
520#578—24no—
521#578—24no—
522#577—24no—
523#577—24no—
524C2×#137—21no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137C22×C4711yescharacteristic
528C2×#137C22×C4711yescharacteristic
529C2×#137C22×C4711yescharacteristic
530C2×#137C22×C4711yescharacteristic, complemented
531C2×AGL(1,ℤ/8)—21no—
532C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
533C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
534C2×#135—21no—
535C2×#135—21no—
536C2×#135C22×C4711yescharacteristic
537C2×#135C22×C4711yescharacteristic
538C22×Q16—21no—
539C22×Q16C22×C4711yescharacteristic, complemented
540C22×SD16—21no—
541C22×SD16C22×C4711yescharacteristic
542C2×#131C22×C4711yescharacteristic
543C2×#131C22×C4711yescharacteristic, complemented
544#537C22×C4711yescharacteristic
545C2×#124C22×C4711yescharacteristic
546#455—24no—
547#454—24no—
548#452—21no—
549#452—21no—
550#451—21no—
551#450—21no—
552#449—21no—
553#449—21no—
554#448—21no—
555#447—21no—
556C2×#104C22×C4711yescharacteristic
557C2×#104C22×C4711yescharacteristic
558C2×#104C22×C4711yescharacteristic, complemented
559C2×#104C22×C4711yescharacteristic, complemented
560#417C22×C4711yescharacteristic
561#417C22×C4711yescharacteristic, complemented
562C2×#103C22×C4711yescharacteristic, complemented
563C2×#102C22×C4711yescharacteristic
564C2×#101C22×C4711yescharacteristic, complemented
565C2×#101C22×C4711yescharacteristic, complemented
566C2×#100C22×C4711yescharacteristic
567#408C22×C4711yescharacteristic
568#408C22×C4711yescharacteristic, complemented
569#391C22×C4711yescharacteristic, complemented
570#343C22×C4711yescharacteristic, complemented
571#341C22×C4711yescharacteristic, complemented
572#341C22×C4711yescharacteristic, complemented
573#336C22×C4711yescharacteristic, complemented
574C47#2388911yescharacteristic, direct product factor, Sylow
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C4714yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C4711yescharacteristic
596C2×#41C23×C4711yescharacteristic
597C2×#41C23×C4711yescharacteristic
598C2×#41C23×C4711yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C4711yescharacteristic
604C22×Q8C23×C4711yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C4711yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C4714yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C4714yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C4711yescharacteristic
641C2×Q16D4×C4711yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C4711yescharacteristic
654C2×SD16D4×C4711yescharacteristic
655C2×SD16D4×C4711yescharacteristic
656C2×SD16D4×C4711yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C4711yescharacteristic
660C2×D8D4×C4711yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C4711yescharacteristic
668C2×M16C23×C4711yescharacteristic
669C2×M16C23×C4711yescharacteristic
670C2×M16C23×C4711yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C4711yescharacteristic
674C22×C8C23×C4711yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C4711yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C4711yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C4712yes—
736#41C2×D4×C4712yes—
737#41C2×D4×C4712yes—
738#41C2×D4×C4712yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C4711yescharacteristic
760C2×Q8C2×D4×C4711yescharacteristic
761C2×Q8C2×D4×C4712yes—
762C2×Q8C2×D4×C4712yes—
763C2×Q8C2×D4×C4711yescharacteristic
764C2×Q8C2×D4×C4711yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C4711yescharacteristic
786C2×D4C2×D4×C4711yescharacteristic
787C2×D4C2×D4×C4712yes—
788C2×D4C2×D4×C4711yescharacteristic
789C2×D4C2×D4×C4711yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C4711yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C4712yes—
837M16C2×D4×C4712yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C4711yescharacteristic
849C2×C8C2×D4×C4711yescharacteristic
850C2×C8C2×D4×C4711yescharacteristic
851C2×C8C2×D4×C4711yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C4711yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C4712yes—
890Q8#120×C4712yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C4712yes—
915D4#120×C4712yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C4711yescharacteristic
945C2×C4C22×D4×C4711yescharacteristic
946C2×C4C22×D4×C4711yescharacteristic
947C2×C4C22×D4×C4711yescharacteristic
948C2×C4C22×D4×C4711yescharacteristic
949C2×C4H(5,𝔽2)×C4711yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22C47×#53411yescharacteristic
979C22D42×C4711yescharacteristic
980C22D42×C4711yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C4711yescharacteristic
990C4C2×#120×C4711yescharacteristic
991C4D42×C4711yescharacteristic
992C4D42×C4711yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C47×#240311yescharacteristic
1001C2C47×#328911yescharacteristic
1002C2C47×#329011yescharacteristic
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. C2×C47×#578C2semidirect
2. C2×C47×#577C2semidirect
3. C2×C47×#454C2semidirect
4. C2×C47×#455C2semidirect
5. C47×#3013C2semidirect
6. C47×#3012C2semidirect
7. C47×#2020C2semidirect
8. C47×#2019C2semidirect
9. C47×#2015C2semidirect
10. C47×#2007C2semidirect
11. C47×#1908C2semidirect
12. C47×#1907C2semidirect
13. C47×#1876C2semidirect
14. C47×#1876C2semidirect
15. C47×#1793C2semidirect
17. C2×2−1+4×C47C22semidirect
29. C2×#137×C47C22semidirect
38. C22×Q16×C47C22semidirect
42. C2×#131×C47C22semidirect
57. C2×#104×C47C22semidirect
58. C2×#104×C47C22semidirect
60. C47×#417C22semidirect
61. C2×#103×C47C22semidirect
63. C2×#101×C47C22semidirect
64. C2×#101×C47C22semidirect
67. C47×#408C22semidirect
68. C47×#391C22semidirect
69. C47×#343C22semidirect
70. C47×#341C22semidirect
71. C47×#341C22semidirect
72. C47×#336C22semidirect
80. 2−1+4×C47D4semidirect
117. #137×C47D4semidirect
122. AGL(1,ℤ/8)×C47D4semidirect
456. #23889C47direct (N × H)
492. C2×#578C2×C47semidirect
493. C2×#577C2×C47semidirect
494. C2×#454C2×C47semidirect
495. C2×#455C2×C47semidirect
496. #3013C2×C47semidirect
497. #3012C2×C47semidirect
498. #2020C2×C47semidirect
499. #2019C2×C47semidirect
500. #2015C2×C47semidirect
501. #2007C2×C47semidirect
502. #1908C2×C47semidirect
503. #1907C2×C47semidirect
504. #1876C2×C47semidirect
505. #1876C2×C47semidirect
506. #1793C2×C47semidirect
518. C2×2−1+4C22×C47semidirect
530. C2×#137C22×C47semidirect
539. C22×Q16C22×C47semidirect
543. C2×#131C22×C47semidirect
558. C2×#104C22×C47semidirect
559. C2×#104C22×C47semidirect
561. #417C22×C47semidirect
562. C2×#103C22×C47semidirect
564. C2×#101C22×C47semidirect
565. C2×#101C22×C47semidirect
568. #408C22×C47semidirect
569. #391C22×C47semidirect
570. #343C22×C47semidirect
571. #341C22×C47semidirect
572. #341C22×C47semidirect
573. #336C22×C47semidirect
574. C47#23889direct (N × H)
582. 2−1+4D4×C47semidirect
619. #137D4×C47semidirect
624. AGL(1,ℤ/8)D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5782
C2×C47×#5772
C2×C47×#4542
C2×C47×#4552
C47×#30132
C47×#30122
C47×#20202
C47×#20192
C47×#20152
C47×#20072
C47×#19082
C47×#19072
C47×#18762
C47×#17932
#2388947