Finite Group Databasebeta

← C47×#23860 #26063558

Subgroups — C47×#23860 #26063558

Order 12032.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
2C2×D42×C47C211yesmaximal, characteristic, complemented
3C2×C47×#449C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C2×C47×#447C211yesmaximal, characteristic, complemented
6C47×#2407C211yesmaximal, characteristic, complemented
7C47×#2014C211yesmaximal, characteristic, complemented
8C47×#2011C211yesmaximal, characteristic, complemented
9C47×#2000C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1895C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1870C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic, complemented
17C23×D4×C47—21no—
18C23×D4×C47C2211yescharacteristic
19C23×D4×C47C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C47—24no—
21C2×AGL(1,ℤ/8)×C47—24no—
22C2×AGL(1,ℤ/8)×C47—24no—
23C22×SD16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic, complemented
25C22×SD16×C47C2211yescharacteristic, complemented
26C22×D8×C47C2211yescharacteristic
27C22×D8×C47C2211yescharacteristic, complemented
28C22×D8×C47C2211yescharacteristic, complemented
29C22×M16×C47C2211yescharacteristic, complemented
30D42×C47—24no—
31D42×C47—24no—
32C2×#127×C47C2211yescharacteristic
33C2×C22⋊Q8×C47C2211yescharacteristic, complemented
34C2×#121×C47—21no—
35C2×#121×C47C2211yescharacteristic
36C2×#121×C47C2211yescharacteristic
37C2×#121×C47C2211yescharacteristic, complemented
38C2×#120×C47—21no—
39C2×#120×C47—21no—
40C2×C4×D4×C47C2211yescharacteristic
41C2×C4×D4×C47C2211yescharacteristic
42C47×#450—24no—
43C47×#449—24no—
44C47×#447—24no—
45C2×#103×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic, complemented
49C2×#102×C47C2211yescharacteristic, complemented
50C2×#102×C47C2211yescharacteristic, complemented
51C2×#102×C47C2211yescharacteristic, complemented
52C2×#102×C47C2211yescharacteristic, complemented
53C2×C22⋊C8×C47C2211yescharacteristic, complemented
54C2×C22⋊C8×C47C2211yescharacteristic, complemented
55C2×C22⋊C8×C47C2211yescharacteristic, complemented
56C47×#394—21no—
57C47×#392—21no—
58C47×#391C2211yescharacteristic, complemented
59C47×#390C2211yescharacteristic, complemented
60C47×#386—21no—
61C47×#385—21no—
62C47×#380C2211yescharacteristic, complemented
63C47×#340C2211yescharacteristic, complemented
64C47×#340C2211yescharacteristic, complemented
65C47×#336C2211yescharacteristic, complemented
66C47×#336C2211yescharacteristic, complemented
67C25×C47—21no—
68C25×C47—21no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—22no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C22×Q8×C47C2311yescharacteristic
76C22×D4×C47—22no—
77C22×D4×C47—22no—
78C22×D4×C47—28no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—22no—
82C22×D4×C47—22no—
83C22×D4×C47—22no—
84C22×D4×C47—22no—
85C22×D4×C47—21no—
86C22×D4×C47—21no—
87C22×D4×C47—21no—
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—22no—
91C22×D4×C47—21no—
92C22×D4×C47—41no—
93C22×D4×C47—41no—
94C22×D4×C47—41no—
95C22×D4×C47—41no—
96C22×D4×C47—44no—
97C22×D4×C47—44no—
98C22×D4×C47D411yescharacteristic
99C22×D4×C47D414yescomplemented
100C22×D4×C47C2311yescharacteristic
101C22×D4×C47C2311yescharacteristic
102C22×D4×C47C2311yescharacteristic
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C23×C4×C47—21no—
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108AGL(1,ℤ/8)×C47—232no—
109C2×SD16×C47—22no—
110C2×SD16×C47—22no—
111C2×SD16×C47—22no—
112C2×SD16×C47—22no—
113C2×SD16×C47—22no—
114C2×SD16×C47—22no—
115C2×SD16×C47—22no—
116C2×SD16×C47—41no—
117C2×SD16×C47D414yescomplemented
118C2×D8×C47—22no—
119C2×D8×C47—22no—
120C2×D8×C47—22no—
121C2×D8×C47—22no—
122C2×D8×C47—22no—
123C2×D8×C47—22no—
124C2×D8×C47—22no—
125C2×D8×C47—41no—
126C2×D8×C47D414yescomplemented
127C2×M16×C47—22no—
128C2×M16×C47—22no—
129C2×M16×C47—22no—
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134#127×C47—22no—
135#127×C47—22no—
136C22⋊Q8×C47—22no—
137C22⋊Q8×C47—41no—
138#121×C47—28no—
139#121×C47—22no—
140#121×C47—22no—
141#121×C47—22no—
142#121×C47—22no—
143#121×C47—41no—
144#121×C47D414yescomplemented
145#120×C47—28no—
146#120×C47—28no—
147C4×D4×C47—22no—
148C4×D4×C47—22no—
149C4×D4×C47—22no—
150C4×D4×C47—22no—
151C2×C4⋊C4×C47—21no—
152C2×C4⋊C4×C47D411yescharacteristic
153C2×C4⋊C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C22⋊C4×C47—21no—
157C2×C22⋊C4×C47—21no—
158C2×C22⋊C4×C47—21no—
159C2×C22⋊C4×C47—21no—
160C2×C22⋊C4×C47—21no—
161C2×C22⋊C4×C47—21no—
162C2×C22⋊C4×C47—21no—
163C2×C22⋊C4×C47—21no—
164C2×C22⋊C4×C47D411yescharacteristic
165C2×C22⋊C4×C47D411yescharacteristic
166C2×C42×C47C2311yescharacteristic
167#103×C47—22no—
168#102×C47—22no—
169#102×C47—22no—
170#102×C47—22no—
171#102×C47—22no—
172#102×C47—22no—
173#102×C47—41no—
174#102×C47—41no—
175C22⋊C8×C47—22no—
176C22⋊C8×C47—22no—
177C22⋊C8×C47—22no—
178#95×C47—21no—
179#95×C47—21no—
180#95×C47—21no—
181C24×C47—21no—
182C24×C47—24no—
183C24×C47—21no—
184C24×C47—21no—
185C24×C47—21no—
186C24×C47—24no—
187C24×C47—42no—
188C24×C47—42no—
189C24×C47—42no—
190C24×C47—42no—
191C24×C47—42no—
192C24×C47—42no—
193C24×C47—42no—
194C24×C47—42no—
195C24×C47—81no—
196C24×C47—81no—
197C24×C47—81no—
198C24×C47—81no—
199C24×C47C2×D411yescharacteristic
200C24×C47C2×D411yescharacteristic
201#41×C47—28no—
202#41×C47—44no—
203#41×C47—44no—
204#41×C47—44no—
205C2×Q8×C47—21no—
206C2×Q8×C47—21no—
207C2×Q8×C47—21no—
208C2×Q8×C47—21no—
209C2×Q8×C47—21no—
210C2×Q8×C47C2×D412yescomplemented
211C2×D4×C47—22no—
212C2×D4×C47—22no—
213C2×D4×C47—28no—
214C2×D4×C47—24no—
215C2×D4×C47—24no—
216C2×D4×C47—24no—
217C2×D4×C47—24no—
218C2×D4×C47—24no—
219C2×D4×C47—24no—
220C2×D4×C47—22no—
221C2×D4×C47—21no—
222C2×D4×C47—21no—
223C2×D4×C47—21no—
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—21no—
239C2×D4×C47—44no—
240C2×D4×C47—44no—
241C2×D4×C47—44no—
242C2×D4×C47—42no—
243C2×D4×C47—42no—
244C2×D4×C47—42no—
245C2×D4×C47—42no—
246C2×D4×C47—42no—
247C2×D4×C47—42no—
248C2×D4×C47—44no—
249C2×D4×C47—44no—
250C2×D4×C47—432no—
251C2×D4×C47—44no—
252C2×D4×C47—42no—
253C2×D4×C47—42no—
254C2×D4×C47—42no—
255C2×D4×C47—42no—
256C2×D4×C47—42no—
257C2×D4×C47—42no—
258C2×D4×C47—44no—
259C2×D4×C47—42no—
260C2×D4×C47—42no—
261C2×D4×C47—42no—
262C2×D4×C47—81no—
263C2×D4×C47—81no—
264C2×D4×C47—81no—
265C2×D4×C47C2×D412yes—
266C2×D4×C47C2×D412yes—
267C2×D4×C47C2×D412yes—
268C2×D4×C47C2×D412yes—
269C2×D4×C47C2×D412yes—
270C2×D4×C47C2×D412yescomplemented
271C22×C4×C47—21no—
272C22×C4×C47—21no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—24no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—21no—
279C22×C4×C47—21no—
280C22×C4×C47—21no—
281C22×C4×C47—21no—
282C22×C4×C47—21no—
283C22×C4×C47—21no—
284C22×C4×C47—21no—
285C22×C4×C47—21no—
286C22×C4×C47—42no—
287C22×C4×C47—42no—
288C22×C4×C47—42no—
289C22×C4×C47—42no—
290C22×C4×C47—42no—
291C22×C4×C47C2×D411yescharacteristic
292C22×C4×C47C2×D411yescharacteristic
293C22×C4×C47C2×D411yescharacteristic
294C22×C4×C47C2×D412yes—
295C22×C4×C47C2×D412yes—
296C22×C4×C47C2×D411yescharacteristic
297C22×C4×C47C2411yescharacteristic
298SD16×C47—28no—
299SD16×C47—28no—
300SD16×C47—44no—
301D8×C47—28no—
302D8×C47—28no—
303D8×C47—44no—
304M16×C47—28no—
305C2×C8×C47—21no—
306C2×C8×C47—21no—
307C2×C8×C47—21no—
308C2×C8×C47—21no—
309C2×C8×C47—21no—
310C2×C8×C47—21no—
311C2×C8×C47—21no—
312C2×C8×C47—21no—
313C2×C8×C47—21no—
314C2×C8×C47—21no—
315C2×C8×C47C2×D412yescomplemented
316C2×C8×C47C2×D412yescomplemented
317C4⋊C4×C47—22no—
318C4⋊C4×C47—21no—
319C4⋊C4×C47—21no—
320C4⋊C4×C47—21no—
321C4⋊C4×C47—21no—
322C4⋊C4×C47—21no—
323C4⋊C4×C47—42no—
324C4⋊C4×C47C2×D412yes—
325C22⋊C4×C47—24no—
326C22⋊C4×C47—24no—
327C22⋊C4×C47—22no—
328C22⋊C4×C47—24no—
329C22⋊C4×C47—22no—
330C22⋊C4×C47—42no—
331C22⋊C4×C47—42no—
332C22⋊C4×C47—42no—
333C22⋊C4×C47—81no—
334C22⋊C4×C47—81no—
335C42×C47—21no—
336C42×C47—21no—
337C23×C47—21no—
338C23×C47—22no—
339C23×C47—21no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—21no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—21no—
346C23×C47—21no—
347C23×C47—21no—
348C23×C47—21no—
349C23×C47—21no—
350C23×C47—21no—
351C23×C47—21no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—48no—
356C23×C47—48no—
357C23×C47—48no—
358C23×C47—48no—
359C23×C47—41no—
360C23×C47—41no—
361C23×C47—41no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—41no—
367C23×C47—41no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—41no—
377C23×C47—41no—
378C23×C47—41no—
379C23×C47—41no—
380C23×C47—41no—
381C23×C47—84no—
382C23×C47—84no—
383C23×C47—84no—
384C23×C47—84no—
385C23×C47—84no—
386C23×C47—84no—
387C23×C47—84no—
388C23×C47—84no—
389C23×C47—84no—
390C23×C47—84no—
391C23×C47#12012yes—
392C23×C47AGL(1,ℤ/8)12yescomplemented
393C23×C47C22×D411yescharacteristic
394Q8×C47—22no—
395Q8×C47—22no—
396Q8×C47—41no—
397Q8×C47—41no—
398D4×C47—28no—
399D4×C47—22no—
400D4×C47—22no—
401D4×C47—22no—
402D4×C47—22no—
403D4×C47—22no—
404D4×C47—22no—
405D4×C47—22no—
406D4×C47—22no—
407D4×C47—22no—
408D4×C47—48no—
409D4×C47—48no—
410D4×C47—48no—
411D4×C47—48no—
412D4×C47—48no—
413D4×C47—48no—
414D4×C47—41no—
415D4×C47—41no—
416D4×C47—41no—
417D4×C47—41no—
418D4×C47—41no—
419D4×C47—41no—
420D4×C47—84no—
421D4×C47—84no—
422D4×C47#12014yes—
423C2×C4×C47—21no—
424C2×C4×C47—21no—
425C2×C4×C47—21no—
426C2×C4×C47—21no—
427C2×C4×C47—22no—
428C2×C4×C47—22no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—21no—
432C2×C4×C47—21no—
433C2×C4×C47—22no—
434C2×C4×C47—21no—
435C2×C4×C47—22no—
436C2×C4×C47—21no—
437C2×C4×C47—21no—
438C2×C4×C47—21no—
439C2×C4×C47—48no—
440C2×C4×C47—48no—
441C2×C4×C47—41no—
442C2×C4×C47—41no—
443C2×C4×C47—41no—
444C2×C4×C47—41no—
445C2×C4×C47—41no—
446C2×C4×C47—41no—
447C2×C4×C47—41no—
448C2×C4×C47—41no—
449C2×C4×C47—41no—
450C2×C4×C47—41no—
451C2×C4×C47—41no—
452C2×C4×C47—41no—
453C2×C4×C47—41no—
454C2×C4×C47—41no—
455C2×C4×C47#12012yes—
456C2×C4×C47AGL(1,ℤ/8)12yescomplemented
457C2×C4×C47C22×D411yescharacteristic
458C2×C4×C47C22×D411yescharacteristic
459C2×C4×C47C22×D411yescharacteristic
460C2×C4×C47C22×D411yescharacteristic
461C2×C4×C47H(5,𝔽2)11yescharacteristic
462C2×C4×C47H(5,𝔽2)11yescharacteristic
463C8×C47—22no—
464C8×C47—22no—
465C8×C47—41no—
466C8×C47—41no—
467#23860C4711yesmaximal, characteristic, direct product factor, Sylow
468C22×C47—22no—
469C22×C47—24no—
470C22×C47—22no—
471C22×C47—22no—
472C22×C47—22no—
473C22×C47—22no—
474C22×C47—22no—
475C22×C47—41no—
476C22×C47—42no—
477C22×C47—41no—
478C22×C47—42no—
479C22×C47—41no—
480C22×C47—42no—
481C22×C47—41no—
482C22×C47—42no—
483C22×C47—41no—
484C22×C47—41no—
485C22×C47—42no—
486C22×C47—41no—
487C22×C47—41no—
488C22×C47—42no—
489C22×C47—42no—
490C22×C47—42no—
491C22×C47—42no—
492C22×C47—42no—
493C22×C47—42no—
494C22×C47—42no—
495C22×C47—42no—
496C22×C47—42no—
497C22×C47—42no—
498C22×C47—816no—
499C22×C47—816no—
500C22×C47—81no—
501C22×C47—81no—
502C22×C47—81no—
503C22×C47—81no—
504C22×C47—81no—
505C22×C47—81no—
506C22×C47—81no—
507C22×C47—81no—
508C22×C47—81no—
509C22×C47—81no—
510C22×C47—81no—
511C22×C47—81no—
512C22×C47C2×#12011yescharacteristic
513C22×C47D4211yescharacteristic
514C22×C47D4211yescharacteristic
515C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
517C22×C47#57611yescharacteristic
518C22×C47#57711yescharacteristic
519C4×C47—22no—
520C4×C47—22no—
521C4×C47—41no—
522C4×C47—42no—
523C4×C47—42no—
524C4×C47—41no—
525C4×C47—81no—
526C4×C47—81no—
527C4×C47C2×#12011yescharacteristic
528C4×C47#53411yescharacteristic
529C4×C47D4211yescharacteristic
530C4×C47D4211yescharacteristic
531C22×AGL(1,ℤ/8)C2×C4711yescharacteristic, complemented
532C2×D42C2×C4711yescharacteristic, complemented
533C2×#449C2×C4711yescharacteristic, complemented
534C2×#450C2×C4711yescharacteristic, complemented
535C2×#447C2×C4711yescharacteristic, complemented
536#2407C2×C4711yescharacteristic, complemented
537#2014C2×C4711yescharacteristic, complemented
538#2011C2×C4711yescharacteristic, complemented
539#2000C2×C4711yescharacteristic, complemented
540#1999C2×C4711yescharacteristic, complemented
541#1895C2×C4711yescharacteristic, complemented
542#1879C2×C4711yescharacteristic, complemented
543#1877C2×C4711yescharacteristic, complemented
544#1870C2×C4711yescharacteristic, complemented
545#1786C2×C4711yescharacteristic, complemented
546C2×C47—42no—
547C2×C47—42no—
548C2×C47—44no—
549C2×C47—82no—
550C2×C47—82no—
551C2×C47—82no—
552C2×C47#240311yescharacteristic
553C2×C47#300311yescharacteristic
554C2×C47#301211yescharacteristic
555C2×C47#326411yescharacteristic
556C2×C47#326511yescharacteristic
557C2×C47#327211yescharacteristic
558C2×C47#327411yescharacteristic
559C22×#41C22×C4711yescharacteristic, complemented
560C23×D4—21no—
561C23×D4C22×C4711yescharacteristic
562C23×D4C22×C4711yescharacteristic
563C2×AGL(1,ℤ/8)—24no—
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C22×SD16C22×C4711yescharacteristic
567C22×SD16C22×C4711yescharacteristic, complemented
568C22×SD16C22×C4711yescharacteristic, complemented
569C22×D8C22×C4711yescharacteristic
570C22×D8C22×C4711yescharacteristic, complemented
571C22×D8C22×C4711yescharacteristic, complemented
572C22×M16C22×C4711yescharacteristic, complemented
573D42—24no—
574D42—24no—
575C2×#127C22×C4711yescharacteristic
576C2×C22⋊Q8C22×C4711yescharacteristic, complemented
577C2×#121—21no—
578C2×#121C22×C4711yescharacteristic
579C2×#121C22×C4711yescharacteristic
580C2×#121C22×C4711yescharacteristic, complemented
581C2×#120—21no—
582C2×#120—21no—
583C2×C4×D4C22×C4711yescharacteristic
584C2×C4×D4C22×C4711yescharacteristic
585#450—24no—
586#449—24no—
587#447—24no—
588C2×#103C22×C4711yescharacteristic, complemented
589C2×#102C22×C4711yescharacteristic
590C2×#102C22×C4711yescharacteristic
591C2×#102C22×C4711yescharacteristic, complemented
592C2×#102C22×C4711yescharacteristic, complemented
593C2×#102C22×C4711yescharacteristic, complemented
594C2×#102C22×C4711yescharacteristic, complemented
595C2×#102C22×C4711yescharacteristic, complemented
596C2×C22⋊C8C22×C4711yescharacteristic, complemented
597C2×C22⋊C8C22×C4711yescharacteristic, complemented
598C2×C22⋊C8C22×C4711yescharacteristic, complemented
599#394—21no—
600#392—21no—
601#391C22×C4711yescharacteristic, complemented
602#390C22×C4711yescharacteristic, complemented
603#386—21no—
604#385—21no—
605#380C22×C4711yescharacteristic, complemented
606#340C22×C4711yescharacteristic, complemented
607#340C22×C4711yescharacteristic, complemented
608#336C22×C4711yescharacteristic, complemented
609#336C22×C4711yescharacteristic, complemented
610C47#2386011yescharacteristic, direct product factor, Sylow
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C4711yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C4711yescharacteristic
643C22×D4D4×C4714yescomplemented
644C22×D4C23×C4711yescharacteristic
645C22×D4C23×C4711yescharacteristic
646C22×D4C23×C4711yescharacteristic
647C22×D4C23×C4711yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C4711yescharacteristic
651C23×C4C23×C4711yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C4714yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C4714yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C4711yescharacteristic
675C22×C8C23×C4711yescharacteristic
676C22×C8C23×C4711yescharacteristic
677C22×C8C23×C4711yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C4714yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C4711yescharacteristic
697C2×C4⋊C4C23×C4711yescharacteristic
698C2×C4⋊C4C23×C4711yescharacteristic
699C2×C4⋊C4C23×C4711yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C4711yescharacteristic
709C2×C22⋊C4D4×C4711yescharacteristic
710C2×C42C23×C4711yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C4711yescharacteristic
744C24C2×D4×C4711yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C4712yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C4712yes—
810C2×D4C2×D4×C4712yes—
811C2×D4C2×D4×C4712yes—
812C2×D4C2×D4×C4712yes—
813C2×D4C2×D4×C4712yes—
814C2×D4C2×D4×C4712yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C4711yescharacteristic
836C22×C4C2×D4×C4711yescharacteristic
837C22×C4C2×D4×C4711yescharacteristic
838C22×C4C2×D4×C4712yes—
839C22×C4C2×D4×C4712yes—
840C22×C4C2×D4×C4711yescharacteristic
841C22×C4C24×C4711yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C4712yescomplemented
860C2×C8C2×D4×C4712yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C4712yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C4712yes—
936C23AGL(1,ℤ/8)×C4712yescomplemented
937C23C22×D4×C4711yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C4714yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C4712yes—
1000C2×C4AGL(1,ℤ/8)×C4712yescomplemented
1001C2×C4C22×D4×C4711yescharacteristic
1002C2×C4C22×D4×C4711yescharacteristic
1003C2×C4C22×D4×C4711yescharacteristic
1004C2×C4C22×D4×C4711yescharacteristic
1005C2×C4H(5,𝔽2)×C4711yescharacteristic
1006C2×C4H(5,𝔽2)×C4711yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C4711yescharacteristic
1056C22D42×C4711yescharacteristic
1057C22D42×C4711yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
1060C22C47×#57611yescharacteristic
1061C22C47×#57711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C4711yescharacteristic
1071C4C47×#53411yescharacteristic
1072C4D42×C4711yescharacteristic
1073C4D42×C4711yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C47×#240311yescharacteristic
1081C2C47×#300311yescharacteristic
1082C2C47×#301211yescharacteristic
1083C2C47×#326411yescharacteristic
1084C2C47×#326511yescharacteristic
1085C2C47×#327211yescharacteristic
1086C2C47×#327411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C47C2semidirect
2. C2×D42×C47C2semidirect
3. C2×C47×#449C2semidirect
4. C2×C47×#450C2semidirect
5. C2×C47×#447C2semidirect
6. C47×#2407C2semidirect
7. C47×#2014C2semidirect
8. C47×#2011C2semidirect
9. C47×#2000C2semidirect
10. C47×#1999C2semidirect
11. C47×#1895C2semidirect
12. C47×#1879C2semidirect
13. C47×#1877C2semidirect
14. C47×#1870C2semidirect
15. C47×#1786C2semidirect
16. C22×#41×C47C22semidirect
24. C22×SD16×C47C22semidirect
25. C22×SD16×C47C22semidirect
27. C22×D8×C47C22semidirect
28. C22×D8×C47C22semidirect
29. C22×M16×C47C22semidirect
33. C2×C22⋊Q8×C47C22semidirect
37. C2×#121×C47C22semidirect
45. C2×#103×C47C22semidirect
48. C2×#102×C47C22semidirect
49. C2×#102×C47C22semidirect
50. C2×#102×C47C22semidirect
51. C2×#102×C47C22semidirect
52. C2×#102×C47C22semidirect
53. C2×C22⋊C8×C47C22semidirect
54. C2×C22⋊C8×C47C22semidirect
55. C2×C22⋊C8×C47C22semidirect
58. C47×#391C22semidirect
59. C47×#390C22semidirect
62. C47×#380C22semidirect
63. C47×#340C22semidirect
64. C47×#340C22semidirect
65. C47×#336C22semidirect
66. C47×#336C22semidirect
99. C22×D4×C47D4semidirect
117. C2×SD16×C47D4semidirect
126. C2×D8×C47D4semidirect
144. #121×C47D4semidirect
210. C2×Q8×C47C2×D4semidirect
270. C2×D4×C47C2×D4semidirect
315. C2×C8×C47C2×D4semidirect
316. C2×C8×C47C2×D4semidirect
392. C23×C47AGL(1,ℤ/8)semidirect
456. C2×C4×C47AGL(1,ℤ/8)semidirect
467. #23860C47direct (N × H)
531. C22×AGL(1,ℤ/8)C2×C47semidirect
532. C2×D42C2×C47semidirect
533. C2×#449C2×C47semidirect
534. C2×#450C2×C47semidirect
535. C2×#447C2×C47semidirect
536. #2407C2×C47semidirect
537. #2014C2×C47semidirect
538. #2011C2×C47semidirect
539. #2000C2×C47semidirect
540. #1999C2×C47semidirect
541. #1895C2×C47semidirect
542. #1879C2×C47semidirect
543. #1877C2×C47semidirect
544. #1870C2×C47semidirect
545. #1786C2×C47semidirect
559. C22×#41C22×C47semidirect
567. C22×SD16C22×C47semidirect
568. C22×SD16C22×C47semidirect
570. C22×D8C22×C47semidirect
571. C22×D8C22×C47semidirect
572. C22×M16C22×C47semidirect
576. C2×C22⋊Q8C22×C47semidirect
580. C2×#121C22×C47semidirect
588. C2×#103C22×C47semidirect
591. C2×#102C22×C47semidirect
592. C2×#102C22×C47semidirect
593. C2×#102C22×C47semidirect
594. C2×#102C22×C47semidirect
595. C2×#102C22×C47semidirect
596. C2×C22⋊C8C22×C47semidirect
597. C2×C22⋊C8C22×C47semidirect
598. C2×C22⋊C8C22×C47semidirect
601. #391C22×C47semidirect
602. #390C22×C47semidirect
605. #380C22×C47semidirect
606. #340C22×C47semidirect
607. #340C22×C47semidirect
608. #336C22×C47semidirect
609. #336C22×C47semidirect
610. C47#23860direct (N × H)
643. C22×D4D4×C47semidirect
661. C2×SD16D4×C47semidirect
670. C2×D8D4×C47semidirect
688. #121D4×C47semidirect
754. C2×Q8C2×D4×C47semidirect
814. C2×D4C2×D4×C47semidirect
859. C2×C8C2×D4×C47semidirect
860. C2×C8C2×D4×C47semidirect
936. C23AGL(1,ℤ/8)×C47semidirect
1000. C2×C4AGL(1,ℤ/8)×C47semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C472
C2×D42×C472
C2×C47×#4492
C2×C47×#4502
C2×C47×#4472
C47×#24072
C47×#20142
C47×#20112
C47×#20002
C47×#19992
C47×#18952
C47×#18792
C47×#18772
C47×#18702
C47×#17862
#2386047