Finite Group Databasebeta

← C47×#24464 #26064162

Subgroups — C47×#24464 #26064162

Order 12032.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3488C211yesmaximal, characteristic, complemented
2C47×#3055C211yesmaximal, characteristic, complemented
3C2×C47×#453C211yesmaximal, characteristic, complemented
4C47×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C47C211yesmaximal, characteristic, complemented
6C47×#2856C211yesmaximal, characteristic, complemented
7C47×#2039C211yesmaximal, characteristic, complemented
8C47×#2037C211yesmaximal, characteristic, complemented
9C47×#2006C211yesmaximal, characteristic, complemented
10C47×#2002C211yesmaximal, characteristic, complemented
11C47×#1900C211yesmaximal, characteristic, complemented
12C47×#1896C211yesmaximal, characteristic, complemented
13C47×#1883C211yesmaximal, characteristic, complemented
14C47×#1859C211yesmaximal, characteristic, complemented
15C47×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C47C2211yescharacteristic, complemented
21C22×M16×C47C2211yescharacteristic, complemented
22C47×#550—21no—
23C47×#548—21no—
24C47×#546—21no—
25C47×#546—22no—
26D42×C47—22no—
27D42×C47—21no—
28C47×#537—21no—
29C47×#537C2211yescharacteristic
30C47×#535—21no—
31C47×#535C2211yescharacteristic
32C2×#127×C47C2211yescharacteristic, complemented
33C47×#525—21no—
34C47×#525C2211yescharacteristic
35C2×#121×C47—21no—
36C2×#121×C47—22no—
37C2×#121×C47C2211yescharacteristic
38C2×#121×C47C2211yescharacteristic, complemented
39C47×#520C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic, complemented
41C47×#469—21no—
42C47×#468—21no—
43C47×#466—21no—
44C47×#465—21no—
45C47×#453—24no—
46C47×#449—21no—
47C47×#449—21no—
48C47×#448—21no—
49C47×#447—21no—
50C47×#428C2211yescharacteristic, complemented
51C2×#104×C47—24no—
52C2×#104×C47C2211yescharacteristic
53C2×#104×C47C2211yescharacteristic
54C2×#104×C47C2211yescharacteristic, complemented
55C2×#104×C47C2211yescharacteristic, complemented
56C2×#104×C47C2211yescharacteristic, complemented
57C2×#104×C47C2211yescharacteristic, complemented
58C47×#418C2211yescharacteristic, complemented
59C47×#417C2211yescharacteristic
60C47×#417C2211yescharacteristic, complemented
61C47×#417C2211yescharacteristic, complemented
62C2×#100×C47C2211yescharacteristic, complemented
63C2×#100×C47C2211yescharacteristic, complemented
64C47×#407C2211yescharacteristic, complemented
65C47×#390—22no—
66C47×#390C2211yescharacteristic, complemented
67C47×#390C2211yescharacteristic, complemented
68C47×#384C2211yescharacteristic, complemented
69C47×#343C2211yescharacteristic, complemented
70C47×#343C2211yescharacteristic, complemented
71C47×#339C2211yescharacteristic, complemented
72C47×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C47—22no—
74H(5,𝔽2)×C47—22no—
75H(5,𝔽2)×C47—41no—
76H(5,𝔽2)×C47—41no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47—21no—
80C2×#41×C47—21no—
81C2×#41×C47—22no—
82C2×#41×C47—22no—
83C2×#41×C47—41no—
84C2×#41×C47—41no—
85C2×#41×C47D411yescharacteristic, complemented
86C2×#41×C47D411yescharacteristic, complemented
87C2×#41×C47C2311yescharacteristic
88C2×#41×C47C2311yescharacteristic
89C2×#41×C47C2311yescharacteristic
90C22×Q8×C47D411yescharacteristic, complemented
91C22×D4×C47—21no—
92C22×D4×C47—22no—
93C22×D4×C47—22no—
94C22×D4×C47—21no—
95C22×D4×C47—21no—
96C22×D4×C47—21no—
97C22×D4×C47—22no—
98C22×D4×C47D412yes—
99C22×D4×C47D411yescharacteristic, complemented
100C22×D4×C47C2311yescharacteristic
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47—21no—
103C23×C4×C47—21no—
104C23×C4×C47C2311yescharacteristic
105AGL(1,ℤ/8)×C47—22no—
106AGL(1,ℤ/8)×C47—22no—
107AGL(1,ℤ/8)×C47—22no—
108AGL(1,ℤ/8)×C47—41no—
109AGL(1,ℤ/8)×C47—41no—
110AGL(1,ℤ/8)×C47—41no—
111C2×SD16×C47—21no—
112C2×SD16×C47—21no—
113C2×SD16×C47—21no—
114C2×D8×C47—21no—
115C2×D8×C47—21no—
116C2×D8×C47—21no—
117C2×M16×C47—21no—
118C2×M16×C47—22no—
119C2×M16×C47—41no—
120C2×M16×C47C2311yescharacteristic
121C2×M16×C47C2311yescharacteristic
122C2×M16×C47C2311yescharacteristic
123C2×M16×C47C2311yescharacteristic
124C22×C8×C47—21no—
125#127×C47—22no—
126#127×C47—21no—
127#127×C47—22no—
128#127×C47—41no—
129#124×C47—22no—
130#124×C47—21no—
131#123×C47—22no—
132#123×C47—21no—
133C22⋊Q8×C47—22no—
134C22⋊Q8×C47—21no—
135C22⋊Q8×C47—21no—
136C22⋊Q8×C47D411yescharacteristic, complemented
137C22⋊Q8×C47D411yescharacteristic, complemented
138#121×C47—22no—
139#121×C47—22no—
140#121×C47—22no—
141#121×C47—22no—
142#121×C47—22no—
143#121×C47—21no—
144#121×C47—21no—
145#121×C47—21no—
146#121×C47—21no—
147#121×C47—21no—
148#121×C47—21no—
149#121×C47—22no—
150#121×C47—21no—
151#121×C47—21no—
152#121×C47—21no—
153#121×C47—21no—
154#121×C47—21no—
155#121×C47—21no—
156#121×C47—48no—
157#121×C47D411yescharacteristic, complemented
158#121×C47D411yescharacteristic, complemented
159#120×C47—22no—
160#120×C47—22no—
161#120×C47—22no—
162#120×C47—21no—
163#120×C47—22no—
164C4×Q8×C47—21no—
165C4×D4×C47—22no—
166C4×D4×C47—22no—
167C4×D4×C47—21no—
168C4×D4×C47—22no—
169C4×D4×C47—21no—
170C4×D4×C47—21no—
171#117×C47—21no—
172#117×C47C2311yescharacteristic
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47—22no—
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C22⋊C4×C47—22no—
178C2×C22⋊C4×C47—22no—
179C2×C22⋊C4×C47—22no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47D412yes—
182C2×C42×C47—22no—
183C2×C42×C47—21no—
184C2×C42×C47—41no—
185C2×C42×C47C2311yescharacteristic
186C2×C42×C47C2311yescharacteristic
187#107×C47—21no—
188#106×C47—21no—
189#104×C47—22no—
190#104×C47—22no—
191#104×C47—22no—
192#104×C47—22no—
193#104×C47—41no—
194#104×C47D414yescomplemented
195#103×C47—21no—
196#103×C47—21no—
197#103×C47—21no—
198#102×C47—21no—
199#102×C47—21no—
200#102×C47—21no—
201#102×C47—21no—
202#102×C47—21no—
203#100×C47—22no—
204#100×C47—41no—
205C22⋊C8×C47—21no—
206C22⋊C8×C47—21no—
207C24×C47—22no—
208C24×C47—21no—
209C24×C47—21no—
210C24×C47C2×D411yescharacteristic
211C24×C47C2×D412yes—
212#41×C47—21no—
213#41×C47—21no—
214#41×C47—22no—
215#41×C47—22no—
216#41×C47—21no—
217#41×C47—21no—
218#41×C47—21no—
219#41×C47—21no—
220#41×C47—21no—
221#41×C47—21no—
222#41×C47—21no—
223#41×C47—21no—
224#41×C47—42no—
225#41×C47—42no—
226#41×C47—41no—
227#41×C47—41no—
228#41×C47—42no—
229#41×C47—42no—
230#41×C47—42no—
231#41×C47—42no—
232#41×C47—42no—
233#41×C47—42no—
234#41×C47C2×D412yes—
235#41×C47#4112yes—
236C2×Q8×C47—21no—
237C2×Q8×C47—22no—
238C2×Q8×C47—41no—
239C2×Q8×C47C2×D411yescharacteristic
240C2×Q8×C47C2×D411yescharacteristic
241C2×Q8×C47C2×D411yescharacteristic
242C2×D4×C47—21no—
243C2×D4×C47—22no—
244C2×D4×C47—22no—
245C2×D4×C47—22no—
246C2×D4×C47—22no—
247C2×D4×C47—21no—
248C2×D4×C47—21no—
249C2×D4×C47—21no—
250C2×D4×C47—21no—
251C2×D4×C47—21no—
252C2×D4×C47—22no—
253C2×D4×C47—22no—
254C2×D4×C47—22no—
255C2×D4×C47—21no—
256C2×D4×C47—22no—
257C2×D4×C47—21no—
258C2×D4×C47—21no—
259C2×D4×C47—21no—
260C2×D4×C47—21no—
261C2×D4×C47—21no—
262C2×D4×C47—21no—
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—21no—
266C2×D4×C47—21no—
267C2×D4×C47—21no—
268C2×D4×C47—21no—
269C2×D4×C47—21no—
270C2×D4×C47—41no—
271C2×D4×C47—42no—
272C2×D4×C47—42no—
273C2×D4×C47—44no—
274C2×D4×C47—44no—
275C2×D4×C47—44no—
276C2×D4×C47—42no—
277C2×D4×C47—42no—
278C2×D4×C47—44no—
279C2×D4×C47—44no—
280C2×D4×C47—42no—
281C2×D4×C47—42no—
282C2×D4×C47—44no—
283C2×D4×C47—44no—
284C2×D4×C47—41no—
285C2×D4×C47—41no—
286C2×D4×C47—84no—
287C2×D4×C47C2×D411yescharacteristic
288C2×D4×C47C2×D411yescharacteristic
289C2×D4×C47C2×D411yescharacteristic
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—22no—
297C22×C4×C47—24no—
298C22×C4×C47—21no—
299C22×C4×C47—21no—
300C22×C4×C47—22no—
301C22×C4×C47—21no—
302C22×C4×C47—21no—
303C22×C4×C47—21no—
304C22×C4×C47—21no—
305C22×C4×C47—21no—
306C22×C4×C47—42no—
307C22×C4×C47—42no—
308C22×C4×C47—42no—
309C22×C4×C47—42no—
310C22×C4×C47C2×D411yescharacteristic
311C22×C4×C47C2×D411yescharacteristic
312C22×C4×C47C2×D411yescharacteristic
313C22×C4×C47C2×D411yescharacteristic
314C22×C4×C47C2×D411yescharacteristic
315C22×C4×C47C2×D412yes—
316C22×C4×C47C2411yescharacteristic
317SD16×C47—42no—
318SD16×C47—42no—
319SD16×C47—42no—
320D8×C47—42no—
321D8×C47—42no—
322D8×C47—42no—
323M16×C47—21no—
324M16×C47—21no—
325M16×C47—21no—
326M16×C47—21no—
327M16×C47—21no—
328M16×C47—21no—
329M16×C47—21no—
330M16×C47—42no—
331M16×C47C2×D412yescomplemented
332C2×C8×C47—21no—
333C2×C8×C47—21no—
334C2×C8×C47—21no—
335C2×C8×C47—21no—
336C2×C8×C47—42no—
337C4⋊C4×C47—22no—
338C4⋊C4×C47—22no—
339C4⋊C4×C47—21no—
340C4⋊C4×C47—21no—
341C4⋊C4×C47—21no—
342C4⋊C4×C47—21no—
343C4⋊C4×C47—21no—
344C4⋊C4×C47—21no—
345C4⋊C4×C47—44no—
346C4⋊C4×C47C2×D411yescharacteristic
347C4⋊C4×C47C2×D411yescharacteristic
348C22⋊C4×C47—22no—
349C22⋊C4×C47—22no—
350C22⋊C4×C47—22no—
351C22⋊C4×C47—22no—
352C22⋊C4×C47—22no—
353C22⋊C4×C47—21no—
354C22⋊C4×C47—21no—
355C22⋊C4×C47—21no—
356C22⋊C4×C47—21no—
357C22⋊C4×C47—22no—
358C22⋊C4×C47—22no—
359C22⋊C4×C47—21no—
360C22⋊C4×C47—44no—
361C22⋊C4×C47—44no—
362C22⋊C4×C47—41no—
363C22⋊C4×C47—41no—
364C42×C47—22no—
365C42×C47—21no—
366C42×C47—21no—
367C42×C47—21no—
368C42×C47—21no—
369C42×C47—42no—
370C42×C47C2×D412yescomplemented
371C23×C47—21no—
372C23×C47—21no—
373C23×C47—21no—
374C23×C47—22no—
375C23×C47—22no—
376C23×C47—21no—
377C23×C47—21no—
378C23×C47—22no—
379C23×C47—22no—
380C23×C47—41no—
381C23×C47—42no—
382C23×C47—44no—
383C23×C47—42no—
384C23×C47—42no—
385C23×C47—42no—
386C23×C47—42no—
387C23×C47—42no—
388C23×C47—41no—
389C23×C47—41no—
390C23×C47—41no—
391C23×C47—81no—
392C23×C47—82no—
393C23×C47—82no—
394C23×C47#12011yescharacteristic
395C23×C47#12011yescharacteristic
396C23×C47C22×D411yescharacteristic
397Q8×C47—21no—
398Q8×C47—21no—
399Q8×C47—21no—
400Q8×C47—21no—
401Q8×C47—21no—
402Q8×C47—42no—
403Q8×C47#12112yescomplemented
404D4×C47—22no—
405D4×C47—22no—
406D4×C47—21no—
407D4×C47—21no—
408D4×C47—21no—
409D4×C47—21no—
410D4×C47—21no—
411D4×C47—42no—
412D4×C47—42no—
413D4×C47—44no—
414D4×C47—42no—
415D4×C47—44no—
416D4×C47—41no—
417D4×C47—41no—
418D4×C47—41no—
419D4×C47—41no—
420D4×C47—44no—
421D4×C47—42no—
422D4×C47—41no—
423D4×C47—41no—
424D4×C47—41no—
425D4×C47—41no—
426D4×C47—41no—
427D4×C47—41no—
428D4×C47—41no—
429D4×C47—41no—
430D4×C47—88no—
431D4×C47—81no—
432D4×C47—82no—
433D4×C47—82no—
434D4×C47—82no—
435D4×C47—82no—
436D4×C47—82no—
437D4×C47—82no—
438D4×C47#12112yescomplemented
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—21no—
442C2×C4×C47—22no—
443C2×C4×C47—21no—
444C2×C4×C47—21no—
445C2×C4×C47—21no—
446C2×C4×C47—21no—
447C2×C4×C47—21no—
448C2×C4×C47—21no—
449C2×C4×C47—21no—
450C2×C4×C47—21no—
451C2×C4×C47—22no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—22no—
455C2×C4×C47—22no—
456C2×C4×C47—21no—
457C2×C4×C47—22no—
458C2×C4×C47—21no—
459C2×C4×C47—21no—
460C2×C4×C47—21no—
461C2×C4×C47—42no—
462C2×C4×C47—42no—
463C2×C4×C47—42no—
464C2×C4×C47—48no—
465C2×C4×C47—44no—
466C2×C4×C47—41no—
467C2×C4×C47—41no—
468C2×C4×C47—41no—
469C2×C4×C47—41no—
470C2×C4×C47—41no—
471C2×C4×C47—41no—
472C2×C4×C47—42no—
473C2×C4×C47—42no—
474C2×C4×C47—41no—
475C2×C4×C47—82no—
476C2×C4×C47#12011yescharacteristic
477C2×C4×C47#12011yescharacteristic
478C2×C4×C47C22×D411yescharacteristic
479C2×C4×C47C22×D411yescharacteristic
480C2×C4×C47C22×D411yescharacteristic
481C2×C4×C47C2×#4111yescharacteristic
482C2×C4×C47H(5,𝔽2)11yescharacteristic
483C2×C4×C47H(5,𝔽2)11yescharacteristic
484C8×C47—22no—
485C8×C47—41no—
486C8×C47—41no—
487C8×C47—41no—
488#24464C4711yesmaximal, characteristic, direct product factor, Sylow
489C22×C47—21no—
490C22×C47—21no—
491C22×C47—21no—
492C22×C47—21no—
493C22×C47—21no—
494C22×C47—22no—
495C22×C47—21no—
496C22×C47—21no—
497C22×C47—42no—
498C22×C47—42no—
499C22×C47—41no—
500C22×C47—41no—
501C22×C47—41no—
502C22×C47—41no—
503C22×C47—42no—
504C22×C47—42no—
505C22×C47—41no—
506C22×C47—41no—
507C22×C47—41no—
508C22×C47—42no—
509C22×C47—41no—
510C22×C47—84no—
511C22×C47—82no—
512C22×C47—82no—
513C22×C47—82no—
514C22×C47—82no—
515C22×C47—81no—
516C22×C47—81no—
517C22×C47—81no—
518C22×C47—164no—
519C22×C47#45312yescomplemented
520C22×C47C2×#12011yescharacteristic
521C22×C47D4211yescharacteristic
522C22×C47#54611yescharacteristic
523C4×C47—24no—
524C4×C47—21no—
525C4×C47—21no—
526C4×C47—22no—
527C4×C47—42no—
528C4×C47—41no—
529C4×C47—41no—
530C4×C47—42no—
531C4×C47—41no—
532C4×C47—41no—
533C4×C47—81no—
534C4×C47C2×#12111yescharacteristic
535C4×C47#53411yescharacteristic
536C4×C47D4211yescharacteristic
537C4×C47#54611yescharacteristic
538#3488C2×C4711yescharacteristic, complemented
539#3055C2×C4711yescharacteristic, complemented
540C2×#453C2×C4711yescharacteristic, complemented
541#3006C2×C4711yescharacteristic, complemented
542C22×#104C2×C4711yescharacteristic, complemented
543#2856C2×C4711yescharacteristic, complemented
544#2039C2×C4711yescharacteristic, complemented
545#2037C2×C4711yescharacteristic, complemented
546#2006C2×C4711yescharacteristic, complemented
547#2002C2×C4711yescharacteristic, complemented
548#1900C2×C4711yescharacteristic, complemented
549#1896C2×C4711yescharacteristic, complemented
550#1883C2×C4711yescharacteristic, complemented
551#1859C2×C4711yescharacteristic, complemented
552#1792C2×C4711yescharacteristic, complemented
553C2×C47—21no—
554C2×C47—21no—
555C2×C47—22no—
556C2×C47—41no—
557C2×C47—42no—
558C2×C47—81no—
559C2×C47—82no—
560C2×C47—81no—
561C2×C47—161no—
562C2×C47#241011yescharacteristic
563C2×C47C2×#45311yescharacteristic
564C2×C47#301811yescharacteristic
565C2×H(5,𝔽2)C22×C4711yescharacteristic
566C22×#41C22×C4711yescharacteristic
567C2×AGL(1,ℤ/8)C22×C4711yescharacteristic
568C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
569C2×AGL(1,ℤ/8)C22×C4711yescharacteristic, complemented
570C22×M16C22×C4711yescharacteristic, complemented
571#550—21no—
572#548—21no—
573#546—21no—
574#546—22no—
575D42—22no—
576D42—21no—
577#537—21no—
578#537C22×C4711yescharacteristic
579#535—21no—
580#535C22×C4711yescharacteristic
581C2×#127C22×C4711yescharacteristic, complemented
582#525—21no—
583#525C22×C4711yescharacteristic
584C2×#121—21no—
585C2×#121—22no—
586C2×#121C22×C4711yescharacteristic
587C2×#121C22×C4711yescharacteristic, complemented
588#520C22×C4711yescharacteristic
589C22×C42C22×C4711yescharacteristic, complemented
590#469—21no—
591#468—21no—
592#466—21no—
593#465—21no—
594#453—24no—
595#449—21no—
596#449—21no—
597#448—21no—
598#447—21no—
599#428C22×C4711yescharacteristic, complemented
600C2×#104—24no—
601C2×#104C22×C4711yescharacteristic
602C2×#104C22×C4711yescharacteristic
603C2×#104C22×C4711yescharacteristic, complemented
604C2×#104C22×C4711yescharacteristic, complemented
605C2×#104C22×C4711yescharacteristic, complemented
606C2×#104C22×C4711yescharacteristic, complemented
607#418C22×C4711yescharacteristic, complemented
608#417C22×C4711yescharacteristic
609#417C22×C4711yescharacteristic, complemented
610#417C22×C4711yescharacteristic, complemented
611C2×#100C22×C4711yescharacteristic, complemented
612C2×#100C22×C4711yescharacteristic, complemented
613#407C22×C4711yescharacteristic, complemented
614#390—22no—
615#390C22×C4711yescharacteristic, complemented
616#390C22×C4711yescharacteristic, complemented
617#384C22×C4711yescharacteristic, complemented
618#343C22×C4711yescharacteristic, complemented
619#343C22×C4711yescharacteristic, complemented
620#339C22×C4711yescharacteristic, complemented
621#339C22×C4711yescharacteristic, complemented
622C47#2446411yescharacteristic, direct product factor, Sylow
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C4711yescharacteristic, complemented
636C2×#41D4×C4711yescharacteristic, complemented
637C2×#41C23×C4711yescharacteristic
638C2×#41C23×C4711yescharacteristic
639C2×#41C23×C4711yescharacteristic
640C22×Q8D4×C4711yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C4712yes—
649C22×D4D4×C4711yescharacteristic, complemented
650C22×D4C23×C4711yescharacteristic
651C22×D4C23×C4711yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C4711yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C4711yescharacteristic
671C2×M16C23×C4711yescharacteristic
672C2×M16C23×C4711yescharacteristic
673C2×M16C23×C4711yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C4711yescharacteristic, complemented
687C22⋊Q8D4×C4711yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C4711yescharacteristic, complemented
708#121D4×C4711yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C4711yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C4711yescharacteristic
726C2×C4⋊C4C23×C4711yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C4712yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C4711yescharacteristic
736C2×C42C23×C4711yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C4714yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C4711yescharacteristic
761C24C2×D4×C4712yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C4712yes—
785#41#41×C4712yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C4711yescharacteristic
790C2×Q8C2×D4×C4711yescharacteristic
791C2×Q8C2×D4×C4711yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C4711yescharacteristic
838C2×D4C2×D4×C4711yescharacteristic
839C2×D4C2×D4×C4711yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C4711yescharacteristic
861C22×C4C2×D4×C4711yescharacteristic
862C22×C4C2×D4×C4711yescharacteristic
863C22×C4C2×D4×C4711yescharacteristic
864C22×C4C2×D4×C4711yescharacteristic
865C22×C4C2×D4×C4712yes—
866C22×C4C24×C4711yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C4712yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C4711yescharacteristic
897C4⋊C4C2×D4×C4711yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C4712yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C4711yescharacteristic
945C23#120×C4711yescharacteristic
946C23C22×D4×C4711yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C4712yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C4712yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C4711yescharacteristic
1027C2×C4#120×C4711yescharacteristic
1028C2×C4C22×D4×C4711yescharacteristic
1029C2×C4C22×D4×C4711yescharacteristic
1030C2×C4C22×D4×C4711yescharacteristic
1031C2×C4C2×#41×C4711yescharacteristic
1032C2×C4H(5,𝔽2)×C4711yescharacteristic
1033C2×C4H(5,𝔽2)×C4711yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C47×#45312yescomplemented
1069C22C2×#120×C4711yescharacteristic
1070C22D42×C4711yescharacteristic
1071C22C47×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C4711yescharacteristic
1084C4C47×#53411yescharacteristic
1085C4D42×C4711yescharacteristic
1086C4C47×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C47×#241011yescharacteristic
1097C2C2×C47×#45311yescharacteristic
1098C2C47×#301811yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC22×C4C24×C47
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3488C2semidirect
2. C47×#3055C2semidirect
3. C2×C47×#453C2semidirect
4. C47×#3006C2semidirect
5. C22×#104×C47C2semidirect
6. C47×#2856C2semidirect
7. C47×#2039C2semidirect
8. C47×#2037C2semidirect
9. C47×#2006C2semidirect
10. C47×#2002C2semidirect
11. C47×#1900C2semidirect
12. C47×#1896C2semidirect
13. C47×#1883C2semidirect
14. C47×#1859C2semidirect
15. C47×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C47C22semidirect
20. C2×AGL(1,ℤ/8)×C47C22semidirect
21. C22×M16×C47C22semidirect
32. C2×#127×C47C22semidirect
38. C2×#121×C47C22semidirect
40. C22×C42×C47C22semidirect
50. C47×#428C22semidirect
54. C2×#104×C47C22semidirect
55. C2×#104×C47C22semidirect
56. C2×#104×C47C22semidirect
57. C2×#104×C47C22semidirect
58. C47×#418C22semidirect
60. C47×#417C22semidirect
61. C47×#417C22semidirect
62. C2×#100×C47C22semidirect
63. C2×#100×C47C22semidirect
64. C47×#407C22semidirect
66. C47×#390C22semidirect
67. C47×#390C22semidirect
68. C47×#384C22semidirect
69. C47×#343C22semidirect
70. C47×#343C22semidirect
71. C47×#339C22semidirect
72. C47×#339C22semidirect
85. C2×#41×C47D4semidirect
86. C2×#41×C47D4semidirect
90. C22×Q8×C47D4semidirect
99. C22×D4×C47D4semidirect
136. C22⋊Q8×C47D4semidirect
137. C22⋊Q8×C47D4semidirect
157. #121×C47D4semidirect
158. #121×C47D4semidirect
194. #104×C47D4semidirect
331. M16×C47C2×D4semidirect
370. C42×C47C2×D4semidirect
403. Q8×C47#121semidirect
438. D4×C47#121semidirect
488. #24464C47direct (N × H)
519. C22×C47#453semidirect
538. #3488C2×C47semidirect
539. #3055C2×C47semidirect
540. C2×#453C2×C47semidirect
541. #3006C2×C47semidirect
542. C22×#104C2×C47semidirect
543. #2856C2×C47semidirect
544. #2039C2×C47semidirect
545. #2037C2×C47semidirect
546. #2006C2×C47semidirect
547. #2002C2×C47semidirect
548. #1900C2×C47semidirect
549. #1896C2×C47semidirect
550. #1883C2×C47semidirect
551. #1859C2×C47semidirect
552. #1792C2×C47semidirect
568. C2×AGL(1,ℤ/8)C22×C47semidirect
569. C2×AGL(1,ℤ/8)C22×C47semidirect
570. C22×M16C22×C47semidirect
581. C2×#127C22×C47semidirect
587. C2×#121C22×C47semidirect
589. C22×C42C22×C47semidirect
599. #428C22×C47semidirect
603. C2×#104C22×C47semidirect
604. C2×#104C22×C47semidirect
605. C2×#104C22×C47semidirect
606. C2×#104C22×C47semidirect
607. #418C22×C47semidirect
609. #417C22×C47semidirect
610. #417C22×C47semidirect
611. C2×#100C22×C47semidirect
612. C2×#100C22×C47semidirect
613. #407C22×C47semidirect
615. #390C22×C47semidirect
616. #390C22×C47semidirect
617. #384C22×C47semidirect
618. #343C22×C47semidirect
619. #343C22×C47semidirect
620. #339C22×C47semidirect
621. #339C22×C47semidirect
622. C47#24464direct (N × H)
635. C2×#41D4×C47semidirect
636. C2×#41D4×C47semidirect
640. C22×Q8D4×C47semidirect
649. C22×D4D4×C47semidirect
686. C22⋊Q8D4×C47semidirect
687. C22⋊Q8D4×C47semidirect
707. #121D4×C47semidirect
708. #121D4×C47semidirect
744. #104D4×C47semidirect
881. M16C2×D4×C47semidirect
920. C42C2×D4×C47semidirect
953. Q8#121×C47semidirect
988. D4#121×C47semidirect
1068. C22C47×#453semidirect

Maximal subgroups

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

subgroupindex
C47×#34882
C47×#30552
C2×C47×#4532
C47×#30062
C22×#104×C472
C47×#28562
C47×#20392
C47×#20372
C47×#20062
C47×#20022
C47×#19002
C47×#18962
C47×#18832
C47×#18592
C47×#17922
#2446447