Finite Group Databasebeta

← C47×#22422 #26062120

Subgroups — C47×#22422 #26062120

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#550C211yesmaximal, characteristic
2C2×C47×#435C211yesmaximal, characteristic, complemented
3C2×C47×#417C211yesmaximal, characteristic, complemented
4C2×C47×#416C211yesmaximal, characteristic, complemented
5C47×#2352C211yesmaximal, characteristic, complemented
6C47×#1982C211yesmaximal, characteristic, complemented
7C47×#1961C211yesmaximal, characteristic, complemented
8C47×#1895C211yesmaximal, characteristic, complemented
9C47×#1893C211yesmaximal, characteristic, complemented
10C47×#1875C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1805C211yesmaximal, characteristic, complemented
13C47×#1788C211yesmaximal, characteristic, complemented
14C47×#1788C211yesmaximal, characteristic, complemented
15C47×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C47×#550—24no—
21C47×#550C418yescomplemented
22C2×#127×C47—21no—
23C2×#127×C47C2211yescharacteristic
24C2×#121×C47—21no—
25C2×#121×C47—21no—
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×D4×C47—21no—
30C2×C4×D4×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C47×#435—24no—
34C2×C4⋊C8×C47C2211yescharacteristic
35C47×#417—24no—
36C47×#416—24no—
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×#97×C47C2211yescharacteristic
52C47×#388—21no—
53C47×#387—21no—
54C47×#386—21no—
55C47×#382C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47—21no—
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47C2×C414yes—
75C2×#41×C47C2×C414yescomplemented
76C22×Q8×C47C2311yescharacteristic
77C22×D4×C47—21no—
78C22×D4×C47—21no—
79C22×D4×C47—21no—
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47D411yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C22×D4×C47C2311yescharacteristic
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C2×M16×C47—22no—
92C2×M16×C47—22no—
93C2×M16×C47—41no—
94C22×C8×C47—22no—
95C22×C8×C47—22no—
96C22×C8×C47—41no—
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C22×C8×C47C2311yescharacteristic
101#127×C47—28no—
102#127×C47—22no—
103#127×C47C2×C414yescomplemented
104#121×C47—22no—
105#121×C47—22no—
106#121×C47—28no—
107#121×C47—28no—
108#121×C47C2×C414yes—
109#121×C47C2×C414yescomplemented
110C4×Q8×C47—22no—
111C4×Q8×C47C2×C414yescomplemented
112C4×D4×C47—28no—
113C4×D4×C47C2×C414yes—
114C4×D4×C47D414yes—
115#117×C47—22no—
116#117×C47—41no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—22no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—41no—
121C2×C4⋊C4×C47D411yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C4⋊C4×C47C2311yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47—21no—
136C2×C42×C47—21no—
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139#103×C47—22no—
140#103×C47—22no—
141#103×C47—22no—
142#103×C47D414yescomplemented
143#102×C47—22no—
144#102×C47—22no—
145#102×C47—22no—
146#102×C47—22no—
147#102×C47—41no—
148#102×C47—41no—
149#102×C47—41no—
150#102×C47—41no—
151C22⋊C8×C47—22no—
152C22⋊C8×C47—22no—
153#97×C47—22no—
154#95×C47—21no—
155#95×C47—21no—
156#95×C47—21no—
157#95×C47—21no—
158#95×C47—21no—
159C24×C47—21no—
160C24×C47—21no—
161C24×C47C2×D411yescharacteristic
162C24×C47C2×D411yescharacteristic
163#41×C47—28no—
164#41×C47—28no—
165#41×C47—44no—
166#41×C47—44no—
167#41×C47—44no—
168#41×C47—44no—
169#41×C47—44no—
170#41×C47—44no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47C22×C412yes—
175C2×Q8×C47C2×D412yes—
176C2×Q8×C47#4112yes—
177C2×D4×C47—24no—
178C2×D4×C47—24no—
179C2×D4×C47—24no—
180C2×D4×C47—24no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—41no—
194C2×D4×C47—41no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C22⋊C414yes—
208C2×D4×C47C22×C412yes—
209C2×D4×C47C22×C412yes—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—24no—
222C22×C4×C47—24no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—42no—
227C22×C4×C47—42no—
228C22×C4×C47—42no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—81no—
233C22×C4×C47C22×C412yes—
234C22×C4×C47C22×C412yes—
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D412yes—
240C22×C4×C47C2×D412yes—
241C22×C4×C47C2411yescharacteristic
242M16×C47—44no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—44no—
255C2×C8×C47C2×D412yes—
256C4⋊C4×C47—24no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47—21no—
259C4⋊C4×C47—21no—
260C4⋊C4×C47—21no—
261C4⋊C4×C47—21no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—42no—
266C4⋊C4×C47C22⋊C414yes—
267C4⋊C4×C47C22×C412yes—
268C4⋊C4×C47C2×D412yes—
269C22⋊C4×C47—24no—
270C22⋊C4×C47—24no—
271C22⋊C4×C47—42no—
272C22⋊C4×C47—42no—
273C22⋊C4×C47—81no—
274C22⋊C4×C47C22⋊C414yes—
275C22⋊C4×C47C22⋊C414yes—
276C42×C47—24no—
277C42×C47—42no—
278C42×C47—81no—
279C42×C47C22×C412yes—
280C42×C47C2×D412yes—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—22no—
294C23×C47—22no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47C2×C22⋊C412yes—
308C23×C47C2×C22⋊C412yes—
309C23×C47C22×D411yescharacteristic
310Q8×C47—22no—
311Q8×C47—22no—
312Q8×C47—22no—
313Q8×C47C4×D414yes—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—22no—
318D4×C47—44no—
319D4×C47—48no—
320D4×C47—48no—
321D4×C47—48no—
322D4×C47—41no—
323D4×C47—41no—
324D4×C47—41no—
325D4×C47—41no—
326D4×C47—84no—
327D4×C47—84no—
328D4×C47—84no—
329C2×C4×C47—22no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—22no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—22no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—48no—
351C2×C4×C47—48no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—84no—
366C2×C4×C47C2×C22⋊C412yes—
367C2×C4×C47C2×C22⋊C412yes—
368C2×C4×C47C2×C22⋊C412yes—
369C2×C4×C47C2×C22⋊C412yes—
370C2×C4×C47C23×C411yescharacteristic
371C2×C4×C47C22×D411yescharacteristic
372C2×C4×C47C22×D411yescharacteristic
373C2×C4×C47C2×#4111yescharacteristic
374C2×C4×C47H(5,𝔽2)11yescharacteristic
375C2×C4×C47H(5,𝔽2)11yescharacteristic
376C8×C47—22no—
377C8×C47—41no—
378C8×C47—41no—
379C8×C47—41no—
380#22422C4711yesmaximal, characteristic, direct product factor, Sylow
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—41no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47—81no—
409C22×C47C22×C22⋊C411yescharacteristic
410C22×C47D4211yescharacteristic
411C22×C47#54611yescharacteristic
412C22×C47#57511yescharacteristic
413C22×C47#57511yescharacteristic
414C22×C47#57611yescharacteristic
415C22×C47#57711yescharacteristic
416C4×C47—22no—
417C4×C47—22no—
418C4×C47—24no—
419C4×C47—22no—
420C4×C47—22no—
421C4×C47—42no—
422C4×C47—42no—
423C4×C47—81no—
424C4×C47—81no—
425C4×C47—81no—
426C4×C47C2×C4×D411yescharacteristic
427C4×C47#51811yescharacteristic
428C4×C47D4211yescharacteristic
429C4×C47#54611yescharacteristic
430C2×#550C2×C4711yescharacteristic
431C2×#435C2×C4711yescharacteristic, complemented
432C2×#417C2×C4711yescharacteristic, complemented
433C2×#416C2×C4711yescharacteristic, complemented
434#2352C2×C4711yescharacteristic, complemented
435#1982C2×C4711yescharacteristic, complemented
436#1961C2×C4711yescharacteristic, complemented
437#1895C2×C4711yescharacteristic, complemented
438#1893C2×C4711yescharacteristic, complemented
439#1875C2×C4711yescharacteristic, complemented
440#1874C2×C4711yescharacteristic, complemented
441#1805C2×C4711yescharacteristic, complemented
442#1788C2×C4711yescharacteristic, complemented
443#1788C2×C4711yescharacteristic, complemented
444#1763C2×C4711yescharacteristic, complemented
445C2×C47—42no—
446C2×C47—42no—
447C2×C47—82no—
448C2×C47—82no—
449C2×C47D4×C22⋊C411yescharacteristic
450C2×C47#289611yescharacteristic
451C2×C47#289711yescharacteristic
452C2×C47#326811yescharacteristic
453C2×C47#327111yescharacteristic
454C2×C47#330911yescharacteristic
455C2×C47#331711yescharacteristic
456C22×#41C22×C4711yescharacteristic
457C22×#41C22×C4711yescharacteristic
458C22×M16C22×C4711yescharacteristic
459C23×C8C22×C4711yescharacteristic
460#550—24no—
461#550C4×C4718yescomplemented
462C2×#127—21no—
463C2×#127C22×C4711yescharacteristic
464C2×#121—21no—
465C2×#121—21no—
466C2×#121C22×C4711yescharacteristic
467C2×#121C22×C4711yescharacteristic
468C2×C4×Q8C22×C4711yescharacteristic
469C2×C4×D4—21no—
470C2×C4×D4C22×C4711yescharacteristic
471C2×#117C22×C4711yescharacteristic
472C22×C4⋊C4C22×C4711yescharacteristic
473#435—24no—
474C2×C4⋊C8C22×C4711yescharacteristic
475#417—24no—
476#416—24no—
477C2×#103C22×C4711yescharacteristic
478C2×#103C22×C4711yescharacteristic
479C2×#103C22×C4711yescharacteristic
480C2×#103C22×C4711yescharacteristic
481C2×#102C22×C4711yescharacteristic
482C2×#102C22×C4711yescharacteristic
483C2×#102C22×C4711yescharacteristic
484C2×#102C22×C4711yescharacteristic
485C2×#102C22×C4711yescharacteristic
486C2×#102C22×C4711yescharacteristic
487C2×#102C22×C4711yescharacteristic
488C2×#102C22×C4711yescharacteristic
489C2×C22⋊C8C22×C4711yescharacteristic
490C2×C22⋊C8C22×C4711yescharacteristic
491C2×#97C22×C4711yescharacteristic
492#388—21no—
493#387—21no—
494#386—21no—
495#382C22×C4711yescharacteristic
496#380C22×C4711yescharacteristic
497#380C22×C4711yescharacteristic
498C4×C4⋊C4C22×C4711yescharacteristic
499C4×C22⋊C4—21no—
500#340C22×C4711yescharacteristic
501#340C22×C4711yescharacteristic
502#340C22×C4711yescharacteristic
503#340C22×C4711yescharacteristic
504C47#2242211yescharacteristic, direct product factor, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C4714yes—
516C2×#41C2×C4×C4714yescomplemented
517C22×Q8C23×C4711yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4D4×C4711yescharacteristic
525C22×D4C23×C4711yescharacteristic
526C22×D4C23×C4711yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C4711yescharacteristic
531C23×C4C23×C4711yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C23×C4711yescharacteristic
539C22×C8C23×C4711yescharacteristic
540C22×C8C23×C4711yescharacteristic
541C22×C8C23×C4711yescharacteristic
542#127—28no—
543#127—22no—
544#127C2×C4×C4714yescomplemented
545#121—22no—
546#121—22no—
547#121—28no—
548#121—28no—
549#121C2×C4×C4714yes—
550#121C2×C4×C4714yescomplemented
551C4×Q8—22no—
552C4×Q8C2×C4×C4714yescomplemented
553C4×D4—28no—
554C4×D4C2×C4×C4714yes—
555C4×D4D4×C4714yes—
556#117—22no—
557#117—41no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4D4×C4711yescharacteristic
563C2×C4⋊C4C23×C4711yescharacteristic
564C2×C4⋊C4C23×C4711yescharacteristic
565C2×C4⋊C4C23×C4711yescharacteristic
566C2×C4⋊C4C23×C4711yescharacteristic
567C2×C4⋊C4C23×C4711yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4D4×C4711yescharacteristic
574C2×C22⋊C4D4×C4711yescharacteristic
575C2×C42—21no—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C23×C4711yescharacteristic
579C4⋊C8—22no—
580#103—22no—
581#103—22no—
582#103—22no—
583#103D4×C4714yescomplemented
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593C22⋊C8—22no—
594#97—22no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95—21no—
600C24—21no—
601C24—21no—
602C24C2×D4×C4711yescharacteristic
603C24C2×D4×C4711yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22×C4×C4712yes—
616C2×Q8C2×D4×C4712yes—
617C2×Q8#41×C4712yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C4714yes—
649C2×D4C22×C4×C4712yes—
650C2×D4C22×C4×C4712yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4C22×C4×C4712yes—
675C22×C4C22×C4×C4712yes—
676C22×C4C2×D4×C4711yescharacteristic
677C22×C4C2×D4×C4711yescharacteristic
678C22×C4C2×D4×C4711yescharacteristic
679C22×C4C2×D4×C4711yescharacteristic
680C22×C4C2×D4×C4712yes—
681C22×C4C2×D4×C4712yes—
682C22×C4C24×C4711yescharacteristic
683M16—44no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—44no—
696C2×C8C2×D4×C4712yes—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4C22⋊C4×C4714yes—
708C4⋊C4C22×C4×C4712yes—
709C4⋊C4C2×D4×C4712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4C22⋊C4×C4714yes—
716C22⋊C4C22⋊C4×C4714yes—
717C42—24no—
718C42—42no—
719C42—81no—
720C42C22×C4×C4712yes—
721C42C2×D4×C4712yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊C4×C4712yes—
749C23C2×C22⋊C4×C4712yes—
750C23C22×D4×C4711yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×D4×C4714yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—84no—
807C2×C4C2×C22⋊C4×C4712yes—
808C2×C4C2×C22⋊C4×C4712yes—
809C2×C4C2×C22⋊C4×C4712yes—
810C2×C4C2×C22⋊C4×C4712yes—
811C2×C4C23×C4×C4711yescharacteristic
812C2×C4C22×D4×C4711yescharacteristic
813C2×C4C22×D4×C4711yescharacteristic
814C2×C4C2×#41×C4711yescharacteristic
815C2×C4H(5,𝔽2)×C4711yescharacteristic
816C2×C4H(5,𝔽2)×C4711yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊C4×C4711yescharacteristic
850C22D42×C4711yescharacteristic
851C22C47×#54611yescharacteristic
852C22C47×#57511yescharacteristic
853C22C47×#57511yescharacteristic
854C22C47×#57611yescharacteristic
855C22C47×#57711yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4C2×C4×D4×C4711yescharacteristic
867C4C47×#51811yescharacteristic
868C4D42×C4711yescharacteristic
869C4C47×#54611yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊C4×C4711yescharacteristic
875C2C47×#289611yescharacteristic
876C2C47×#289711yescharacteristic
877C2C47×#326811yescharacteristic
878C2C47×#327111yescharacteristic
879C2C47×#330911yescharacteristic
880C2C47×#331711yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#550C2
LCSG ▷ C2×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
2. C2×C47×#435C2semidirect
3. C2×C47×#417C2semidirect
4. C2×C47×#416C2semidirect
5. C47×#2352C2semidirect
6. C47×#1982C2semidirect
7. C47×#1961C2semidirect
8. C47×#1895C2semidirect
9. C47×#1893C2semidirect
10. C47×#1875C2semidirect
11. C47×#1874C2semidirect
12. C47×#1805C2semidirect
13. C47×#1788C2semidirect
14. C47×#1788C2semidirect
15. C47×#1763C2semidirect
21. C47×#550C4semidirect
75. C2×#41×C47C2×C4semidirect
103. #127×C47C2×C4semidirect
109. #121×C47C2×C4semidirect
111. C4×Q8×C47C2×C4semidirect
142. #103×C47D4semidirect
380. #22422C47direct (N × H)
431. C2×#435C2×C47semidirect
432. C2×#417C2×C47semidirect
433. C2×#416C2×C47semidirect
434. #2352C2×C47semidirect
435. #1982C2×C47semidirect
436. #1961C2×C47semidirect
437. #1895C2×C47semidirect
438. #1893C2×C47semidirect
439. #1875C2×C47semidirect
440. #1874C2×C47semidirect
441. #1805C2×C47semidirect
442. #1788C2×C47semidirect
443. #1788C2×C47semidirect
444. #1763C2×C47semidirect
461. #550C4×C47semidirect
504. C47#22422direct (N × H)
516. C2×#41C2×C4×C47semidirect
544. #127C2×C4×C47semidirect
550. #121C2×C4×C47semidirect
552. C4×Q8C2×C4×C47semidirect
583. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5502
C2×C47×#4352
C2×C47×#4172
C2×C47×#4162
C47×#23522
C47×#19822
C47×#19612
C47×#18952
C47×#18932
C47×#18752
C47×#18742
C47×#18052
C47×#17882
C47×#17632
#2242247