Finite Group Databasebeta

← C2×C47×#3370 #26101010

Subgroups — C2×C47×#3370 #26101010

Order 12032.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#559C211yesmaximal, characteristic, complemented
2C2×C47×#554C211yesmaximal, characteristic, complemented
3C47×#3370C2116yesmaximal, direct product factor
4C2×C47×#490C211yesmaximal, characteristic, complemented
5C2×C47×#489C211yesmaximal, characteristic, complemented
6C2×C47×#488C211yesmaximal, characteristic, complemented
7C2×C47×#479C211yesmaximal, characteristic, complemented
8C2×C47×#478C211yesmaximal, characteristic, complemented
9C2×C47×#474C211yesmaximal, characteristic, complemented
10C2×C47×#463C211yesmaximal, characteristic, complemented
11C2×C47×#463C211yesmaximal, characteristic, complemented
12C2×C47×#459C211yesmaximal, characteristic
13C2×C47×#446C211yesmaximal, characteristic, complemented
14C2×C47×#442C211yesmaximal, characteristic, complemented
15C2×C47×#440C211yesmaximal, characteristic, complemented
16C2×C4×D8×C47C211yesmaximal, characteristic, complemented
17C22×SD16×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×D8×C47C2211yescharacteristic
20C47×#559—24no—
21C47×#559C2218yescomplemented
22C47×#554—24no—
23C47×#554C2218yescomplemented
24C2×C4⋊Q8×C47C2211yescharacteristic
25C2×#127×C47C2211yescharacteristic
26C2×#125×C47C2211yescharacteristic
27C2×#125×C47C2211yescharacteristic
28C2×#124×C47—21no—
29C2×#124×C47C2211yescharacteristic
30C2×#124×C47C2211yescharacteristic
31C2×#123×C47—21no—
32C2×#123×C47—21no—
33C2×C22⋊Q8×C47—21no—
34C2×C22⋊Q8×C47—21no—
35C2×C22⋊Q8×C47—21no—
36C2×C4×Q8×C47C2211yescharacteristic
37C2×C4×Q8×C47C2211yescharacteristic
38C2×C4×D4×C47—21no—
39C2×C4×D4×C47C2211yescharacteristic
40C2×C4×D4×C47C2211yescharacteristic
41C2×C4×D4×C47C2211yescharacteristic
42C2×C4×D4×C47C2211yescharacteristic
43C2×C4×D4×C47C2211yescharacteristic
44C22×C4⋊C4×C47—21no—
45C47×#490C2218yescomplemented
46C47×#489C2218yescomplemented
47C47×#488C2218yescomplemented
48C47×#479C2218yescomplemented
49C47×#478C2218yescomplemented
50C47×#474C2218yescomplemented
51C47×#463C2218yescomplemented
52C47×#463C2218yescomplemented
53C47×#459C2218yes—
54C47×#446C2218yescomplemented
55C47×#442C2218yescomplemented
56C47×#440C2218yescomplemented
57C4×D8×C47C2218yescomplemented
58C2×#107×C47C2211yescharacteristic
59C2×#107×C47C2211yescharacteristic
60C2×#106×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C2×C4⋊C8×C47C2211yescharacteristic
64C2×#103×C47C2211yescharacteristic
65C2×#103×C47C2211yescharacteristic
66C2×#103×C47C2211yescharacteristic
67C2×#102×C47C2211yescharacteristic
68C2×#102×C47C2211yescharacteristic
69C2×#102×C47C2211yescharacteristic
70C2×#102×C47C2211yescharacteristic
71C2×#102×C47C2211yescharacteristic
72C2×#102×C47C2211yescharacteristic
73C2×#102×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Q8×C47—21no—
78C22×Q8×C47D411yescharacteristic
79C22×Q8×C47C2311yescharacteristic
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47—21no—
90C2×SD16×C47—24no—
91C2×SD16×C47C2314yes—
92C2×D8×C47—24no—
93C2×D8×C47—24no—
94C2×D8×C47C2314yes—
95C2×D8×C47C2314yes—
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C4⋊Q8×C47—22no—
101C4⋊Q8×C47C2314yes—
102#127×C47—22no—
103#127×C47C2314yes—
104#125×C47—22no—
105#125×C47—22no—
106#125×C47C2314yes—
107#125×C47C2314yes—
108#124×C47—28no—
109#124×C47—22no—
110#124×C47—22no—
111#124×C47C2314yes—
112#124×C47C2314yes—
113#123×C47—28no—
114#123×C47—28no—
115C22⋊Q8×C47—28no—
116C22⋊Q8×C47—28no—
117C22⋊Q8×C47—28no—
118C4×Q8×C47—22no—
119C4×Q8×C47D414yes—
120C4×Q8×C47C2314yes—
121C4×Q8×C47C2314yes—
122C4×D4×C47—28no—
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47C2314yes—
129C4×D4×C47C2314yes—
130C4×D4×C47C2314yes—
131C4×D4×C47C2314yes—
132C4×D4×C47C2314yes—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—21no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47—28no—
140C2×C4⋊C4×C47D411yescharacteristic
141C2×C4⋊C4×C47D411yescharacteristic
142C2×C4⋊C4×C47D411yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C4⋊C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47C2311yescharacteristic
147C2×C22⋊C4×C47—21no—
148C2×C22⋊C4×C47—21no—
149C2×C22⋊C4×C47—21no—
150C2×C22⋊C4×C47—21no—
151C2×C22⋊C4×C47—21no—
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47—21no—
156C2×C42×C47—21no—
157C2×C42×C47C2311yescharacteristic
158C2×C42×C47C2311yescharacteristic
159C2×C42×C47C2311yescharacteristic
160#107×C47C2314yes—
161#107×C47C2314yes—
162#106×C47C2314yes—
163C4⋊C8×C47C2314yes—
164C4⋊C8×C47C2314yes—
165C4⋊C8×C47C2314yes—
166#103×C47C2314yes—
167#103×C47C2314yes—
168#103×C47C2314yes—
169#102×C47C2314yes—
170#102×C47C2314yes—
171#102×C47C2314yes—
172#102×C47C2314yes—
173#102×C47C2314yes—
174#102×C47C2314yes—
175#102×C47C2314yes—
176#97×C47C2314yes—
177#97×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—24no—
184C2×Q8×C47—22no—
185C2×Q8×C47—22no—
186C2×Q8×C47—42no—
187C2×Q8×C47—82no—
188C2×Q8×C47C2×D414yes—
189C2×Q8×C47C2412yes—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—24no—
194C2×D4×C47—24no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—44no—
201C2×D4×C47—82no—
202C2×D4×C47#4114yes—
203C2×D4×C47C2412yes—
204C2×D4×C47C2412yes—
205C2×D4×C47C2412yes—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—24no—
213C22×C4×C47—24no—
214C22×C4×C47—24no—
215C22×C4×C47—24no—
216C22×C4×C47—44no—
217C22×C4×C47—82no—
218C22×C4×C47—82no—
219C22×C4×C47—82no—
220C22×C4×C47—82no—
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D411yescharacteristic
225C22×C4×C47C2×D411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2411yescharacteristic
228SD16×C47—28no—
229D8×C47—28no—
230D8×C47—28no—
231C2×C8×C47—22no—
232C2×C8×C47—22no—
233C2×C8×C47—22no—
234C2×C8×C47—22no—
235C2×C8×C47C2412yes—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—24no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2×D414yes—
250C4⋊C4×C47C2×D414yes—
251C4⋊C4×C47C2×D414yes—
252C4⋊C4×C47C2412yes—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—24no—
265C42×C47—24no—
266C42×C47C2×D412yes—
267C42×C47C2×D412yes—
268C42×C47C2×D412yes—
269C42×C47C2412yes—
270C42×C47C2412yes—
271C42×C47C2412yes—
272C23×C47—24no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—42no—
277C23×C47—42no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—44no—
288Q8×C47—42no—
289Q8×C47—84no—
290D4×C47—24no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—48no—
297D4×C47—42no—
298D4×C47—42no—
299D4×C47—84no—
300D4×C47C2×#4114yes—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—48no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—84no—
319C2×C4×C47—84no—
320C2×C4×C47—84no—
321C2×C4×C47—84no—
322C2×C4×C47C22×D412yes—
323C2×C4×C47C22×D412yes—
324C2×C4×C47C22×D412yes—
325C2×C4×C47C22×D412yes—
326C2×C4×C47C22×D412yes—
327C2×C4×C47C22×D412yes—
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4112yes—
330C2×C4×C472−1+412yes—
331C2×C4×C47C2511yescharacteristic
332C8×C47—22no—
333C8×C47—22no—
334C8×C47—22no—
335C8×C47—22no—
336C2×#3370C4711yesmaximal, characteristic, direct product factor, Sylow
337C22×C47—24no—
338C22×C47—48no—
339C22×C47—42no—
340C22×C47—42no—
341C22×C47—42no—
342C22×C47—42no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—84no—
348C22×C47—84no—
349C22×C47#54812yes—
350C22×C47#57512yes—
351C22×C47#57612yes—
352C22×C47C23×D411yescharacteristic
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47#54812yes—
365C4×C47C22×#4111yescharacteristic
366C4×C47C2×2−1+411yescharacteristic
367C2×#559C2×C4711yescharacteristic, complemented
368C2×#554C2×C4711yescharacteristic, complemented
369#3370C2×C47116yesdirect product factor
370C2×#490C2×C4711yescharacteristic, complemented
371C2×#489C2×C4711yescharacteristic, complemented
372C2×#488C2×C4711yescharacteristic, complemented
373C2×#479C2×C4711yescharacteristic, complemented
374C2×#478C2×C4711yescharacteristic, complemented
375C2×#474C2×C4711yescharacteristic, complemented
376C2×#463C2×C4711yescharacteristic, complemented
377C2×#463C2×C4711yescharacteristic, complemented
378C2×#459C2×C4711yescharacteristic
379C2×#446C2×C4711yescharacteristic, complemented
380C2×#442C2×C4711yescharacteristic, complemented
381C2×#440C2×C4711yescharacteristic, complemented
382C2×C4×D8C2×C4711yescharacteristic, complemented
383C2×C47—44no—
384C2×C47—82no—
385C2×C47—82no—
386C2×C47#337014yesdirect product factor
387C2×C47C2×#54811yescharacteristic
388C2×C47C2×#57511yescharacteristic
389C2×C47C2×#57611yescharacteristic
390C22×SD16C22×C4711yescharacteristic
391C22×D8C22×C4711yescharacteristic
392C22×D8C22×C4711yescharacteristic
393#559—24no—
394#559C22×C4718yescomplemented
395#554—24no—
396#554C22×C4718yescomplemented
397C2×C4⋊Q8C22×C4711yescharacteristic
398C2×#127C22×C4711yescharacteristic
399C2×#125C22×C4711yescharacteristic
400C2×#125C22×C4711yescharacteristic
401C2×#124—21no—
402C2×#124C22×C4711yescharacteristic
403C2×#124C22×C4711yescharacteristic
404C2×#123—21no—
405C2×#123—21no—
406C2×C22⋊Q8—21no—
407C2×C22⋊Q8—21no—
408C2×C22⋊Q8—21no—
409C2×C4×Q8C22×C4711yescharacteristic
410C2×C4×Q8C22×C4711yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4C22×C4711yescharacteristic
413C2×C4×D4C22×C4711yescharacteristic
414C2×C4×D4C22×C4711yescharacteristic
415C2×C4×D4C22×C4711yescharacteristic
416C2×C4×D4C22×C4711yescharacteristic
417C22×C4⋊C4—21no—
418#490C22×C4718yescomplemented
419#489C22×C4718yescomplemented
420#488C22×C4718yescomplemented
421#479C22×C4718yescomplemented
422#478C22×C4718yescomplemented
423#474C22×C4718yescomplemented
424#463C22×C4718yescomplemented
425#463C22×C4718yescomplemented
426#459C22×C4718yes—
427#446C22×C4718yescomplemented
428#442C22×C4718yescomplemented
429#440C22×C4718yescomplemented
430C4×D8C22×C4718yescomplemented
431C2×#107C22×C4711yescharacteristic
432C2×#107C22×C4711yescharacteristic
433C2×#106C22×C4711yescharacteristic
434C2×C4⋊C8C22×C4711yescharacteristic
435C2×C4⋊C8C22×C4711yescharacteristic
436C2×C4⋊C8C22×C4711yescharacteristic
437C2×#103C22×C4711yescharacteristic
438C2×#103C22×C4711yescharacteristic
439C2×#103C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic
441C2×#102C22×C4711yescharacteristic
442C2×#102C22×C4711yescharacteristic
443C2×#102C22×C4711yescharacteristic
444C2×#102C22×C4711yescharacteristic
445C2×#102C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#97C22×C4711yescharacteristic
448C2×#97C22×C4711yescharacteristic
449C2×C4×C8C22×C4711yescharacteristic
450C47C2×#337011yescharacteristic, direct product factor, Sylow
451C22×Q8—21no—
452C22×Q8D4×C4711yescharacteristic
453C22×Q8C23×C4711yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4C23×C4711yescharacteristic
457C22×D4C23×C4711yescharacteristic
458C22×D4C23×C4711yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C2×SD16—24no—
465C2×SD16C23×C4714yes—
466C2×D8—24no—
467C2×D8—24no—
468C2×D8C23×C4714yes—
469C2×D8C23×C4714yes—
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473C22×C8C23×C4711yescharacteristic
474C4⋊Q8—22no—
475C4⋊Q8C23×C4714yes—
476#127—22no—
477#127C23×C4714yes—
478#125—22no—
479#125—22no—
480#125C23×C4714yes—
481#125C23×C4714yes—
482#124—28no—
483#124—22no—
484#124—22no—
485#124C23×C4714yes—
486#124C23×C4714yes—
487#123—28no—
488#123—28no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C22⋊Q8—28no—
492C4×Q8—22no—
493C4×Q8D4×C4714yes—
494C4×Q8C23×C4714yes—
495C4×Q8C23×C4714yes—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4C23×C4714yes—
503C4×D4C23×C4714yes—
504C4×D4C23×C4714yes—
505C4×D4C23×C4714yes—
506C4×D4C23×C4714yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4D4×C4711yescharacteristic
515C2×C4⋊C4D4×C4711yescharacteristic
516C2×C4⋊C4D4×C4711yescharacteristic
517C2×C4⋊C4C23×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C42—21no—
531C2×C42C23×C4711yescharacteristic
532C2×C42C23×C4711yescharacteristic
533C2×C42C23×C4711yescharacteristic
534#107C23×C4714yes—
535#107C23×C4714yes—
536#106C23×C4714yes—
537C4⋊C8C23×C4714yes—
538C4⋊C8C23×C4714yes—
539C4⋊C8C23×C4714yes—
540#103C23×C4714yes—
541#103C23×C4714yes—
542#103C23×C4714yes—
543#102C23×C4714yes—
544#102C23×C4714yes—
545#102C23×C4714yes—
546#102C23×C4714yes—
547#102C23×C4714yes—
548#102C23×C4714yes—
549#102C23×C4714yes—
550#97C23×C4714yes—
551#97C23×C4714yes—
552C4×C8C23×C4714yes—
553C24—21no—
554C24—21no—
555C24—21no—
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—42no—
561C2×Q8—82no—
562C2×Q8C2×D4×C4714yes—
563C2×Q8C24×C4712yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4#41×C4714yes—
577C2×D4C24×C4712yes—
578C2×D4C24×C4712yes—
579C2×D4C24×C4712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—44no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4C2×D4×C4711yescharacteristic
596C22×C4C2×D4×C4711yescharacteristic
597C22×C4C2×D4×C4711yescharacteristic
598C22×C4C2×D4×C4711yescharacteristic
599C22×C4C2×D4×C4711yescharacteristic
600C22×C4C2×D4×C4711yescharacteristic
601C22×C4C24×C4711yescharacteristic
602SD16—28no—
603D8—28no—
604D8—28no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8C24×C4712yes—
610C2×C8C24×C4712yes—
611C2×C8C24×C4712yes—
612C2×C8C24×C4712yes—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C4714yes—
624C4⋊C4C2×D4×C4714yes—
625C4⋊C4C2×D4×C4714yes—
626C4⋊C4C24×C4712yes—
627C4⋊C4C24×C4712yes—
628C4⋊C4C24×C4712yes—
629C4⋊C4C24×C4712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C42—24no—
640C42C2×D4×C4712yes—
641C42C2×D4×C4712yes—
642C42C2×D4×C4712yes—
643C42C24×C4712yes—
644C42C24×C4712yes—
645C42C24×C4712yes—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C22×D4×C4711yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—84no—
664D4—24no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—42no—
672D4—42no—
673D4—84no—
674D4C2×#41×C4714yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—84no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4C22×D4×C4712yes—
697C2×C4C22×D4×C4712yes—
698C2×C4C22×D4×C4712yes—
699C2×C4C22×D4×C4712yes—
700C2×C4C22×D4×C4712yes—
701C2×C4C22×D4×C4712yes—
702C2×C4C22×D4×C4711yescharacteristic
703C2×C4C2×#41×C4712yes—
704C2×C42−1+4×C4712yes—
705C2×C4C25×C4711yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22—84no—
722C22C47×#54812yes—
723C22C47×#57512yes—
724C22C47×#57612yes—
725C22C23×D4×C4711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4C47×#54812yes—
738C4C22×#41×C4711yescharacteristic
739C4C2×2−1+4×C4711yescharacteristic
740C2—44no—
741C2—82no—
742C2—82no—
743C2C47×#337014yesdirect product factor
744C2C2×C47×#54811yescharacteristic
745C2C2×C47×#57511yescharacteristic
746C2C2×C47×#57611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC2×C47×#459C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×Q8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#559C2semidirect
2. C2×C47×#554C2semidirect
3. C47×#3370C2direct (N × H)
4. C2×C47×#490C2semidirect
5. C2×C47×#489C2semidirect
6. C2×C47×#488C2semidirect
7. C2×C47×#479C2semidirect
8. C2×C47×#478C2semidirect
9. C2×C47×#474C2semidirect
10. C2×C47×#463C2semidirect
11. C2×C47×#463C2semidirect
13. C2×C47×#446C2semidirect
14. C2×C47×#442C2semidirect
15. C2×C47×#440C2semidirect
16. C2×C4×D8×C47C2semidirect
21. C47×#559C22semidirect
23. C47×#554C22semidirect
45. C47×#490C22semidirect
46. C47×#489C22semidirect
47. C47×#488C22semidirect
48. C47×#479C22semidirect
49. C47×#478C22semidirect
50. C47×#474C22semidirect
51. C47×#463C22semidirect
52. C47×#463C22semidirect
54. C47×#446C22semidirect
55. C47×#442C22semidirect
56. C47×#440C22semidirect
57. C4×D8×C47C22semidirect
336. C2×#3370C47direct (N × H)
367. C2×#559C2×C47semidirect
368. C2×#554C2×C47semidirect
369. #3370C2×C47direct (N × H)
370. C2×#490C2×C47semidirect
371. C2×#489C2×C47semidirect
372. C2×#488C2×C47semidirect
373. C2×#479C2×C47semidirect
374. C2×#478C2×C47semidirect
375. C2×#474C2×C47semidirect
376. C2×#463C2×C47semidirect
377. C2×#463C2×C47semidirect
379. C2×#446C2×C47semidirect
380. C2×#442C2×C47semidirect
381. C2×#440C2×C47semidirect
382. C2×C4×D8C2×C47semidirect
386. C2×C47#3370direct (N × H)
394. #559C22×C47semidirect
396. #554C22×C47semidirect
418. #490C22×C47semidirect
419. #489C22×C47semidirect
420. #488C22×C47semidirect
421. #479C22×C47semidirect
422. #478C22×C47semidirect
423. #474C22×C47semidirect
424. #463C22×C47semidirect
425. #463C22×C47semidirect
427. #446C22×C47semidirect
428. #442C22×C47semidirect
429. #440C22×C47semidirect
430. C4×D8C22×C47semidirect
450. C47C2×#3370direct (N × H)
743. C2C47×#3370direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5592
C2×C47×#5542
C47×#33702
C2×C47×#4902
C2×C47×#4892
C2×C47×#4882
C2×C47×#4792
C2×C47×#4782
C2×C47×#4742
C2×C47×#4632
C2×C47×#4592
C2×C47×#4462
C2×C47×#4422
C2×C47×#4402
C2×C4×D8×C472
C2×#337047