Finite Group Databasebeta

← C47×#24395 #26064093

Subgroups — C47×#24395 #26064093

Order 12032.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#537C211yesmaximal, characteristic
2C2×C47×#470C211yesmaximal, characteristic, complemented
3C2×C47×#465C211yesmaximal, characteristic, complemented
4C2×C47×#452C211yesmaximal, characteristic, complemented
5C2×C47×#408C211yesmaximal, characteristic, complemented
6C47×#2616C211yesmaximal, characteristic, complemented
7C47×#2035C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2001C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1895C211yesmaximal, characteristic, complemented
12C47×#1892C211yesmaximal, characteristic, complemented
13C47×#1872C211yesmaximal, characteristic, complemented
14C47×#1853C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C22×#41×C47C2211yescharacteristic
18C22×Q16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic
21C23×C8×C47C2211yescharacteristic
22C47×#537—24no—
23C47×#537—24no—
24C2×C22⋊Q8×C47—21no—
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C22⋊Q8×C47C2211yescharacteristic
29C2×C22⋊Q8×C47C2211yescharacteristic
30C2×#121×C47—21no—
31C2×#121×C47—21no—
32C2×#121×C47—21no—
33C2×#121×C47C2211yescharacteristic
34C2×#121×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C47×#470—24no—
37C47×#465—24no—
38C47×#452—24no—
39C2×#106×C47C2211yescharacteristic
40C2×#106×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×#103×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×#102×C47C2211yescharacteristic
48C2×#102×C47C2211yescharacteristic
49C47×#408—24no—
50C2×C22⋊C8×C47C2211yescharacteristic
51C2×C22⋊C8×C47C2211yescharacteristic
52C2×C22⋊C8×C47C2211yescharacteristic
53C2×C22⋊C8×C47C2211yescharacteristic
54C47×#395—21no—
55C47×#394—21no—
56C47×#394—21no—
57C47×#394—21no—
58C47×#380C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#380C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C47×#340C2211yescharacteristic
64C47×#340C2211yescharacteristic
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—22no—
72C2×#41×C47—22no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47—41no—
77C22×Q8×C47D411yescharacteristic
78C22×Q8×C47C2311yescharacteristic
79C22×Q8×C47C2311yescharacteristic
80C22×D4×C47—21no—
81C22×D4×C47—21no—
82C22×D4×C47—21no—
83C22×D4×C47D411yescharacteristic
84C22×D4×C47D411yescharacteristic
85C22×D4×C47D411yescharacteristic
86C22×D4×C47C2311yescharacteristic
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C2×Q16×C47—22no—
93C2×Q16×C47—22no—
94C2×Q16×C47—41no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—41no—
98C2×M16×C47—22no—
99C2×M16×C47—22no—
100C2×M16×C47—41no—
101C22×C8×C47—22no—
102C22×C8×C47—22no—
103C22×C8×C47—41no—
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22⋊Q8×C47—28no—
109C22⋊Q8×C47—22no—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—22no—
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47—22no—
115C22⋊Q8×C47—22no—
116C22⋊Q8×C47—41no—
117C22⋊Q8×C47—41no—
118C22⋊Q8×C47D414yes—
119#121×C47—28no—
120#121×C47—28no—
121#121×C47—28no—
122#121×C47—22no—
123#121×C47—22no—
124#121×C47—22no—
125#121×C47D414yes—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47—21no—
129C2×C4⋊C4×C47—22no—
130C2×C4⋊C4×C47—22no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47—21no—
148C2×C22⋊C4×C47—21no—
149#106×C47—22no—
150#106×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#103×C47—22no—
154#103×C47—22no—
155#103×C47—41no—
156#102×C47—22no—
157#102×C47—22no—
158#102×C47—41no—
159C22⋊C8×C47—22no—
160C22⋊C8×C47—22no—
161C22⋊C8×C47—22no—
162C22⋊C8×C47D414yescomplemented
163#95×C47—21no—
164#95×C47—21no—
165#95×C47—21no—
166C24×C47—21no—
167C24×C47C2×D411yescharacteristic
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D411yescharacteristic
170#41×C47—44no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174#41×C47—44no—
175#41×C47—44no—
176#41×C47—44no—
177#41×C47—44no—
178C2×Q8×C47—22no—
179C2×Q8×C47—22no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—21no—
191C2×Q8×C47—41no—
192C2×Q8×C47C2×D412yes—
193C2×D4×C47—24no—
194C2×D4×C47—22no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—24no—
199C2×D4×C47—24no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—41no—
208C2×D4×C47—41no—
209C2×D4×C47—41no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—81no—
213C2×D4×C47—81no—
214C2×D4×C47—81no—
215C2×D4×C47—81no—
216C2×D4×C47C2×D412yes—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—24no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—24no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—42no—
241C22×C4×C47—42no—
242C22×C4×C47—81no—
243C22×C4×C47—81no—
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D412yes—
247C22×C4×C47C2×D412yes—
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D412yes—
250C22×C4×C47#4112yes—
251C22×C4×C47C2411yescharacteristic
252Q16×C47—44no—
253SD16×C47—44no—
254M16×C47—44no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47—21no—
263C2×C8×C47—21no—
264C2×C8×C47—21no—
265C2×C8×C47—44no—
266C2×C8×C47C2×D412yes—
267C2×C8×C47C2×D412yes—
268C4⋊C4×C47—24no—
269C4⋊C4×C47—24no—
270C4⋊C4×C47—24no—
271C4⋊C4×C47—21no—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—21no—
276C4⋊C4×C47—21no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47—42no—
280C4⋊C4×C47—42no—
281C4⋊C4×C47—42no—
282C4⋊C4×C47C2×D412yes—
283C4⋊C4×C47C2×D412yes—
284C22⋊C4×C47—24no—
285C22⋊C4×C47—24no—
286C22⋊C4×C47—24no—
287C22⋊C4×C47—24no—
288C22⋊C4×C47—42no—
289C22⋊C4×C47—42no—
290C22⋊C4×C47—42no—
291C22⋊C4×C47—81no—
292C22⋊C4×C47—81no—
293C22⋊C4×C47—81no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—21no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—21no—
306C23×C47—21no—
307C23×C47—22no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—21no—
311C23×C47—21no—
312C23×C47—21no—
313C23×C47—21no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47#12012yes—
321C23×C47#12112yes—
322C23×C47C22×D411yescharacteristic
323Q8×C47—22no—
324Q8×C47—22no—
325Q8×C47—44no—
326Q8×C47—41no—
327Q8×C47—41no—
328Q8×C47—41no—
329Q8×C47—41no—
330Q8×C47—41no—
331Q8×C47—41no—
332D4×C47—22no—
333D4×C47—22no—
334D4×C47—44no—
335D4×C47—44no—
336D4×C47—44no—
337D4×C47—48no—
338D4×C47—41no—
339D4×C47—41no—
340D4×C47—84no—
341D4×C47—84no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—48no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—84no—
384C2×C4×C47#12012yes—
385C2×C4×C47#12112yes—
386C2×C4×C47C22×D411yescharacteristic
387C2×C4×C47C22×D411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C2×#4111yescharacteristic
390C2×C4×C47H(5,𝔽2)11yescharacteristic
391C2×C4×C47H(5,𝔽2)11yescharacteristic
392C8×C47—22no—
393C8×C47—22no—
394C8×C47—41no—
395C8×C47—41no—
396#24395C4711yesmaximal, characteristic, direct product factor, Sylow
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—22no—
402C22×C47—22no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—41no—
406C22×C47—41no—
407C22×C47—41no—
408C22×C47—41no—
409C22×C47—41no—
410C22×C47—41no—
411C22×C47—42no—
412C22×C47—41no—
413C22×C47—41no—
414C22×C47—41no—
415C22×C47—41no—
416C22×C47—42no—
417C22×C47—41no—
418C22×C47—42no—
419C22×C47—41no—
420C22×C47—41no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47—81no—
424C22×C47—81no—
425C22×C47C2×#12011yescharacteristic
426C22×C47C2×#12111yescharacteristic
427C22×C47#53411yescharacteristic
428C22×C47#57711yescharacteristic
429C22×C47#57711yescharacteristic
430C22×C47#57711yescharacteristic
431C22×C47#57811yescharacteristic
432C4×C47—22no—
433C4×C47—22no—
434C4×C47—41no—
435C4×C47—42no—
436C4×C47—42no—
437C4×C47—42no—
438C4×C47—81no—
439C4×C47—81no—
440C4×C47—81no—
441C4×C47—81no—
442C4×C47D4211yescharacteristic
443C4×C47D4211yescharacteristic
444C4×C47#54611yescharacteristic
445C4×C47#54611yescharacteristic
446C2×#537C2×C4711yescharacteristic
447C2×#470C2×C4711yescharacteristic, complemented
448C2×#465C2×C4711yescharacteristic, complemented
449C2×#452C2×C4711yescharacteristic, complemented
450C2×#408C2×C4711yescharacteristic, complemented
451#2616C2×C4711yescharacteristic, complemented
452#2035C2×C4711yescharacteristic, complemented
453#2034C2×C4711yescharacteristic, complemented
454#2001C2×C4711yescharacteristic, complemented
455#2000C2×C4711yescharacteristic, complemented
456#1895C2×C4711yescharacteristic, complemented
457#1892C2×C4711yescharacteristic, complemented
458#1872C2×C4711yescharacteristic, complemented
459#1853C2×C4711yescharacteristic, complemented
460#1788C2×C4711yescharacteristic, complemented
461C2×C47—42no—
462C2×C47—42no—
463C2×C47—81no—
464C2×C47—82no—
465C2×C47#241011yescharacteristic
466C2×C47#300911yescharacteristic
467C2×C47#301311yescharacteristic
468C2×C47#306011yescharacteristic
469C2×C47#306311yescharacteristic
470C2×C47#320111yescharacteristic
471C2×C47#320411yescharacteristic
472C22×#41C22×C4711yescharacteristic
473C22×#41C22×C4711yescharacteristic
474C22×Q16C22×C4711yescharacteristic
475C22×SD16C22×C4711yescharacteristic
476C22×M16C22×C4711yescharacteristic
477C23×C8C22×C4711yescharacteristic
478#537—24no—
479#537—24no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C4711yescharacteristic
482C2×C22⋊Q8C22×C4711yescharacteristic
483C2×C22⋊Q8C22×C4711yescharacteristic
484C2×C22⋊Q8C22×C4711yescharacteristic
485C2×C22⋊Q8C22×C4711yescharacteristic
486C2×#121—21no—
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C4711yescharacteristic
490C2×#121C22×C4711yescharacteristic
491C22×C4⋊C4C22×C4711yescharacteristic
492#470—24no—
493#465—24no—
494#452—24no—
495C2×#106C22×C4711yescharacteristic
496C2×#106C22×C4711yescharacteristic
497C2×#103C22×C4711yescharacteristic
498C2×#103C22×C4711yescharacteristic
499C2×#103C22×C4711yescharacteristic
500C2×#103C22×C4711yescharacteristic
501C2×#103C22×C4711yescharacteristic
502C2×#102C22×C4711yescharacteristic
503C2×#102C22×C4711yescharacteristic
504C2×#102C22×C4711yescharacteristic
505#408—24no—
506C2×C22⋊C8C22×C4711yescharacteristic
507C2×C22⋊C8C22×C4711yescharacteristic
508C2×C22⋊C8C22×C4711yescharacteristic
509C2×C22⋊C8C22×C4711yescharacteristic
510#395—21no—
511#394—21no—
512#394—21no—
513#394—21no—
514#380C22×C4711yescharacteristic
515#380C22×C4711yescharacteristic
516#380C22×C4711yescharacteristic
517#340C22×C4711yescharacteristic
518#340C22×C4711yescharacteristic
519#340C22×C4711yescharacteristic
520#340C22×C4711yescharacteristic
521C47#2439511yescharacteristic, direct product factor, Sylow
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8D4×C4711yescharacteristic
535C22×Q8C23×C4711yescharacteristic
536C22×Q8C23×C4711yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C4711yescharacteristic
541C22×D4D4×C4711yescharacteristic
542C22×D4D4×C4711yescharacteristic
543C22×D4C23×C4711yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C4711yescharacteristic
547C23×C4C23×C4711yescharacteristic
548C23×C4C23×C4711yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C4711yescharacteristic
562C22×C8C23×C4711yescharacteristic
563C22×C8C23×C4711yescharacteristic
564C22×C8C23×C4711yescharacteristic
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C4714yes—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121D4×C4714yes—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C23×C4711yescharacteristic
592C2×C4⋊C4C23×C4711yescharacteristic
593C2×C4⋊C4C23×C4711yescharacteristic
594C2×C4⋊C4C23×C4711yescharacteristic
595C2×C4⋊C4C23×C4711yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606#106—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C4714yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C4711yescharacteristic
625C24C2×D4×C4711yescharacteristic
626C24C2×D4×C4711yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C4712yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C4712yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C4711yescharacteristic
702C22×C4C2×D4×C4711yescharacteristic
703C22×C4C2×D4×C4712yes—
704C22×C4C2×D4×C4712yes—
705C22×C4C2×D4×C4711yescharacteristic
706C22×C4C2×D4×C4712yes—
707C22×C4#41×C4712yes—
708C22×C4C24×C4711yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C4712yes—
724C2×C8C2×D4×C4712yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C4712yes—
740C4⋊C4C2×D4×C4712yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C4712yes—
778C23#121×C4712yes—
779C23C22×D4×C4711yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4#120×C4712yes—
842C2×C4#121×C4712yes—
843C2×C4C22×D4×C4711yescharacteristic
844C2×C4C22×D4×C4711yescharacteristic
845C2×C4C22×D4×C4711yescharacteristic
846C2×C4C2×#41×C4711yescharacteristic
847C2×C4H(5,𝔽2)×C4711yescharacteristic
848C2×C4H(5,𝔽2)×C4711yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C4711yescharacteristic
882C22C2×#121×C4711yescharacteristic
883C22C47×#53411yescharacteristic
884C22C47×#57711yescharacteristic
885C22C47×#57711yescharacteristic
886C22C47×#57711yescharacteristic
887C22C47×#57811yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C4711yescharacteristic
899C4D42×C4711yescharacteristic
900C4C47×#54611yescharacteristic
901C4C47×#54611yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C47×#241011yescharacteristic
907C2C47×#300911yescharacteristic
908C2C47×#301311yescharacteristic
909C2C47×#306011yescharacteristic
910C2C47×#306311yescharacteristic
911C2C47×#320111yescharacteristic
912C2C47×#320411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#470C2semidirect
3. C2×C47×#465C2semidirect
4. C2×C47×#452C2semidirect
5. C2×C47×#408C2semidirect
6. C47×#2616C2semidirect
7. C47×#2035C2semidirect
8. C47×#2034C2semidirect
9. C47×#2001C2semidirect
10. C47×#2000C2semidirect
11. C47×#1895C2semidirect
12. C47×#1892C2semidirect
13. C47×#1872C2semidirect
14. C47×#1853C2semidirect
15. C47×#1788C2semidirect
162. C22⋊C8×C47D4semidirect
396. #24395C47direct (N × H)
447. C2×#470C2×C47semidirect
448. C2×#465C2×C47semidirect
449. C2×#452C2×C47semidirect
450. C2×#408C2×C47semidirect
451. #2616C2×C47semidirect
452. #2035C2×C47semidirect
453. #2034C2×C47semidirect
454. #2001C2×C47semidirect
455. #2000C2×C47semidirect
456. #1895C2×C47semidirect
457. #1892C2×C47semidirect
458. #1872C2×C47semidirect
459. #1853C2×C47semidirect
460. #1788C2×C47semidirect
521. C47#24395direct (N × H)
619. C22⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5372
C2×C47×#4702
C2×C47×#4652
C2×C47×#4522
C2×C47×#4082
C47×#26162
C47×#20352
C47×#20342
C47×#20012
C47×#20002
C47×#18952
C47×#18922
C47×#18722
C47×#18532
C47×#17882
#2439547