Finite Group Databasebeta

← C47×#21871 #26061569

Subgroups — C47×#21871 #26061569

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#542C211yesmaximal, characteristic
2C2×C47×#433C211yesmaximal, characteristic, complemented
3C47×#2317C211yesmaximal, characteristic, complemented
4C47×#1993C211yesmaximal, characteristic, complemented
5C47×#1990C211yesmaximal, characteristic, complemented
6C47×#1959C211yesmaximal, characteristic, complemented
7C47×#1958C211yesmaximal, characteristic, complemented
8C47×#1875C211yesmaximal, characteristic
9C47×#1874C211yesmaximal, characteristic
10C47×#1873C211yesmaximal, characteristic, complemented
11C47×#1872C211yesmaximal, characteristic, complemented
12C47×#1805C211yesmaximal, characteristic, complemented
13C47×#1804C211yesmaximal, characteristic, complemented
14C47×#1803C211yesmaximal, characteristic, complemented
15C47×#1802C211yesmaximal, characteristic, complemented
16C47×#542—24no—
17C47×#542C418yescomplemented
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×#126×C47—21no—
20C2×#124×C47—21no—
21C2×#124×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×C22⋊Q8×C47—21no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×C4×Q8×C47C2211yescharacteristic
27C2×C4×D4×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C47×#433—24no—
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×#97×C47C2211yescharacteristic
45C2×C4×C8×C47C2211yescharacteristic
46C47×#389—21no—
47C47×#389—21no—
48C47×#385—21no—
49C47×#385—21no—
50C47×#384C2211yescharacteristic
51C47×#384C2211yescharacteristic
52C47×#382C2211yescharacteristic
53C47×#382C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Q8×C47—21no—
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47C2311yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47C2311yescharacteristic
69C22×C8×C47C2311yescharacteristic
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C4⋊Q8×C47—22no—
74C4⋊Q8×C47C2×C414yescomplemented
75#126×C47—28no—
76#124×C47—28no—
77#124×C47—22no—
78#124×C47C2×C414yescomplemented
79#123×C47—28no—
80C22⋊Q8×C47—22no—
81C22⋊Q8×C47—28no—
82C22⋊Q8×C47C2×C414yes—
83#121×C47—22no—
84#121×C47C2×C414yes—
85C4×Q8×C47—22no—
86C4×Q8×C47C2×C414yescomplemented
87C4×D4×C47—22no—
88C4×D4×C47C2×C414yescomplemented
89#117×C47—41no—
90#117×C47—41no—
91#117×C47C2×C414yes—
92#117×C47D414yes—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—41no—
102C2×C4⋊C4×C47—41no—
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47D411yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123C4⋊C8×C47—22no—
124C4⋊C8×C47—22no—
125#103×C47—41no—
126#103×C47—41no—
127#103×C47—41no—
128#103×C47—41no—
129#102×C47—41no—
130#102×C47—41no—
131#102×C47—41no—
132#102×C47—41no—
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135#97×C47—22no—
136C4×C8×C47—22no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143C2×Q8×C47—24no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—81no—
150C2×Q8×C47—81no—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—24no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—81no—
159C2×D4×C47—81no—
160C2×D4×C47C22×C412yes—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—24no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—42no—
174C22×C4×C47—81no—
175C22×C4×C47—81no—
176C22×C4×C47—81no—
177C22×C4×C47—81no—
178C22×C4×C47C22×C412yes—
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D412yes—
185C22×C4×C47C2411yescharacteristic
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C4⋊C4×C47—24no—
199C4⋊C4×C47—24no—
200C4⋊C4×C47—24no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47—81no—
213C4⋊C4×C47—81no—
214C4⋊C4×C47—81no—
215C4⋊C4×C47—81no—
216C4⋊C4×C47C22⋊C414yes—
217C4⋊C4×C47C22⋊C414yes—
218C4⋊C4×C47C22×C412yes—
219C4⋊C4×C47C22×C412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—24no—
223C22⋊C4×C47—24no—
224C22⋊C4×C47—24no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47C22⋊C414yes—
227C22⋊C4×C47C22⋊C414yes—
228C42×C47—24no—
229C42×C47—42no—
230C42×C47C22×C412yes—
231C42×C47C22×C412yes—
232C42×C47C2×D412yes—
233C42×C47C2×D412yes—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—22no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47C2×C22⋊C412yes—
248C23×C47C22×D411yescharacteristic
249Q8×C47—22no—
250Q8×C47—22no—
251Q8×C47—41no—
252Q8×C47—41no—
253Q8×C47—84no—
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—41no—
257D4×C47—41no—
258D4×C47—84no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—84no—
295C2×C4×C47—84no—
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47C23×C411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C2×C4×C47H(5,𝔽2)11yescharacteristic
305C2×C4×C472−1+411yescharacteristic
306C2×C4×C472−1+411yescharacteristic
307C8×C47—41no—
308C8×C47—41no—
309C8×C47—41no—
310C8×C47—41no—
311#21871C4711yesmaximal, characteristic, direct product factor, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—42no—
320C22×C47—42no—
321C22×C47—42no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47C22×C22⋊C411yescharacteristic
327C22×C47#53511yescharacteristic
328C22×C47#53611yescharacteristic
329C22×C47#57611yescharacteristic
330C22×C47#57711yescharacteristic
331C22×C47#57711yescharacteristic
332C22×C47#57811yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—81no—
342C4×C47—81no—
343C4×C47—81no—
344C4×C47—81no—
345C4×C47#52011yescharacteristic
346C4×C47#52011yescharacteristic
347C4×C47#53711yescharacteristic
348C4×C47#53711yescharacteristic
349C2×#542C2×C4711yescharacteristic
350C2×#433C2×C4711yescharacteristic, complemented
351#2317C2×C4711yescharacteristic, complemented
352#1993C2×C4711yescharacteristic, complemented
353#1990C2×C4711yescharacteristic, complemented
354#1959C2×C4711yescharacteristic, complemented
355#1958C2×C4711yescharacteristic, complemented
356#1875C2×C4711yescharacteristic
357#1874C2×C4711yescharacteristic
358#1873C2×C4711yescharacteristic, complemented
359#1872C2×C4711yescharacteristic, complemented
360#1805C2×C4711yescharacteristic, complemented
361#1804C2×C4711yescharacteristic, complemented
362#1803C2×C4711yescharacteristic, complemented
363#1802C2×C4711yescharacteristic, complemented
364C2×C47—42no—
365C2×C47—82no—
366C2×C47#231111yescharacteristic
367C2×C47#289711yescharacteristic
368C2×C47#289811yescharacteristic
369C2×C47#322411yescharacteristic
370C2×C47#322511yescharacteristic
371C2×C47#324311yescharacteristic
372C2×C47#324411yescharacteristic
373#542—24no—
374#542C4×C4718yescomplemented
375C2×C4⋊Q8C22×C4711yescharacteristic
376C2×#126—21no—
377C2×#124—21no—
378C2×#124C22×C4711yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C22×C4711yescharacteristic
382C2×#121C22×C4711yescharacteristic
383C2×C4×Q8C22×C4711yescharacteristic
384C2×C4×D4C22×C4711yescharacteristic
385C2×#117C22×C4711yescharacteristic
386C2×#117C22×C4711yescharacteristic
387C22×C4⋊C4C22×C4711yescharacteristic
388#433—24no—
389C2×C4⋊C8C22×C4711yescharacteristic
390C2×C4⋊C8C22×C4711yescharacteristic
391C2×#103C22×C4711yescharacteristic
392C2×#103C22×C4711yescharacteristic
393C2×#103C22×C4711yescharacteristic
394C2×#103C22×C4711yescharacteristic
395C2×#102C22×C4711yescharacteristic
396C2×#102C22×C4711yescharacteristic
397C2×#102C22×C4711yescharacteristic
398C2×#102C22×C4711yescharacteristic
399C2×C22⋊C8C22×C4711yescharacteristic
400C2×C22⋊C8C22×C4711yescharacteristic
401C2×#97C22×C4711yescharacteristic
402C2×C4×C8C22×C4711yescharacteristic
403#389—21no—
404#389—21no—
405#385—21no—
406#385—21no—
407#384C22×C4711yescharacteristic
408#384C22×C4711yescharacteristic
409#382C22×C4711yescharacteristic
410#382C22×C4711yescharacteristic
411#340C22×C4711yescharacteristic
412#340C22×C4711yescharacteristic
413#340C22×C4711yescharacteristic
414#340C22×C4711yescharacteristic
415#340C22×C4711yescharacteristic
416#340C22×C4711yescharacteristic
417#340C22×C4711yescharacteristic
418#340C22×C4711yescharacteristic
419C47#2187111yescharacteristic, direct product factor, Sylow
420C22×Q8—21no—
421C22×Q8C23×C4711yescharacteristic
422C22×D4—21no—
423C22×D4C23×C4711yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C4711yescharacteristic
427C22×C8C23×C4711yescharacteristic
428C22×C8C23×C4711yescharacteristic
429C22×C8C23×C4711yescharacteristic
430C22×C8C23×C4711yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8C2×C4×C4714yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×C4×C4714yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×C4×C4714yes—
441#121—22no—
442#121C2×C4×C4714yes—
443C4×Q8—22no—
444C4×Q8C2×C4×C4714yescomplemented
445C4×D4—22no—
446C4×D4C2×C4×C4714yescomplemented
447#117—41no—
448#117—41no—
449#117C2×C4×C4714yes—
450#117D4×C4714yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4D4×C4711yescharacteristic
462C2×C4⋊C4D4×C4711yescharacteristic
463C2×C4⋊C4C23×C4711yescharacteristic
464C2×C4⋊C4C23×C4711yescharacteristic
465C2×C4⋊C4C23×C4711yescharacteristic
466C2×C4⋊C4C23×C4711yescharacteristic
467C2×C4⋊C4C23×C4711yescharacteristic
468C2×C4⋊C4C23×C4711yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4D4×C4711yescharacteristic
476C2×C22⋊C4D4×C4711yescharacteristic
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C4711yescharacteristic
480C2×C42C23×C4711yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—41no—
484#103—41no—
485#103—41no—
486#103—41no—
487#102—41no—
488#102—41no—
489#102—41no—
490#102—41no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—21no—
500C24C2×D4×C4711yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×C4×C4712yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×C4×C4712yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C22×C4×C4712yes—
537C22×C4C2×D4×C4711yescharacteristic
538C22×C4C2×D4×C4711yescharacteristic
539C22×C4C2×D4×C4711yescharacteristic
540C22×C4C2×D4×C4711yescharacteristic
541C22×C4C2×D4×C4711yescharacteristic
542C22×C4C2×D4×C4712yes—
543C22×C4C24×C4711yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4—81no—
572C4⋊C4—81no—
573C4⋊C4—81no—
574C4⋊C4C22⋊C4×C4714yes—
575C4⋊C4C22⋊C4×C4714yes—
576C4⋊C4C22×C4×C4712yes—
577C4⋊C4C22×C4×C4712yes—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—42no—
584C22⋊C4C22⋊C4×C4714yes—
585C22⋊C4C22⋊C4×C4714yes—
586C42—24no—
587C42—42no—
588C42C22×C4×C4712yes—
589C42C22×C4×C4712yes—
590C42C2×D4×C4712yes—
591C42C2×D4×C4712yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊C4×C4712yes—
606C23C22×D4×C4711yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—84no—
654C2×C4C2×C22⋊C4×C4712yes—
655C2×C4C2×C22⋊C4×C4712yes—
656C2×C4C2×C22⋊C4×C4712yes—
657C2×C4C2×C22⋊C4×C4712yes—
658C2×C4C2×C22⋊C4×C4712yes—
659C2×C4C23×C4×C4711yescharacteristic
660C2×C4C22×D4×C4711yescharacteristic
661C2×C4H(5,𝔽2)×C4711yescharacteristic
662C2×C4H(5,𝔽2)×C4711yescharacteristic
663C2×C42−1+4×C4711yescharacteristic
664C2×C42−1+4×C4711yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊C4×C4711yescharacteristic
684C22C47×#53511yescharacteristic
685C22C47×#53611yescharacteristic
686C22C47×#57611yescharacteristic
687C22C47×#57711yescharacteristic
688C22C47×#57711yescharacteristic
689C22C47×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C47×#52011yescharacteristic
703C4C47×#52011yescharacteristic
704C4C47×#53711yescharacteristic
705C4C47×#53711yescharacteristic
706C2—42no—
707C2—82no—
708C2C47×#231111yescharacteristic
709C2C47×#289711yescharacteristic
710C2C47×#289811yescharacteristic
711C2C47×#322411yescharacteristic
712C2C47×#322511yescharacteristic
713C2C47×#324311yescharacteristic
714C2C47×#324411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×#121×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×#117×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#433C2semidirect
3. C47×#2317C2semidirect
4. C47×#1993C2semidirect
5. C47×#1990C2semidirect
6. C47×#1959C2semidirect
7. C47×#1958C2semidirect
10. C47×#1873C2semidirect
11. C47×#1872C2semidirect
12. C47×#1805C2semidirect
13. C47×#1804C2semidirect
14. C47×#1803C2semidirect
15. C47×#1802C2semidirect
17. C47×#542C4semidirect
74. C4⋊Q8×C47C2×C4semidirect
78. #124×C47C2×C4semidirect
86. C4×Q8×C47C2×C4semidirect
88. C4×D4×C47C2×C4semidirect
311. #21871C47direct (N × H)
350. C2×#433C2×C47semidirect
351. #2317C2×C47semidirect
352. #1993C2×C47semidirect
353. #1990C2×C47semidirect
354. #1959C2×C47semidirect
355. #1958C2×C47semidirect
358. #1873C2×C47semidirect
359. #1872C2×C47semidirect
360. #1805C2×C47semidirect
361. #1804C2×C47semidirect
362. #1803C2×C47semidirect
363. #1802C2×C47semidirect
374. #542C4×C47semidirect
419. C47#21871direct (N × H)
432. C4⋊Q8C2×C4×C47semidirect
436. #124C2×C4×C47semidirect
444. C4×Q8C2×C4×C47semidirect
446. C4×D4C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5422
C2×C47×#4332
C47×#23172
C47×#19932
C47×#19902
C47×#19592
C47×#19582
C47×#18752
C47×#18742
C47×#18732
C47×#18722
C47×#18052
C47×#18042
C47×#18032
C47×#18022
#2187147