Finite Group Databasebeta

← C47×#22549 #26062247

Subgroups — C47×#22549 #26062247

Order 12032.

1118 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×#559C211yesmaximal, characteristic
2C2×C47×#446C211yesmaximal, characteristic, complemented
3C47×#2355C211yesmaximal, characteristic, complemented
4C47×#1983C211yesmaximal, characteristic, complemented
5C47×#1983C211yesmaximal, characteristic, complemented
6C47×#1982C211yesmaximal, characteristic
7C47×#1961C211yesmaximal, characteristic
8C47×#1959C211yesmaximal, characteristic, complemented
9C47×#1958C211yesmaximal, characteristic, complemented
10C47×#1805C211yesmaximal, characteristic, complemented
11C47×#1804C211yesmaximal, characteristic, complemented
12C47×#1802C211yesmaximal, characteristic, complemented
13C47×#1763C211yesmaximal, characteristic, complemented
14C47×#1762C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C47×#559—24no—
17C47×#559C418yescomplemented
18C2×#127×C47C2211yescharacteristic
19C2×#124×C47—21no—
20C2×#124×C47C2211yescharacteristic
21C2×#124×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×#123×C47—21no—
24C2×C4×Q8×C47C2211yescharacteristic
25C2×C4×Q8×C47C2211yescharacteristic
26C2×C4×D4×C47—21no—
27C2×C4×D4×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C47×#446—24no—
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×C4⋊C8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#103×C47C2211yescharacteristic
35C2×#103×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#97×C47C2211yescharacteristic
46C2×#97×C47C2211yescharacteristic
47C2×C4×C8×C47C2211yescharacteristic
48C47×#391—21no—
49C47×#387—21no—
50C47×#387—21no—
51C47×#384C2211yescharacteristic
52C47×#382C2211yescharacteristic
53C47×#382C2211yescharacteristic
54C4×C4⋊C4×C47—21no—
55C4×C4⋊C4×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Q8×C47D411yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2311yescharacteristic
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C22×C8×C47C2311yescharacteristic
71C22×C8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74#127×C47—22no—
75#127×C47C2×C414yes—
76#124×C47—28no—
77#124×C47—22no—
78#124×C47—22no—
79#124×C47C2×C414yes—
80#124×C47C2×C414yes—
81#123×C47—28no—
82#123×C47—28no—
83C4×Q8×C47—22no—
84C4×Q8×C47C2×C414yes—
85C4×Q8×C47C2×C414yes—
86C4×Q8×C47D414yes—
87C4×D4×C47—28no—
88C4×D4×C47—22no—
89C4×D4×C47—22no—
90C4×D4×C47C2×C414yes—
91C4×D4×C47C2×C414yes—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47D411yescharacteristic
96C2×C4⋊C4×C47D411yescharacteristic
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C42×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C4⋊C8×C47—22no—
117C4⋊C8×C47—22no—
118C4⋊C8×C47—22no—
119#103×C47—22no—
120#103×C47—22no—
121#103×C47—41no—
122#103×C47—41no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—41no—
128#102×C47—41no—
129#102×C47—41no—
130#102×C47—41no—
131#97×C47—22no—
132#97×C47—22no—
133C4×C8×C47—22no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47—21no—
142C24×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47C22⋊C414yes—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—24no—
153C2×D4×C47—24no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—21no—
162C2×D4×C47—21no—
163C2×D4×C47—21no—
164C2×D4×C47—42no—
165C2×D4×C47—42no—
166C2×D4×C47—81no—
167C2×D4×C47—81no—
168C2×D4×C47C22×C412yes—
169C2×D4×C47C22×C412yes—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—24no—
174C22×C4×C47—24no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—81no—
179C22×C4×C47—81no—
180C22×C4×C47—81no—
181C22×C4×C47—81no—
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2411yescharacteristic
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—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47#4112yes—
201C4⋊C4×C47—24no—
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—42no—
211C4⋊C4×C47—81no—
212C4⋊C4×C47C22⋊C414yes—
213C4⋊C4×C47C22⋊C414yes—
214C4⋊C4×C47C22⋊C414yes—
215C4⋊C4×C47C22×C412yes—
216C4⋊C4×C47#4112yes—
217C22⋊C4×C47—24no—
218C22⋊C4×C47—24no—
219C22⋊C4×C47—24no—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—24no—
223C42×C47—24no—
224C42×C47—42no—
225C42×C47—81no—
226C42×C47—81no—
227C42×C47C22×C412yes—
228C42×C47C22×C412yes—
229C42×C47C22×C412yes—
230C42×C47C2×D412yes—
231C42×C47C2×D412yes—
232C42×C47C2×D412yes—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47C22×D411yescharacteristic
248Q8×C47—22no—
249Q8×C47—22no—
250Q8×C47—44no—
251Q8×C47—41no—
252Q8×C47—41no—
253D4×C47—22no—
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—22no—
257D4×C47—48no—
258D4×C47—41no—
259D4×C47—41no—
260D4×C47—41no—
261D4×C47—41no—
262D4×C47—84no—
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—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
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—84no—
294C2×C4×C47—84no—
295C2×C4×C47C2×C22⋊C412yes—
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×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C2×C4×C472−1+411yescharacteristic
307C8×C47—22no—
308C8×C47—41no—
309C8×C47—41no—
310C8×C47—41no—
311#22549C4711yesmaximal, characteristic, direct product factor, Sylow
312C22×C47—42no—
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—42no—
317C22×C47—42no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47—81no—
321C22×C47—81no—
322C22×C47—81no—
323C22×C47—81no—
324C22×C47—81no—
325C22×C47—81no—
326C22×C47C22×C22⋊C411yescharacteristic
327C22×C47#54811yescharacteristic
328C22×C47#55011yescharacteristic
329C22×C47#57511yescharacteristic
330C22×C47#57511yescharacteristic
331C22×C47#57611yescharacteristic
332C22×C47#57711yescharacteristic
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—81no—
343C4×C47—81no—
344C4×C47—81no—
345C4×C47C4×#4111yescharacteristic
346C4×C47#52011yescharacteristic
347C4×C47#54811yescharacteristic
348C4×C47#55011yescharacteristic
349C2×#559C2×C4711yescharacteristic
350C2×#446C2×C4711yescharacteristic, complemented
351#2355C2×C4711yescharacteristic, complemented
352#1983C2×C4711yescharacteristic, complemented
353#1983C2×C4711yescharacteristic, complemented
354#1982C2×C4711yescharacteristic
355#1961C2×C4711yescharacteristic
356#1959C2×C4711yescharacteristic, complemented
357#1958C2×C4711yescharacteristic, complemented
358#1805C2×C4711yescharacteristic, complemented
359#1804C2×C4711yescharacteristic, complemented
360#1802C2×C4711yescharacteristic, complemented
361#1763C2×C4711yescharacteristic, complemented
362#1762C2×C4711yescharacteristic, complemented
363C4×#102C2×C4711yescharacteristic, complemented
364C2×C47—82no—
365C2×C47—82no—
366C2×C47#234111yescharacteristic
367C2×C47#289611yescharacteristic
368C2×C47#289711yescharacteristic
369C2×C47#337011yescharacteristic
370C2×C47#337111yescharacteristic
371C2×C47#340111yescharacteristic
372C2×C47#340311yescharacteristic
373#559—24no—
374#559C4×C4718yescomplemented
375C2×#127C22×C4711yescharacteristic
376C2×#124—21no—
377C2×#124C22×C4711yescharacteristic
378C2×#124C22×C4711yescharacteristic
379C2×#123—21no—
380C2×#123—21no—
381C2×C4×Q8C22×C4711yescharacteristic
382C2×C4×Q8C22×C4711yescharacteristic
383C2×C4×D4—21no—
384C2×C4×D4C22×C4711yescharacteristic
385C2×C4×D4C22×C4711yescharacteristic
386#446—24no—
387C2×C4⋊C8C22×C4711yescharacteristic
388C2×C4⋊C8C22×C4711yescharacteristic
389C2×C4⋊C8C22×C4711yescharacteristic
390C2×#103C22×C4711yescharacteristic
391C2×#103C22×C4711yescharacteristic
392C2×#103C22×C4711yescharacteristic
393C2×#103C22×C4711yescharacteristic
394C2×#102C22×C4711yescharacteristic
395C2×#102C22×C4711yescharacteristic
396C2×#102C22×C4711yescharacteristic
397C2×#102C22×C4711yescharacteristic
398C2×#102C22×C4711yescharacteristic
399C2×#102C22×C4711yescharacteristic
400C2×#102C22×C4711yescharacteristic
401C2×#102C22×C4711yescharacteristic
402C2×#97C22×C4711yescharacteristic
403C2×#97C22×C4711yescharacteristic
404C2×C4×C8C22×C4711yescharacteristic
405#391—21no—
406#387—21no—
407#387—21no—
408#384C22×C4711yescharacteristic
409#382C22×C4711yescharacteristic
410#382C22×C4711yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C22×C4711yescharacteristic
413C4×C4⋊C4C22×C4711yescharacteristic
414C4×C4⋊C4C22×C4711yescharacteristic
415#340C22×C4711yescharacteristic
416#340C22×C4711yescharacteristic
417#340C22×C4711yescharacteristic
418#340C22×C4711yescharacteristic
419C47#2254911yescharacteristic, direct product factor, Sylow
420C22×Q8D4×C4711yescharacteristic
421C22×Q8C23×C4711yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C4711yescharacteristic
425C22×D4C23×C4711yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C22×C8C23×C4711yescharacteristic
429C22×C8C23×C4711yescharacteristic
430C22×C8C23×C4711yescharacteristic
431C22×C8C23×C4711yescharacteristic
432#127—22no—
433#127C2×C4×C4714yes—
434#124—28no—
435#124—22no—
436#124—22no—
437#124C2×C4×C4714yes—
438#124C2×C4×C4714yes—
439#123—28no—
440#123—28no—
441C4×Q8—22no—
442C4×Q8C2×C4×C4714yes—
443C4×Q8C2×C4×C4714yes—
444C4×Q8D4×C4714yes—
445C4×D4—28no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4C2×C4×C4714yes—
449C4×D4C2×C4×C4714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C4711yescharacteristic
454C2×C4⋊C4D4×C4711yescharacteristic
455C2×C4⋊C4D4×C4711yescharacteristic
456C2×C4⋊C4C23×C4711yescharacteristic
457C2×C4⋊C4C23×C4711yescharacteristic
458C2×C4⋊C4C23×C4711yescharacteristic
459C2×C4⋊C4C23×C4711yescharacteristic
460C2×C4⋊C4C23×C4711yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C4711yescharacteristic
472C2×C42C23×C4711yescharacteristic
473C2×C42C23×C4711yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—22no—
476C4⋊C8—22no—
477#103—22no—
478#103—22no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—41no—
486#102—41no—
487#102—41no—
488#102—41no—
489#97—22no—
490#97—22no—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—21no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C22⋊C4×C4714yes—
509C2×Q8C22×C4×C4712yes—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×C4×C4712yes—
527C2×D4C22×C4×C4712yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C4711yescharacteristic
541C22×C4C2×D4×C4711yescharacteristic
542C22×C4C2×D4×C4711yescharacteristic
543C22×C4C2×D4×C4711yescharacteristic
544C22×C4C2×D4×C4711yescharacteristic
545C22×C4C2×D4×C4711yescharacteristic
546C22×C4C24×C4711yescharacteristic
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—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8#41×C4712yes—
559C4⋊C4—24no—
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—42no—
569C4⋊C4—81no—
570C4⋊C4C22⋊C4×C4714yes—
571C4⋊C4C22⋊C4×C4714yes—
572C4⋊C4C22⋊C4×C4714yes—
573C4⋊C4C22×C4×C4712yes—
574C4⋊C4#41×C4712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C42—24no—
582C42—42no—
583C42—81no—
584C42—81no—
585C42C22×C4×C4712yes—
586C42C22×C4×C4712yes—
587C42C22×C4×C4712yes—
588C42C2×D4×C4712yes—
589C42C2×D4×C4712yes—
590C42C2×D4×C4712yes—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×D4×C4711yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
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—84no—
652C2×C4—84no—
653C2×C4C2×C22⋊C4×C4712yes—
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×C4C2×#41×C4711yescharacteristic
662C2×C4C2×#41×C4711yescharacteristic
663C2×C4H(5,𝔽2)×C4711yescharacteristic
664C2×C42−1+4×C4711yescharacteristic
665C8—22no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊C4×C4711yescharacteristic
684C22C47×#54811yescharacteristic
685C22C47×#55011yescharacteristic
686C22C47×#57511yescharacteristic
687C22C47×#57511yescharacteristic
688C22C47×#57611yescharacteristic
689C22C47×#57711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C4×#41×C4711yescharacteristic
703C4C47×#52011yescharacteristic
704C4C47×#54811yescharacteristic
705C4C47×#55011yescharacteristic
706C2—82no—
707C2—82no—
708C2C47×#234111yescharacteristic
709C2C47×#289611yescharacteristic
710C2C47×#289711yescharacteristic
711C2C47×#337011yescharacteristic
712C2C47×#337111yescharacteristic
713C2C47×#340111yescharacteristic
714C2C47×#340311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×#127×C47C22
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
2. C2×C47×#446C2semidirect
3. C47×#2355C2semidirect
4. C47×#1983C2semidirect
5. C47×#1983C2semidirect
8. C47×#1959C2semidirect
9. C47×#1958C2semidirect
10. C47×#1805C2semidirect
11. C47×#1804C2semidirect
12. C47×#1802C2semidirect
13. C47×#1763C2semidirect
14. C47×#1762C2semidirect
15. C4×#102×C47C2semidirect
17. C47×#559C4semidirect
311. #22549C47direct (N × H)
350. C2×#446C2×C47semidirect
351. #2355C2×C47semidirect
352. #1983C2×C47semidirect
353. #1983C2×C47semidirect
356. #1959C2×C47semidirect
357. #1958C2×C47semidirect
358. #1805C2×C47semidirect
359. #1804C2×C47semidirect
360. #1802C2×C47semidirect
361. #1763C2×C47semidirect
362. #1762C2×C47semidirect
363. C4×#102C2×C47semidirect
374. #559C4×C47semidirect
419. C47#22549direct (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×#4462
C47×#23552
C47×#19832
C47×#19822
C47×#19612
C47×#19592
C47×#19582
C47×#18052
C47×#18042
C47×#18022
C47×#17632
C47×#17622
C4×#102×C472
#2254947