Finite Group Databasebeta

← C47×#25562 #26065260

Subgroups — C47×#25562 #26065260

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#552C211yesmaximal, characteristic
2C2×C47×#485C211yesmaximal, characteristic, complemented
3C2×C47×#470C211yesmaximal, characteristic, complemented
4C47×#2417C211yesmaximal, characteristic
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2036C211yesmaximal, characteristic, complemented
7C47×#2026C211yesmaximal, characteristic, complemented
8C47×#2001C211yesmaximal, characteristic, complemented
9C47×#1878C211yesmaximal, characteristic, complemented
10C47×#1872C211yesmaximal, characteristic, complemented
11C47×#1872C211yesmaximal, characteristic, complemented
12C47×#1870C211yesmaximal, characteristic
13C47×#1865C211yesmaximal, characteristic, complemented
14C47×#1853C211yesmaximal, characteristic, complemented
15C47×#1736C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C47×#552—24no—
19C47×#552—24no—
20C2×#126×C47—21no—
21C2×#125×C47—21no—
22C2×#125×C47C2211yescharacteristic
23C2×#123×C47—21no—
24C2×C22⋊Q8×C47C2211yescharacteristic
25C2×C22⋊Q8×C47C2211yescharacteristic
26C2×C22⋊Q8×C47C2211yescharacteristic
27C2×C22⋊Q8×C47C2211yescharacteristic
28C2×C4×Q8×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47—21no—
31C2×#117×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C47×#485—24no—
35C47×#470—24no—
36C2×#107×C47C2211yescharacteristic
37C2×#106×C47C2211yescharacteristic
38C2×#106×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×#103×C47C2211yescharacteristic
43C2×#103×C47C2211yescharacteristic
44C2×#103×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#398—21no—
49C47×#396—21no—
50C47×#391C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#386—21no—
53C47×#380—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47D411yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47C2311yescharacteristic
69C23×C4×C47C2311yescharacteristic
70C2×Q16×C47—22no—
71C2×Q16×C47—22no—
72C2×Q16×C47—41no—
73C2×M16×C47—22no—
74C2×M16×C47—22no—
75C2×M16×C47—41no—
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80#126×C47—28no—
81#125×C47—28no—
82#125×C47—22no—
83#125×C47—22no—
84#123×C47—28no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—22no—
89C22⋊Q8×C47—22no—
90C22⋊Q8×C47—22no—
91C22⋊Q8×C47—41no—
92C22⋊Q8×C47D414yes—
93C4×Q8×C47—22no—
94C4×Q8×C47—22no—
95C4×D4×C47—22no—
96C4×D4×C47—22no—
97#117×C47—28no—
98#117×C47—22no—
99#117×C47D414yes—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—22no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—41no—
114C2×C4⋊C4×C47D411yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47D411yescharacteristic
128C2×C22⋊C4×C47D411yescharacteristic
129C2×C42×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#106×C47—22no—
134#106×C47—22no—
135#103×C47—22no—
136#103×C47—22no—
137#103×C47—22no—
138#103×C47—22no—
139#103×C47—22no—
140#103×C47—41no—
141C22⋊C8×C47—22no—
142C22⋊C8×C47—22no—
143C22⋊C8×C47—41no—
144#95×C47—21no—
145#95×C47—21no—
146#95×C47—21no—
147#95×C47—21no—
148C24×C47C2×D411yescharacteristic
149C24×C47C2×D411yescharacteristic
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47C2×D412yes—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—41no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—24no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—42no—
185C22×C4×C47—42no—
186C22×C4×C47—42no—
187C22×C4×C47—42no—
188C22×C4×C47—81no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2411yescharacteristic
196Q16×C47—44no—
197M16×C47—44no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47#4112yes—
210C4⋊C4×C47—24no—
211C4⋊C4×C47—24no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—24no—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—42no—
226C4⋊C4×C47—42no—
227C4⋊C4×C47—42no—
228C4⋊C4×C47—81no—
229C4⋊C4×C47C2×D412yes—
230C4⋊C4×C47C2×D412yes—
231C4⋊C4×C47C2×D412yes—
232C4⋊C4×C47#4112yes—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—24no—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—81no—
241C42×C47—24no—
242C42×C47—24no—
243C42×C47—21no—
244C42×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47#12012yes—
258C23×C47#13712yes—
259C23×C47C22×D411yescharacteristic
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—41no—
263Q8×C47—41no—
264Q8×C47—41no—
265Q8×C47—41no—
266Q8×C47—41no—
267Q8×C47—41no—
268D4×C47—44no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—48no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—84no—
314C2×C4×C47#12012yes—
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×C4×C47H(5,𝔽2)11yescharacteristic
320C2×C4×C472−1+411yescharacteristic
321C8×C47—22no—
322C8×C47—41no—
323C8×C47—41no—
324C8×C47—41no—
325#25562C4711yesmaximal, characteristic, direct product factor, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—41no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47C2×#12011yescharacteristic
341C22×C47#54611yescharacteristic
342C22×C47#54711yescharacteristic
343C22×C47C2×#13711yescharacteristic
344C22×C47#57511yescharacteristic
345C22×C47#57711yescharacteristic
346C22×C47#57811yescharacteristic
347C4×C47—22no—
348C4×C47—41no—
349C4×C47—42no—
350C4×C47—41no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—41no—
354C4×C47—42no—
355C4×C47—42no—
356C4×C47—81no—
357C4×C47—81no—
358C4×C47—81no—
359C4×C47#53211yescharacteristic
360C4×C47#53711yescharacteristic
361C4×C47#54611yescharacteristic
362C4×C47#54711yescharacteristic
363C2×#552C2×C4711yescharacteristic
364C2×#485C2×C4711yescharacteristic, complemented
365C2×#470C2×C4711yescharacteristic, complemented
366#2417C2×C4711yescharacteristic
367#2059C2×C4711yescharacteristic, complemented
368#2036C2×C4711yescharacteristic, complemented
369#2026C2×C4711yescharacteristic, complemented
370#2001C2×C4711yescharacteristic, complemented
371#1878C2×C4711yescharacteristic, complemented
372#1872C2×C4711yescharacteristic, complemented
373#1872C2×C4711yescharacteristic, complemented
374#1870C2×C4711yescharacteristic
375#1865C2×C4711yescharacteristic, complemented
376#1853C2×C4711yescharacteristic, complemented
377#1736C2×C4711yescharacteristic, complemented
378C2×C47—42no—
379C2×C47—42no—
380C2×C47#243011yescharacteristic
381C2×C47#300711yescharacteristic
382C2×C47#301311yescharacteristic
383C2×C47#331211yescharacteristic
384C2×C47#332311yescharacteristic
385C2×C47#334411yescharacteristic
386C2×C47#335211yescharacteristic
387C22×Q16C22×C4711yescharacteristic
388C22×M16C22×C4711yescharacteristic
389#552—24no—
390#552—24no—
391C2×#126—21no—
392C2×#125—21no—
393C2×#125C22×C4711yescharacteristic
394C2×#123—21no—
395C2×C22⋊Q8C22×C4711yescharacteristic
396C2×C22⋊Q8C22×C4711yescharacteristic
397C2×C22⋊Q8C22×C4711yescharacteristic
398C2×C22⋊Q8C22×C4711yescharacteristic
399C2×C4×Q8C22×C4711yescharacteristic
400C2×C4×D4C22×C4711yescharacteristic
401C2×#117—21no—
402C2×#117C22×C4711yescharacteristic
403C22×C4⋊C4C22×C4711yescharacteristic
404C22×C4⋊C4C22×C4711yescharacteristic
405#485—24no—
406#470—24no—
407C2×#107C22×C4711yescharacteristic
408C2×#106C22×C4711yescharacteristic
409C2×#106C22×C4711yescharacteristic
410C2×#103C22×C4711yescharacteristic
411C2×#103C22×C4711yescharacteristic
412C2×#103C22×C4711yescharacteristic
413C2×#103C22×C4711yescharacteristic
414C2×#103C22×C4711yescharacteristic
415C2×#103C22×C4711yescharacteristic
416C2×C22⋊C8C22×C4711yescharacteristic
417C2×C22⋊C8C22×C4711yescharacteristic
418C2×C22⋊C8C22×C4711yescharacteristic
419#398—21no—
420#396—21no—
421#391C22×C4711yescharacteristic
422#389C22×C4711yescharacteristic
423#386—21no—
424#380—21no—
425#380C22×C4711yescharacteristic
426#340C22×C4711yescharacteristic
427#340C22×C4711yescharacteristic
428#340C22×C4711yescharacteristic
429#340C22×C4711yescharacteristic
430#340C22×C4711yescharacteristic
431#340C22×C4711yescharacteristic
432#336C22×C4711yescharacteristic
433#336C22×C4711yescharacteristic
434C47#2556211yescharacteristic, direct product factor, Sylow
435C22×Q8C23×C4711yescharacteristic
436C22×Q8C23×C4711yescharacteristic
437C22×D4D4×C4711yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4C23×C4711yescharacteristic
441C23×C4C23×C4711yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—41no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8C23×C4711yescharacteristic
449C22×C8C23×C4711yescharacteristic
450C22×C8C23×C4711yescharacteristic
451C22×C8C23×C4711yescharacteristic
452#126—28no—
453#125—28no—
454#125—22no—
455#125—22no—
456#123—28no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—41no—
464C22⋊Q8D4×C4714yes—
465C4×Q8—22no—
466C4×Q8—22no—
467C4×D4—22no—
468C4×D4—22no—
469#117—28no—
470#117—22no—
471#117D4×C4714yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4D4×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C4⋊C4C23×C4711yescharacteristic
492C2×C4⋊C4C23×C4711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4D4×C4711yescharacteristic
500C2×C22⋊C4D4×C4711yescharacteristic
501C2×C42—21no—
502C2×C42—21no—
503C2×C42C23×C4711yescharacteristic
504#107—22no—
505#106—22no—
506#106—22no—
507#103—22no—
508#103—22no—
509#103—22no—
510#103—22no—
511#103—22no—
512#103—41no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—41no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24C2×D4×C4711yescharacteristic
521C24C2×D4×C4711yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×D4×C4712yes—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4C2×D4×C4711yescharacteristic
562C22×C4C2×D4×C4711yescharacteristic
563C22×C4C2×D4×C4711yescharacteristic
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C2×D4×C4712yes—
566C22×C4C2×D4×C4712yes—
567C22×C4C24×C4711yescharacteristic
568Q16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8#41×C4712yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—81no—
601C4⋊C4C2×D4×C4712yes—
602C4⋊C4C2×D4×C4712yes—
603C4⋊C4C2×D4×C4712yes—
604C4⋊C4#41×C4712yes—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C42—24no—
614C42—24no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23#120×C4712yes—
630C23#137×C4712yes—
631C23C22×D4×C4711yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—44no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—48no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4#120×C4712yes—
687C2×C4C22×D4×C4711yescharacteristic
688C2×C4C22×D4×C4711yescharacteristic
689C2×C4C2×#41×C4711yescharacteristic
690C2×C4C2×#41×C4711yescharacteristic
691C2×C4H(5,𝔽2)×C4711yescharacteristic
692C2×C42−1+4×C4711yescharacteristic
693C8—22no—
694C8—41no—
695C8—41no—
696C8—41no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C2×#120×C4711yescharacteristic
712C22C47×#54611yescharacteristic
713C22C47×#54711yescharacteristic
714C22C2×#137×C4711yescharacteristic
715C22C47×#57511yescharacteristic
716C22C47×#57711yescharacteristic
717C22C47×#57811yescharacteristic
718C4—22no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4C47×#53211yescharacteristic
731C4C47×#53711yescharacteristic
732C4C47×#54611yescharacteristic
733C4C47×#54711yescharacteristic
734C2—42no—
735C2—42no—
736C2C47×#243011yescharacteristic
737C2C47×#300711yescharacteristic
738C2C47×#301311yescharacteristic
739C2C47×#331211yescharacteristic
740C2C47×#332311yescharacteristic
741C2C47×#334411yescharacteristic
742C2C47×#335211yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47D4
LCSG ▷ C22×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×#485C2semidirect
3. C2×C47×#470C2semidirect
5. C47×#2059C2semidirect
6. C47×#2036C2semidirect
7. C47×#2026C2semidirect
8. C47×#2001C2semidirect
9. C47×#1878C2semidirect
10. C47×#1872C2semidirect
11. C47×#1872C2semidirect
13. C47×#1865C2semidirect
14. C47×#1853C2semidirect
15. C47×#1736C2semidirect
325. #25562C47direct (N × H)
364. C2×#485C2×C47semidirect
365. C2×#470C2×C47semidirect
367. #2059C2×C47semidirect
368. #2036C2×C47semidirect
369. #2026C2×C47semidirect
370. #2001C2×C47semidirect
371. #1878C2×C47semidirect
372. #1872C2×C47semidirect
373. #1872C2×C47semidirect
375. #1865C2×C47semidirect
376. #1853C2×C47semidirect
377. #1736C2×C47semidirect
434. C47#25562direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5522
C2×C47×#4852
C2×C47×#4702
C47×#24172
C47×#20592
C47×#20362
C47×#20262
C47×#20012
C47×#18782
C47×#18722
C47×#18702
C47×#18652
C47×#18532
C47×#17362
#2556247