Finite Group Databasebeta

← C47×#25550 #26065248

Subgroups — C47×#25550 #26065248

Order 12032.

1242 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#553C211yesmaximal, characteristic, complemented
2C2×C47×#482C211yesmaximal, characteristic, complemented
3C2×C47×#469C211yesmaximal, characteristic, complemented
4C47×#2416C211yesmaximal, characteristic, complemented
5C47×#2059C211yesmaximal, characteristic, complemented
6C47×#2033C211yesmaximal, characteristic, complemented
7C47×#2025C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic, complemented
9C47×#1879C211yesmaximal, characteristic, complemented
10C47×#1874C211yesmaximal, characteristic, complemented
11C47×#1874C211yesmaximal, characteristic, complemented
12C47×#1870C211yesmaximal, characteristic, complemented
13C47×#1864C211yesmaximal, characteristic, complemented
14C47×#1853C211yesmaximal, characteristic, complemented
15C47×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C47×#553—24no—
19C47×#553—24no—
20C2×#126×C47—21no—
21C2×#125×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×#121×C47—21no—
24C2×#121×C47—21no—
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×#121×C47C2211yescharacteristic
29C2×C4×D4×C47—21no—
30C2×C4×D4×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C47×#482—24no—
36C47×#469—24no—
37C2×#107×C47C2211yescharacteristic
38C2×#106×C47C2211yescharacteristic
39C2×#106×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C47×#396—21no—
50C47×#394—21no—
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#386—21no—
54C47×#380C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×D4×C47—21no—
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47D411yescharacteristic
68C22×D4×C47C2311yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74C23×C4×C47C2311yescharacteristic
75C2×D8×C47—22no—
76C2×D8×C47—22no—
77C2×D8×C47—41no—
78C2×M16×C47—22no—
79C2×M16×C47—22no—
80C2×M16×C47—41no—
81C22×C8×C47C2311yescharacteristic
82C22×C8×C47C2311yescharacteristic
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85#126×C47—28no—
86#125×C47—22no—
87#125×C47—22no—
88#123×C47—28no—
89#121×C47—28no—
90#121×C47—22no—
91#121×C47—22no—
92#121×C47—22no—
93#121×C47—22no—
94#121×C47—22no—
95#121×C47—22no—
96#121×C47—41no—
97#121×C47—44no—
98#121×C47D414yescomplemented
99C4×D4×C47—28no—
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104#117×C47—22no—
105#117×C47D414yescomplemented
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—41no—
115C2×C4⋊C4×C47D411yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
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×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135#107×C47—22no—
136#106×C47—22no—
137#106×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—41no—
144C22⋊C8×C47—22no—
145C22⋊C8×C47—22no—
146C22⋊C8×C47—41no—
147#95×C47—21no—
148#95×C47—21no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47C2×D411yescharacteristic
152C24×C47C2×D411yescharacteristic
153C2×D4×C47—24no—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—24no—
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—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—41no—
169C2×D4×C47—42no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—42no—
173C2×D4×C47—42no—
174C2×D4×C47—42no—
175C2×D4×C47—42no—
176C2×D4×C47—81no—
177C2×D4×C47—81no—
178C2×D4×C47—81no—
179C2×D4×C47C2×D412yes—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—24no—
189C22×C4×C47—24no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—42no—
199C22×C4×C47—42no—
200C22×C4×C47—81no—
201C22×C4×C47—81no—
202C22×C4×C47—81no—
203C22×C4×C47—81no—
204C22×C4×C47—81no—
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2×D412yes—
211C22×C4×C47C2411yescharacteristic
212D8×C47—44no—
213M16×C47—44no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47—21no—
218C2×C8×C47—21no—
219C2×C8×C47—21no—
220C2×C8×C47—21no—
221C2×C8×C47—21no—
222C2×C8×C47—21no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47#4112yes—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—22no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47—21no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—42no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47C2×D412yes—
241C4⋊C4×C47C2×D412yes—
242C4⋊C4×C47C2×D412yes—
243C4⋊C4×C47#4112yes—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—81no—
255C42×C47—24no—
256C42×C47—21no—
257C42×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—22no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47#12012yes—
285C23×C47AGL(1,ℤ/8)12yes—
286C23×C47C22×D411yescharacteristic
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—44no—
290D4×C47—48no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—41no—
296D4×C47—41no—
297D4×C47—84no—
298D4×C47—84no—
299D4×C47—84no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—21no—
309C2×C4×C47—22no—
310C2×C4×C47—21no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—41no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—84no—
338C2×C4×C47—84no—
339C2×C4×C47—84no—
340C2×C4×C47#12012yes—
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C2×#4111yescharacteristic
344C2×C4×C47C2×#4111yescharacteristic
345C2×C4×C47H(5,𝔽2)11yescharacteristic
346C2×C4×C472−1+411yescharacteristic
347C8×C47—22no—
348C8×C47—41no—
349C8×C47—41no—
350C8×C47—41no—
351#25550C4711yesmaximal, characteristic, direct product factor, Sylow
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47C2×#12011yescharacteristic
381C22×C47#54611yescharacteristic
382C22×C47#54711yescharacteristic
383C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C47#57511yescharacteristic
385C22×C47#57611yescharacteristic
386C22×C47#57711yescharacteristic
387C4×C47—22no—
388C4×C47—41no—
389C4×C47—41no—
390C4×C47—42no—
391C4×C47—41no—
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—42no—
395C4×C47—81no—
396C4×C47—81no—
397C4×C47#53211yescharacteristic
398C4×C47#53711yescharacteristic
399C4×C47#54611yescharacteristic
400C4×C47#54711yescharacteristic
401C2×#553C2×C4711yescharacteristic, complemented
402C2×#482C2×C4711yescharacteristic, complemented
403C2×#469C2×C4711yescharacteristic, complemented
404#2416C2×C4711yescharacteristic, complemented
405#2059C2×C4711yescharacteristic, complemented
406#2033C2×C4711yescharacteristic, complemented
407#2025C2×C4711yescharacteristic, complemented
408#1999C2×C4711yescharacteristic, complemented
409#1879C2×C4711yescharacteristic, complemented
410#1874C2×C4711yescharacteristic, complemented
411#1874C2×C4711yescharacteristic, complemented
412#1870C2×C4711yescharacteristic, complemented
413#1864C2×C4711yescharacteristic, complemented
414#1853C2×C4711yescharacteristic, complemented
415#1736C2×C4711yescharacteristic, complemented
416C2×C47—42no—
417C2×C47—42no—
418C2×C47—82no—
419C2×C47—161no—
420C2×C47#243011yescharacteristic
421C2×C47#300611yescharacteristic
422C2×C47#301211yescharacteristic
423C2×C47#331811yescharacteristic
424C2×C47#332611yescharacteristic
425C2×C47#334511yescharacteristic
426C2×C47#335511yescharacteristic
427C22×D8C22×C4711yescharacteristic
428C22×M16C22×C4711yescharacteristic
429#553—24no—
430#553—24no—
431C2×#126—21no—
432C2×#125C22×C4711yescharacteristic
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C4711yescharacteristic
437C2×#121C22×C4711yescharacteristic
438C2×#121C22×C4711yescharacteristic
439C2×#121C22×C4711yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4C22×C4711yescharacteristic
442C2×C4×D4C22×C4711yescharacteristic
443C2×#117C22×C4711yescharacteristic
444C22×C4⋊C4C22×C4711yescharacteristic
445C22×C4⋊C4C22×C4711yescharacteristic
446#482—24no—
447#469—24no—
448C2×#107C22×C4711yescharacteristic
449C2×#106C22×C4711yescharacteristic
450C2×#106C22×C4711yescharacteristic
451C2×#102C22×C4711yescharacteristic
452C2×#102C22×C4711yescharacteristic
453C2×#102C22×C4711yescharacteristic
454C2×#102C22×C4711yescharacteristic
455C2×#102C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×C22⋊C8C22×C4711yescharacteristic
458C2×C22⋊C8C22×C4711yescharacteristic
459C2×C22⋊C8C22×C4711yescharacteristic
460#396—21no—
461#394—21no—
462#390C22×C4711yescharacteristic
463#389C22×C4711yescharacteristic
464#386—21no—
465#380C22×C4711yescharacteristic
466#340C22×C4711yescharacteristic
467#340C22×C4711yescharacteristic
468#340C22×C4711yescharacteristic
469#340C22×C4711yescharacteristic
470#340C22×C4711yescharacteristic
471#340C22×C4711yescharacteristic
472#336C22×C4711yescharacteristic
473#336C22×C4711yescharacteristic
474C47#2555011yescharacteristic, direct product factor, Sylow
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4D4×C4711yescharacteristic
480C22×D4C23×C4711yescharacteristic
481C22×D4C23×C4711yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C4711yescharacteristic
486C23×C4C23×C4711yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C4711yescharacteristic
494C22×C8C23×C4711yescharacteristic
495C22×C8C23×C4711yescharacteristic
496C22×C8C23×C4711yescharacteristic
497#126—28no—
498#125—22no—
499#125—22no—
500#123—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C4714yescomplemented
511C4×D4—28no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516#117—22no—
517#117D4×C4714yescomplemented
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4D4×C4711yescharacteristic
528C2×C4⋊C4C23×C4711yescharacteristic
529C2×C4⋊C4C23×C4711yescharacteristic
530C2×C4⋊C4C23×C4711yescharacteristic
531C2×C4⋊C4C23×C4711yescharacteristic
532C2×C4⋊C4C23×C4711yescharacteristic
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4D4×C4711yescharacteristic
544C2×C22⋊C4D4×C4711yescharacteristic
545C2×C42—21no—
546C2×C42C23×C4711yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C4711yescharacteristic
564C24C2×D4×C4711yescharacteristic
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4C2×D4×C4712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4C2×D4×C4711yescharacteristic
618C22×C4C2×D4×C4711yescharacteristic
619C22×C4C2×D4×C4711yescharacteristic
620C22×C4C2×D4×C4711yescharacteristic
621C22×C4C2×D4×C4712yes—
622C22×C4C2×D4×C4712yes—
623C22×C4C24×C4711yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8#41×C4712yes—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4C2×D4×C4712yes—
653C4⋊C4C2×D4×C4712yes—
654C4⋊C4C2×D4×C4712yes—
655C4⋊C4#41×C4712yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—22no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#120×C4712yes—
697C23AGL(1,ℤ/8)×C4712yes—
698C23C22×D4×C4711yescharacteristic
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4#120×C4712yes—
753C2×C4C22×D4×C4711yescharacteristic
754C2×C4C22×D4×C4711yescharacteristic
755C2×C4C2×#41×C4711yescharacteristic
756C2×C4C2×#41×C4711yescharacteristic
757C2×C4H(5,𝔽2)×C4711yescharacteristic
758C2×C42−1+4×C4711yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C4711yescharacteristic
792C22C47×#54611yescharacteristic
793C22C47×#54711yescharacteristic
794C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
795C22C47×#57511yescharacteristic
796C22C47×#57611yescharacteristic
797C22C47×#57711yescharacteristic
798C4—22no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4C47×#53211yescharacteristic
809C4C47×#53711yescharacteristic
810C4C47×#54611yescharacteristic
811C4C47×#54711yescharacteristic
812C2—42no—
813C2—42no—
814C2—82no—
815C2—161no—
816C2C47×#243011yescharacteristic
817C2C47×#300611yescharacteristic
818C2C47×#301211yescharacteristic
819C2C47×#331811yescharacteristic
820C2C47×#332611yescharacteristic
821C2C47×#334511yescharacteristic
822C2C47×#335511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
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
1. C2×C47×#553C2semidirect
2. C2×C47×#482C2semidirect
3. C2×C47×#469C2semidirect
4. C47×#2416C2semidirect
5. C47×#2059C2semidirect
6. C47×#2033C2semidirect
7. C47×#2025C2semidirect
8. C47×#1999C2semidirect
9. C47×#1879C2semidirect
10. C47×#1874C2semidirect
11. C47×#1874C2semidirect
12. C47×#1870C2semidirect
13. C47×#1864C2semidirect
14. C47×#1853C2semidirect
15. C47×#1736C2semidirect
98. #121×C47D4semidirect
105. #117×C47D4semidirect
351. #25550C47direct (N × H)
401. C2×#553C2×C47semidirect
402. C2×#482C2×C47semidirect
403. C2×#469C2×C47semidirect
404. #2416C2×C47semidirect
405. #2059C2×C47semidirect
406. #2033C2×C47semidirect
407. #2025C2×C47semidirect
408. #1999C2×C47semidirect
409. #1879C2×C47semidirect
410. #1874C2×C47semidirect
411. #1874C2×C47semidirect
412. #1870C2×C47semidirect
413. #1864C2×C47semidirect
414. #1853C2×C47semidirect
415. #1736C2×C47semidirect
474. C47#25550direct (N × H)
510. #121D4×C47semidirect
517. #117D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5532
C2×C47×#4822
C2×C47×#4692
C47×#24162
C47×#20592
C47×#20332
C47×#20252
C47×#19992
C47×#18792
C47×#18742
C47×#18702
C47×#18642
C47×#18532
C47×#17362
#2555047