Finite Group Databasebeta

← C47×#25401 #26065099

Subgroups — C47×#25401 #26065099

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#469C211yesmaximal, characteristic, complemented
2C2×C47×#465C211yesmaximal, characteristic, complemented
3C2×C47×#463C211yesmaximal, characteristic, complemented
4C2×C47×#435C211yesmaximal, characteristic, complemented
5C47×#2540C211yesmaximal, characteristic, complemented
6C47×#2537C211yesmaximal, characteristic, complemented
7C47×#2035C211yesmaximal, characteristic, complemented
8C47×#2034C211yesmaximal, characteristic, complemented
9C47×#2000C211yesmaximal, characteristic, complemented
10C47×#1999C211yesmaximal, characteristic, complemented
11C47×#1959C211yesmaximal, characteristic, complemented
12C47×#1948C211yesmaximal, characteristic, complemented
13C47×#1894C211yesmaximal, characteristic, complemented
14C47×#1893C211yesmaximal, characteristic, complemented
15C47×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C23×C8×C47C2211yescharacteristic
20C2×#124×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×#121×C47—21no—
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#121×C47C2211yescharacteristic
27C2×#121×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C47×#469—24no—
31C47×#465—24no—
32C47×#463—24no—
33C47×#435—24no—
34C2×#106×C47C2211yescharacteristic
35C2×#106×C47C2211yescharacteristic
36C2×C4⋊C8×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2211yescharacteristic
47C2×#97×C47C2211yescharacteristic
48C47×#399—21no—
49C47×#394—21no—
50C47×#394—21no—
51C47×#392—21no—
52C47×#390—21no—
53C47×#390—21no—
54C47×#384C2211yescharacteristic
55C47×#380—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×D4×C47—21no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47D411yescharacteristic
69C22×D4×C47C2311yescharacteristic
70C22×D4×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47C2311yescharacteristic
73C23×C4×C47C2311yescharacteristic
74C2×SD16×C47—22no—
75C2×SD16×C47—22no—
76C2×SD16×C47—41no—
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—41no—
80C2×M16×C47—22no—
81C2×M16×C47—22no—
82C2×M16×C47—41no—
83C22×C8×C47—22no—
84C22×C8×C47—22no—
85C22×C8×C47—41no—
86C22×C8×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90#124×C47—22no—
91#124×C47—22no—
92C22⋊Q8×C47—22no—
93C22⋊Q8×C47—22no—
94C22⋊Q8×C47—41no—
95C22⋊Q8×C47—41no—
96#121×C47—22no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—41no—
101#121×C47—41no—
102#121×C47—41no—
103#121×C47—41no—
104#121×C47—44no—
105C4×D4×C47—22no—
106C4×D4×C47—22no—
107C4×D4×C47—22no—
108C4×D4×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×C47D411yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
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×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134#106×C47—22no—
135#106×C47—22no—
136C4⋊C8×C47D414yescomplemented
137#103×C47—22no—
138#103×C47—22no—
139#103×C47—41no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—41no—
144#102×C47D414yescomplemented
145C22⋊C8×C47—22no—
146C22⋊C8×C47—22no—
147#97×C47—22no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47C2×D411yescharacteristic
154C24×C47C2×D411yescharacteristic
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×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—21no—
164C2×D4×C47—21no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—41no—
175C2×D4×C47—42no—
176C2×D4×C47—42no—
177C2×D4×C47—42no—
178C2×D4×C47—42no—
179C2×D4×C47—42no—
180C2×D4×C47—42no—
181C2×D4×C47—42no—
182C2×D4×C47—42no—
183C2×D4×C47—81no—
184C2×D4×C47—81no—
185C2×D4×C47—81no—
186C2×D4×C47—81no—
187C2×D4×C47C2×D412yes—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
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—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—42no—
207C22×C4×C47—42no—
208C22×C4×C47—42no—
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2411yescharacteristic
214SD16×C47—44no—
215D8×C47—44no—
216M16×C47—44no—
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—21no—
226C2×C8×C47—44no—
227C2×C8×C47C2×D412yes—
228C2×C8×C47C2×D412yes—
229C2×C8×C47C2×D412yes—
230C4⋊C4×C47—22no—
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—21no—
239C4⋊C4×C47—42no—
240C4⋊C4×C47—42no—
241C4⋊C4×C47—42no—
242C4⋊C4×C47—81no—
243C4⋊C4×C47C2×D412yes—
244C4⋊C4×C47#4112yes—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—42no—
248C22⋊C4×C47—42no—
249C22⋊C4×C47—42no—
250C22⋊C4×C47—42no—
251C22⋊C4×C47—42no—
252C22⋊C4×C47—42no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C42×C47—81no—
259C42×C47C2×D412yes—
260C42×C47#4112yes—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—22no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
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—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47AGL(1,ℤ/8)12yes—
289C23×C47C22×D411yescharacteristic
290Q8×C47—41no—
291Q8×C47—41no—
292Q8×C47—41no—
293Q8×C47—41no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—44no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—84no—
304D4×C47—84no—
305D4×C47—84no—
306D4×C47—84no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—22no—
315C2×C4×C47—21no—
316C2×C4×C47—22no—
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—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—84no—
344C2×C4×C47#12112yes—
345C2×C4×C47#12112yes—
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47H(5,𝔽2)11yescharacteristic
351C2×C4×C47H(5,𝔽2)11yescharacteristic
352C8×C47—22no—
353C8×C47—22no—
354C8×C47—22no—
355C8×C47—41no—
356#25401C4711yesmaximal, characteristic, direct product factor, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—42no—
366C22×C47—41no—
367C22×C47—42no—
368C22×C47—41no—
369C22×C47—42no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—81no—
375C22×C47—81no—
376C22×C47—81no—
377C22×C47—81no—
378C22×C47—81no—
379C22×C47—81no—
380C22×C47—81no—
381C22×C47—81no—
382C22×C47—81no—
383C22×C47—81no—
384C22×C47—81no—
385C22×C47C2×#12111yescharacteristic
386C22×C47D4211yescharacteristic
387C22×C47#54611yescharacteristic
388C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C47#57511yescharacteristic
390C22×C47#57711yescharacteristic
391C22×C47#57711yescharacteristic
392C4×C47—22no—
393C4×C47—22no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—42no—
397C4×C47—42no—
398C4×C47—81no—
399C4×C47—81no—
400C4×C47—81no—
401C4×C47—81no—
402C4×C47#53211yescharacteristic
403C4×C47#54011yescharacteristic
404C4×C47D4211yescharacteristic
405C4×C47#55011yescharacteristic
406C2×#469C2×C4711yescharacteristic, complemented
407C2×#465C2×C4711yescharacteristic, complemented
408C2×#463C2×C4711yescharacteristic, complemented
409C2×#435C2×C4711yescharacteristic, complemented
410#2540C2×C4711yescharacteristic, complemented
411#2537C2×C4711yescharacteristic, complemented
412#2035C2×C4711yescharacteristic, complemented
413#2034C2×C4711yescharacteristic, complemented
414#2000C2×C4711yescharacteristic, complemented
415#1999C2×C4711yescharacteristic, complemented
416#1959C2×C4711yescharacteristic, complemented
417#1948C2×C4711yescharacteristic, complemented
418#1894C2×C4711yescharacteristic, complemented
419#1893C2×C4711yescharacteristic, complemented
420#1762C2×C4711yescharacteristic, complemented
421C2×C47—42no—
422C2×C47—81no—
423C2×C47—82no—
424C2×C47—161no—
425C2×C47#242811yescharacteristic
426C2×C47#305511yescharacteristic
427C2×C47#306011yescharacteristic
428C2×C47#326511yescharacteristic
429C2×C47#326711yescharacteristic
430C2×C47#330611yescharacteristic
431C2×C47#332111yescharacteristic
432C22×SD16C22×C4711yescharacteristic
433C22×D8C22×C4711yescharacteristic
434C22×M16C22×C4711yescharacteristic
435C23×C8C22×C4711yescharacteristic
436C2×#124C22×C4711yescharacteristic
437C2×C22⋊Q8C22×C4711yescharacteristic
438C2×C22⋊Q8C22×C4711yescharacteristic
439C2×#121—21no—
440C2×#121C22×C4711yescharacteristic
441C2×#121C22×C4711yescharacteristic
442C2×#121C22×C4711yescharacteristic
443C2×#121C22×C4711yescharacteristic
444C2×C4×D4C22×C4711yescharacteristic
445C2×C4×D4C22×C4711yescharacteristic
446#469—24no—
447#465—24no—
448#463—24no—
449#435—24no—
450C2×#106C22×C4711yescharacteristic
451C2×#106C22×C4711yescharacteristic
452C2×C4⋊C8C22×C4711yescharacteristic
453C2×#103C22×C4711yescharacteristic
454C2×#103C22×C4711yescharacteristic
455C2×#103C22×C4711yescharacteristic
456C2×#102C22×C4711yescharacteristic
457C2×#102C22×C4711yescharacteristic
458C2×#102C22×C4711yescharacteristic
459C2×#102C22×C4711yescharacteristic
460C2×#102C22×C4711yescharacteristic
461C2×C22⋊C8C22×C4711yescharacteristic
462C2×C22⋊C8C22×C4711yescharacteristic
463C2×#97C22×C4711yescharacteristic
464#399—21no—
465#394—21no—
466#394—21no—
467#392—21no—
468#390—21no—
469#390—21no—
470#384C22×C4711yescharacteristic
471#380—21no—
472#380C22×C4711yescharacteristic
473#380C22×C4711yescharacteristic
474C4×C4⋊C4C22×C4711yescharacteristic
475#340C22×C4711yescharacteristic
476#340C22×C4711yescharacteristic
477#340C22×C4711yescharacteristic
478#340C22×C4711yescharacteristic
479C47#2540111yescharacteristic, direct product factor, Sylow
480C22×Q8C23×C4711yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C4711yescharacteristic
486C22×D4C23×C4711yescharacteristic
487C22×D4C23×C4711yescharacteristic
488C23×C4—21no—
489C23×C4C23×C4711yescharacteristic
490C23×C4C23×C4711yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505C22×C8C23×C4711yescharacteristic
506C22×C8C23×C4711yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C4711yescharacteristic
531C2×C4⋊C4C23×C4711yescharacteristic
532C2×C4⋊C4C23×C4711yescharacteristic
533C2×C4⋊C4C23×C4711yescharacteristic
534C2×C4⋊C4C23×C4711yescharacteristic
535C2×C4⋊C4C23×C4711yescharacteristic
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⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C4711yescharacteristic
548C2×C22⋊C4D4×C4711yescharacteristic
549C2×C42—21no—
550C2×C42C23×C4711yescharacteristic
551#106—22no—
552#106—22no—
553C4⋊C8D4×C4714yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C4714yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C4711yescharacteristic
571C24C2×D4×C4711yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C4712yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C4711yescharacteristic
627C22×C4C2×D4×C4711yescharacteristic
628C22×C4C2×D4×C4711yescharacteristic
629C22×C4C2×D4×C4711yescharacteristic
630C22×C4C24×C4711yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C4712yes—
645C2×C8C2×D4×C4712yes—
646C2×C8C2×D4×C4712yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C4712yes—
661C4⋊C4#41×C4712yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C4712yes—
677C42#41×C4712yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C4712yes—
706C23C22×D4×C4711yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
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—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—84no—
761C2×C4#121×C4712yes—
762C2×C4#121×C4712yes—
763C2×C4C22×D4×C4711yescharacteristic
764C2×C4C22×D4×C4711yescharacteristic
765C2×C4C2×#41×C4711yescharacteristic
766C2×C4C2×#41×C4711yescharacteristic
767C2×C4H(5,𝔽2)×C4711yescharacteristic
768C2×C4H(5,𝔽2)×C4711yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C4711yescharacteristic
802C22D42×C4711yescharacteristic
803C22C47×#54611yescharacteristic
804C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
805C22C47×#57511yescharacteristic
806C22C47×#57711yescharacteristic
807C22C47×#57711yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C47×#53211yescharacteristic
819C4C47×#54011yescharacteristic
820C4D42×C4711yescharacteristic
821C4C47×#55011yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C47×#242811yescharacteristic
827C2C47×#305511yescharacteristic
828C2C47×#306011yescharacteristic
829C2C47×#326511yescharacteristic
830C2C47×#326711yescharacteristic
831C2C47×#330611yescharacteristic
832C2C47×#332111yescharacteristic
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×#469C2semidirect
2. C2×C47×#465C2semidirect
3. C2×C47×#463C2semidirect
4. C2×C47×#435C2semidirect
5. C47×#2540C2semidirect
6. C47×#2537C2semidirect
7. C47×#2035C2semidirect
8. C47×#2034C2semidirect
9. C47×#2000C2semidirect
10. C47×#1999C2semidirect
11. C47×#1959C2semidirect
12. C47×#1948C2semidirect
13. C47×#1894C2semidirect
14. C47×#1893C2semidirect
15. C47×#1762C2semidirect
136. C4⋊C8×C47D4semidirect
144. #102×C47D4semidirect
356. #25401C47direct (N × H)
406. C2×#469C2×C47semidirect
407. C2×#465C2×C47semidirect
408. C2×#463C2×C47semidirect
409. C2×#435C2×C47semidirect
410. #2540C2×C47semidirect
411. #2537C2×C47semidirect
412. #2035C2×C47semidirect
413. #2034C2×C47semidirect
414. #2000C2×C47semidirect
415. #1999C2×C47semidirect
416. #1959C2×C47semidirect
417. #1948C2×C47semidirect
418. #1894C2×C47semidirect
419. #1893C2×C47semidirect
420. #1762C2×C47semidirect
479. C47#25401direct (N × H)
553. C4⋊C8D4×C47semidirect
561. #102D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4692
C2×C47×#4652
C2×C47×#4632
C2×C47×#4352
C47×#25402
C47×#25372
C47×#20352
C47×#20342
C47×#20002
C47×#19992
C47×#19592
C47×#19482
C47×#18942
C47×#18932
C47×#17622
#2540147