Finite Group Databasebeta

← C47×#25136 #26064834

Subgroups — C47×#25136 #26064834

Order 12032.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#450C211yesmaximal, characteristic, complemented
3C2×C47×#436C211yesmaximal, characteristic, complemented
4C2×C47×#418C211yesmaximal, characteristic, complemented
5C47×#2415C211yesmaximal, characteristic, complemented
6C47×#2408C211yesmaximal, characteristic
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2034C211yesmaximal, characteristic, complemented
10C47×#2000C211yesmaximal, characteristic, complemented
11C47×#1968C211yesmaximal, characteristic, complemented
12C47×#1934C211yesmaximal, characteristic, complemented
13C47×#1895C211yesmaximal, characteristic, complemented
14C47×#1894C211yesmaximal, characteristic, complemented
15C47×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C22×M16×C47C2211yescharacteristic, complemented
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic, complemented
23C2×#121×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#120×C47—21no—
26C2×C4×D4×C47C2211yescharacteristic
27C2×#117×C47C2211yescharacteristic
28C47×#468—24no—
29C47×#450—24no—
30C47×#436—24no—
31C2×#107×C47C2211yescharacteristic, complemented
32C2×#106×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C47×#418—24no—
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C22⋊C8×C47C2211yescharacteristic, complemented
45C2×C4×C8×C47C2211yescharacteristic, complemented
46C47×#397—21no—
47C47×#394—21no—
48C47×#394—21no—
49C47×#392—21no—
50C47×#391C2211yescharacteristic, complemented
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#389—21no—
54C47×#389C2211yescharacteristic, complemented
55C47×#388—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic, complemented
58C47×#379—21no—
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—22no—
70C22×D4×C47—21no—
71C22×D4×C47—22no—
72C22×D4×C47—41no—
73C22×D4×C47—41no—
74C22×D4×C47D411yescharacteristic
75C22×D4×C47C2311yescharacteristic
76C22×D4×C47C2311yescharacteristic
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C2×SD16×C47—22no—
80C2×SD16×C47—22no—
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—41no—
84C2×SD16×C47—41no—
85C2×M16×C47—22no—
86C2×M16×C47—22no—
87C2×M16×C47—22no—
88C2×M16×C47—22no—
89C2×M16×C47—41no—
90C2×M16×C47—41no—
91C22×C8×C47C2311yescharacteristic
92C22×C8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22⋊Q8×C47—22no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98C22⋊Q8×C47—41no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—41no—
102#121×C47—41no—
103#120×C47—44no—
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106#117×C47—22no—
107#117×C47—41no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47D411yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
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×C47D411yescharacteristic
129C2×C22⋊C4×C47D411yescharacteristic
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133#106×C47—41no—
134C4⋊C8×C47—22no—
135#103×C47—22no—
136#103×C47—41no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47D414yescomplemented
143C22⋊C8×C47—22no—
144C22⋊C8×C47D414yescomplemented
145C4×C8×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47—21no—
151C24×C47—21no—
152C24×C47—21no—
153C24×C47—42no—
154C24×C47—42no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47C2×D411yescharacteristic
161C24×C47C2×D411yescharacteristic
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×D4×C47—28no—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C2×D4×C47—21no—
181C2×D4×C47—44no—
182C2×D4×C47—44no—
183C2×D4×C47—41no—
184C2×D4×C47—42no—
185C2×D4×C47—42no—
186C2×D4×C47—44no—
187C2×D4×C47—42no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—42no—
192C2×D4×C47—81no—
193C2×D4×C47—81no—
194C2×D4×C47C2×D412yes—
195C2×D4×C47#4112yes—
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—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47#4112yes—
218C22×C4×C47C2411yescharacteristic
219SD16×C47—44no—
220SD16×C47—44no—
221M16×C47—44no—
222M16×C47—44no—
223C2×C8×C47—21no—
224C2×C8×C47—21no—
225C2×C8×C47—21no—
226C2×C8×C47—21no—
227C2×C8×C47—21no—
228C2×C8×C47—21no—
229C2×C8×C47—21no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47C2×D412yes—
233C2×C8×C47C2×D412yes—
234C2×C8×C47C2×D412yes—
235C4⋊C4×C47—22no—
236C4⋊C4×C47—21no—
237C4⋊C4×C47—21no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—42no—
246C4⋊C4×C47—42no—
247C4⋊C4×C47—42no—
248C4⋊C4×C47C2×D412yes—
249C22⋊C4×C47—22no—
250C22⋊C4×C47—22no—
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—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—81no—
261C22⋊C4×C47—81no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—42no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—21no—
276C23×C47—21no—
277C23×C47—21no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—48no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—84no—
294C23×C47—84no—
295C23×C47—84no—
296C23×C47—84no—
297C23×C47—84no—
298C23×C47—84no—
299C23×C47#12112yes—
300C23×C47C22×D411yescharacteristic
301Q8×C47—41no—
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47—41no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—44no—
310D4×C47—48no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—84no—
316D4×C47—84no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—22no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
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—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47#12112yes—
354C2×C4×C47AGL(1,ℤ/8)12yes—
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C2×#4111yescharacteristic
358C2×C4×C47C2×#4111yescharacteristic
359C2×C4×C47H(5,𝔽2)11yescharacteristic
360C2×C4×C47H(5,𝔽2)11yescharacteristic
361C8×C47—22no—
362C8×C47—22no—
363C8×C47—22no—
364C8×C47—41no—
365#25136C4711yesmaximal, characteristic, direct product factor, Sylow
366C22×C47—22no—
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—42no—
375C22×C47—42no—
376C22×C47—41no—
377C22×C47—42no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—42no—
384C22×C47—41no—
385C22×C47—42no—
386C22×C47—816no—
387C22×C47—81no—
388C22×C47—81no—
389C22×C47—81no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47—81no—
395C22×C47C2×#12111yescharacteristic
396C22×C47D4211yescharacteristic
397C22×C47#54611yescharacteristic
398C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C47#57511yescharacteristic
400C22×C47#57711yescharacteristic
401C22×C47#57711yescharacteristic
402C4×C47—22no—
403C4×C47—22no—
404C4×C47—41no—
405C4×C47—42no—
406C4×C47—41no—
407C4×C47—81no—
408C4×C47—81no—
409C4×C47—81no—
410C4×C47—81no—
411C4×C47—81no—
412C4×C47#52511yescharacteristic
413C4×C47#53811yescharacteristic
414C4×C47D4211yescharacteristic
415C4×C47#54611yescharacteristic
416C2×#468C2×C4711yescharacteristic, complemented
417C2×#450C2×C4711yescharacteristic, complemented
418C2×#436C2×C4711yescharacteristic, complemented
419C2×#418C2×C4711yescharacteristic, complemented
420#2415C2×C4711yescharacteristic, complemented
421#2408C2×C4711yescharacteristic
422#2067C2×C4711yescharacteristic, complemented
423#2055C2×C4711yescharacteristic, complemented
424#2034C2×C4711yescharacteristic, complemented
425#2000C2×C4711yescharacteristic, complemented
426#1968C2×C4711yescharacteristic, complemented
427#1934C2×C4711yescharacteristic, complemented
428#1895C2×C4711yescharacteristic, complemented
429#1894C2×C4711yescharacteristic, complemented
430#1854C2×C4711yescharacteristic, complemented
431C2×C47—42no—
432C2×C47—81no—
433C2×C47—82no—
434C2×C47—82no—
435C2×C47#242411yescharacteristic
436C2×C47#305511yescharacteristic
437C2×C47#305711yescharacteristic
438C2×C47#327211yescharacteristic
439C2×C47#327511yescharacteristic
440C2×C47#332311yescharacteristic
441C2×C47#332411yescharacteristic
442C23×D4C22×C4711yescharacteristic
443C22×SD16C22×C4711yescharacteristic
444C22×SD16C22×C4711yescharacteristic
445C22×M16C22×C4711yescharacteristic
446C22×M16C22×C4711yescharacteristic, complemented
447C2×C22⋊Q8C22×C4711yescharacteristic
448C2×C22⋊Q8C22×C4711yescharacteristic, complemented
449C2×#121C22×C4711yescharacteristic
450C2×#121C22×C4711yescharacteristic
451C2×#120—21no—
452C2×C4×D4C22×C4711yescharacteristic
453C2×#117C22×C4711yescharacteristic
454#468—24no—
455#450—24no—
456#436—24no—
457C2×#107C22×C4711yescharacteristic, complemented
458C2×#106C22×C4711yescharacteristic, complemented
459C2×C4⋊C8C22×C4711yescharacteristic, complemented
460#418—24no—
461C2×#103C22×C4711yescharacteristic, complemented
462C2×#103C22×C4711yescharacteristic, complemented
463C2×#102C22×C4711yescharacteristic
464C2×#102C22×C4711yescharacteristic
465C2×#102C22×C4711yescharacteristic
466C2×#102C22×C4711yescharacteristic
467C2×#102C22×C4711yescharacteristic
468C2×#102C22×C4711yescharacteristic
469C2×C22⋊C8C22×C4711yescharacteristic
470C2×C22⋊C8C22×C4711yescharacteristic, complemented
471C2×C4×C8C22×C4711yescharacteristic, complemented
472#397—21no—
473#394—21no—
474#394—21no—
475#392—21no—
476#391C22×C4711yescharacteristic, complemented
477#390C22×C4711yescharacteristic
478#390C22×C4711yescharacteristic
479#389—21no—
480#389C22×C4711yescharacteristic, complemented
481#388—21no—
482#380C22×C4711yescharacteristic
483#380C22×C4711yescharacteristic, complemented
484#379—21no—
485#340C22×C4711yescharacteristic, complemented
486#340C22×C4711yescharacteristic, complemented
487#340C22×C4711yescharacteristic, complemented
488#340C22×C4711yescharacteristic, complemented
489C47#2513611yescharacteristic, direct product factor, Sylow
490C25—21no—
491C22×Q8C23×C4711yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C4711yescharacteristic
502C22×D4C23×C4711yescharacteristic
503C22×D4C23×C4711yescharacteristic
504C23×C4C23×C4711yescharacteristic
505C23×C4C23×C4711yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C4711yescharacteristic
519C22×C8C23×C4711yescharacteristic
520C22×C8C23×C4711yescharacteristic
521C22×C8C23×C4711yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C4711yescharacteristic
539C2×C4⋊C4C23×C4711yescharacteristic
540C2×C4⋊C4C23×C4711yescharacteristic
541C2×C4⋊C4C23×C4711yescharacteristic
542C2×C4⋊C4C23×C4711yescharacteristic
543C2×C4⋊C4C23×C4711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C4711yescharacteristic
556C2×C22⋊C4D4×C4711yescharacteristic
557C2×C42—21no—
558C2×C42C23×C4711yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C4714yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C4714yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C4711yescharacteristic
588C24C2×D4×C4711yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C4712yes—
622C2×D4#41×C4712yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C4711yescharacteristic
640C22×C4C2×D4×C4711yescharacteristic
641C22×C4C2×D4×C4711yescharacteristic
642C22×C4C2×D4×C4712yes—
643C22×C4C2×D4×C4711yescharacteristic
644C22×C4#41×C4712yes—
645C22×C4C24×C4711yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C4712yes—
660C2×C8C2×D4×C4712yes—
661C2×C8C2×D4×C4712yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C4712yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C4712yes—
727C23C22×D4×C4711yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C4712yes—
781C2×C4AGL(1,ℤ/8)×C4712yes—
782C2×C4C22×D4×C4711yescharacteristic
783C2×C4C22×D4×C4711yescharacteristic
784C2×C4C2×#41×C4711yescharacteristic
785C2×C4C2×#41×C4711yescharacteristic
786C2×C4H(5,𝔽2)×C4711yescharacteristic
787C2×C4H(5,𝔽2)×C4711yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C4711yescharacteristic
822C22D42×C4711yescharacteristic
823C22C47×#54611yescharacteristic
824C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
825C22C47×#57511yescharacteristic
826C22C47×#57711yescharacteristic
827C22C47×#57711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4C47×#52511yescharacteristic
839C4C47×#53811yescharacteristic
840C4D42×C4711yescharacteristic
841C4C47×#54611yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C47×#242411yescharacteristic
847C2C47×#305511yescharacteristic
848C2C47×#305711yescharacteristic
849C2C47×#327211yescharacteristic
850C2C47×#327511yescharacteristic
851C2C47×#332311yescharacteristic
852C2C47×#332411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2408C2
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×#468C2semidirect
2. C2×C47×#450C2semidirect
3. C2×C47×#436C2semidirect
4. C2×C47×#418C2semidirect
5. C47×#2415C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2034C2semidirect
10. C47×#2000C2semidirect
11. C47×#1968C2semidirect
12. C47×#1934C2semidirect
13. C47×#1895C2semidirect
14. C47×#1894C2semidirect
15. C47×#1854C2semidirect
20. C22×M16×C47C22semidirect
22. C2×C22⋊Q8×C47C22semidirect
31. C2×#107×C47C22semidirect
32. C2×#106×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
44. C2×C22⋊C8×C47C22semidirect
45. C2×C4×C8×C47C22semidirect
50. C47×#391C22semidirect
54. C47×#389C22semidirect
57. C47×#380C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
142. #102×C47D4semidirect
144. C22⋊C8×C47D4semidirect
365. #25136C47direct (N × H)
416. C2×#468C2×C47semidirect
417. C2×#450C2×C47semidirect
418. C2×#436C2×C47semidirect
419. C2×#418C2×C47semidirect
420. #2415C2×C47semidirect
422. #2067C2×C47semidirect
423. #2055C2×C47semidirect
424. #2034C2×C47semidirect
425. #2000C2×C47semidirect
426. #1968C2×C47semidirect
427. #1934C2×C47semidirect
428. #1895C2×C47semidirect
429. #1894C2×C47semidirect
430. #1854C2×C47semidirect
446. C22×M16C22×C47semidirect
448. C2×C22⋊Q8C22×C47semidirect
457. C2×#107C22×C47semidirect
458. C2×#106C22×C47semidirect
459. C2×C4⋊C8C22×C47semidirect
461. C2×#103C22×C47semidirect
462. C2×#103C22×C47semidirect
470. C2×C22⋊C8C22×C47semidirect
471. C2×C4×C8C22×C47semidirect
476. #391C22×C47semidirect
480. #389C22×C47semidirect
483. #380C22×C47semidirect
485. #340C22×C47semidirect
486. #340C22×C47semidirect
487. #340C22×C47semidirect
488. #340C22×C47semidirect
489. C47#25136direct (N × H)
569. #102D4×C47semidirect
571. C22⋊C8D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4682
C2×C47×#4502
C2×C47×#4362
C2×C47×#4182
C47×#24152
C47×#24082
C47×#20672
C47×#20552
C47×#20342
C47×#20002
C47×#19682
C47×#19342
C47×#18952
C47×#18942
C47×#18542
#2513647