Finite Group Databasebeta

← C47×#25093 #26064791

Subgroups — C47×#25093 #26064791

Order 12032.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#468C211yesmaximal, characteristic, complemented
2C2×C47×#460C211yesmaximal, characteristic, complemented
3C2×C47×#450C211yesmaximal, characteristic, complemented
4C2×C47×#418C211yesmaximal, characteristic, complemented
5C47×#2433C211yesmaximal, characteristic
6C47×#2362C211yesmaximal, characteristic, complemented
7C47×#2067C211yesmaximal, characteristic, complemented
8C47×#2055C211yesmaximal, characteristic, complemented
9C47×#2041C211yesmaximal, characteristic, complemented
10C47×#2014C211yesmaximal, characteristic, complemented
11C47×#1982C211yesmaximal, characteristic, complemented
12C47×#1925C211yesmaximal, characteristic, complemented
13C47×#1880C211yesmaximal, characteristic, complemented
14C47×#1875C211yesmaximal, characteristic, complemented
15C47×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×SD16×C47C2211yescharacteristic
18C22×SD16×C47C2211yescharacteristic
19C22×SD16×C47C2211yescharacteristic, complemented
20C22×M16×C47C2211yescharacteristic
21C2×#127×C47C2211yescharacteristic
22C2×#127×C47C2211yescharacteristic
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47C2211yescharacteristic
25C2×#120×C47—21no—
26C2×#120×C47—21no—
27C2×C4×Q8×C47C2211yescharacteristic, complemented
28C2×#117×C47C2211yescharacteristic
29C47×#468—24no—
30C47×#460—24no—
31C47×#450—24no—
32C2×#107×C47C2211yescharacteristic, complemented
33C2×C4⋊C8×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C47×#418—24no—
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×C22⋊C8×C47C2211yescharacteristic
47C47×#392—21no—
48C47×#392—21no—
49C47×#391C2211yescharacteristic, complemented
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic, complemented
53C47×#388—21no—
54C47×#388—21no—
55C47×#387—21no—
56C4×C4⋊C4×C47—21no—
57C4×C4⋊C4×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—22no—
69C22×D4×C47—21no—
70C22×D4×C47—21no—
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—41no—
76C22×D4×C47—41no—
77C22×D4×C47C2311yescharacteristic
78C22×D4×C47C2311yescharacteristic
79C22×D4×C47C2311yescharacteristic
80C23×C4×C47C2311yescharacteristic
81C2×SD16×C47—22no—
82C2×SD16×C47—22no—
83C2×SD16×C47—22no—
84C2×SD16×C47—22no—
85C2×SD16×C47—22no—
86C2×SD16×C47—22no—
87C2×SD16×C47—41no—
88C2×SD16×C47—41no—
89C2×SD16×C47—41no—
90C2×M16×C47—22no—
91C2×M16×C47—22no—
92C2×M16×C47—41no—
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C22×C8×C47C2311yescharacteristic
96C22×C8×C47C2311yescharacteristic
97#127×C47—22no—
98#127×C47—22no—
99#127×C47—41no—
100#127×C47—41no—
101C22⋊Q8×C47—22no—
102C22⋊Q8×C47D414yescomplemented
103#121×C47—22no—
104#121×C47—22no—
105#120×C47—44no—
106#120×C47—44no—
107C4×Q8×C47—22no—
108C4×Q8×C47—41no—
109#117×C47—22no—
110#117×C47—41no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
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×C47D411yescharacteristic
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C42×C47—21no—
128C2×C42×C47—21no—
129C2×C42×C47—21no—
130C2×C42×C47C2311yescharacteristic
131C2×C42×C47C2311yescharacteristic
132#107×C47—22no—
133C4⋊C8×C47—22no—
134C4⋊C8×C47—41no—
135#103×C47—22no—
136#102×C47—22no—
137#102×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—
144#102×C47D414yescomplemented
145C22⋊C8×C47—22no—
146#95×C47—21no—
147#95×C47—21no—
148#95×C47—21no—
149#95×C47—21no—
150#95×C47D411yescharacteristic
151#95×C47D411yescharacteristic
152C24×C47—21no—
153C24×C47—21no—
154C24×C47—21no—
155C24×C47—42no—
156C24×C47—42no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—42no—
160C24×C47—81no—
161C24×C47—81no—
162C24×C47C2×D411yescharacteristic
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47C2×D412yes—
169C2×D4×C47—28no—
170C2×D4×C47—21no—
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—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—44no—
187C2×D4×C47—44no—
188C2×D4×C47—42no—
189C2×D4×C47—42no—
190C2×D4×C47—44no—
191C2×D4×C47—42no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47—42no—
203C2×D4×C47—81no—
204C2×D4×C47—81no—
205C2×D4×C47—81no—
206C2×D4×C47—81no—
207C2×D4×C47C2×D412yes—
208C2×D4×C47#4112yes—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47C2×D411yescharacteristic
219C22×C4×C47C2×D411yescharacteristic
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D412yes—
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47#4112yes—
225C22×C4×C47C2411yescharacteristic
226SD16×C47—44no—
227SD16×C47—44no—
228SD16×C47—44no—
229M16×C47—44no—
230C2×C8×C47—21no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47C2×D412yes—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—42no—
250C4⋊C4×C47—42no—
251C4⋊C4×C47C2×D412yes—
252C4⋊C4×C47C2×D412yes—
253C22⋊C4×C47—24no—
254C22⋊C4×C47—22no—
255C22⋊C4×C47—22no—
256C22⋊C4×C47—42no—
257C22⋊C4×C47—42no—
258C22⋊C4×C47—42no—
259C22⋊C4×C47—42no—
260C22⋊C4×C47—42no—
261C22⋊C4×C47—42no—
262C42×C47—21no—
263C42×C47—21no—
264C42×C47—21no—
265C42×C47—21no—
266C42×C47—42no—
267C42×C47—42no—
268C42×C47—42no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—48no—
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×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—84no—
298C23×C47—84no—
299C23×C47—84no—
300C23×C47—84no—
301C23×C47—84no—
302C23×C47—84no—
303C23×C47#12112yes—
304C23×C47C22×D411yescharacteristic
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—41no—
308Q8×C47—41no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47—22no—
313D4×C47—48no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—41no—
319D4×C47—41no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—84no—
323D4×C47—84no—
324D4×C47—84no—
325D4×C47—84no—
326D4×C47—84no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—21no—
340C2×C4×C47—22no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
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—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47#12112yes—
359C2×C4×C47AGL(1,ℤ/8)12yes—
360C2×C4×C47AGL(1,ℤ/8)12yes—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4111yescharacteristic
364C2×C4×C47C2×#4111yescharacteristic
365C2×C4×C47H(5,𝔽2)11yescharacteristic
366C2×C4×C47H(5,𝔽2)11yescharacteristic
367C8×C47—22no—
368C8×C47—41no—
369C8×C47—41no—
370C8×C47—41no—
371#25093C4711yesmaximal, characteristic, direct product factor, Sylow
372C22×C47—22no—
373C22×C47—22no—
374C22×C47—22no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—816no—
386C22×C47—81no—
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×C47—81no—
396C22×C47—81no—
397C22×C47—81no—
398C22×C47—81no—
399C22×C47—81no—
400C22×C47—81no—
401C22×C47C2×#12111yescharacteristic
402C22×C47D4211yescharacteristic
403C22×C47#54611yescharacteristic
404C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C47#57711yescharacteristic
407C22×C47#57711yescharacteristic
408C4×C47—22no—
409C4×C47—22no—
410C4×C47—22no—
411C4×C47—42no—
412C4×C47—41no—
413C4×C47—42no—
414C4×C47—42no—
415C4×C47—41no—
416C4×C47—81no—
417C4×C47—81no—
418C4×C47#52511yescharacteristic
419C4×C47#53811yescharacteristic
420C4×C47D4211yescharacteristic
421C4×C47#54611yescharacteristic
422C2×#468C2×C4711yescharacteristic, complemented
423C2×#460C2×C4711yescharacteristic, complemented
424C2×#450C2×C4711yescharacteristic, complemented
425C2×#418C2×C4711yescharacteristic, complemented
426#2433C2×C4711yescharacteristic
427#2362C2×C4711yescharacteristic, complemented
428#2067C2×C4711yescharacteristic, complemented
429#2055C2×C4711yescharacteristic, complemented
430#2041C2×C4711yescharacteristic, complemented
431#2014C2×C4711yescharacteristic, complemented
432#1982C2×C4711yescharacteristic, complemented
433#1925C2×C4711yescharacteristic, complemented
434#1880C2×C4711yescharacteristic, complemented
435#1875C2×C4711yescharacteristic, complemented
436#1851C2×C4711yescharacteristic, complemented
437C2×C47—42no—
438C2×C47—82no—
439C2×C47—82no—
440C2×C47—161no—
441C2×C47#242411yescharacteristic
442C2×C47#303811yescharacteristic
443C2×C47#304311yescharacteristic
444C2×C47#326511yescharacteristic
445C2×C47#327211yescharacteristic
446C2×C47#331011yescharacteristic
447C2×C47#332411yescharacteristic
448C23×D4C22×C4711yescharacteristic
449C22×SD16C22×C4711yescharacteristic
450C22×SD16C22×C4711yescharacteristic
451C22×SD16C22×C4711yescharacteristic, complemented
452C22×M16C22×C4711yescharacteristic
453C2×#127C22×C4711yescharacteristic
454C2×#127C22×C4711yescharacteristic
455C2×C22⋊Q8C22×C4711yescharacteristic
456C2×#121C22×C4711yescharacteristic
457C2×#120—21no—
458C2×#120—21no—
459C2×C4×Q8C22×C4711yescharacteristic, complemented
460C2×#117C22×C4711yescharacteristic
461#468—24no—
462#460—24no—
463#450—24no—
464C2×#107C22×C4711yescharacteristic, complemented
465C2×C4⋊C8C22×C4711yescharacteristic, complemented
466C2×C4⋊C8C22×C4711yescharacteristic, complemented
467#418—24no—
468C2×#103C22×C4711yescharacteristic, complemented
469C2×#102C22×C4711yescharacteristic
470C2×#102C22×C4711yescharacteristic
471C2×#102C22×C4711yescharacteristic
472C2×#102C22×C4711yescharacteristic
473C2×#102C22×C4711yescharacteristic
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic, complemented
476C2×#102C22×C4711yescharacteristic, complemented
477C2×#102C22×C4711yescharacteristic, complemented
478C2×C22⋊C8C22×C4711yescharacteristic
479#392—21no—
480#392—21no—
481#391C22×C4711yescharacteristic, complemented
482#390C22×C4711yescharacteristic
483#390C22×C4711yescharacteristic
484#389C22×C4711yescharacteristic, complemented
485#388—21no—
486#388—21no—
487#387—21no—
488C4×C4⋊C4—21no—
489C4×C4⋊C4C22×C4711yescharacteristic, complemented
490C4×C22⋊C4C22×C4711yescharacteristic
491#340C22×C4711yescharacteristic, complemented
492#340C22×C4711yescharacteristic, complemented
493#336C22×C4711yescharacteristic, complemented
494#336C22×C4711yescharacteristic, complemented
495C47#2509311yescharacteristic, direct product factor, Sylow
496C25—21no—
497C22×Q8C23×C4711yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C4711yescharacteristic
511C22×D4C23×C4711yescharacteristic
512C22×D4C23×C4711yescharacteristic
513C23×C4C23×C4711yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C22×C8C23×C4711yescharacteristic
527C22×C8C23×C4711yescharacteristic
528C22×C8C23×C4711yescharacteristic
529C22×C8C23×C4711yescharacteristic
530#127—22no—
531#127—22no—
532#127—41no—
533#127—41no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C4714yescomplemented
536#121—22no—
537#121—22no—
538#120—44no—
539#120—44no—
540C4×Q8—22no—
541C4×Q8—41no—
542#117—22no—
543#117—41no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4C23×C4711yescharacteristic
548C2×C4⋊C4C23×C4711yescharacteristic
549C2×C4⋊C4C23×C4711yescharacteristic
550C2×C4⋊C4C23×C4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4D4×C4711yescharacteristic
559C2×C22⋊C4D4×C4711yescharacteristic
560C2×C42—21no—
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C4711yescharacteristic
564C2×C42C23×C4711yescharacteristic
565#107—22no—
566C4⋊C8—22no—
567C4⋊C8—41no—
568#103—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102D4×C4714yescomplemented
578C22⋊C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95D4×C4711yescharacteristic
584#95D4×C4711yescharacteristic
585C24—21no—
586C24—21no—
587C24—21no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—81no—
594C24—81no—
595C24C2×D4×C4711yescharacteristic
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C4712yes—
602C2×D4—28no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4C2×D4×C4712yes—
641C2×D4#41×C4712yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4C2×D4×C4711yescharacteristic
652C22×C4C2×D4×C4711yescharacteristic
653C22×C4C2×D4×C4711yescharacteristic
654C22×C4C2×D4×C4712yes—
655C22×C4C2×D4×C4711yescharacteristic
656C22×C4C2×D4×C4711yescharacteristic
657C22×C4#41×C4712yes—
658C22×C4C24×C4711yescharacteristic
659SD16—44no—
660SD16—44no—
661SD16—44no—
662M16—44no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8C2×D4×C4712yes—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4C2×D4×C4712yes—
685C4⋊C4C2×D4×C4712yes—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23#121×C4712yes—
737C23C22×D4×C4711yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#121×C4712yes—
792C2×C4AGL(1,ℤ/8)×C4712yes—
793C2×C4AGL(1,ℤ/8)×C4712yes—
794C2×C4C22×D4×C4711yescharacteristic
795C2×C4C22×D4×C4711yescharacteristic
796C2×C4C2×#41×C4711yescharacteristic
797C2×C4C2×#41×C4711yescharacteristic
798C2×C4H(5,𝔽2)×C4711yescharacteristic
799C2×C4H(5,𝔽2)×C4711yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22C2×#121×C4711yescharacteristic
834C22D42×C4711yescharacteristic
835C22C47×#54611yescharacteristic
836C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
837C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
838C22C47×#57711yescharacteristic
839C22C47×#57711yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—42no—
844C4—41no—
845C4—42no—
846C4—41no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4C47×#52511yescharacteristic
851C4C47×#53811yescharacteristic
852C4D42×C4711yescharacteristic
853C4C47×#54611yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2C47×#242411yescharacteristic
859C2C47×#303811yescharacteristic
860C2C47×#304311yescharacteristic
861C2C47×#326511yescharacteristic
862C2C47×#327211yescharacteristic
863C2C47×#331011yescharacteristic
864C2C47×#332411yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2433C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C47×#468C2semidirect
2. C2×C47×#460C2semidirect
3. C2×C47×#450C2semidirect
4. C2×C47×#418C2semidirect
6. C47×#2362C2semidirect
7. C47×#2067C2semidirect
8. C47×#2055C2semidirect
9. C47×#2041C2semidirect
10. C47×#2014C2semidirect
11. C47×#1982C2semidirect
12. C47×#1925C2semidirect
13. C47×#1880C2semidirect
14. C47×#1875C2semidirect
15. C47×#1851C2semidirect
19. C22×SD16×C47C22semidirect
27. C2×C4×Q8×C47C22semidirect
32. C2×#107×C47C22semidirect
33. C2×C4⋊C8×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
36. C2×#103×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
49. C47×#391C22semidirect
52. C47×#389C22semidirect
57. C4×C4⋊C4×C47C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
102. C22⋊Q8×C47D4semidirect
144. #102×C47D4semidirect
371. #25093C47direct (N × H)
422. C2×#468C2×C47semidirect
423. C2×#460C2×C47semidirect
424. C2×#450C2×C47semidirect
425. C2×#418C2×C47semidirect
427. #2362C2×C47semidirect
428. #2067C2×C47semidirect
429. #2055C2×C47semidirect
430. #2041C2×C47semidirect
431. #2014C2×C47semidirect
432. #1982C2×C47semidirect
433. #1925C2×C47semidirect
434. #1880C2×C47semidirect
435. #1875C2×C47semidirect
436. #1851C2×C47semidirect
451. C22×SD16C22×C47semidirect
459. C2×C4×Q8C22×C47semidirect
464. C2×#107C22×C47semidirect
465. C2×C4⋊C8C22×C47semidirect
466. C2×C4⋊C8C22×C47semidirect
468. C2×#103C22×C47semidirect
475. C2×#102C22×C47semidirect
476. C2×#102C22×C47semidirect
477. C2×#102C22×C47semidirect
481. #391C22×C47semidirect
484. #389C22×C47semidirect
489. C4×C4⋊C4C22×C47semidirect
491. #340C22×C47semidirect
492. #340C22×C47semidirect
493. #336C22×C47semidirect
494. #336C22×C47semidirect
495. C47#25093direct (N × H)
535. C22⋊Q8D4×C47semidirect
577. #102D4×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×#4602
C2×C47×#4502
C2×C47×#4182
C47×#24332
C47×#23622
C47×#20672
C47×#20552
C47×#20412
C47×#20142
C47×#19822
C47×#19252
C47×#18802
C47×#18752
C47×#18512
#2509347