Finite Group Databasebeta

← C47×#22868 #26062566

Subgroups — C47×#22868 #26062566

Order 12032.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#447C211yesmaximal, characteristic
2C2×C47×#442C211yesmaximal, characteristic, complemented
3C2×C47×#418C211yesmaximal, characteristic, complemented
4C47×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
6C47×#1970C211yesmaximal, characteristic, complemented
7C47×#1936C211yesmaximal, characteristic, complemented
8C47×#1926C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1879C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1862C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C47C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic, complemented
24C2×#117×C47C2211yescharacteristic
25C22×C22⋊C4×C47—21no—
26C47×#447C418yescomplemented
27C47×#442—24no—
28C2×#107×C47C2211yescharacteristic, complemented
29C2×#106×C47C2211yescharacteristic, complemented
30C47×#418—24no—
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic, complemented
38C2×#102×C47C2211yescharacteristic, complemented
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×#97×C47C2211yescharacteristic, complemented
41C2×C4×C8×C47C2211yescharacteristic, complemented
42C47×#390—21no—
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic
45C47×#390C2211yescharacteristic, complemented
46C47×#389C2211yescharacteristic, complemented
47C47×#388—21no—
48C47×#386—21no—
49C47×#386—21no—
50C47×#386—21no—
51C47×#380C2211yescharacteristic
52C47×#379—21no—
53C4×C4⋊C4×C47C2211yescharacteristic, complemented
54C4×C22⋊C4×C47—21no—
55C4×C22⋊C4×C47C2211yescharacteristic
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#340C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C25×C47—21no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—21no—
66C22×D4×C47—21no—
67C22×D4×C47—22no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47C2×C414yescomplemented
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C22×D4×C47C2311yescharacteristic
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47—21no—
77C23×C4×C47C2311yescharacteristic
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—41no—
81C2×D8×C47—41no—
82C2×D8×C47C2×C414yes—
83C2×D8×C47C2×C414yescomplemented
84C2×M16×C47—22no—
85C2×M16×C47—22no—
86C2×M16×C47—41no—
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91#121×C47—22no—
92#121×C47C2×C414yescomplemented
93C4×D4×C47—22no—
94C4×D4×C47—22no—
95C4×D4×C47—22no—
96C4×D4×C47—41no—
97C4×D4×C47—41no—
98C4×D4×C47—41no—
99#117×C47—22no—
100#117×C47—41no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—44no—
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C22⋊C4×C47D411yescharacteristic
122C2×C42×C47—21no—
123C2×C42×C47—21no—
124C2×C42×C47C2311yescharacteristic
125C2×C42×C47C2311yescharacteristic
126#107×C47—41no—
127#106×C47—22no—
128#102×C47—22no—
129#102×C47—22no—
130#102×C47—22no—
131#102×C47—22no—
132#102×C47—41no—
133#102×C47C2×C414yescomplemented
134#102×C47C2×C414yescomplemented
135#102×C47D414yescomplemented
136C22⋊C8×C47C2×C414yescomplemented
137#97×C47—22no—
138C4×C8×C47—41no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—24no—
148C24×C47—42no—
149C24×C47—42no—
150C24×C47—42no—
151C24×C47—42no—
152C24×C47—81no—
153C24×C47—81no—
154C24×C47C2×D411yescharacteristic
155C2×D4×C47—28no—
156C2×D4×C47—24no—
157C2×D4×C47—24no—
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—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—44no—
172C2×D4×C47—44no—
173C2×D4×C47—44no—
174C2×D4×C47—42no—
175C2×D4×C47—42no—
176C2×D4×C47—81no—
177C2×D4×C47—81no—
178C2×D4×C47C22×C412yes—
179C2×D4×C47C22×C412yes—
180C2×D4×C47C22×C412yes—
181C2×D4×C47C2×D412yes—
182C2×D4×C47#4112yes—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47—42no—
196C22×C4×C47—42no—
197C22×C4×C47—42no—
198C22×C4×C47—81no—
199C22×C4×C47—81no—
200C22×C4×C47—81no—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47#4112yes—
208C22×C4×C47C2411yescharacteristic
209D8×C47—28no—
210D8×C47—44no—
211M16×C47—44no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
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×C47C22×C412yes—
222C2×C8×C47C22×C412yes—
223C2×C8×C47C2×D412yes—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—81no—
233C4⋊C4×C47C22×C412yes—
234C4⋊C4×C47C2×D412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—41no—
238C22⋊C4×C47—42no—
239C22⋊C4×C47—42no—
240C22⋊C4×C47—42no—
241C22⋊C4×C47—42no—
242C22⋊C4×C47—42no—
243C22⋊C4×C47—42no—
244C22⋊C4×C47—42no—
245C22⋊C4×C47—42no—
246C22⋊C4×C47—81no—
247C22⋊C4×C47—81no—
248C22⋊C4×C47—81no—
249C42×C47—21no—
250C42×C47—21no—
251C42×C47—21no—
252C42×C47—21no—
253C42×C47—42no—
254C42×C47—81no—
255C23×C47—22no—
256C23×C47—21no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—48no—
267C23×C47—48no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
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—84no—
285C23×C47—84no—
286C23×C47—84no—
287C23×C47—84no—
288C23×C47—84no—
289C23×C47C4×D412yes—
290C23×C47C22×D411yescharacteristic
291D4×C47—22no—
292D4×C47—22no—
293D4×C47—22no—
294D4×C47—22no—
295D4×C47—22no—
296D4×C47—22no—
297D4×C47—22no—
298D4×C47—48no—
299D4×C47—41no—
300D4×C47—41no—
301D4×C47—41no—
302D4×C47—41no—
303D4×C47—84no—
304D4×C47C4×D414yes—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—22no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
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×C47C4×D412yes—
341C2×C4×C47AGL(1,ℤ/8)12yes—
342C2×C4×C47C23×C411yescharacteristic
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C2×#4111yescharacteristic
345C2×C4×C47C2×#4111yescharacteristic
346C2×C4×C47H(5,𝔽2)11yescharacteristic
347C2×C4×C47H(5,𝔽2)11yescharacteristic
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—22no—
351C8×C47—41no—
352#22868C4711yesmaximal, characteristic, direct product factor, Sylow
353C22×C47—22no—
354C22×C47—24no—
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—41no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—816no—
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×C47C2×C4×D411yescharacteristic
383C22×C47D4211yescharacteristic
384C22×C47#54611yescharacteristic
385C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
386C22×C47#57511yescharacteristic
387C22×C47#57611yescharacteristic
388C22×C47#57611yescharacteristic
389C4×C47—22no—
390C4×C47—22no—
391C4×C47—42no—
392C4×C47—41no—
393C4×C47—42no—
394C4×C47—41no—
395C4×C47—41no—
396C4×C47—81no—
397C4×C47—81no—
398C4×C47—81no—
399C4×C47C2×C4×D411yescharacteristic
400C4×C47#51811yescharacteristic
401C4×C47#54611yescharacteristic
402C4×C47#55111yescharacteristic
403C2×#447C2×C4711yescharacteristic
404C2×#442C2×C4711yescharacteristic, complemented
405C2×#418C2×C4711yescharacteristic, complemented
406#2363C2×C4711yescharacteristic, complemented
407D4×C22⋊C4C2×C4711yescharacteristic, complemented
408#1970C2×C4711yescharacteristic, complemented
409#1936C2×C4711yescharacteristic, complemented
410#1926C2×C4711yescharacteristic, complemented
411#1895C2×C4711yescharacteristic, complemented
412#1879C2×C4711yescharacteristic, complemented
413#1879C2×C4711yescharacteristic, complemented
414#1862C2×C4711yescharacteristic, complemented
415#1854C2×C4711yescharacteristic, complemented
416C4×#102C2×C4711yescharacteristic, complemented
417#1753C2×C4711yescharacteristic, complemented
418C2×C47—42no—
419C2×C47—44no—
420C2×C47—82no—
421C2×C47—82no—
422C2×C47#235811yescharacteristic
423C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C47#294811yescharacteristic
425C2×C47#327311yescharacteristic
426C2×C47#327411yescharacteristic
427C2×C47#331811yescharacteristic
428C2×C47#331911yescharacteristic
429C23×D4C22×C4711yescharacteristic
430C22×D8C22×C4711yescharacteristic
431C22×D8C22×C4711yescharacteristic
432C22×M16C22×C4711yescharacteristic
433C2×#121C22×C4711yescharacteristic
434C2×C4×D4C22×C4711yescharacteristic
435C2×C4×D4C22×C4711yescharacteristic
436C2×C4×D4C22×C4711yescharacteristic, complemented
437C2×#117C22×C4711yescharacteristic
438C22×C22⋊C4—21no—
439#447C4×C4718yescomplemented
440#442—24no—
441C2×#107C22×C4711yescharacteristic, complemented
442C2×#106C22×C4711yescharacteristic, complemented
443#418—24no—
444C2×#102C22×C4711yescharacteristic
445C2×#102C22×C4711yescharacteristic
446C2×#102C22×C4711yescharacteristic
447C2×#102C22×C4711yescharacteristic
448C2×#102C22×C4711yescharacteristic
449C2×#102C22×C4711yescharacteristic
450C2×#102C22×C4711yescharacteristic, complemented
451C2×#102C22×C4711yescharacteristic, complemented
452C2×C22⋊C8C22×C4711yescharacteristic
453C2×#97C22×C4711yescharacteristic, complemented
454C2×C4×C8C22×C4711yescharacteristic, complemented
455#390—21no—
456#390C22×C4711yescharacteristic
457#390C22×C4711yescharacteristic
458#390C22×C4711yescharacteristic, complemented
459#389C22×C4711yescharacteristic, complemented
460#388—21no—
461#386—21no—
462#386—21no—
463#386—21no—
464#380C22×C4711yescharacteristic
465#379—21no—
466C4×C4⋊C4C22×C4711yescharacteristic, complemented
467C4×C22⋊C4—21no—
468C4×C22⋊C4C22×C4711yescharacteristic
469#340C22×C4711yescharacteristic, complemented
470#340C22×C4711yescharacteristic, complemented
471#340C22×C4711yescharacteristic, complemented
472#340C22×C4711yescharacteristic, complemented
473#336C22×C4711yescharacteristic, complemented
474#336C22×C4711yescharacteristic, complemented
475C47#2286811yescharacteristic, direct product factor, Sylow
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C4714yescomplemented
485C22×D4C23×C4711yescharacteristic
486C22×D4C23×C4711yescharacteristic
487C22×D4C23×C4711yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C4711yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C4714yes—
497C2×D8C2×C4×C4714yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C4711yescharacteristic
502C22×C8C23×C4711yescharacteristic
503C22×C8C23×C4711yescharacteristic
504C22×C8C23×C4711yescharacteristic
505#121—22no—
506#121C2×C4×C4714yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C4711yescharacteristic
517C2×C4⋊C4C23×C4711yescharacteristic
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4711yescharacteristic
520C2×C4⋊C4C23×C4711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C4711yescharacteristic
535C2×C22⋊C4D4×C4711yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C4711yescharacteristic
539C2×C42C23×C4711yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C4714yescomplemented
548#102C2×C4×C4714yescomplemented
549#102D4×C4714yescomplemented
550C22⋊C8C2×C4×C4714yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C4711yescharacteristic
557#95D4×C4711yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C4711yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
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—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C4712yes—
593C2×D4C22×C4×C4712yes—
594C2×D4C22×C4×C4712yes—
595C2×D4C2×D4×C4712yes—
596C2×D4#41×C4712yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C4712yes—
616C22×C4C2×D4×C4711yescharacteristic
617C22×C4C2×D4×C4711yescharacteristic
618C22×C4C2×D4×C4711yescharacteristic
619C22×C4C2×D4×C4711yescharacteristic
620C22×C4C2×D4×C4711yescharacteristic
621C22×C4#41×C4712yes—
622C22×C4C24×C4711yescharacteristic
623D8—28no—
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×C8C22×C4×C4712yes—
636C2×C8C22×C4×C4712yes—
637C2×C8C2×D4×C4712yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C4712yes—
648C4⋊C4C2×D4×C4712yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
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—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C4712yes—
704C23C22×D4×C4711yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C4714yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
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—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C4712yes—
755C2×C4AGL(1,ℤ/8)×C4712yes—
756C2×C4C23×C4×C4711yescharacteristic
757C2×C4C22×D4×C4711yescharacteristic
758C2×C4C2×#41×C4711yescharacteristic
759C2×C4C2×#41×C4711yescharacteristic
760C2×C4H(5,𝔽2)×C4711yescharacteristic
761C2×C4H(5,𝔽2)×C4711yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C4711yescharacteristic
796C22D42×C4711yescharacteristic
797C22C47×#54611yescharacteristic
798C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
799C22C47×#57511yescharacteristic
800C22C47×#57611yescharacteristic
801C22C47×#57611yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—42no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C4711yescharacteristic
813C4C47×#51811yescharacteristic
814C4C47×#54611yescharacteristic
815C4C47×#55111yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C47×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C4711yescharacteristic
822C2C47×#294811yescharacteristic
823C2C47×#327311yescharacteristic
824C2C47×#327411yescharacteristic
825C2C47×#331811yescharacteristic
826C2C47×#331911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
LCSG ▷ C2×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
2. C2×C47×#442C2semidirect
3. C2×C47×#418C2semidirect
4. C47×#2363C2semidirect
5. D4×C22⋊C4×C47C2semidirect
6. C47×#1970C2semidirect
7. C47×#1936C2semidirect
8. C47×#1926C2semidirect
9. C47×#1895C2semidirect
10. C47×#1879C2semidirect
11. C47×#1879C2semidirect
12. C47×#1862C2semidirect
13. C47×#1854C2semidirect
14. C4×#102×C47C2semidirect
15. C47×#1753C2semidirect
23. C2×C4×D4×C47C22semidirect
26. C47×#447C4semidirect
28. C2×#107×C47C22semidirect
29. C2×#106×C47C22semidirect
37. C2×#102×C47C22semidirect
38. C2×#102×C47C22semidirect
40. C2×#97×C47C22semidirect
41. C2×C4×C8×C47C22semidirect
45. C47×#390C22semidirect
46. C47×#389C22semidirect
53. C4×C4⋊C4×C47C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#340C22semidirect
60. C47×#336C22semidirect
61. C47×#336C22semidirect
70. C22×D4×C47C2×C4semidirect
83. C2×D8×C47C2×C4semidirect
92. #121×C47C2×C4semidirect
133. #102×C47C2×C4semidirect
134. #102×C47C2×C4semidirect
135. #102×C47D4semidirect
136. C22⋊C8×C47C2×C4semidirect
352. #22868C47direct (N × H)
404. C2×#442C2×C47semidirect
405. C2×#418C2×C47semidirect
406. #2363C2×C47semidirect
407. D4×C22⋊C4C2×C47semidirect
408. #1970C2×C47semidirect
409. #1936C2×C47semidirect
410. #1926C2×C47semidirect
411. #1895C2×C47semidirect
412. #1879C2×C47semidirect
413. #1879C2×C47semidirect
414. #1862C2×C47semidirect
415. #1854C2×C47semidirect
416. C4×#102C2×C47semidirect
417. #1753C2×C47semidirect
436. C2×C4×D4C22×C47semidirect
439. #447C4×C47semidirect
441. C2×#107C22×C47semidirect
442. C2×#106C22×C47semidirect
450. C2×#102C22×C47semidirect
451. C2×#102C22×C47semidirect
453. C2×#97C22×C47semidirect
454. C2×C4×C8C22×C47semidirect
458. #390C22×C47semidirect
459. #389C22×C47semidirect
466. C4×C4⋊C4C22×C47semidirect
469. #340C22×C47semidirect
470. #340C22×C47semidirect
471. #340C22×C47semidirect
472. #340C22×C47semidirect
473. #336C22×C47semidirect
474. #336C22×C47semidirect
475. C47#22868direct (N × H)
484. C22×D4C2×C4×C47semidirect
497. C2×D8C2×C4×C47semidirect
506. #121C2×C4×C47semidirect
547. #102C2×C4×C47semidirect
548. #102C2×C4×C47semidirect
549. #102D4×C47semidirect
550. C22⋊C8C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4472
C2×C47×#4422
C2×C47×#4182
C47×#23632
D4×C22⋊C4×C472
C47×#19702
C47×#19362
C47×#19262
C47×#18952
C47×#18792
C47×#18622
C47×#18542
C4×#102×C472
C47×#17532
#2286847