Finite Group Databasebeta

← C47×#24909 #26064607

Subgroups — C47×#24909 #26064607

Order 12032.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 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
3C47×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
5C47×#2092C211yesmaximal, characteristic, complemented
6C47×#2077C211yesmaximal, characteristic, complemented
7C47×#2054C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1936C211yesmaximal, characteristic, complemented
10C47×#1924C211yesmaximal, characteristic, complemented
11C47×#1879C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1862C211yesmaximal, characteristic, complemented
14C47×#1804C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C22×D8×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic, complemented
23C22×C22⋊C4×C47—21no—
24C47×#447—24no—
25C47×#442—24no—
26C2×#107×C47C2211yescharacteristic, complemented
27C2×#106×C47C2211yescharacteristic, complemented
28C2×C4⋊C8×C47C2211yescharacteristic, complemented
29C2×#102×C47C2211yescharacteristic
30C2×#102×C47C2211yescharacteristic
31C2×#102×C47C2211yescharacteristic
32C2×#102×C47C2211yescharacteristic
33C2×#102×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic, complemented
36C2×#102×C47C2211yescharacteristic, complemented
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C2×#97×C47C2211yescharacteristic, complemented
40C47×#397—21no—
41C47×#394—21no—
42C47×#390C2211yescharacteristic
43C47×#390C2211yescharacteristic
44C47×#390C2211yescharacteristic, complemented
45C47×#389C2211yescharacteristic, complemented
46C47×#386—21no—
47C47×#386—21no—
48C47×#386—21no—
49C47×#382C2211yescharacteristic, complemented
50C47×#381—21no—
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C47×#379—21no—
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic, complemented
56C47×#340C2211yescharacteristic, complemented
57C47×#340C2211yescharacteristic, complemented
58C47×#340C2211yescharacteristic, complemented
59C47×#336C2211yescharacteristic, complemented
60C47×#336C2211yescharacteristic, complemented
61C25×C47—21no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—41no—
69C22×D4×C47—41no—
70C22×D4×C47C2311yescharacteristic
71C22×D4×C47C2311yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47—21no—
74C23×C4×C47—21no—
75C23×C4×C47—21no—
76C23×C4×C47C2311yescharacteristic
77C2×D8×C47—22no—
78C2×D8×C47—22no—
79C2×D8×C47—22no—
80C2×D8×C47—22no—
81C2×D8×C47—41no—
82C2×D8×C47D414yes—
83C22×C8×C47C2311yescharacteristic
84C22×C8×C47C2311yescharacteristic
85C22×C8×C47C2311yescharacteristic
86C22×C8×C47C2311yescharacteristic
87#121×C47—22no—
88#121×C47—41no—
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C4×D4×C47—41no—
93C4×D4×C47—41no—
94C4×D4×C47—41no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
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—44no—
114C2×C22⋊C4×C47D411yescharacteristic
115C2×C22⋊C4×C47D411yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#107×C47—41no—
119#106×C47—22no—
120C4⋊C8×C47—41no—
121#102×C47—22no—
122#102×C47—22no—
123#102×C47—22no—
124#102×C47—22no—
125#102×C47—22no—
126#102×C47—22no—
127#102×C47—41no—
128#102×C47—41no—
129C22⋊C8×C47—22no—
130C22⋊C8×C47—41no—
131#97×C47—22no—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47D411yescharacteristic
138#95×C47D411yescharacteristic
139C24×C47—21no—
140C24×C47—24no—
141C24×C47—21no—
142C24×C47—21no—
143C24×C47—42no—
144C24×C47—42no—
145C24×C47—42no—
146C24×C47—42no—
147C24×C47—81no—
148C24×C47—81no—
149C24×C47C2×D411yescharacteristic
150C2×D4×C47—24no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
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—42no—
165C2×D4×C47—42no—
166C2×D4×C47—44no—
167C2×D4×C47—44no—
168C2×D4×C47—44no—
169C2×D4×C47—44no—
170C2×D4×C47—42no—
171C2×D4×C47—42no—
172C2×D4×C47—81no—
173C2×D4×C47C2×D412yes—
174C2×D4×C47C2×D412yes—
175C2×D4×C47#4112yes—
176C2×D4×C47#4112yes—
177C2×D4×C47#4112yes—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
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—21no—
189C22×C4×C47—42no—
190C22×C4×C47—42no—
191C22×C4×C47—42no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47—81no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2411yescharacteristic
204D8×C47—28no—
205D8×C47—44no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47—21no—
214C2×C8×C47—21no—
215C2×C8×C47—21no—
216C2×C8×C47—21no—
217C2×C8×C47C2×D412yes—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—81no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—41no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—42no—
233C22⋊C4×C47—42no—
234C22⋊C4×C47—42no—
235C22⋊C4×C47—42no—
236C22⋊C4×C47—42no—
237C22⋊C4×C47—42no—
238C22⋊C4×C47—81no—
239C22⋊C4×C47—81no—
240C22⋊C4×C47—81no—
241C22⋊C4×C47—81no—
242C22⋊C4×C47—81no—
243C42×C47—21no—
244C42×C47—21no—
245C42×C47—21no—
246C42×C47—21no—
247C23×C47—21no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—21no—
251C23×C47—22no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—48no—
259C23×C47—48no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
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—84no—
277C23×C47—84no—
278C23×C47—84no—
279C23×C47—84no—
280C23×C47—84no—
281C23×C47AGL(1,ℤ/8)12yes—
282C23×C47C22×D411yescharacteristic
283D4×C47—22no—
284D4×C47—22no—
285D4×C47—22no—
286D4×C47—22no—
287D4×C47—22no—
288D4×C47—22no—
289D4×C47—22no—
290D4×C47—48no—
291D4×C47—41no—
292D4×C47—41no—
293D4×C47—41no—
294D4×C47—41no—
295D4×C47—84no—
296D4×C47#12314yes—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
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—84no—
332C2×C4×C47—84no—
333C2×C4×C47—84no—
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47C2×#4111yescharacteristic
338C2×C4×C47H(5,𝔽2)11yescharacteristic
339C2×C4×C47H(5,𝔽2)11yescharacteristic
340C8×C47—22no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344#24909C4711yesmaximal, characteristic, direct product factor, Sylow
345C22×C47—22no—
346C22×C47—24no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—42no—
350C22×C47—41no—
351C22×C47—42no—
352C22×C47—41no—
353C22×C47—42no—
354C22×C47—41no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—41no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47—816no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—81no—
369C22×C47—81no—
370C22×C47—81no—
371C22×C47—81no—
372C22×C47—81no—
373C22×C47—81no—
374C22×C47#52511yescharacteristic
375C22×C47D4211yescharacteristic
376C22×C47#54611yescharacteristic
377C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C47#57511yescharacteristic
379C22×C47#57611yescharacteristic
380C22×C47#57611yescharacteristic
381C4×C47—41no—
382C4×C47—41no—
383C4×C47—41no—
384C4×C47—41no—
385C4×C47—41no—
386C4×C47—81no—
387C4×C47—81no—
388C4×C47—81no—
389C4×C47—81no—
390C4×C47—81no—
391C4×C47C2×#12311yescharacteristic
392C4×C47#53811yescharacteristic
393C4×C47#54611yescharacteristic
394C4×C47#55111yescharacteristic
395C2×#447C2×C4711yescharacteristic
396C2×#442C2×C4711yescharacteristic, complemented
397#2420C2×C4711yescharacteristic, complemented
398D4×C22⋊C4C2×C4711yescharacteristic, complemented
399#2092C2×C4711yescharacteristic, complemented
400#2077C2×C4711yescharacteristic, complemented
401#2054C2×C4711yescharacteristic, complemented
402#2033C2×C4711yescharacteristic, complemented
403#1936C2×C4711yescharacteristic, complemented
404#1924C2×C4711yescharacteristic, complemented
405#1879C2×C4711yescharacteristic, complemented
406#1879C2×C4711yescharacteristic, complemented
407#1862C2×C4711yescharacteristic, complemented
408#1804C2×C4711yescharacteristic, complemented
409#1786C2×C4711yescharacteristic, complemented
410C2×C47—42no—
411C2×C47—44no—
412C2×C47—82no—
413C2×C47—82no—
414C2×C47#241811yescharacteristic
415C2×C47#311411yescharacteristic
416C2×C47#312211yescharacteristic
417C2×C47#326411yescharacteristic
418C2×C47#327311yescharacteristic
419C2×C47#331811yescharacteristic
420C2×C47#331911yescharacteristic
421C23×D4C22×C4711yescharacteristic
422C22×D8C22×C4711yescharacteristic
423C22×D8C22×C4711yescharacteristic
424C2×#121C22×C4711yescharacteristic
425C2×C4×D4C22×C4711yescharacteristic
426C2×C4×D4C22×C4711yescharacteristic
427C2×C4×D4C22×C4711yescharacteristic, complemented
428C22×C22⋊C4—21no—
429#447—24no—
430#442—24no—
431C2×#107C22×C4711yescharacteristic, complemented
432C2×#106C22×C4711yescharacteristic, complemented
433C2×C4⋊C8C22×C4711yescharacteristic, complemented
434C2×#102C22×C4711yescharacteristic
435C2×#102C22×C4711yescharacteristic
436C2×#102C22×C4711yescharacteristic
437C2×#102C22×C4711yescharacteristic
438C2×#102C22×C4711yescharacteristic
439C2×#102C22×C4711yescharacteristic
440C2×#102C22×C4711yescharacteristic, complemented
441C2×#102C22×C4711yescharacteristic, complemented
442C2×C22⋊C8C22×C4711yescharacteristic
443C2×C22⋊C8C22×C4711yescharacteristic
444C2×#97C22×C4711yescharacteristic, complemented
445#397—21no—
446#394—21no—
447#390C22×C4711yescharacteristic
448#390C22×C4711yescharacteristic
449#390C22×C4711yescharacteristic, complemented
450#389C22×C4711yescharacteristic, complemented
451#386—21no—
452#386—21no—
453#386—21no—
454#382C22×C4711yescharacteristic, complemented
455#381—21no—
456#380C22×C4711yescharacteristic
457#380C22×C4711yescharacteristic
458#379—21no—
459C4×C22⋊C4C22×C4711yescharacteristic
460#340C22×C4711yescharacteristic, complemented
461#340C22×C4711yescharacteristic, complemented
462#340C22×C4711yescharacteristic, complemented
463#340C22×C4711yescharacteristic, complemented
464#336C22×C4711yescharacteristic, complemented
465#336C22×C4711yescharacteristic, complemented
466C47#2490911yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C4711yescharacteristic
477C22×D4C23×C4711yescharacteristic
478C22×D4C23×C4711yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C4711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C4714yes—
489C22×C8C23×C4711yescharacteristic
490C22×C8C23×C4711yescharacteristic
491C22×C8C23×C4711yescharacteristic
492C22×C8C23×C4711yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C4711yescharacteristic
503C2×C4⋊C4C23×C4711yescharacteristic
504C2×C4⋊C4C23×C4711yescharacteristic
505C2×C4⋊C4C23×C4711yescharacteristic
506C2×C4⋊C4C23×C4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C4711yescharacteristic
521C2×C22⋊C4D4×C4711yescharacteristic
522C2×C42C23×C4711yescharacteristic
523C2×C42C23×C4711yescharacteristic
524#107—41no—
525#106—22no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C4711yescharacteristic
544#95D4×C4711yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C4711yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C4712yes—
580C2×D4C2×D4×C4712yes—
581C2×D4#41×C4712yes—
582C2×D4#41×C4712yes—
583C2×D4#41×C4712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C4711yescharacteristic
605C22×C4C2×D4×C4711yescharacteristic
606C22×C4C2×D4×C4711yescharacteristic
607C22×C4C2×D4×C4711yescharacteristic
608C22×C4C2×D4×C4711yescharacteristic
609C22×C4C24×C4711yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C4712yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23AGL(1,ℤ/8)×C4712yes—
688C23C22×D4×C4711yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C4714yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C22×D4×C4711yescharacteristic
741C2×C4C2×#41×C4711yescharacteristic
742C2×C4C2×#41×C4711yescharacteristic
743C2×C4C2×#41×C4711yescharacteristic
744C2×C4H(5,𝔽2)×C4711yescharacteristic
745C2×C4H(5,𝔽2)×C4711yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C47×#52511yescharacteristic
780C22D42×C4711yescharacteristic
781C22C47×#54611yescharacteristic
782C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
783C22C47×#57511yescharacteristic
784C22C47×#57611yescharacteristic
785C22C47×#57611yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C4711yescharacteristic
797C4C47×#53811yescharacteristic
798C4C47×#54611yescharacteristic
799C4C47×#55111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C47×#241811yescharacteristic
805C2C47×#311411yescharacteristic
806C2C47×#312211yescharacteristic
807C2C47×#326411yescharacteristic
808C2C47×#327311yescharacteristic
809C2C47×#331811yescharacteristic
810C2C47×#331911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#447C2
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
2. C2×C47×#442C2semidirect
3. C47×#2420C2semidirect
4. D4×C22⋊C4×C47C2semidirect
5. C47×#2092C2semidirect
6. C47×#2077C2semidirect
7. C47×#2054C2semidirect
8. C47×#2033C2semidirect
9. C47×#1936C2semidirect
10. C47×#1924C2semidirect
11. C47×#1879C2semidirect
12. C47×#1879C2semidirect
13. C47×#1862C2semidirect
14. C47×#1804C2semidirect
15. C47×#1786C2semidirect
22. C2×C4×D4×C47C22semidirect
26. C2×#107×C47C22semidirect
27. C2×#106×C47C22semidirect
28. C2×C4⋊C8×C47C22semidirect
35. C2×#102×C47C22semidirect
36. C2×#102×C47C22semidirect
39. C2×#97×C47C22semidirect
44. C47×#390C22semidirect
45. C47×#389C22semidirect
49. C47×#382C22semidirect
55. C47×#340C22semidirect
56. C47×#340C22semidirect
57. C47×#340C22semidirect
58. C47×#340C22semidirect
59. C47×#336C22semidirect
60. C47×#336C22semidirect
344. #24909C47direct (N × H)
396. C2×#442C2×C47semidirect
397. #2420C2×C47semidirect
398. D4×C22⋊C4C2×C47semidirect
399. #2092C2×C47semidirect
400. #2077C2×C47semidirect
401. #2054C2×C47semidirect
402. #2033C2×C47semidirect
403. #1936C2×C47semidirect
404. #1924C2×C47semidirect
405. #1879C2×C47semidirect
406. #1879C2×C47semidirect
407. #1862C2×C47semidirect
408. #1804C2×C47semidirect
409. #1786C2×C47semidirect
427. C2×C4×D4C22×C47semidirect
431. C2×#107C22×C47semidirect
432. C2×#106C22×C47semidirect
433. C2×C4⋊C8C22×C47semidirect
440. C2×#102C22×C47semidirect
441. C2×#102C22×C47semidirect
444. C2×#97C22×C47semidirect
449. #390C22×C47semidirect
450. #389C22×C47semidirect
454. #382C22×C47semidirect
460. #340C22×C47semidirect
461. #340C22×C47semidirect
462. #340C22×C47semidirect
463. #340C22×C47semidirect
464. #336C22×C47semidirect
465. #336C22×C47semidirect
466. C47#24909direct (N × H)

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
C47×#24202
D4×C22⋊C4×C472
C47×#20922
C47×#20772
C47×#20542
C47×#20332
C47×#19362
C47×#19242
C47×#18792
C47×#18622
C47×#18042
C47×#17862
#2490947