Finite Group Databasebeta

← C47×#26929 #26066627

Subgroups — C47×#26929 #26066627

Order 12032.

982 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#484C211yesmaximal, characteristic, complemented
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C47×#2426C211yesmaximal, characteristic, complemented
4C47×#2361C211yesmaximal, characteristic, complemented
5C47×#2087C211yesmaximal, characteristic, complemented
6C47×#2042C211yesmaximal, characteristic, complemented
7C47×#2000C211yesmaximal, characteristic, complemented
8C47×#1999C211yesmaximal, characteristic
9C47×#1970C211yesmaximal, characteristic, complemented
10C47×#1925C211yesmaximal, characteristic, complemented
11C47×#1923C211yesmaximal, characteristic, complemented
12C47×#1880C211yesmaximal, characteristic, complemented
13C47×#1874C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic, complemented
15C4×#103×C47C211yesmaximal, characteristic, complemented
16C22×SD16×C47C2211yescharacteristic
17C22×D8×C47C2211yescharacteristic
18C2×#124×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×#121×C47C2211yescharacteristic
21C2×#121×C47C2211yescharacteristic
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4×D4×C47—21no—
24C2×C4×D4×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C47×#484—24no—
27C47×#463—24no—
28C2×#107×C47C2211yescharacteristic
29C2×#107×C47C2211yescharacteristic
30C2×C4⋊C8×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×C22⋊C8×C47C2211yescharacteristic
40C2×C22⋊C8×C47C2211yescharacteristic
41C2×C4×C8×C47C2211yescharacteristic
42C47×#396—21no—
43C47×#394—21no—
44C47×#390—21no—
45C47×#390C2211yescharacteristic
46C47×#390C2211yescharacteristic
47C47×#389C2211yescharacteristic
48C47×#389C2211yescharacteristic
49C47×#388—21no—
50C47×#388—21no—
51C47×#386—21no—
52C47×#385—21no—
53C4×C4⋊C4×C47C2211yescharacteristic
54C4×C22⋊C4×C47C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Q8×C47C2311yescharacteristic
62C22×D4×C47—21no—
63C22×D4×C47—21no—
64C22×D4×C47C2311yescharacteristic
65C22×D4×C47C2311yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47C2311yescharacteristic
69C2×SD16×C47—22no—
70C2×SD16×C47—22no—
71C2×SD16×C47—41no—
72C2×D8×C47—22no—
73C2×D8×C47—22no—
74C2×D8×C47—41no—
75C22×C8×C47C2311yescharacteristic
76C22×C8×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79#124×C47—22no—
80#124×C47—41no—
81C22⋊Q8×C47—22no—
82C22⋊Q8×C47—41no—
83#121×C47—22no—
84#121×C47—22no—
85#121×C47—22no—
86#121×C47—41no—
87C4×Q8×C47—22no—
88C4×Q8×C47—41no—
89C4×D4×C47—22no—
90C4×D4×C47—41no—
91C4×D4×C47—44no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—41no—
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C47D411yescharacteristic
115C2×C22⋊C4×C47D411yescharacteristic
116C2×C42×C47—21no—
117C2×C42×C47—21no—
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120#107×C47—22no—
121#107×C47—22no—
122C4⋊C8×C47—22no—
123#103×C47—22no—
124#103×C47—22no—
125#103×C47D414yescomplemented
126#102×C47—22no—
127#102×C47—22no—
128#102×C47—22no—
129#102×C47—41no—
130#102×C47—41no—
131C22⋊C8×C47—22no—
132C22⋊C8×C47—41no—
133C4×C8×C47—41no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47D411yescharacteristic
138#95×C47D411yescharacteristic
139C24×C47—21no—
140C24×C47—21no—
141C24×C47C2×D411yescharacteristic
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47C2×D412yes—
148C2×D4×C47—24no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
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—42no—
161C2×D4×C47—42no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47—81no—
165C2×D4×C47#4112yes—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—81no—
183C22×C4×C47—81no—
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2411yescharacteristic
190SD16×C47—44no—
191D8×C47—44no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47C2×D412yes—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47—42no—
213C4⋊C4×C47—42no—
214C4⋊C4×C47—42no—
215C4⋊C4×C47—81no—
216C4⋊C4×C47C2×D412yes—
217C4⋊C4×C47#4112yes—
218C4⋊C4×C47#4112yes—
219C22⋊C4×C47—24no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—42no—
223C22⋊C4×C47—42no—
224C22⋊C4×C47—42no—
225C22⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—81no—
230C22⋊C4×C47—81no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—42no—
236C42×C47—42no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—22no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47#13512yes—
258C23×C47C22×D411yescharacteristic
259Q8×C47—22no—
260Q8×C47—22no—
261Q8×C47—41no—
262Q8×C47—41no—
263D4×C47—22no—
264D4×C47—22no—
265D4×C47—48no—
266D4×C47—41no—
267D4×C47—41no—
268D4×C47—41no—
269D4×C47—41no—
270D4×C47—41no—
271D4×C47—41no—
272D4×C47—84no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—22no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—22no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—84no—
310C2×C4×C47—84no—
311C2×C4×C47AGL(1,ℤ/8)12yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47C2×#4111yescharacteristic
314C2×C4×C47C2×#4111yescharacteristic
315C2×C4×C47C2×#4111yescharacteristic
316C2×C4×C47H(5,𝔽2)11yescharacteristic
317C2×C4×C47H(5,𝔽2)11yescharacteristic
318C8×C47—22no—
319C8×C47—41no—
320C8×C47—41no—
321C8×C47—41no—
322#26929C4711yesmaximal, characteristic, direct product factor, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—81no—
334C22×C47—81no—
335C22×C47—81no—
336C22×C47—81no—
337C22×C47—81no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47—81no—
341C22×C47—81no—
342C22×C47—81no—
343C22×C47—81no—
344C22×C47#52511yescharacteristic
345C22×C47D4211yescharacteristic
346C22×C47#54611yescharacteristic
347C22×C47C2×#13511yescharacteristic
348C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C47#57611yescharacteristic
350C22×C47#57811yescharacteristic
351C4×C47—22no—
352C4×C47—42no—
353C4×C47—41no—
354C4×C47—42no—
355C4×C47—41no—
356C4×C47—42no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—42no—
360C4×C47—81no—
361C4×C47—81no—
362C4×C47#53211yescharacteristic
363C4×C47#54011yescharacteristic
364C4×C47#54611yescharacteristic
365C4×C47#55311yescharacteristic
366C2×#484C2×C4711yescharacteristic, complemented
367C2×#463C2×C4711yescharacteristic, complemented
368#2426C2×C4711yescharacteristic, complemented
369#2361C2×C4711yescharacteristic, complemented
370#2087C2×C4711yescharacteristic, complemented
371#2042C2×C4711yescharacteristic, complemented
372#2000C2×C4711yescharacteristic, complemented
373#1999C2×C4711yescharacteristic
374#1970C2×C4711yescharacteristic, complemented
375#1925C2×C4711yescharacteristic, complemented
376#1923C2×C4711yescharacteristic, complemented
377#1880C2×C4711yescharacteristic, complemented
378#1874C2×C4711yescharacteristic, complemented
379#1862C2×C4711yescharacteristic, complemented
380C4×#103C2×C4711yescharacteristic, complemented
381C2×C47—42no—
382C2×C47—82no—
383C2×C47—161no—
384C2×C47#246411yescharacteristic
385C2×C47#310511yescharacteristic
386C2×C47#312411yescharacteristic
387C2×C47#327411yescharacteristic
388C2×C47#328511yescharacteristic
389C2×C47#329711yescharacteristic
390C2×C47#330811yescharacteristic
391C22×SD16C22×C4711yescharacteristic
392C22×D8C22×C4711yescharacteristic
393C2×#124C22×C4711yescharacteristic
394C2×C22⋊Q8C22×C4711yescharacteristic
395C2×#121C22×C4711yescharacteristic
396C2×#121C22×C4711yescharacteristic
397C2×C4×Q8C22×C4711yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C22×C4711yescharacteristic
400C22×C4⋊C4C22×C4711yescharacteristic
401#484—24no—
402#463—24no—
403C2×#107C22×C4711yescharacteristic
404C2×#107C22×C4711yescharacteristic
405C2×C4⋊C8C22×C4711yescharacteristic
406C2×#103C22×C4711yescharacteristic
407C2×#103C22×C4711yescharacteristic
408C2×#103C22×C4711yescharacteristic
409C2×#102C22×C4711yescharacteristic
410C2×#102C22×C4711yescharacteristic
411C2×#102C22×C4711yescharacteristic
412C2×#102C22×C4711yescharacteristic
413C2×#102C22×C4711yescharacteristic
414C2×C22⋊C8C22×C4711yescharacteristic
415C2×C22⋊C8C22×C4711yescharacteristic
416C2×C4×C8C22×C4711yescharacteristic
417#396—21no—
418#394—21no—
419#390—21no—
420#390C22×C4711yescharacteristic
421#390C22×C4711yescharacteristic
422#389C22×C4711yescharacteristic
423#389C22×C4711yescharacteristic
424#388—21no—
425#388—21no—
426#386—21no—
427#385—21no—
428C4×C4⋊C4C22×C4711yescharacteristic
429C4×C22⋊C4C22×C4711yescharacteristic
430#340C22×C4711yescharacteristic
431#340C22×C4711yescharacteristic
432#340C22×C4711yescharacteristic
433#340C22×C4711yescharacteristic
434#336C22×C4711yescharacteristic
435#336C22×C4711yescharacteristic
436C47#2692911yescharacteristic, direct product factor, Sylow
437C22×Q8C23×C4711yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C23×C4711yescharacteristic
441C22×D4C23×C4711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C4711yescharacteristic
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—41no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8—41no—
451C22×C8C23×C4711yescharacteristic
452C22×C8C23×C4711yescharacteristic
453C22×C8C23×C4711yescharacteristic
454C22×C8C23×C4711yescharacteristic
455#124—22no—
456#124—41no—
457C22⋊Q8—22no—
458C22⋊Q8—41no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121—41no—
463C4×Q8—22no—
464C4×Q8—41no—
465C4×D4—22no—
466C4×D4—41no—
467C4×D4—44no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4C23×C4711yescharacteristic
476C2×C4⋊C4C23×C4711yescharacteristic
477C2×C4⋊C4C23×C4711yescharacteristic
478C2×C4⋊C4C23×C4711yescharacteristic
479C2×C4⋊C4C23×C4711yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4D4×C4711yescharacteristic
491C2×C22⋊C4D4×C4711yescharacteristic
492C2×C42—21no—
493C2×C42—21no—
494C2×C42C23×C4711yescharacteristic
495C2×C42C23×C4711yescharacteristic
496#107—22no—
497#107—22no—
498C4⋊C8—22no—
499#103—22no—
500#103—22no—
501#103D4×C4714yescomplemented
502#102—22no—
503#102—22no—
504#102—22no—
505#102—41no—
506#102—41no—
507C22⋊C8—22no—
508C22⋊C8—41no—
509C4×C8—41no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95D4×C4711yescharacteristic
514#95D4×C4711yescharacteristic
515C24—21no—
516C24—21no—
517C24C2×D4×C4711yescharacteristic
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8C2×D4×C4712yes—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—81no—
541C2×D4#41×C4712yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4C2×D4×C4711yescharacteristic
561C22×C4C2×D4×C4711yescharacteristic
562C22×C4C2×D4×C4711yescharacteristic
563C22×C4C2×D4×C4711yescharacteristic
564C22×C4C2×D4×C4711yescharacteristic
565C22×C4C24×C4711yescharacteristic
566SD16—44no—
567D8—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8C2×D4×C4712yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4C2×D4×C4712yes—
593C4⋊C4#41×C4712yes—
594C4⋊C4#41×C4712yes—
595C22⋊C4—24no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—42no—
612C42—42no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23#135×C4712yes—
634C23C22×D4×C4711yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—41no—
638Q8—41no—
639D4—22no—
640D4—22no—
641D4—48no—
642D4—41no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4AGL(1,ℤ/8)×C4712yes—
688C2×C4C22×D4×C4711yescharacteristic
689C2×C4C2×#41×C4711yescharacteristic
690C2×C4C2×#41×C4711yescharacteristic
691C2×C4C2×#41×C4711yescharacteristic
692C2×C4H(5,𝔽2)×C4711yescharacteristic
693C2×C4H(5,𝔽2)×C4711yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C47×#52511yescharacteristic
720C22D42×C4711yescharacteristic
721C22C47×#54611yescharacteristic
722C22C2×#135×C4711yescharacteristic
723C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
724C22C47×#57611yescharacteristic
725C22C47×#57811yescharacteristic
726C4—22no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—81no—
736C4—81no—
737C4C47×#53211yescharacteristic
738C4C47×#54011yescharacteristic
739C4C47×#54611yescharacteristic
740C4C47×#55311yescharacteristic
741C2—42no—
742C2—82no—
743C2—161no—
744C2C47×#246411yescharacteristic
745C2C47×#310511yescharacteristic
746C2C47×#312411yescharacteristic
747C2C47×#327411yescharacteristic
748C2C47×#328511yescharacteristic
749C2C47×#329711yescharacteristic
750C2C47×#330811yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#1999C2
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×#484C2semidirect
2. C2×C47×#463C2semidirect
3. C47×#2426C2semidirect
4. C47×#2361C2semidirect
5. C47×#2087C2semidirect
6. C47×#2042C2semidirect
7. C47×#2000C2semidirect
9. C47×#1970C2semidirect
10. C47×#1925C2semidirect
11. C47×#1923C2semidirect
12. C47×#1880C2semidirect
13. C47×#1874C2semidirect
14. C47×#1862C2semidirect
15. C4×#103×C47C2semidirect
125. #103×C47D4semidirect
322. #26929C47direct (N × H)
366. C2×#484C2×C47semidirect
367. C2×#463C2×C47semidirect
368. #2426C2×C47semidirect
369. #2361C2×C47semidirect
370. #2087C2×C47semidirect
371. #2042C2×C47semidirect
372. #2000C2×C47semidirect
374. #1970C2×C47semidirect
375. #1925C2×C47semidirect
376. #1923C2×C47semidirect
377. #1880C2×C47semidirect
378. #1874C2×C47semidirect
379. #1862C2×C47semidirect
380. C4×#103C2×C47semidirect
436. C47#26929direct (N × H)
501. #103D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4842
C2×C47×#4632
C47×#24262
C47×#23612
C47×#20872
C47×#20422
C47×#20002
C47×#19992
C47×#19702
C47×#19252
C47×#19232
C47×#18802
C47×#18742
C47×#18622
C4×#103×C472
#2692947