Finite Group Databasebeta

← C47×#14041 #26053739

Subgroups — C47×#14041 #26053739

Order 12032.

1386 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#389C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
4C47×#1445C212yesmaximal
5C47×#1442C212yesmaximal
6C47×#1436C212yesmaximal
7C47×#1436C212yesmaximal
8C47×C4⋊#95C211yesmaximal, characteristic
9C47×C4⋊#95C211yesmaximal, characteristic
10C47×C4⋊#95C211yesmaximal, characteristic
11C47×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C47C2211yescharacteristic
13C22×C4⋊C4×C47C2211yescharacteristic
14C22×C4⋊C4×C47C2211yescharacteristic
15C22×C4⋊C4×C47C2211yescharacteristic
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2212yes—
19C22×C42×C47C2211yescharacteristic
20C22×C42×C47C2211yescharacteristic
21C22×C42×C47C2211yescharacteristic
22C22×C42×C47C2212yes—
23C47×#389C418yescomplemented
24C4×C4⋊C4×C47—24no—
25C4×C4⋊C4×C47—24no—
26C2×#95×C47C2211yescharacteristic
27C2×#95×C47C2212yes—
28C2×#95×C47C2211yescharacteristic
29C2×#95×C47C2212yes—
30C2×#95×C47C2212yes—
31C2×#95×C47C2212yes—
32C2×#95×C47C2212yes—
33C2×#95×C47C2212yes—
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C2×#95×C47C2212yes—
37C2×#95×C47C2212yes—
38C23×C4×C47C2312yes—
39C23×C4×C47C2312yes—
40C23×C4×C47C2311yescharacteristic
41C23×C4×C47C2312yes—
42C23×C4×C47C2311yescharacteristic
43C23×C4×C47C2311yescharacteristic
44C23×C4×C47C2312yes—
45C23×C4×C47C2311yescharacteristic
46C23×C4×C47C2311yescharacteristic
47C23×C4×C47C2311yescharacteristic
48C23×C4×C47C2311yescharacteristic
49C2×C4⋊C4×C47—22no—
50C2×C4⋊C4×C47—22no—
51C2×C4⋊C4×C47—22no—
52C2×C4⋊C4×C47—22no—
53C2×C4⋊C4×C47—22no—
54C2×C4⋊C4×C47—22no—
55C2×C4⋊C4×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—22no—
58C2×C4⋊C4×C47—22no—
59C2×C4⋊C4×C47—22no—
60C2×C4⋊C4×C47—22no—
61C2×C4⋊C4×C47—22no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—42no—
64C2×C4⋊C4×C47—42no—
65C2×C4⋊C4×C47C2×C414yes—
66C2×C4⋊C4×C47C2×C414yes—
67C2×C4⋊C4×C47C2×C418yes—
68C2×C4⋊C4×C47Q814yes—
69C2×C4⋊C4×C47Q814yes—
70C2×C42×C47—22no—
71C2×C42×C47—22no—
72C2×C42×C47—22no—
73C2×C42×C47—22no—
74C2×C42×C47—24no—
75C2×C42×C47—22no—
76C2×C42×C47—22no—
77C2×C42×C47—22no—
78C2×C42×C47—42no—
79C2×C42×C47—42no—
80C2×C42×C47C2×C414yes—
81C2×C42×C47D414yes—
82#95×C47—24no—
83#95×C47—22no—
84#95×C47—22no—
85#95×C47—24no—
86#95×C47—24no—
87#95×C47—24no—
88#95×C47—42no—
89#95×C47—42no—
90#95×C47—42no—
91#95×C47—42no—
92#95×C47—42no—
93#95×C47C2×C418yes—
94C24×C47C2411yescharacteristic
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—22no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C22×C414yes—
154C22×C4×C47C22×C414yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C22×C412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×D412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×Q814yes—
161C22×C4×C47C2×Q812yes—
162C22×C4×C47C2×Q812yes—
163C22×C4×C47C2×Q812yes—
164C22×C4×C47C2×Q812yes—
165C22×C4×C47#4112yes—
166C22×C4×C47#4112yes—
167C22×C4×C47#4112yes—
168C22×C4×C47#4112yes—
169C22×C4×C47#4112yes—
170C22×C4×C47#4112yes—
171C22×C4×C47#4112yes—
172C4⋊C4×C47—28no—
173C4⋊C4×C47—28no—
174C4⋊C4×C47—28no—
175C4⋊C4×C47—28no—
176C4⋊C4×C47—28no—
177C4⋊C4×C47—48no—
178C4⋊C4×C47—44no—
179C42×C47—28no—
180C42×C47—28no—
181C42×C47—48no—
182C42×C47—44no—
183C23×C47C23×C411yescharacteristic
184C23×C47C22×D411yescharacteristic
185C23×C47C22×Q811yescharacteristic
186C23×C47C22×Q811yescharacteristic
187C23×C47C2×#4111yescharacteristic
188C23×C47C2×#4111yescharacteristic
189C23×C47C2×#4111yescharacteristic
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4111yescharacteristic
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4111yescharacteristic
194C23×C47H(5,𝔽2)11yescharacteristic
195C23×C47H(5,𝔽2)11yescharacteristic
196C23×C47H(5,𝔽2)11yescharacteristic
197C23×C472−1+411yescharacteristic
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—24no—
211C2×C4×C47—22no—
212C2×C4×C47—24no—
213C2×C4×C47—24no—
214C2×C4×C47—22no—
215C2×C4×C47—24no—
216C2×C4×C47—24no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—24no—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—42no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—42no—
243C2×C4×C47—41no—
244C2×C4×C47—42no—
245C2×C4×C47—41no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—42no—
256C2×C4×C47—42no—
257C2×C4×C47—42no—
258C2×C4×C47—42no—
259C2×C4×C47—42no—
260C2×C4×C47—42no—
261C2×C4×C47—42no—
262C2×C4×C47—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47#11714yes—
267C2×C4×C47C4×D414yes—
268C2×C4×C47C4×Q814yes—
269C2×C4×C47C4×Q814yes—
270C2×C4×C47C22⋊Q814yes—
271C2×C4×C47C22⋊Q814yes—
272C2×C4×C47#12314yes—
273C2×C4×C47#12514yes—
274C2×C4×C47#12614yes—
275#14041C4711yesmaximal, characteristic, direct product factor, Sylow
276C22×C47C2×#11711yescharacteristic
277C22×C47C2×C4×D411yescharacteristic
278C22×C47C2×C4×Q811yescharacteristic
279C22×C47C2×C4×Q811yescharacteristic
280C22×C47C4×#4111yescharacteristic
281C22×C47#51811yescharacteristic
282C22×C47#52011yescharacteristic
283C22×C47C2×C22⋊Q811yescharacteristic
284C22×C47C2×C22⋊Q811yescharacteristic
285C22×C47C2×#12311yescharacteristic
286C22×C47#52511yescharacteristic
287C22×C47C2×#12511yescharacteristic
288C22×C47C2×#12611yescharacteristic
289C22×C47#52911yescharacteristic
290C22×C47#53311yescharacteristic
291C22×C47#53511yescharacteristic
292C22×C47#53711yescharacteristic
293C22×C47#54011yescharacteristic
294C22×C47#54211yescharacteristic
295C22×C47#55211yescharacteristic
296C22×C47#55311yescharacteristic
297C22×C47#55311yescharacteristic
298C22×C47#55311yescharacteristic
299C22×C47#55411yescharacteristic
300C22×C47#55411yescharacteristic
301C22×C47#55411yescharacteristic
302C22×C47#55411yescharacteristic
303C22×C47#55511yescharacteristic
304C22×C47#55611yescharacteristic
305C22×C47#55711yescharacteristic
306C22×C47#55711yescharacteristic
307C22×C47Q8211yescharacteristic
308C22×C47#55911yescharacteristic
309C22×C47#55911yescharacteristic
310C22×C47#55911yescharacteristic
311C4×C47—24no—
312C4×C47—24no—
313C4×C47—42no—
314C4×C47—44no—
315C4×C47—44no—
316C4×C47—44no—
317C4×C47—42no—
318C4×C47—42no—
319C4×C47—42no—
320C4×C47—82no—
321C4×C47#38718yes—
322C2×#389C2×C4711yescharacteristic
323C2×C4×C4⋊C4C2×C4711yescharacteristic
324C2×C4×C4⋊C4C2×C4711yescharacteristic
325#1445C2×C4712yes—
326#1442C2×C4712yes—
327#1436C2×C4712yes—
328#1436C2×C4712yes—
329C4⋊#95C2×C4711yescharacteristic
330C4⋊#95C2×C4711yescharacteristic
331C4⋊#95C2×C4711yescharacteristic
332C4⋊#95C2×C4711yescharacteristic
333C2×C47C2×#38711yescharacteristic
334C2×C47C4×C22⋊Q811yescharacteristic
335C2×C47#232411yescharacteristic
336C2×C47#235511yescharacteristic
337C2×C47#235711yescharacteristic
338C2×C47#236911yescharacteristic
339C2×C47#237011yescharacteristic
340C2×C47#248511yescharacteristic
341C2×C47#248711yescharacteristic
342C2×C47#250711yescharacteristic
343C2×C47#250911yescharacteristic
344C2×C47#251111yescharacteristic
345C2×C47#251311yescharacteristic
346C2×C47#258011yescharacteristic
347C2×C47#258211yescharacteristic
348C22×C4⋊C4C22×C4711yescharacteristic
349C22×C4⋊C4C22×C4711yescharacteristic
350C22×C4⋊C4C22×C4711yescharacteristic
351C22×C4⋊C4C22×C4711yescharacteristic
352C22×C4⋊C4C22×C4711yescharacteristic
353C22×C4⋊C4C22×C4711yescharacteristic
354C22×C4⋊C4C22×C4712yes—
355C22×C42C22×C4711yescharacteristic
356C22×C42C22×C4711yescharacteristic
357C22×C42C22×C4711yescharacteristic
358C22×C42C22×C4712yes—
359#389C4×C4718yescomplemented
360C4×C4⋊C4—24no—
361C4×C4⋊C4—24no—
362C2×#95C22×C4712yes—
363C2×#95C22×C4712yes—
364C2×#95C22×C4712yes—
365C2×#95C22×C4711yescharacteristic
366C2×#95C22×C4712yes—
367C2×#95C22×C4711yescharacteristic
368C2×#95C22×C4712yes—
369C2×#95C22×C4712yes—
370C2×#95C22×C4712yes—
371C2×#95C22×C4712yes—
372C2×#95C22×C4712yes—
373C2×#95C22×C4712yes—
374C47#1404111yescharacteristic, direct product factor, Sylow
375C23×C4C23×C4712yes—
376C23×C4C23×C4712yes—
377C23×C4C23×C4711yescharacteristic
378C23×C4C23×C4712yes—
379C23×C4C23×C4711yescharacteristic
380C23×C4C23×C4712yes—
381C23×C4C23×C4711yescharacteristic
382C23×C4C23×C4711yescharacteristic
383C23×C4C23×C4711yescharacteristic
384C23×C4C23×C4711yescharacteristic
385C23×C4C23×C4711yescharacteristic
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4C2×C4×C4714yes—
403C2×C4⋊C4C2×C4×C4714yes—
404C2×C4⋊C4C2×C4×C4718yes—
405C2×C4⋊C4Q8×C4714yes—
406C2×C4⋊C4Q8×C4714yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42C2×C4×C4714yes—
418C2×C42D4×C4714yes—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95C2×C4×C4718yes—
431C24C24×C4711yescharacteristic
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4C22×C4×C4714yes—
490C22×C4C22×C4×C4714yes—
491C22×C4C22×C4×C4712yes—
492C22×C4C22×C4×C4712yes—
493C22×C4C22×C4×C4712yes—
494C22×C4C2×D4×C4712yes—
495C22×C4C2×D4×C4712yes—
496C22×C4C2×D4×C4712yes—
497C22×C4C2×Q8×C4714yes—
498C22×C4C2×Q8×C4712yes—
499C22×C4C2×Q8×C4712yes—
500C22×C4C2×Q8×C4712yes—
501C22×C4C2×Q8×C4712yes—
502C22×C4#41×C4712yes—
503C22×C4#41×C4712yes—
504C22×C4#41×C4712yes—
505C22×C4#41×C4712yes—
506C22×C4#41×C4712yes—
507C22×C4#41×C4712yes—
508C22×C4#41×C4712yes—
509C4⋊C4—28no—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—28no—
513C4⋊C4—28no—
514C4⋊C4—48no—
515C4⋊C4—44no—
516C42—28no—
517C42—28no—
518C42—48no—
519C42—44no—
520C23C23×C4×C4711yescharacteristic
521C23C22×D4×C4711yescharacteristic
522C23C22×Q8×C4711yescharacteristic
523C23C22×Q8×C4711yescharacteristic
524C23C2×#41×C4711yescharacteristic
525C23C2×#41×C4711yescharacteristic
526C23C2×#41×C4711yescharacteristic
527C23C2×#41×C4711yescharacteristic
528C23C2×#41×C4711yescharacteristic
529C23C2×#41×C4711yescharacteristic
530C23C2×#41×C4711yescharacteristic
531C23H(5,𝔽2)×C4711yescharacteristic
532C23H(5,𝔽2)×C4711yescharacteristic
533C23H(5,𝔽2)×C4711yescharacteristic
534C232−1+4×C4711yescharacteristic
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4#117×C4714yes—
604C2×C4C4×D4×C4714yes—
605C2×C4C4×Q8×C4714yes—
606C2×C4C4×Q8×C4714yes—
607C2×C4C22⋊Q8×C4714yes—
608C2×C4C22⋊Q8×C4714yes—
609C2×C4#123×C4714yes—
610C2×C4#125×C4714yes—
611C2×C4#126×C4714yes—
612C22C2×#117×C4711yescharacteristic
613C22C2×C4×D4×C4711yescharacteristic
614C22C2×C4×Q8×C4711yescharacteristic
615C22C2×C4×Q8×C4711yescharacteristic
616C22C4×#41×C4711yescharacteristic
617C22C47×#51811yescharacteristic
618C22C47×#52011yescharacteristic
619C22C2×C22⋊Q8×C4711yescharacteristic
620C22C2×C22⋊Q8×C4711yescharacteristic
621C22C2×#123×C4711yescharacteristic
622C22C47×#52511yescharacteristic
623C22C2×#125×C4711yescharacteristic
624C22C2×#126×C4711yescharacteristic
625C22C47×#52911yescharacteristic
626C22C47×#53311yescharacteristic
627C22C47×#53511yescharacteristic
628C22C47×#53711yescharacteristic
629C22C47×#54011yescharacteristic
630C22C47×#54211yescharacteristic
631C22C47×#55211yescharacteristic
632C22C47×#55311yescharacteristic
633C22C47×#55311yescharacteristic
634C22C47×#55311yescharacteristic
635C22C47×#55411yescharacteristic
636C22C47×#55411yescharacteristic
637C22C47×#55411yescharacteristic
638C22C47×#55411yescharacteristic
639C22C47×#55511yescharacteristic
640C22C47×#55611yescharacteristic
641C22C47×#55711yescharacteristic
642C22C47×#55711yescharacteristic
643C22Q82×C4711yescharacteristic
644C22C47×#55911yescharacteristic
645C22C47×#55911yescharacteristic
646C22C47×#55911yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—42no—
655C4—42no—
656C4—82no—
657C4C47×#38718yes—
658C2C2×C47×#38711yescharacteristic
659C2C4×C22⋊Q8×C4711yescharacteristic
660C2C47×#232411yescharacteristic
661C2C47×#235511yescharacteristic
662C2C47×#235711yescharacteristic
663C2C47×#236911yescharacteristic
664C2C47×#237011yescharacteristic
665C2C47×#248511yescharacteristic
666C2C47×#248711yescharacteristic
667C2C47×#250711yescharacteristic
668C2C47×#250911yescharacteristic
669C2C47×#251111yescharacteristic
670C2C47×#251311yescharacteristic
671C2C47×#258011yescharacteristic
672C2C47×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
23. C47×#389C4semidirect
275. #14041C47direct (N × H)
359. #389C4×C47semidirect
374. C47#14041direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#3892
C2×C4×C4⋊C4×C472
C47×#14452
C47×#14422
C47×#14362
C47×C4⋊#952
#1404147