Finite Group Databasebeta

← C47×#25890 #26065588

Subgroups — C47×#25890 #26065588

Order 12032.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#546C211yesmaximal, characteristic
2C2×C47×#488C211yesmaximal, characteristic, complemented
3C2×C47×#478C211yesmaximal, characteristic, complemented
4C47×#2562C211yesmaximal, characteristic, complemented
5C47×#2036C211yesmaximal, characteristic, complemented
6C47×#2035C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1983C211yesmaximal, characteristic, complemented
10C47×#1954C211yesmaximal, characteristic, complemented
11C47×#1788C211yesmaximal, characteristic, complemented
12C47×#1788C211yesmaximal, characteristic, complemented
13C47×#1786C211yesmaximal, characteristic, complemented
14C47×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C47C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C47×#546—24no—
19C47×#546—24no—
20C2×#125×C47C2211yescharacteristic, complemented
21C2×#124×C47C2211yescharacteristic
22C2×#123×C47—21no—
23C2×C22⋊Q8×C47C2211yescharacteristic
24C2×#121×C47—21no—
25C2×#121×C47C2211yescharacteristic
26C2×#120×C47—21no—
27C2×C4×D4×C47C2211yescharacteristic
28C2×C4×D4×C47C2211yescharacteristic
29C22×C22⋊C4×C47—21no—
30C47×#488—24no—
31C47×#478—24no—
32C2×#107×C47C2211yescharacteristic, complemented
33C2×#106×C47C2211yescharacteristic, complemented
34C2×C4⋊C8×C47C2211yescharacteristic, complemented
35C2×#103×C47C2211yescharacteristic, complemented
36C2×#103×C47C2211yescharacteristic, complemented
37C2×#103×C47C2211yescharacteristic, complemented
38C2×#103×C47C2211yescharacteristic, complemented
39C2×#102×C47C2211yescharacteristic
40C2×#102×C47C2211yescharacteristic
41C2×#102×C47C2211yescharacteristic
42C2×#102×C47C2211yescharacteristic
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic
46C2×#102×C47C2211yescharacteristic
47C2×C22⋊C8×C47C2211yescharacteristic
48C2×C22⋊C8×C47C2211yescharacteristic
49C2×C22⋊C8×C47C2211yescharacteristic, complemented
50C2×C22⋊C8×C47C2211yescharacteristic, complemented
51C2×C4×C8×C47C2211yescharacteristic, complemented
52C47×#400—21no—
53C47×#394—21no—
54C47×#388—21no—
55C47×#388—21no—
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic, complemented
59C47×#380C2211yescharacteristic, complemented
60C4×C4⋊C4×C47C2211yescharacteristic, complemented
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C25×C47—21no—
64C2×#41×C47—22no—
65C2×#41×C47—22no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—41no—
69C2×#41×C47—41no—
70C22×Q8×C47C2311yescharacteristic
71C22×D4×C47—21no—
72C22×D4×C47—21no—
73C22×D4×C47—22no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—21no—
78C22×D4×C47—41no—
79C22×D4×C47—41no—
80C22×D4×C47D411yescharacteristic
81C22×D4×C47C2311yescharacteristic
82C22×D4×C47C2311yescharacteristic
83C23×C4×C47—21no—
84C23×C4×C47—21no—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91#125×C47—22no—
92#125×C47—22no—
93#124×C47—22no—
94#124×C47D414yes—
95#123×C47—28no—
96C22⋊Q8×C47—22no—
97C22⋊Q8×C47—22no—
98#121×C47—28no—
99#121×C47—22no—
100#121×C47—22no—
101#120×C47—28no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104C4×D4×C47—22no—
105C4×D4×C47D414yes—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47D411yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C22⋊C4×C47—28no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—21no—
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×C47C2311yescharacteristic
129#107×C47—22no—
130#106×C47—22no—
131C4⋊C8×C47—22no—
132#103×C47—22no—
133#103×C47—22no—
134#103×C47—41no—
135#103×C47—41no—
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—41no—
143#102×C47—41no—
144C22⋊C8×C47—41no—
145C22⋊C8×C47—41no—
146C22⋊C8×C47—41no—
147C22⋊C8×C47—41no—
148C4×C8×C47—22no—
149#95×C47—21no—
150#95×C47—21no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154C24×C47—21no—
155C24×C47—24no—
156C24×C47—21no—
157C24×C47—42no—
158C24×C47—42no—
159C24×C47—42no—
160C24×C47—42no—
161C24×C47—81no—
162C24×C47—81no—
163C24×C47C2×D411yescharacteristic
164C24×C47C2×D411yescharacteristic
165#41×C47—44no—
166#41×C47—44no—
167#41×C47—44no—
168#41×C47—44no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—21no—
173C2×Q8×C47—21no—
174C2×Q8×C47C2×D412yes—
175C2×D4×C47—24no—
176C2×D4×C47—24no—
177C2×D4×C47—22no—
178C2×D4×C47—24no—
179C2×D4×C47—22no—
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—21no—
187C2×D4×C47—21no—
188C2×D4×C47—41no—
189C2×D4×C47—42no—
190C2×D4×C47—42no—
191C2×D4×C47—44no—
192C2×D4×C47—44no—
193C2×D4×C47—44no—
194C2×D4×C47—42no—
195C2×D4×C47—42no—
196C2×D4×C47—44no—
197C2×D4×C47—81no—
198C2×D4×C47—81no—
199C2×D4×C47C2×D412yes—
200C2×D4×C47C2×D412yes—
201C2×D4×C47#4112yes—
202C2×D4×C47#4112yes—
203C22×C4×C47—24no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
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×C47—24no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—42no—
224C22×C4×C47—42no—
225C22×C4×C47—81no—
226C22×C4×C47—81no—
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2411yescharacteristic
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×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—42no—
256C4⋊C4×C47—42no—
257C4⋊C4×C47C2×D412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—22no—
265C22⋊C4×C47—42no—
266C22⋊C4×C47—42no—
267C22⋊C4×C47—81no—
268C22⋊C4×C47—81no—
269C42×C47—81no—
270C42×C47C2×D412yes—
271C42×C47C2×D412yes—
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—22no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—48no—
290C23×C47—48no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—41no—
298C23×C47—41no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—84no—
302C23×C47—84no—
303C23×C47—84no—
304C23×C47—84no—
305C23×C47—84no—
306C23×C47#13512yes—
307C23×C47C22×D411yescharacteristic
308Q8×C47—22no—
309Q8×C47—22no—
310Q8×C47—41no—
311Q8×C47—41no—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—22no—
316D4×C47—22no—
317D4×C47—44no—
318D4×C47—48no—
319D4×C47—48no—
320D4×C47—41no—
321D4×C47—41no—
322D4×C47—84no—
323D4×C47#12414yes—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—22no—
329C2×C4×C47—21no—
330C2×C4×C47—22no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—48no—
337C2×C4×C47—41no—
338C2×C4×C47—41no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
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—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—84no—
362C2×C4×C47#12012yes—
363C2×C4×C47#12012yes—
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C2×#4111yescharacteristic
367C2×C4×C47C2×#4111yescharacteristic
368C2×C4×C47H(5,𝔽2)11yescharacteristic
369C2×C4×C47H(5,𝔽2)11yescharacteristic
370C8×C47—41no—
371C8×C47—41no—
372C8×C47—41no—
373C8×C47—41no—
374#25890C4711yesmaximal, characteristic, direct product factor, Sylow
375C22×C47—24no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—41no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—41no—
386C22×C47—42no—
387C22×C47—41no—
388C22×C47—42no—
389C22×C47—41no—
390C22×C47—42no—
391C22×C47—41no—
392C22×C47—42no—
393C22×C47—41no—
394C22×C47—42no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—816no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47C2×#12011yescharacteristic
405C22×C47#54611yescharacteristic
406C22×C47#54611yescharacteristic
407C22×C47C2×#13511yescharacteristic
408C22×C47#57511yescharacteristic
409C22×C47#57611yescharacteristic
410C22×C47#57711yescharacteristic
411C4×C47—22no—
412C4×C47—22no—
413C4×C47—41no—
414C4×C47—41no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47—81no—
418C4×C47—81no—
419C4×C47—81no—
420C4×C47—81no—
421C4×C47C2×#12411yescharacteristic
422C4×C47#53511yescharacteristic
423C4×C47#54611yescharacteristic
424C4×C47#54611yescharacteristic
425C2×#546C2×C4711yescharacteristic
426C2×#488C2×C4711yescharacteristic, complemented
427C2×#478C2×C4711yescharacteristic, complemented
428#2562C2×C4711yescharacteristic, complemented
429#2036C2×C4711yescharacteristic, complemented
430#2035C2×C4711yescharacteristic, complemented
431#2034C2×C4711yescharacteristic, complemented
432#2033C2×C4711yescharacteristic, complemented
433#1983C2×C4711yescharacteristic, complemented
434#1954C2×C4711yescharacteristic, complemented
435#1788C2×C4711yescharacteristic, complemented
436#1788C2×C4711yescharacteristic, complemented
437#1786C2×C4711yescharacteristic, complemented
438#1786C2×C4711yescharacteristic, complemented
439C4×#102C2×C4711yescharacteristic, complemented
440C2×C47—42no—
441C2×C47—44no—
442C2×C47—81no—
443C2×C47—82no—
444C2×C47#243511yescharacteristic
445C2×C47#300211yescharacteristic
446C2×C47#301211yescharacteristic
447C2×C47#329611yescharacteristic
448C2×C47#329711yescharacteristic
449C2×C47#332211yescharacteristic
450C2×C47#332311yescharacteristic
451C22×#41C22×C4711yescharacteristic
452C23×D4C22×C4711yescharacteristic
453#546—24no—
454#546—24no—
455C2×#125C22×C4711yescharacteristic, complemented
456C2×#124C22×C4711yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C22×C4711yescharacteristic
459C2×#121—21no—
460C2×#121C22×C4711yescharacteristic
461C2×#120—21no—
462C2×C4×D4C22×C4711yescharacteristic
463C2×C4×D4C22×C4711yescharacteristic
464C22×C22⋊C4—21no—
465#488—24no—
466#478—24no—
467C2×#107C22×C4711yescharacteristic, complemented
468C2×#106C22×C4711yescharacteristic, complemented
469C2×C4⋊C8C22×C4711yescharacteristic, complemented
470C2×#103C22×C4711yescharacteristic, complemented
471C2×#103C22×C4711yescharacteristic, complemented
472C2×#103C22×C4711yescharacteristic, complemented
473C2×#103C22×C4711yescharacteristic, complemented
474C2×#102C22×C4711yescharacteristic
475C2×#102C22×C4711yescharacteristic
476C2×#102C22×C4711yescharacteristic
477C2×#102C22×C4711yescharacteristic
478C2×#102C22×C4711yescharacteristic
479C2×#102C22×C4711yescharacteristic
480C2×#102C22×C4711yescharacteristic
481C2×#102C22×C4711yescharacteristic
482C2×C22⋊C8C22×C4711yescharacteristic
483C2×C22⋊C8C22×C4711yescharacteristic
484C2×C22⋊C8C22×C4711yescharacteristic, complemented
485C2×C22⋊C8C22×C4711yescharacteristic, complemented
486C2×C4×C8C22×C4711yescharacteristic, complemented
487#400—21no—
488#394—21no—
489#388—21no—
490#388—21no—
491#380C22×C4711yescharacteristic
492#380C22×C4711yescharacteristic
493#380C22×C4711yescharacteristic, complemented
494#380C22×C4711yescharacteristic, complemented
495C4×C4⋊C4C22×C4711yescharacteristic, complemented
496#340C22×C4711yescharacteristic, complemented
497#340C22×C4711yescharacteristic, complemented
498C47#2589011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C4711yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C4711yescharacteristic
517C22×D4C23×C4711yescharacteristic
518C22×D4C23×C4711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C4711yescharacteristic
522C23×C4C23×C4711yescharacteristic
523C22×C8C23×C4711yescharacteristic
524C22×C8C23×C4711yescharacteristic
525C22×C8C23×C4711yescharacteristic
526C22×C8C23×C4711yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C4714yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C4714yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C4711yescharacteristic
546C2×C4⋊C4C23×C4711yescharacteristic
547C2×C4⋊C4C23×C4711yescharacteristic
548C2×C4⋊C4C23×C4711yescharacteristic
549C2×C4⋊C4C23×C4711yescharacteristic
550C2×C4⋊C4C23×C4711yescharacteristic
551C2×C22⋊C4—28no—
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⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C4711yescharacteristic
562C2×C22⋊C4D4×C4711yescharacteristic
563C2×C42—21no—
564C2×C42C23×C4711yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C4711yescharacteristic
600C24C2×D4×C4711yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C4712yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C4712yes—
636C2×D4C2×D4×C4712yes—
637C2×D4#41×C4712yes—
638C2×D4#41×C4712yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
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×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C4711yescharacteristic
664C22×C4C2×D4×C4711yescharacteristic
665C22×C4C2×D4×C4711yescharacteristic
666C22×C4C2×D4×C4711yescharacteristic
667C22×C4C24×C4711yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C4712yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C4712yes—
707C42C2×D4×C4712yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C4712yes—
743C23C22×D4×C4711yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C4714yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
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—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C4712yes—
799C2×C4#120×C4712yes—
800C2×C4C22×D4×C4711yescharacteristic
801C2×C4C22×D4×C4711yescharacteristic
802C2×C4C2×#41×C4711yescharacteristic
803C2×C4C2×#41×C4711yescharacteristic
804C2×C4H(5,𝔽2)×C4711yescharacteristic
805C2×C4H(5,𝔽2)×C4711yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C4711yescharacteristic
840C22C47×#54611yescharacteristic
841C22C47×#54611yescharacteristic
842C22C2×#135×C4711yescharacteristic
843C22C47×#57511yescharacteristic
844C22C47×#57611yescharacteristic
845C22C47×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C4711yescharacteristic
857C4C47×#53511yescharacteristic
858C4C47×#54611yescharacteristic
859C4C47×#54611yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C47×#243511yescharacteristic
865C2C47×#300211yescharacteristic
866C2C47×#301211yescharacteristic
867C2C47×#329611yescharacteristic
868C2C47×#329711yescharacteristic
869C2C47×#332211yescharacteristic
870C2C47×#332311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×C47×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#488C2semidirect
3. C2×C47×#478C2semidirect
4. C47×#2562C2semidirect
5. C47×#2036C2semidirect
6. C47×#2035C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#1983C2semidirect
10. C47×#1954C2semidirect
11. C47×#1788C2semidirect
12. C47×#1788C2semidirect
13. C47×#1786C2semidirect
14. C47×#1786C2semidirect
15. C4×#102×C47C2semidirect
20. C2×#125×C47C22semidirect
32. C2×#107×C47C22semidirect
33. C2×#106×C47C22semidirect
34. C2×C4⋊C8×C47C22semidirect
35. C2×#103×C47C22semidirect
36. C2×#103×C47C22semidirect
37. C2×#103×C47C22semidirect
38. C2×#103×C47C22semidirect
49. C2×C22⋊C8×C47C22semidirect
50. C2×C22⋊C8×C47C22semidirect
51. C2×C4×C8×C47C22semidirect
58. C47×#380C22semidirect
59. C47×#380C22semidirect
60. C4×C4⋊C4×C47C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
374. #25890C47direct (N × H)
426. C2×#488C2×C47semidirect
427. C2×#478C2×C47semidirect
428. #2562C2×C47semidirect
429. #2036C2×C47semidirect
430. #2035C2×C47semidirect
431. #2034C2×C47semidirect
432. #2033C2×C47semidirect
433. #1983C2×C47semidirect
434. #1954C2×C47semidirect
435. #1788C2×C47semidirect
436. #1788C2×C47semidirect
437. #1786C2×C47semidirect
438. #1786C2×C47semidirect
439. C4×#102C2×C47semidirect
455. C2×#125C22×C47semidirect
467. C2×#107C22×C47semidirect
468. C2×#106C22×C47semidirect
469. C2×C4⋊C8C22×C47semidirect
470. C2×#103C22×C47semidirect
471. C2×#103C22×C47semidirect
472. C2×#103C22×C47semidirect
473. C2×#103C22×C47semidirect
484. C2×C22⋊C8C22×C47semidirect
485. C2×C22⋊C8C22×C47semidirect
486. C2×C4×C8C22×C47semidirect
493. #380C22×C47semidirect
494. #380C22×C47semidirect
495. C4×C4⋊C4C22×C47semidirect
496. #340C22×C47semidirect
497. #340C22×C47semidirect
498. C47#25890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5462
C2×C47×#4882
C2×C47×#4782
C47×#25622
C47×#20362
C47×#20352
C47×#20342
C47×#20332
C47×#19832
C47×#19542
C47×#17882
C47×#17862
C4×#102×C472
#2589047