Finite Group Databasebeta

← C47×#25563 #26065261

Subgroups — C47×#25563 #26065261

Order 12032.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3490C211yesmaximal, characteristic, complemented
2C47×#2410C212yesmaximal, complemented
3C47×#2405C211yesmaximal, characteristic, complemented
4C47×#2062C211yesmaximal, characteristic, complemented
5C47×#2044C211yesmaximal, characteristic, complemented
6C47×#2029C211yesmaximal, characteristic, complemented
7C47×#2021C211yesmaximal, characteristic, complemented
8C47×#1898C212yesmaximal, complemented
9C47×#1889C212yesmaximal, complemented
10C47×#1867C212yesmaximal, complemented
11C2×C47×#342C211yesmaximal, characteristic, complemented
12C23×D4×C47C2211yescharacteristic
13C47×#551—22no—
14C47×#551—22no—
15C47×#546—22no—
16C47×#546—22no—
17C47×#543C2211yescharacteristic
18C47×#538—21no—
19C47×#538—21no—
20C47×#534C2211yescharacteristic
21C47×#525—21no—
22C47×#525—21no—
23C2×#123×C47—21no—
24C2×#121×C47—22no—
25C2×#120×C47C2212yes—
26C2×#120×C47C2212yes—
27C47×#518C2212yes—
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2212yes—
30C2×#99×C47C2212yes—
31C2×#99×C47C2212yes—
32C47×#394—21no—
33C47×#394—21no—
34C47×#394—22no—
35C47×#392—22no—
36C47×#386—21no—
37C47×#386—22no—
38C47×#386C2212yes—
39C47×#385C2211yescharacteristic
40C47×#385C2212yes—
41C47×#385C2211yescharacteristic
42C47×#379C2211yescharacteristic
43C47×#379C2212yes—
44C47×#379C2211yescharacteristic
45C47×#379C2211yescharacteristic
46C47×#342C2211yescharacteristic
47C47×#342C2211yescharacteristic
48C47×#342C2212yes—
49C47×#342C2212yes—
50C47×#342C2212yes—
51C25×C47C2311yescharacteristic
52C25×C47C2311yescharacteristic
53C2×#41×C47—21no—
54C2×#41×C47—21no—
55C22×D4×C47—22no—
56C22×D4×C47—21no—
57C22×D4×C47—22no—
58C22×D4×C47—21no—
59C22×D4×C47—22no—
60C22×D4×C47—44no—
61C22×D4×C47D412yescomplemented
62C22×D4×C47D412yescomplemented
63C22×D4×C47C2312yes—
64C23×C4×C47—22no—
65C23×C4×C47D411yescharacteristic, complemented
66C23×C4×C47D411yescharacteristic, complemented
67C23×C4×C47C2311yescharacteristic
68#126×C47—22no—
69#126×C47—22no—
70#124×C47—22no—
71#124×C47—22no—
72#123×C47—22no—
73#123×C47—22no—
74#123×C47—22no—
75#123×C47—22no—
76#123×C47—22no—
77#123×C47—44no—
78C22⋊Q8×C47—21no—
79C22⋊Q8×C47—21no—
80C22⋊Q8×C47—21no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—22no—
83C22⋊Q8×C47—22no—
84#121×C47—21no—
85#121×C47—21no—
86#121×C47—22no—
87#121×C47—22no—
88#121×C47—21no—
89#121×C47—21no—
90#121×C47—48no—
91#120×C47—22no—
92#120×C47—22no—
93#120×C47—22no—
94#120×C47—22no—
95#120×C47—22no—
96#120×C47—24no—
97#120×C47—42no—
98C4×D4×C47—22no—
99C4×D4×C47—22no—
100C4×D4×C47—22no—
101C4×D4×C47—22no—
102C4×D4×C47—22no—
103C4×D4×C47—22no—
104#117×C47—21no—
105#117×C47—21no—
106#117×C47—22no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—24no—
114C2×C22⋊C4×C47—22no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—22no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—42no—
126C2×C22⋊C4×C47D411yescharacteristic, complemented
127C2×C22⋊C4×C47D411yescharacteristic, complemented
128C2×C22⋊C4×C47D412yescomplemented
129C2×C22⋊C4×C47D412yescomplemented
130C2×C22⋊C4×C47C2312yes—
131C2×C22⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47C2311yescharacteristic
133C2×C22⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47C2311yescharacteristic
135C2×C22⋊C4×C47C2312yes—
136C2×C22⋊C4×C47C2312yes—
137#99×C47—24no—
138#99×C47—42no—
139#95×C47—22no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—22no—
143C24×C47—22no—
144C24×C47—21no—
145C24×C47—21no—
146C24×C47—21no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—21no—
150C24×C47—21no—
151C24×C47—42no—
152C24×C47—42no—
153C24×C47—81no—
154C24×C47—81no—
155C24×C47C2×D412yes—
156C24×C47C2×D411yescharacteristic
157C24×C47C2×D412yes—
158C24×C47C2×D412yes—
159C24×C47C2×D411yescharacteristic
160C24×C47C2411yescharacteristic
161#41×C47—82no—
162#41×C47—82no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×D4×C47—28no—
166C2×D4×C47—24no—
167C2×D4×C47—22no—
168C2×D4×C47—22no—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—22no—
172C2×D4×C47—22no—
173C2×D4×C47—22no—
174C2×D4×C47—22no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—22no—
178C2×D4×C47—22no—
179C2×D4×C47—44no—
180C2×D4×C47—42no—
181C2×D4×C47—44no—
182C2×D4×C47—42no—
183C2×D4×C47—44no—
184C2×D4×C47—42no—
185C2×D4×C47—44no—
186C2×D4×C47—42no—
187C2×D4×C47—41no—
188C2×D4×C47—41no—
189C2×D4×C47—44no—
190C2×D4×C47—44no—
191C2×D4×C47—82no—
192C2×D4×C47—82no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—22no—
205C22×C4×C47—42no—
206C22×C4×C47—44no—
207C22×C4×C47—42no—
208C22×C4×C47—44no—
209C22×C4×C47—81no—
210C22×C4×C47—82no—
211C22×C4×C47C2×D412yes—
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D412yes—
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D412yes—
217C22×C4×C47C2×D411yescharacteristic
218C4⋊C4×C47—22no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—22no—
225C4⋊C4×C47—22no—
226C4⋊C4×C47—44no—
227C4⋊C4×C47—42no—
228C4⋊C4×C47—42no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—22no—
231C22⋊C4×C47—22no—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—22no—
236C22⋊C4×C47—22no—
237C22⋊C4×C47—22no—
238C22⋊C4×C47—22no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C22⋊C4×C47—22no—
246C22⋊C4×C47—22no—
247C22⋊C4×C47—21no—
248C22⋊C4×C47—21no—
249C22⋊C4×C47—44no—
250C22⋊C4×C47—44no—
251C22⋊C4×C47—44no—
252C22⋊C4×C47—44no—
253C22⋊C4×C47—42no—
254C22⋊C4×C47—42no—
255C22⋊C4×C47—42no—
256C22⋊C4×C47—81no—
257C22⋊C4×C47—81no—
258C22⋊C4×C47—82no—
259C22⋊C4×C47—81no—
260C22⋊C4×C47#4114yescomplemented
261C42×C47—22no—
262C42×C47—22no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—24no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—24no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—42no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—42no—
289C23×C47—41no—
290C23×C47—42no—
291C23×C47—42no—
292C23×C47—42no—
293C23×C47—42no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47—42no—
298C23×C47—42no—
299C23×C47—84no—
300C23×C47—84no—
301C23×C47—82no—
302C23×C47—82no—
303C23×C47—82no—
304C23×C47—82no—
305C23×C47#12012yes—
306C23×C47#12011yescharacteristic
307C23×C47#12011yescharacteristic
308C23×C47C22×D411yescharacteristic
309C23×C47C22×D412yes—
310C23×C47C2×#4112yes—
311C23×C47H(5,𝔽2)11yescharacteristic
312C23×C472−1+411yescharacteristic
313Q8×C47—81no—
314Q8×C47—81no—
315D4×C47—44no—
316D4×C47—48no—
317D4×C47—44no—
318D4×C47—42no—
319D4×C47—42no—
320D4×C47—42no—
321D4×C47—42no—
322D4×C47—44no—
323D4×C47—44no—
324D4×C47—82no—
325D4×C47—82no—
326D4×C47—81no—
327D4×C47—81no—
328D4×C47—88no—
329C2×C4×C47—24no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—24no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—42no—
342C2×C4×C47—41no—
343C2×C4×C47—42no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47—41no—
347C2×C4×C47—42no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—42no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—42no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—42no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—42no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—42no—
363C2×C4×C47—81no—
364C2×C4×C47—81no—
365C2×C4×C47—82no—
366C2×C4×C47—82no—
367C2×C4×C47—88no—
368#25563C4711yesmaximal, characteristic, direct product factor, Sylow
369C22×C47—21no—
370C22×C47—21no—
371C22×C47—22no—
372C22×C47—21no—
373C22×C47—22no—
374C22×C47—21no—
375C22×C47—21no—
376C22×C47—22no—
377C22×C47—21no—
378C22×C47—22no—
379C22×C47—21no—
380C22×C47—22no—
381C22×C47—42no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—44no—
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—44no—
388C22×C47—44no—
389C22×C47—42no—
390C22×C47—42no—
391C22×C47—44no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—82no—
397C22×C47—81no—
398C22×C47—81no—
399C22×C47—82no—
400C22×C47—82no—
401C22×C47—82no—
402C22×C47—82no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—82no—
406C22×C47—81no—
407C22×C47—81no—
408C22×C47B(4,𝔽2)12yes—
409C22×C47C2×#12011yescharacteristic
410C22×C47#53211yescharacteristic
411C22×C47#53711yescharacteristic
412C22×C47#54612yes—
413C22×C47#54712yes—
414C4×C47—44no—
415C4×C47—42no—
416C4×C47—42no—
417C4×C47—41no—
418C4×C47—41no—
419C4×C47—42no—
420C4×C47—41no—
421C4×C47—41no—
422C4×C47—42no—
423C4×C47—81no—
424C4×C47—81no—
425C4×C47—82no—
426#3490C2×C4711yescharacteristic, complemented
427#2410C2×C4712yescomplemented
428#2405C2×C4711yescharacteristic, complemented
429#2062C2×C4711yescharacteristic, complemented
430#2044C2×C4711yescharacteristic, complemented
431#2029C2×C4711yescharacteristic, complemented
432#2021C2×C4711yescharacteristic, complemented
433#1898C2×C4712yescomplemented
434#1889C2×C4712yescomplemented
435#1867C2×C4712yescomplemented
436C2×#342C2×C4711yescharacteristic, complemented
437C2×C47—22no—
438C2×C47—21no—
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—22no—
442C2×C47—41no—
443C2×C47—42no—
444C2×C47—82no—
445C2×C47—82no—
446C2×C47#243011yescharacteristic
447C2×C47C2×B(4,𝔽2)11yescharacteristic
448C2×C47#302611yescharacteristic
449C23×D4C22×C4711yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C4711yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C4711yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C4712yes—
463C2×#120C22×C4712yes—
464#518C22×C4712yes—
465C22×C22⋊C4C22×C4711yescharacteristic
466C22×C22⋊C4C22×C4712yes—
467C2×#99C22×C4712yes—
468C2×#99C22×C4712yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C4712yes—
476#385C22×C4712yes—
477#385C22×C4711yescharacteristic
478#385C22×C4711yescharacteristic
479#379C22×C4711yescharacteristic
480#379C22×C4712yes—
481#379C22×C4711yescharacteristic
482#379C22×C4711yescharacteristic
483#342C22×C4712yes—
484#342C22×C4711yescharacteristic
485#342C22×C4712yes—
486#342C22×C4712yes—
487#342C22×C4711yescharacteristic
488C47#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C4711yescharacteristic
490C25C23×C4711yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C4712yescomplemented
500C22×D4D4×C4712yescomplemented
501C22×D4C23×C4712yes—
502C23×C4—22no—
503C23×C4D4×C4711yescharacteristic, complemented
504C23×C4D4×C4711yescharacteristic, complemented
505C23×C4C23×C4711yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C4711yescharacteristic, complemented
565C2×C22⋊C4D4×C4711yescharacteristic, complemented
566C2×C22⋊C4D4×C4712yescomplemented
567C2×C22⋊C4D4×C4712yescomplemented
568C2×C22⋊C4C23×C4712yes—
569C2×C22⋊C4C23×C4711yescharacteristic
570C2×C22⋊C4C23×C4711yescharacteristic
571C2×C22⋊C4C23×C4711yescharacteristic
572C2×C22⋊C4C23×C4711yescharacteristic
573C2×C22⋊C4C23×C4712yes—
574C2×C22⋊C4C23×C4712yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C4712yes—
594C24C2×D4×C4711yescharacteristic
595C24C2×D4×C4712yes—
596C24C2×D4×C4712yes—
597C24C2×D4×C4711yescharacteristic
598C24C24×C4711yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C4712yes—
650C22×C4C2×D4×C4711yescharacteristic
651C22×C4C2×D4×C4712yes—
652C22×C4C2×D4×C4711yescharacteristic
653C22×C4C2×D4×C4711yescharacteristic
654C22×C4C2×D4×C4712yes—
655C22×C4C2×D4×C4711yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C4714yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C4712yes—
744C23#120×C4711yescharacteristic
745C23#120×C4711yescharacteristic
746C23C22×D4×C4711yescharacteristic
747C23C22×D4×C4712yes—
748C23C2×#41×C4712yes—
749C23H(5,𝔽2)×C4711yescharacteristic
750C232−1+4×C4711yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C47×B(4,𝔽2)12yes—
846C22C2×#120×C4711yescharacteristic
847C22C47×#53211yescharacteristic
848C22C47×#53711yescharacteristic
849C22C47×#54612yes—
850C22C47×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C47×#243011yescharacteristic
873C2C2×C47×B(4,𝔽2)11yescharacteristic
874C2C47×#302611yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC24C24×C47
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C25×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3490C2semidirect
2. C47×#2410C2semidirect
3. C47×#2405C2semidirect
4. C47×#2062C2semidirect
5. C47×#2044C2semidirect
6. C47×#2029C2semidirect
7. C47×#2021C2semidirect
8. C47×#1898C2semidirect
9. C47×#1889C2semidirect
10. C47×#1867C2semidirect
11. C2×C47×#342C2semidirect
61. C22×D4×C47D4semidirect
62. C22×D4×C47D4semidirect
65. C23×C4×C47D4semidirect
66. C23×C4×C47D4semidirect
126. C2×C22⋊C4×C47D4semidirect
127. C2×C22⋊C4×C47D4semidirect
128. C2×C22⋊C4×C47D4semidirect
129. C2×C22⋊C4×C47D4semidirect
260. C22⋊C4×C47#41semidirect
368. #25563C47direct (N × H)
426. #3490C2×C47semidirect
427. #2410C2×C47semidirect
428. #2405C2×C47semidirect
429. #2062C2×C47semidirect
430. #2044C2×C47semidirect
431. #2029C2×C47semidirect
432. #2021C2×C47semidirect
433. #1898C2×C47semidirect
434. #1889C2×C47semidirect
435. #1867C2×C47semidirect
436. C2×#342C2×C47semidirect
488. C47#25563direct (N × H)
499. C22×D4D4×C47semidirect
500. C22×D4D4×C47semidirect
503. C23×C4D4×C47semidirect
504. C23×C4D4×C47semidirect
564. C2×C22⋊C4D4×C47semidirect
565. C2×C22⋊C4D4×C47semidirect
566. C2×C22⋊C4D4×C47semidirect
567. C2×C22⋊C4D4×C47semidirect
698. C22⋊C4#41×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34902
C47×#24102
C47×#24052
C47×#20622
C47×#20442
C47×#20292
C47×#20212
C47×#18982
C47×#18892
C47×#18672
C2×C47×#3422
#2556347