Finite Group Databasebeta

← C47×#24404 #26064102

Subgroups — C47×#24404 #26064102

Order 12032.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3484C211yesmaximal, characteristic, complemented
2C2×C47×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C47C211yesmaximal, characteristic, complemented
4C47×#2410C212yesmaximal, complemented
5C47×#2403C211yesmaximal, characteristic, complemented
6C47×#2044C212yesmaximal, complemented
7C47×#2021C212yesmaximal, complemented
8C47×#1898C212yesmaximal, complemented
9C47×#1889C211yesmaximal, characteristic, complemented
10C47×#1867C211yesmaximal, characteristic, complemented
11C47×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C47C2211yescharacteristic
13C23×D4×C47C2211yescharacteristic
14C23×D4×C47C2211yescharacteristic, complemented
15C47×#546—22no—
16C47×#546—22no—
17D42×C47—22no—
18D42×C47—22no—
19C47×#535—21no—
20C47×#534—21no—
21C47×#534C2212yes—
22C47×#525—21no—
23C2×#121×C47—22no—
24C2×#120×C47—21no—
25C2×#120×C47—21no—
26C2×#120×C47C2211yescharacteristic
27C2×#120×C47C2212yes—
28C2×#120×C47C2212yescomplemented
29C2×#120×C47C2211yescharacteristic, complemented
30C47×#518C2211yescharacteristic
31C22×C22⋊C4×C47C2212yescomplemented
32C47×B(4,𝔽2)—24no—
33C2×#99×C47—24no—
34C2×#99×C47C2211yescharacteristic
35C2×#99×C47C2211yescharacteristic
36C2×#99×C47C2212yescomplemented
37C2×#99×C47C2212yescomplemented
38C2×#99×C47C2212yescomplemented
39C47×#394—22no—
40C47×#392—21no—
41C47×#392—21no—
42C47×#392—22no—
43C47×#386—21no—
44C47×#386—22no—
45C47×#386C2211yescharacteristic
46C47×#386C2211yescharacteristic, complemented
47C47×#386C2212yescomplemented
48C47×#385C2212yescomplemented
49C47×#379C2212yescomplemented
50C47×#379C2211yescharacteristic, complemented
51C47×#342C2212yescomplemented
52C47×#342C2212yescomplemented
53C25×C47D411yescharacteristic, complemented
54C25×C47C2311yescharacteristic
55C25×C47C2311yescharacteristic
56H(5,𝔽2)×C47—22no—
57H(5,𝔽2)×C47—22no—
58H(5,𝔽2)×C47—42no—
59C2×#41×C47—21no—
60C2×#41×C47—22no—
61C22×D4×C47—21no—
62C22×D4×C47—21no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—22no—
70C22×D4×C47—22no—
71C22×D4×C47—21no—
72C22×D4×C47—22no—
73C22×D4×C47—21no—
74C22×D4×C47—21no—
75C22×D4×C47—22no—
76C22×D4×C47—44no—
77C22×D4×C47—42no—
78C22×D4×C47D411yescharacteristic, complemented
79C22×D4×C47D411yescharacteristic, complemented
80C22×D4×C47D412yescomplemented
81C22×D4×C47D412yescomplemented
82C22×D4×C47C2312yes—
83C22×D4×C47C2311yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C23×C4×C47—22no—
86C23×C4×C47D411yescharacteristic, complemented
87C23×C4×C47C2311yescharacteristic
88#127×C47—22no—
89#124×C47—22no—
90#123×C47—22no—
91#123×C47—22no—
92#123×C47—22no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47—21no—
95#121×C47—21no—
96#121×C47—21no—
97#121×C47—22no—
98#121×C47—22no—
99#121×C47—22no—
100#121×C47—22no—
101#121×C47—22no—
102#121×C47—22no—
103#121×C47—48no—
104#120×C47—22no—
105#120×C47—22no—
106#120×C47—22no—
107#120×C47—22no—
108#120×C47—22no—
109#120×C47—22no—
110#120×C47—22no—
111#120×C47—22no—
112#120×C47—22no—
113#120×C47—22no—
114#120×C47—22no—
115#120×C47—24no—
116#120×C47—42no—
117#120×C47—42no—
118#120×C47—44no—
119C4×D4×C47—22no—
120C4×D4×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123#117×C47—21no—
124C2×C4⋊C4×C47—22no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—24no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—22no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—22no—
137C2×C22⋊C4×C47—22no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—22no—
140C2×C22⋊C4×C47—42no—
141C2×C22⋊C4×C47D412yescomplemented
142C2×C22⋊C4×C47D412yescomplemented
143C2×C22⋊C4×C47C2312yes—
144C2×C22⋊C4×C47C2311yescharacteristic
145C2×C22⋊C4×C47C2311yescharacteristic
146C2×C22⋊C4×C47C2312yes—
147C2×C22⋊C4×C47C2312yes—
148#99×C47—22no—
149#99×C47—24no—
150#99×C47—24no—
151#99×C47—42no—
152#99×C47D414yescomplemented
153#95×C47—22no—
154#95×C47—21no—
155#95×C47—21no—
156#95×C47—22no—
157C24×C47—21no—
158C24×C47—21no—
159C24×C47—22no—
160C24×C47—21no—
161C24×C47—22no—
162C24×C47—21no—
163C24×C47—21no—
164C24×C47—21no—
165C24×C47—22no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47—22no—
169C24×C47—41no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—42no—
173C24×C47—81no—
174C24×C47—81no—
175C24×C47—81no—
176C24×C47C2×D411yescharacteristic
177C24×C47C2×D412yes—
178C24×C47C2×D411yescharacteristic
179C24×C47C2×D412yes—
180C24×C47C2×D412yes—
181C24×C47C2×D411yescharacteristic
182C24×C47C2×D411yescharacteristic
183C24×C47C2411yescharacteristic
184#41×C47—44no—
185#41×C47—44no—
186#41×C47—42no—
187#41×C47—42no—
188C2×Q8×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—22no—
192C2×D4×C47—24no—
193C2×D4×C47—21no—
194C2×D4×C47—28no—
195C2×D4×C47—22no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—22no—
202C2×D4×C47—22no—
203C2×D4×C47—22no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—22no—
207C2×D4×C47—22no—
208C2×D4×C47—22no—
209C2×D4×C47—22no—
210C2×D4×C47—22no—
211C2×D4×C47—22no—
212C2×D4×C47—22no—
213C2×D4×C47—22no—
214C2×D4×C47—22no—
215C2×D4×C47—41no—
216C2×D4×C47—41no—
217C2×D4×C47—42no—
218C2×D4×C47—44no—
219C2×D4×C47—44no—
220C2×D4×C47—44no—
221C2×D4×C47—44no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47—44no—
225C2×D4×C47—44no—
226C2×D4×C47—44no—
227C2×D4×C47—42no—
228C2×D4×C47—42no—
229C2×D4×C47—44no—
230C2×D4×C47—42no—
231C2×D4×C47—41no—
232C2×D4×C47—42no—
233C2×D4×C47—41no—
234C2×D4×C47—42no—
235C2×D4×C47—44no—
236C2×D4×C47—42no—
237C2×D4×C47—42no—
238C2×D4×C47—42no—
239C2×D4×C47—44no—
240C2×D4×C47—42no—
241C2×D4×C47—82no—
242C2×D4×C47—82no—
243C2×D4×C47—81no—
244C2×D4×C47—81no—
245C2×D4×C47—82no—
246C2×D4×C47—82no—
247C2×D4×C47C2×D412yes—
248C2×D4×C47#4112yes—
249C22×C4×C47—21no—
250C22×C4×C47—22no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—22no—
254C22×C4×C47—21no—
255C22×C4×C47—22no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—22no—
259C22×C4×C47—22no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—42no—
263C22×C4×C47—41no—
264C22×C4×C47—44no—
265C22×C4×C47—44no—
266C22×C4×C47—82no—
267C22×C4×C47C2×D412yes—
268C22×C4×C47C2×D411yescharacteristic
269C22×C4×C47C2×D411yescharacteristic
270C22×C4×C47C2×D412yes—
271C22×C4×C47C2×D412yes—
272C4⋊C4×C47—21no—
273C4⋊C4×C47—21no—
274C4⋊C4×C47—22no—
275C4⋊C4×C47—22no—
276C4⋊C4×C47—44no—
277C22⋊C4×C47—22no—
278C22⋊C4×C47—22no—
279C22⋊C4×C47—22no—
280C22⋊C4×C47—22no—
281C22⋊C4×C47—22no—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—22no—
285C22⋊C4×C47—22no—
286C22⋊C4×C47—22no—
287C22⋊C4×C47—22no—
288C22⋊C4×C47—22no—
289C22⋊C4×C47—22no—
290C22⋊C4×C47—21no—
291C22⋊C4×C47—21no—
292C22⋊C4×C47—22no—
293C22⋊C4×C47—22no—
294C22⋊C4×C47—44no—
295C22⋊C4×C47—44no—
296C22⋊C4×C47—42no—
297C22⋊C4×C47—42no—
298C22⋊C4×C47—42no—
299C22⋊C4×C47—44no—
300C22⋊C4×C47—42no—
301C22⋊C4×C47—44no—
302C22⋊C4×C47—42no—
303C22⋊C4×C47—82no—
304C22⋊C4×C47—81no—
305C22⋊C4×C47C2×D414yescomplemented
306C42×C47—22no—
307C23×C47—21no—
308C23×C47—21no—
309C23×C47—21no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—24no—
314C23×C47—21no—
315C23×C47—21no—
316C23×C47—21no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—24no—
320C23×C47—22no—
321C23×C47—21no—
322C23×C47—22no—
323C23×C47—21no—
324C23×C47—21no—
325C23×C47—22no—
326C23×C47—22no—
327C23×C47—41no—
328C23×C47—42no—
329C23×C47—41no—
330C23×C47—41no—
331C23×C47—41no—
332C23×C47—42no—
333C23×C47—41no—
334C23×C47—42no—
335C23×C47—42no—
336C23×C47—42no—
337C23×C47—41no—
338C23×C47—41no—
339C23×C47—41no—
340C23×C47—41no—
341C23×C47—42no—
342C23×C47—42no—
343C23×C47—41no—
344C23×C47—42no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—42no—
348C23×C47—42no—
349C23×C47—42no—
350C23×C47—42no—
351C23×C47—41no—
352C23×C47—41no—
353C23×C47—41no—
354C23×C47—42no—
355C23×C47—42no—
356C23×C47—42no—
357C23×C47—81no—
358C23×C47—81no—
359C23×C47—82no—
360C23×C47—82no—
361C23×C47—82no—
362C23×C47—82no—
363C23×C47—84no—
364C23×C47—84no—
365C23×C47—81no—
366C23×C47—81no—
367C23×C47—84no—
368C23×C47—84no—
369C23×C47#12011yescharacteristic
370C23×C47#12012yes—
371C23×C47#12011yescharacteristic
372C23×C47#12112yescomplemented
373C23×C47C22×D411yescharacteristic
374C23×C47C22×D412yes—
375C23×C47C22×D411yescharacteristic
376C23×C47C2×#4111yescharacteristic
377C23×C47H(5,𝔽2)12yes—
378Q8×C47—42no—
379D4×C47—24no—
380D4×C47—24no—
381D4×C47—44no—
382D4×C47—42no—
383D4×C47—44no—
384D4×C47—48no—
385D4×C47—44no—
386D4×C47—44no—
387D4×C47—44no—
388D4×C47—42no—
389D4×C47—42no—
390D4×C47—42no—
391D4×C47—42no—
392D4×C47—42no—
393D4×C47—42no—
394D4×C47—44no—
395D4×C47—44no—
396D4×C47—82no—
397D4×C47—82no—
398D4×C47—82no—
399D4×C47—82no—
400D4×C47—88no—
401D4×C47—84no—
402D4×C47—84no—
403C2×C4×C47—21no—
404C2×C4×C47—21no—
405C2×C4×C47—22no—
406C2×C4×C47—24no—
407C2×C4×C47—22no—
408C2×C4×C47—22no—
409C2×C4×C47—22no—
410C2×C4×C47—21no—
411C2×C4×C47—21no—
412C2×C4×C47—21no—
413C2×C4×C47—24no—
414C2×C4×C47—22no—
415C2×C4×C47—22no—
416C2×C4×C47—42no—
417C2×C4×C47—42no—
418C2×C4×C47—44no—
419C2×C4×C47—42no—
420C2×C4×C47—42no—
421C2×C4×C47—41no—
422C2×C4×C47—42no—
423C2×C4×C47—42no—
424C2×C4×C47—41no—
425C2×C4×C47—42no—
426C2×C4×C47—42no—
427C2×C4×C47—42no—
428C2×C4×C47—41no—
429C2×C4×C47—41no—
430C2×C4×C47—42no—
431C2×C4×C47—41no—
432C2×C4×C47—41no—
433C2×C4×C47—41no—
434C2×C4×C47—41no—
435C2×C4×C47—42no—
436C2×C4×C47—81no—
437C2×C4×C47—81no—
438C2×C4×C47—88no—
439C2×C4×C47#12112yescomplemented
440#24404C4711yesmaximal, characteristic, direct product factor, Sylow
441C22×C47—21no—
442C22×C47—22no—
443C22×C47—21no—
444C22×C47—22no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47—21no—
448C22×C47—22no—
449C22×C47—22no—
450C22×C47—22no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—22no—
454C22×C47—41no—
455C22×C47—41no—
456C22×C47—42no—
457C22×C47—44no—
458C22×C47—44no—
459C22×C47—42no—
460C22×C47—42no—
461C22×C47—42no—
462C22×C47—44no—
463C22×C47—42no—
464C22×C47—42no—
465C22×C47—42no—
466C22×C47—44no—
467C22×C47—41no—
468C22×C47—41no—
469C22×C47—42no—
470C22×C47—41no—
471C22×C47—42no—
472C22×C47—42no—
473C22×C47—41no—
474C22×C47—42no—
475C22×C47—41no—
476C22×C47—82no—
477C22×C47—81no—
478C22×C47—81no—
479C22×C47—81no—
480C22×C47—82no—
481C22×C47—84no—
482C22×C47—82no—
483C22×C47—82no—
484C22×C47—81no—
485C22×C47—82no—
486C22×C47—81no—
487C22×C47—81no—
488C22×C47—82no—
489C22×C47—84no—
490C22×C47—81no—
491C22×C47—81no—
492C22×C47—162no—
493C22×C47B(4,𝔽2)12yescomplemented
494C22×C47C2×#12011yescharacteristic
495C22×C47C2×#12111yescharacteristic
496C22×C47#53411yescharacteristic
497C22×C47D4212yes—
498C22×C47#54612yes—
499C4×C47—22no—
500C4×C47—44no—
501C4×C47—41no—
502C4×C47—42no—
503C4×C47—42no—
504C4×C47—42no—
505C4×C47—42no—
506C4×C47—82no—
507C4×C47—81no—
508C4×C47—81no—
509#3484C2×C4711yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C4711yescharacteristic, complemented
511C22×#99C2×C4711yescharacteristic, complemented
512#2410C2×C4712yescomplemented
513#2403C2×C4711yescharacteristic, complemented
514#2044C2×C4712yescomplemented
515#2021C2×C4712yescomplemented
516#1898C2×C4712yescomplemented
517#1889C2×C4711yescharacteristic, complemented
518#1867C2×C4711yescharacteristic, complemented
519#1790C2×C4711yescharacteristic, complemented
520C2×C47—22no—
521C2×C47—21no—
522C2×C47—21no—
523C2×C47—22no—
524C2×C47—22no—
525C2×C47—42no—
526C2×C47—41no—
527C2×C47—42no—
528C2×C47—82no—
529C2×C47—81no—
530C2×C47—82no—
531C2×C47#241011yescharacteristic
532C2×C47C2×B(4,𝔽2)11yescharacteristic
533C2×C47#302611yescharacteristic
534C2×H(5,𝔽2)C22×C4711yescharacteristic
535C23×D4C22×C4711yescharacteristic
536C23×D4C22×C4711yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C4712yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C4711yescharacteristic
549C2×#120C22×C4712yes—
550C2×#120C22×C4712yescomplemented
551C2×#120C22×C4711yescharacteristic, complemented
552#518C22×C4711yescharacteristic
553C22×C22⋊C4C22×C4712yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C4711yescharacteristic
557C2×#99C22×C4711yescharacteristic
558C2×#99C22×C4712yescomplemented
559C2×#99C22×C4712yescomplemented
560C2×#99C22×C4712yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C4711yescharacteristic
568#386C22×C4711yescharacteristic, complemented
569#386C22×C4712yescomplemented
570#385C22×C4712yescomplemented
571#379C22×C4712yescomplemented
572#379C22×C4711yescharacteristic, complemented
573#342C22×C4712yescomplemented
574#342C22×C4712yescomplemented
575C47#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C4711yescharacteristic, complemented
577C25C23×C4711yescharacteristic
578C25C23×C4711yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C4711yescharacteristic, complemented
602C22×D4D4×C4711yescharacteristic, complemented
603C22×D4D4×C4712yescomplemented
604C22×D4D4×C4712yescomplemented
605C22×D4C23×C4712yes—
606C22×D4C23×C4711yescharacteristic
607C22×D4C23×C4711yescharacteristic
608C23×C4—22no—
609C23×C4D4×C4711yescharacteristic, complemented
610C23×C4C23×C4711yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C4712yescomplemented
665C2×C22⋊C4D4×C4712yescomplemented
666C2×C22⋊C4C23×C4712yes—
667C2×C22⋊C4C23×C4711yescharacteristic
668C2×C22⋊C4C23×C4711yescharacteristic
669C2×C22⋊C4C23×C4712yes—
670C2×C22⋊C4C23×C4712yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C4714yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C4711yescharacteristic
700C24C2×D4×C4712yes—
701C24C2×D4×C4711yescharacteristic
702C24C2×D4×C4712yes—
703C24C2×D4×C4712yes—
704C24C2×D4×C4711yescharacteristic
705C24C2×D4×C4711yescharacteristic
706C24C24×C4711yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C4712yes—
771C2×D4#41×C4712yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C4712yes—
791C22×C4C2×D4×C4711yescharacteristic
792C22×C4C2×D4×C4711yescharacteristic
793C22×C4C2×D4×C4712yes—
794C22×C4C2×D4×C4712yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C4714yescomplemented
829C42—22no—
830C23—22no—
831C23—24no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C4711yescharacteristic
893C23#120×C4712yes—
894C23#120×C4711yescharacteristic
895C23#121×C4712yescomplemented
896C23C22×D4×C4711yescharacteristic
897C23C22×D4×C4712yes—
898C23C22×D4×C4711yescharacteristic
899C23C2×#41×C4711yescharacteristic
900C23H(5,𝔽2)×C4712yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—44no—
912D4—44no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—42no—
918D4—42no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C4712yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22C47×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C4711yescharacteristic
1017C22C2×#121×C4711yescharacteristic
1018C22C47×#53411yescharacteristic
1019C22D42×C4712yes—
1020C22C47×#54612yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C47×#241011yescharacteristic
1043C2C2×C47×B(4,𝔽2)11yescharacteristic
1044C2C47×#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×#3484C2semidirect
2. C2×C47×B(4,𝔽2)C2semidirect
3. C22×#99×C47C2semidirect
4. C47×#2410C2semidirect
5. C47×#2403C2semidirect
6. C47×#2044C2semidirect
7. C47×#2021C2semidirect
8. C47×#1898C2semidirect
9. C47×#1889C2semidirect
10. C47×#1867C2semidirect
11. C47×#1790C2semidirect
14. C23×D4×C47C22semidirect
28. C2×#120×C47C22semidirect
29. C2×#120×C47C22semidirect
31. C22×C22⋊C4×C47C22semidirect
36. C2×#99×C47C22semidirect
37. C2×#99×C47C22semidirect
38. C2×#99×C47C22semidirect
46. C47×#386C22semidirect
47. C47×#386C22semidirect
48. C47×#385C22semidirect
49. C47×#379C22semidirect
50. C47×#379C22semidirect
51. C47×#342C22semidirect
52. C47×#342C22semidirect
53. C25×C47D4semidirect
78. C22×D4×C47D4semidirect
79. C22×D4×C47D4semidirect
80. C22×D4×C47D4semidirect
81. C22×D4×C47D4semidirect
86. C23×C4×C47D4semidirect
141. C2×C22⋊C4×C47D4semidirect
142. C2×C22⋊C4×C47D4semidirect
152. #99×C47D4semidirect
305. C22⋊C4×C47C2×D4semidirect
372. C23×C47#121semidirect
439. C2×C4×C47#121semidirect
440. #24404C47direct (N × H)
493. C22×C47B(4,𝔽2)semidirect
509. #3484C2×C47semidirect
510. C2×B(4,𝔽2)C2×C47semidirect
511. C22×#99C2×C47semidirect
512. #2410C2×C47semidirect
513. #2403C2×C47semidirect
514. #2044C2×C47semidirect
515. #2021C2×C47semidirect
516. #1898C2×C47semidirect
517. #1889C2×C47semidirect
518. #1867C2×C47semidirect
519. #1790C2×C47semidirect
536. C23×D4C22×C47semidirect
550. C2×#120C22×C47semidirect
551. C2×#120C22×C47semidirect
553. C22×C22⋊C4C22×C47semidirect
558. C2×#99C22×C47semidirect
559. C2×#99C22×C47semidirect
560. C2×#99C22×C47semidirect
568. #386C22×C47semidirect
569. #386C22×C47semidirect
570. #385C22×C47semidirect
571. #379C22×C47semidirect
572. #379C22×C47semidirect
573. #342C22×C47semidirect
574. #342C22×C47semidirect
575. C47#24404direct (N × H)
576. C25D4×C47semidirect
601. C22×D4D4×C47semidirect
602. C22×D4D4×C47semidirect
603. C22×D4D4×C47semidirect
604. C22×D4D4×C47semidirect
609. C23×C4D4×C47semidirect
664. C2×C22⋊C4D4×C47semidirect
665. C2×C22⋊C4D4×C47semidirect
675. #99D4×C47semidirect
828. C22⋊C4C2×D4×C47semidirect
895. C23#121×C47semidirect
962. C2×C4#121×C47semidirect
1015. C22C47×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C47×#34842
C2×C47×B(4,𝔽2)2
C22×#99×C472
C47×#24102
C47×#24032
C47×#20442
C47×#20212
C47×#18982
C47×#18892
C47×#18672
C47×#17902
#2440447