Finite Group Databasebeta

← C41×#24056 #23800257

Subgroups — C41×#24056 #23800257

Order 10496.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3484C211yesmaximal, characteristic
2C41×#2849C212yesmaximal, complemented
3C2×C41×#386C211yesmaximal, characteristic, complemented
4C41×#2044C214yesmaximal, complemented
5C41×#1898C212yesmaximal, complemented
6C41×#1867C212yesmaximal, complemented
7C41×#1790C212yesmaximal, complemented
8C41×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C41C2211yescharacteristic
10C23×D4×C41C2211yescharacteristic
11C24×C4×C41C2211yescharacteristic, complemented
12C41×#546—22no—
13C41×#546—22no—
14D42×C41—22no—
15D42×C41—22no—
16C41×#535—21no—
17C41×#534—21no—
18C41×#534C2212yes—
19C41×#525—21no—
20C2×#123×C41—22no—
21C2×#120×C41—21no—
22C2×#120×C41C2212yes—
23C41×#518C2211yescharacteristic
24C22×C22⋊C4×C41—21no—
25C22×C22⋊C4×C41C2211yescharacteristic, complemented
26C2×#99×C41C2212yes—
27C2×#99×C41C2212yescomplemented
28C2×#99×C41C2214yescomplemented
29C41×#386—21no—
30C41×#386—21no—
31C41×#386—22no—
32C41×#386C2212yes—
33C41×#386C2212yescomplemented
34C41×#386C2214yescomplemented
35C41×#385—22no—
36C41×#385C2214yescomplemented
37C41×#381—22no—
38C41×#379C2212yescomplemented
39C2×#95×C41—21no—
40C41×#342C2214yescomplemented
41C25×C41D411yescharacteristic
42C25×C41C2311yescharacteristic
43H(5,𝔽2)×C41—24no—
44H(5,𝔽2)×C41—42no—
45C2×#41×C41—21no—
46C2×#41×C41—22no—
47C22×D4×C41—21no—
48C22×D4×C41—22no—
49C22×D4×C41—22no—
50C22×D4×C41—22no—
51C22×D4×C41—21no—
52C22×D4×C41—21no—
53C22×D4×C41—24no—
54C22×D4×C41—42no—
55C22×D4×C41D411yescharacteristic
56C22×D4×C41D411yescharacteristic
57C22×D4×C41D412yes—
58C22×D4×C41D412yes—
59C22×D4×C41C2312yes—
60C22×D4×C41C2311yescharacteristic
61C22×D4×C41C2311yescharacteristic
62C23×C4×C41—21no—
63C23×C4×C41—22no—
64C23×C4×C41—21no—
65C23×C4×C41—22no—
66C23×C4×C41—21no—
67C23×C4×C41—44no—
68C23×C4×C41D411yescharacteristic
69C23×C4×C41C2312yes—
70#127×C41—22no—
71#124×C41—22no—
72#123×C41—22no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—48no—
76C22⋊Q8×C41—21no—
77C22⋊Q8×C41—21no—
78#121×C41—21no—
79#121×C41—21no—
80#121×C41—22no—
81#121×C41—22no—
82#121×C41—22no—
83#121×C41—22no—
84#121×C41—22no—
85#121×C41—22no—
86#120×C41—22no—
87#120×C41—22no—
88#120×C41—22no—
89#120×C41—22no—
90#120×C41—22no—
91#120×C41—22no—
92#120×C41—22no—
93#120×C41—22no—
94#120×C41—22no—
95C4×D4×C41—22no—
96C4×D4×C41—22no—
97C4×D4×C41—22no—
98C4×D4×C41—22no—
99#117×C41—21no—
100C2×C4⋊C4×C41—24no—
101C2×C22⋊C4×C41—21no—
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—22no—
105C2×C22⋊C4×C41—22no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—22no—
108C2×C22⋊C4×C41—24no—
109C2×C22⋊C4×C41—22no—
110C2×C22⋊C4×C41—42no—
111C2×C22⋊C4×C41—44no—
112C2×C22⋊C4×C41D412yes—
113C2×C22⋊C4×C41D412yes—
114C2×C22⋊C4×C41C2312yes—
115C2×C22⋊C4×C41C2314yes—
116C2×C22⋊C4×C41C2312yes—
117#99×C41—24no—
118#99×C41—42no—
119#99×C41—44no—
120#95×C41—22no—
121#95×C41—22no—
122#95×C41—24no—
123#95×C41—24no—
124C24×C41—22no—
125C24×C41—22no—
126C24×C41—21no—
127C24×C41—22no—
128C24×C41—21no—
129C24×C41—21no—
130C24×C41—42no—
131C24×C41—42no—
132C24×C41—41no—
133C24×C41—42no—
134C24×C41—42no—
135C24×C41C2×D411yescharacteristic
136C24×C41C2×D412yes—
137C24×C41C2×D412yes—
138C24×C41C2×D411yescharacteristic
139C24×C41C2×D412yes—
140C24×C41C2×D411yescharacteristic
141C24×C41C2×D411yescharacteristic
142C24×C41C2411yescharacteristic
143#41×C41—48no—
144#41×C41—42no—
145#41×C41—42no—
146C2×Q8×C41—21no—
147C2×D4×C41—22no—
148C2×D4×C41—22no—
149C2×D4×C41—22no—
150C2×D4×C41—21no—
151C2×D4×C41—22no—
152C2×D4×C41—22no—
153C2×D4×C41—22no—
154C2×D4×C41—22no—
155C2×D4×C41—22no—
156C2×D4×C41—22no—
157C2×D4×C41—22no—
158C2×D4×C41—22no—
159C2×D4×C41—22no—
160C2×D4×C41—24no—
161C2×D4×C41—22no—
162C2×D4×C41—24no—
163C2×D4×C41—22no—
164C2×D4×C41—22no—
165C2×D4×C41—22no—
166C2×D4×C41—22no—
167C2×D4×C41—22no—
168C2×D4×C41—41no—
169C2×D4×C41—41no—
170C2×D4×C41—48no—
171C2×D4×C41—48no—
172C2×D4×C41—48no—
173C2×D4×C41—42no—
174C2×D4×C41—42no—
175C2×D4×C41—44no—
176C2×D4×C41—44no—
177C2×D4×C41—82no—
178C2×D4×C41—82no—
179C2×D4×C41#4114yes—
180C22×C4×C41—21no—
181C22×C4×C41—24no—
182C22×C4×C41—22no—
183C22×C4×C41—28no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—22no—
187C22×C4×C41—24no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—22no—
191C22×C4×C41—24no—
192C22×C4×C41—22no—
193C22×C4×C41—44no—
194C22×C4×C41—41no—
195C22×C4×C41—44no—
196C22×C4×C41—48no—
197C22×C4×C41—42no—
198C22×C4×C41—44no—
199C22×C4×C41—42no—
200C22×C4×C41—41no—
201C22×C4×C41—41no—
202C22×C4×C41—42no—
203C22×C4×C41—42no—
204C22×C4×C41—42no—
205C22×C4×C41C2×D412yes—
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D412yes—
209C22×C4×C41C2×D412yes—
210C4⋊C4×C41—21no—
211C4⋊C4×C41—21no—
212C4⋊C4×C41—22no—
213C4⋊C4×C41—22no—
214C4⋊C4×C41—48no—
215C22⋊C4×C41—22no—
216C22⋊C4×C41—22no—
217C22⋊C4×C41—22no—
218C22⋊C4×C41—22no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—22no—
221C22⋊C4×C41—22no—
222C22⋊C4×C41—22no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—22no—
225C22⋊C4×C41—22no—
226C22⋊C4×C41—24no—
227C22⋊C4×C41—24no—
228C22⋊C4×C41—24no—
229C22⋊C4×C41—44no—
230C22⋊C4×C41—44no—
231C22⋊C4×C41—48no—
232C22⋊C4×C41—44no—
233C22⋊C4×C41—42no—
234C22⋊C4×C41—44no—
235C42×C41—22no—
236C23×C41—21no—
237C23×C41—21no—
238C23×C41—22no—
239C23×C41—22no—
240C23×C41—21no—
241C23×C41—21no—
242C23×C41—21no—
243C23×C41—24no—
244C23×C41—24no—
245C23×C41—24no—
246C23×C41—24no—
247C23×C41—21no—
248C23×C41—21no—
249C23×C41—22no—
250C23×C41—21no—
251C23×C41—21no—
252C23×C41—24no—
253C23×C41—42no—
254C23×C41—41no—
255C23×C41—41no—
256C23×C41—42no—
257C23×C41—41no—
258C23×C41—41no—
259C23×C41—42no—
260C23×C41—42no—
261C23×C41—48no—
262C23×C41—48no—
263C23×C41—41no—
264C23×C41—41no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—48no—
268C23×C41—42no—
269C23×C41—42no—
270C23×C41—42no—
271C23×C41—42no—
272C23×C41—42no—
273C23×C41—81no—
274C23×C41—81no—
275C23×C41—84no—
276C23×C41—81no—
277C23×C41—81no—
278C23×C41#12012yes—
279C23×C41#12011yescharacteristic
280C23×C41#12011yescharacteristic
281C23×C41#12312yescomplemented
282C23×C41C22×D411yescharacteristic
283C23×C41C22×D412yes—
284C23×C41C2×#4112yes—
285C23×C41H(5,𝔽2)12yes—
286Q8×C41—42no—
287D4×C41—28no—
288D4×C41—44no—
289D4×C41—42no—
290D4×C41—44no—
291D4×C41—44no—
292D4×C41—42no—
293D4×C41—42no—
294D4×C41—44no—
295D4×C41—44no—
296D4×C41—44no—
297D4×C41—44no—
298D4×C41—82no—
299D4×C41—82no—
300D4×C41—82no—
301D4×C41—82no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—24no—
305C2×C4×C41—28no—
306C2×C4×C41—22no—
307C2×C4×C41—22no—
308C2×C4×C41—22no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—24no—
313C2×C4×C41—42no—
314C2×C4×C41—42no—
315C2×C4×C41—44no—
316C2×C4×C41—44no—
317C2×C4×C41—42no—
318C2×C4×C41—44no—
319C2×C4×C41—48no—
320C2×C4×C41—42no—
321C2×C4×C41—42no—
322C2×C4×C41—44no—
323C2×C4×C41—42no—
324C2×C4×C41—42no—
325C2×C4×C41—44no—
326C2×C4×C41—42no—
327C2×C4×C41—44no—
328C2×C4×C41—42no—
329C2×C4×C41—42no—
330C2×C4×C41—44no—
331C2×C4×C41—81no—
332C2×C4×C41—81no—
333C2×C4×C41—84no—
334C2×C4×C41#12312yescomplemented
335#24056C4111yesmaximal, characteristic, direct product factor, Sylow
336C22×C41—24no—
337C22×C41—24no—
338C22×C41—21no—
339C22×C41—21no—
340C22×C41—22no—
341C22×C41—21no—
342C22×C41—21no—
343C22×C41—22no—
344C22×C41—21no—
345C22×C41—21no—
346C22×C41—22no—
347C22×C41—22no—
348C22×C41—22no—
349C22×C41—22no—
350C22×C41—42no—
351C22×C41—42no—
352C22×C41—48no—
353C22×C41—48no—
354C22×C41—42no—
355C22×C41—42no—
356C22×C41—42no—
357C22×C41—42no—
358C22×C41—41no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—41no—
362C22×C41—42no—
363C22×C41—41no—
364C22×C41—42no—
365C22×C41—41no—
366C22×C41—81no—
367C22×C41—84no—
368C22×C41—84no—
369C22×C41—84no—
370C22×C41—81no—
371C22×C41—162no—
372C22×C41B(4,𝔽2)12yes—
373C22×C41#45812yes—
374C22×C41C2×#12011yescharacteristic
375C22×C41C2×#12311yescharacteristic
376C22×C41#53411yescharacteristic
377C22×C41#54614yes—
378C4×C41—22no—
379C4×C41—41no—
380C4×C41—42no—
381C4×C41—44no—
382C4×C41—42no—
383C4×C41—42no—
384C4×C41—84no—
385C4×C41—82no—
386#3484C2×C4111yescharacteristic
387#2849C2×C4112yescomplemented
388C2×#386C2×C4111yescharacteristic, complemented
389#2044C2×C4114yescomplemented
390#1898C2×C4112yescomplemented
391#1867C2×C4112yescomplemented
392#1790C2×C4112yescomplemented
393#1781C2×C4111yescharacteristic, complemented
394C2×C41—21no—
395C2×C41—24no—
396C2×C41—21no—
397C2×C41—22no—
398C2×C41—22no—
399C2×C41—42no—
400C2×C41—42no—
401C2×C41—81no—
402C2×C41—82no—
403C2×C41#240511yescharacteristic
404C2×C41C2×B(4,𝔽2)11yescharacteristic
405C2×C41C2×#45811yescharacteristic
406C2×H(5,𝔽2)C22×C4111yescharacteristic
407C23×D4C22×C4111yescharacteristic
408C24×C4C22×C4111yescharacteristic, complemented
409#546—22no—
410#546—22no—
411D42—22no—
412D42—22no—
413#535—21no—
414#534—21no—
415#534C22×C4112yes—
416#525—21no—
417C2×#123—22no—
418C2×#120—21no—
419C2×#120C22×C4112yes—
420#518C22×C4111yescharacteristic
421C22×C22⋊C4—21no—
422C22×C22⋊C4C22×C4111yescharacteristic, complemented
423C2×#99C22×C4112yes—
424C2×#99C22×C4114yescomplemented
425C2×#99C22×C4112yescomplemented
426#386—22no—
427#386—21no—
428#386—21no—
429#386C22×C4112yes—
430#386C22×C4114yescomplemented
431#386C22×C4112yescomplemented
432#385—22no—
433#385C22×C4114yescomplemented
434#381—22no—
435#379C22×C4112yescomplemented
436C2×#95—21no—
437#342C22×C4114yescomplemented
438C41#2405611yescharacteristic, direct product factor, Sylow
439C25D4×C4111yescharacteristic
440C25C23×C4111yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C4111yescharacteristic
454C22×D4D4×C4111yescharacteristic
455C22×D4D4×C4112yes—
456C22×D4D4×C4112yes—
457C22×D4C23×C4112yes—
458C22×D4C23×C4111yescharacteristic
459C22×D4C23×C4111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C4111yescharacteristic
467C23×C4C23×C4112yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C4112yes—
511C2×C22⋊C4D4×C4112yes—
512C2×C22⋊C4C23×C4112yes—
513C2×C22⋊C4C23×C4114yes—
514C2×C22⋊C4C23×C4112yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C4111yescharacteristic
534C24C2×D4×C4112yes—
535C24C2×D4×C4112yes—
536C24C2×D4×C4111yescharacteristic
537C24C2×D4×C4112yes—
538C24C2×D4×C4111yescharacteristic
539C24C2×D4×C4111yescharacteristic
540C24C24×C4111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C4114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C4112yes—
604C22×C4C2×D4×C4111yescharacteristic
605C22×C4C2×D4×C4111yescharacteristic
606C22×C4C2×D4×C4112yes—
607C22×C4C2×D4×C4112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C4112yes—
677C23#120×C4111yescharacteristic
678C23#120×C4111yescharacteristic
679C23#123×C4112yescomplemented
680C23C22×D4×C4111yescharacteristic
681C23C22×D4×C4112yes—
682C23C2×#41×C4112yes—
683C23H(5,𝔽2)×C4112yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C4112yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22C41×B(4,𝔽2)12yes—
770C22C41×#45812yes—
771C22C2×#120×C4111yescharacteristic
772C22C2×#123×C4111yescharacteristic
773C22C41×#53411yescharacteristic
774C22C41×#54614yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C41×#240511yescharacteristic
793C2C2×C41×B(4,𝔽2)11yescharacteristic
794C2C2×C41×#45811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
prime radicalC41×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2849C2semidirect
3. C2×C41×#386C2semidirect
4. C41×#2044C2semidirect
5. C41×#1898C2semidirect
6. C41×#1867C2semidirect
7. C41×#1790C2semidirect
8. C41×#1781C2semidirect
11. C24×C4×C41C22semidirect
25. C22×C22⋊C4×C41C22semidirect
27. C2×#99×C41C22semidirect
28. C2×#99×C41C22semidirect
33. C41×#386C22semidirect
34. C41×#386C22semidirect
36. C41×#385C22semidirect
38. C41×#379C22semidirect
40. C41×#342C22semidirect
281. C23×C41#123semidirect
334. C2×C4×C41#123semidirect
335. #24056C41direct (N × H)
387. #2849C2×C41semidirect
388. C2×#386C2×C41semidirect
389. #2044C2×C41semidirect
390. #1898C2×C41semidirect
391. #1867C2×C41semidirect
392. #1790C2×C41semidirect
393. #1781C2×C41semidirect
408. C24×C4C22×C41semidirect
422. C22×C22⋊C4C22×C41semidirect
424. C2×#99C22×C41semidirect
425. C2×#99C22×C41semidirect
430. #386C22×C41semidirect
431. #386C22×C41semidirect
433. #385C22×C41semidirect
435. #379C22×C41semidirect
437. #342C22×C41semidirect
438. C41#24056direct (N × H)
679. C23#123×C41semidirect
732. C2×C4#123×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34842
C41×#28492
C2×C41×#3862
C41×#20442
C41×#18982
C41×#18672
C41×#17902
C41×#17812
#2405641