Finite Group Databasebeta

← C41×#18418 #23794619

Subgroups — C41×#18418 #23794619

Order 10496.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3537C211yesmaximal, characteristic, complemented
2C41×#3192C211yesmaximal, characteristic, complemented
3C41×#3188C211yesmaximal, characteristic, complemented
4C41×#2656C211yesmaximal, characteristic, complemented
5C41×#1618C212yesmaximal, complemented
6C41×#1613C212yesmaximal, complemented
7C41×#1600C212yesmaximal, complemented
8C41×#1595C212yesmaximal, complemented
9C41×#1504C211yesmaximal, characteristic, complemented
10C2×C41×#327C211yesmaximal, characteristic, complemented
11C41×#1471C211yesmaximal, characteristic, complemented
12C41×#560—22no—
13C41×#553—21no—
14C41×#553—21no—
15D42×C41—22no—
16D42×C41—21no—
17D42×C41—21no—
18C41×#540—21no—
19C41×#538—21no—
20C41×#538C2212yes—
21C41×#535—21no—
22C41×#534—21no—
23C41×#534C2212yes—
24C41×#525C2211yescharacteristic
25C2×#121×C41—22no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×#121×C41C2211yescharacteristic, complemented
29C41×#484C2211yescharacteristic, complemented
30C41×#482—21no—
31C41×#481—21no—
32C41×#481C2211yescharacteristic, complemented
33C41×#481C2212yescomplemented
34C41×#469—22no—
35C41×#466—21no—
36C41×#465—21no—
37C41×#450C2211yescharacteristic, complemented
38C41×#449—21no—
39C41×#447—21no—
40C41×#447C2211yescharacteristic, complemented
41C41×#447C2212yescomplemented
42C41×#407C2211yescharacteristic, complemented
43C2×C22⋊C8×C41C2211yescharacteristic, complemented
44C41×#399—21no—
45C41×#399C2212yescomplemented
46C41×#392—21no—
47C41×#392C2212yescomplemented
48C2×#95×C41C2211yescharacteristic, complemented
49C41×#328C2212yescomplemented
50C41×#327C2212yescomplemented
51C41×#327C2212yescomplemented
52C41×#327C2212yescomplemented
53C41×#323C2212yescomplemented
54C41×#323C2212yescomplemented
55C2×#41×C41D411yescharacteristic, complemented
56C22×D4×C41—22no—
57C22×D4×C41—21no—
58C22×D4×C41—21no—
59C22×D4×C41—22no—
60C22×D4×C41—21no—
61C22×D4×C41—22no—
62C22×D4×C41D412yes—
63C22×D4×C41D411yescharacteristic
64C22×D4×C41D411yescharacteristic, complemented
65C22×D4×C41C2311yescharacteristic
66C23×C4×C41—21no—
67C23×C4×C41C2311yescharacteristic
68C2×SD16×C41—21no—
69C2×D8×C41—22no—
70C2×D8×C41—21no—
71C2×M16×C41—21no—
72C22×C8×C41—21no—
73#127×C41—22no—
74#127×C41—21no—
75#126×C41—22no—
76#126×C41—22no—
77#125×C41—21no—
78#124×C41—22no—
79#123×C41—22no—
80#123×C41—21no—
81#123×C41—22no—
82#123×C41—22no—
83#123×C41—22no—
84C22⋊Q8×C41D411yescharacteristic, complemented
85C22⋊Q8×C41C2311yescharacteristic
86#121×C41—22no—
87#121×C41—21no—
88#121×C41—21no—
89#121×C41—22no—
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—21no—
94#121×C41—21no—
95#121×C41—21no—
96#121×C41—21no—
97#121×C41—21no—
98#121×C41—21no—
99#121×C41—22no—
100#121×C41—21no—
101#121×C41—21no—
102#121×C41—21no—
103#121×C41—21no—
104#121×C41—48no—
105#121×C41D412yescomplemented
106#121×C41D411yescharacteristic, complemented
107#121×C41C2312yes—
108#121×C41C2311yescharacteristic
109#120×C41—22no—
110#120×C41—22no—
111#120×C41—22no—
112#120×C41—21no—
113#120×C41—22no—
114#120×C41—22no—
115#120×C41—22no—
116C4×D4×C41—22no—
117C4×D4×C41—21no—
118C4×D4×C41—21no—
119C4×D4×C41—21no—
120C4×D4×C41—21no—
121C4×D4×C41—22no—
122#117×C41—21no—
123#117×C41D411yescharacteristic, complemented
124C2×C4⋊C4×C41—22no—
125C2×C4⋊C4×C41D411yescharacteristic
126C2×C4⋊C4×C41D411yescharacteristic, complemented
127C2×C4⋊C4×C41C2311yescharacteristic
128C2×C22⋊C4×C41—21no—
129C2×C22⋊C4×C41—22no—
130C2×C22⋊C4×C41—22no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41C2312yes—
133#107×C41—21no—
134#106×C41—21no—
135#106×C41—22no—
136#103×C41—21no—
137#102×C41—22no—
138#102×C41—21no—
139#102×C41—21no—
140#102×C41—22no—
141#102×C41—21no—
142C22⋊C8×C41—21no—
143C22⋊C8×C41—21no—
144C22⋊C8×C41C2311yescharacteristic
145C22⋊C8×C41C2311yescharacteristic
146C22⋊C8×C41C2312yes—
147#95×C41—21no—
148#95×C41C2312yes—
149C24×C41—22no—
150C24×C41—21no—
151C24×C41—21no—
152C24×C41C2×D411yescharacteristic
153C24×C41C2×D412yes—
154#41×C41—81no—
155C2×Q8×C41C2×D411yescharacteristic
156C2×D4×C41—22no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—22no—
160C2×D4×C41—22no—
161C2×D4×C41—22no—
162C2×D4×C41—22no—
163C2×D4×C41—22no—
164C2×D4×C41—22no—
165C2×D4×C41—21no—
166C2×D4×C41—22no—
167C2×D4×C41—22no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—44no—
174C2×D4×C41—44no—
175C2×D4×C41—44no—
176C2×D4×C41—41no—
177C2×D4×C41—41no—
178C2×D4×C41—81no—
179C2×D4×C41—81no—
180C2×D4×C41—82no—
181C2×D4×C41—81no—
182C2×D4×C41—82no—
183C2×D4×C41—82no—
184C2×D4×C41—81no—
185C2×D4×C41—81no—
186C2×D4×C41—82no—
187C2×D4×C41—82no—
188C2×D4×C41—84no—
189C2×D4×C41C2×D411yescharacteristic
190C2×D4×C41C2×D412yes—
191C22×C4×C41—22no—
192C22×C4×C41—22no—
193C22×C4×C41—22no—
194C22×C4×C41—24no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—81no—
199C22×C4×C41—81no—
200C22×C4×C41—81no—
201C22×C4×C41C2×D412yes—
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2×D411yescharacteristic
204C22×C4×C41C2×D411yescharacteristic
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2411yescharacteristic
208SD16×C41—81no—
209D8×C41—81no—
210D8×C41—82no—
211M16×C41—81no—
212C2×C8×C41—21no—
213C2×C8×C41—22no—
214C2×C8×C41—21no—
215C2×C8×C41—81no—
216C4⋊C4×C41—22no—
217C4⋊C4×C41—22no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—21no—
220C4⋊C4×C41—21no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—44no—
226C4⋊C4×C41C2×D412yes—
227C4⋊C4×C41C2×D411yescharacteristic
228C4⋊C4×C41C2×D411yescharacteristic
229C22⋊C4×C41—22no—
230C22⋊C4×C41—22no—
231C22⋊C4×C41—22no—
232C22⋊C4×C41—22no—
233C22⋊C4×C41—22no—
234C22⋊C4×C41—21no—
235C22⋊C4×C41—21no—
236C22⋊C4×C41—21no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—21no—
239C22⋊C4×C41—22no—
240C22⋊C4×C41—22no—
241C22⋊C4×C41—22no—
242C22⋊C4×C41—21no—
243C22⋊C4×C41—44no—
244C22⋊C4×C41—44no—
245C22⋊C4×C41—41no—
246C22⋊C4×C41—41no—
247C42×C41—22no—
248C42×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—22no—
252C23×C41—22no—
253C23×C41—22no—
254C23×C41—21no—
255C23×C41—22no—
256C23×C41—22no—
257C23×C41—41no—
258C23×C41—42no—
259C23×C41—42no—
260C23×C41—42no—
261C23×C41—42no—
262C23×C41—42no—
263C23×C41—41no—
264C23×C41—41no—
265C23×C41—41no—
266C23×C41—81no—
267C23×C41—81no—
268C23×C41—82no—
269C23×C41—82no—
270C23×C41—82no—
271C23×C41#12011yescharacteristic
272C23×C41#12011yescharacteristic
273C23×C41C22×D411yescharacteristic
274Q8×C41—41no—
275D4×C41—42no—
276D4×C41—41no—
277D4×C41—42no—
278D4×C41—42no—
279D4×C41—42no—
280D4×C41—41no—
281D4×C41—41no—
282D4×C41—42no—
283D4×C41—41no—
284D4×C41—42no—
285D4×C41—41no—
286D4×C41—44no—
287D4×C41—42no—
288D4×C41—81no—
289D4×C41—82no—
290D4×C41—82no—
291D4×C41—81no—
292D4×C41—82no—
293D4×C41—82no—
294D4×C41—82no—
295D4×C41—82no—
296D4×C41—82no—
297D4×C41—88no—
298D4×C41—82no—
299D4×C41—82no—
300C2×C4×C41—24no—
301C2×C4×C41—21no—
302C2×C4×C41—22no—
303C2×C4×C41—22no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—41no—
312C2×C4×C41—42no—
313C2×C4×C41—42no—
314C2×C4×C41—42no—
315C2×C4×C41—42no—
316C2×C4×C41—42no—
317C2×C4×C41—41no—
318C2×C4×C41—81no—
319C2×C4×C41—84no—
320C2×C4×C41—82no—
321C2×C4×C41—82no—
322C2×C4×C41#12011yescharacteristic
323C2×C4×C41#12011yescharacteristic
324C2×C4×C41C22×D411yescharacteristic
325C2×C4×C41C22×D411yescharacteristic
326C8×C41—41no—
327C8×C41—41no—
328C8×C41—42no—
329#18418C4111yesmaximal, characteristic, direct product factor, Sylow
330C22×C41—21no—
331C22×C41—21no—
332C22×C41—21no—
333C22×C41—21no—
334C22×C41—21no—
335C22×C41—21no—
336C22×C41—21no—
337C22×C41—42no—
338C22×C41—42no—
339C22×C41—42no—
340C22×C41—42no—
341C22×C41—41no—
342C22×C41—42no—
343C22×C41—42no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—42no—
348C22×C41—82no—
349C22×C41—82no—
350C22×C41—82no—
351C22×C41—82no—
352C22×C41—81no—
353C22×C41—81no—
354C22×C41—81no—
355C22×C41—162no—
356C22×C41—164no—
357C22×C41#45312yes—
358C22×C41C2×#12011yescharacteristic
359C22×C41#57611yescharacteristic
360C22×C41#57711yescharacteristic
361C4×C41—21no—
362C4×C41—21no—
363C4×C41—21no—
364C4×C41—21no—
365C4×C41—44no—
366C4×C41—42no—
367C4×C41—41no—
368C4×C41—42no—
369C4×C41—41no—
370C4×C41—41no—
371C4×C41—81no—
372#3537C2×C4111yescharacteristic, complemented
373#3192C2×C4111yescharacteristic, complemented
374#3188C2×C4111yescharacteristic, complemented
375#2656C2×C4111yescharacteristic, complemented
376#1618C2×C4112yescomplemented
377#1613C2×C4112yescomplemented
378#1600C2×C4112yescomplemented
379#1595C2×C4112yescomplemented
380#1504C2×C4111yescharacteristic, complemented
381C2×#327C2×C4111yescharacteristic, complemented
382#1471C2×C4111yescharacteristic, complemented
383C2×C41—21no—
384C2×C41—21no—
385C2×C41—22no—
386C2×C41—41no—
387C2×C41—82no—
388C2×C41—82no—
389C2×C41—81no—
390C2×C41—161no—
391C2×C41#301211yescharacteristic
392C2×C41C2×#45311yescharacteristic
393C2×C41#302611yescharacteristic
394#560—22no—
395#553—21no—
396#553—21no—
397D42—22no—
398D42—21no—
399D42—21no—
400#540—21no—
401#538—21no—
402#538C22×C4112yes—
403#535—21no—
404#534—21no—
405#534C22×C4112yes—
406#525C22×C4111yescharacteristic
407C2×#121—22no—
408C2×#121C22×C4111yescharacteristic
409C2×#121C22×C4111yescharacteristic
410C2×#121C22×C4111yescharacteristic, complemented
411#484C22×C4111yescharacteristic, complemented
412#482—21no—
413#481—21no—
414#481C22×C4111yescharacteristic, complemented
415#481C22×C4112yescomplemented
416#469—22no—
417#466—21no—
418#465—21no—
419#450C22×C4111yescharacteristic, complemented
420#449—21no—
421#447—21no—
422#447C22×C4111yescharacteristic, complemented
423#447C22×C4112yescomplemented
424#407C22×C4111yescharacteristic, complemented
425C2×C22⋊C8C22×C4111yescharacteristic, complemented
426#399—21no—
427#399C22×C4112yescomplemented
428#392—21no—
429#392C22×C4112yescomplemented
430C2×#95C22×C4111yescharacteristic, complemented
431#328C22×C4112yescomplemented
432#327C22×C4112yescomplemented
433#327C22×C4112yescomplemented
434#327C22×C4112yescomplemented
435#323C22×C4112yescomplemented
436#323C22×C4112yescomplemented
437C41#1841811yescharacteristic, direct product factor, Sylow
438C2×#41D4×C4111yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C4112yes—
446C22×D4D4×C4111yescharacteristic
447C22×D4D4×C4111yescharacteristic, complemented
448C22×D4C23×C4111yescharacteristic
449C23×C4—21no—
450C23×C4C23×C4111yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C4111yescharacteristic, complemented
468C22⋊Q8C23×C4111yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C4112yescomplemented
489#121D4×C4111yescharacteristic, complemented
490#121C23×C4112yes—
491#121C23×C4111yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C4111yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C4111yescharacteristic
509C2×C4⋊C4D4×C4111yescharacteristic, complemented
510C2×C4⋊C4C23×C4111yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C4112yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C4111yescharacteristic
528C22⋊C8C23×C4111yescharacteristic
529C22⋊C8C23×C4112yes—
530#95—21no—
531#95C23×C4112yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C4111yescharacteristic
536C24C2×D4×C4112yes—
537#41—81no—
538C2×Q8C2×D4×C4111yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C4111yescharacteristic
573C2×D4C2×D4×C4112yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C4112yes—
585C22×C4C2×D4×C4111yescharacteristic
586C22×C4C2×D4×C4111yescharacteristic
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4111yescharacteristic
589C22×C4C2×D4×C4111yescharacteristic
590C22×C4C24×C4111yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C4112yes—
610C4⋊C4C2×D4×C4111yescharacteristic
611C4⋊C4C2×D4×C4111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C4111yescharacteristic
655C23#120×C4111yescharacteristic
656C23C22×D4×C4111yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—42no—
666D4—41no—
667D4—42no—
668D4—41no—
669D4—44no—
670D4—42no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C4111yescharacteristic
706C2×C4#120×C4111yescharacteristic
707C2×C4C22×D4×C4111yescharacteristic
708C2×C4C22×D4×C4111yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22C41×#45312yes—
740C22C2×#120×C4111yescharacteristic
741C22C41×#57611yescharacteristic
742C22C41×#57711yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C41×#301211yescharacteristic
763C2C2×C41×#45311yescharacteristic
764C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3537C2semidirect
2. C41×#3192C2semidirect
3. C41×#3188C2semidirect
4. C41×#2656C2semidirect
5. C41×#1618C2semidirect
6. C41×#1613C2semidirect
7. C41×#1600C2semidirect
8. C41×#1595C2semidirect
9. C41×#1504C2semidirect
10. C2×C41×#327C2semidirect
11. C41×#1471C2semidirect
28. C2×#121×C41C22semidirect
29. C41×#484C22semidirect
32. C41×#481C22semidirect
33. C41×#481C22semidirect
37. C41×#450C22semidirect
40. C41×#447C22semidirect
41. C41×#447C22semidirect
42. C41×#407C22semidirect
43. C2×C22⋊C8×C41C22semidirect
45. C41×#399C22semidirect
47. C41×#392C22semidirect
48. C2×#95×C41C22semidirect
49. C41×#328C22semidirect
50. C41×#327C22semidirect
51. C41×#327C22semidirect
52. C41×#327C22semidirect
53. C41×#323C22semidirect
54. C41×#323C22semidirect
55. C2×#41×C41D4semidirect
64. C22×D4×C41D4semidirect
84. C22⋊Q8×C41D4semidirect
105. #121×C41D4semidirect
106. #121×C41D4semidirect
123. #117×C41D4semidirect
126. C2×C4⋊C4×C41D4semidirect
329. #18418C41direct (N × H)
372. #3537C2×C41semidirect
373. #3192C2×C41semidirect
374. #3188C2×C41semidirect
375. #2656C2×C41semidirect
376. #1618C2×C41semidirect
377. #1613C2×C41semidirect
378. #1600C2×C41semidirect
379. #1595C2×C41semidirect
380. #1504C2×C41semidirect
381. C2×#327C2×C41semidirect
382. #1471C2×C41semidirect
410. C2×#121C22×C41semidirect
411. #484C22×C41semidirect
414. #481C22×C41semidirect
415. #481C22×C41semidirect
419. #450C22×C41semidirect
422. #447C22×C41semidirect
423. #447C22×C41semidirect
424. #407C22×C41semidirect
425. C2×C22⋊C8C22×C41semidirect
427. #399C22×C41semidirect
429. #392C22×C41semidirect
430. C2×#95C22×C41semidirect
431. #328C22×C41semidirect
432. #327C22×C41semidirect
433. #327C22×C41semidirect
434. #327C22×C41semidirect
435. #323C22×C41semidirect
436. #323C22×C41semidirect
437. C41#18418direct (N × H)
438. C2×#41D4×C41semidirect
447. C22×D4D4×C41semidirect
467. C22⋊Q8D4×C41semidirect
488. #121D4×C41semidirect
489. #121D4×C41semidirect
506. #117D4×C41semidirect
509. C2×C4⋊C4D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#35372
C41×#31922
C41×#31882
C41×#26562
C41×#16182
C41×#16132
C41×#16002
C41×#15952
C41×#15042
C2×C41×#3272
C41×#14712
#1841841