Finite Group Databasebeta

← C41×#24404 #23800605

Subgroups — C41×#24404 #23800605

Order 10496.

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
1C41×#3484C211yesmaximal, characteristic, complemented
2C2×C41×B(4,𝔽2)C211yesmaximal, characteristic, complemented
3C22×#99×C41C211yesmaximal, characteristic, complemented
4C41×#2410C212yesmaximal, complemented
5C41×#2403C211yesmaximal, characteristic, complemented
6C41×#2044C212yesmaximal, complemented
7C41×#2021C212yesmaximal, complemented
8C41×#1898C212yesmaximal, complemented
9C41×#1889C211yesmaximal, characteristic, complemented
10C41×#1867C211yesmaximal, characteristic, complemented
11C41×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C41C2211yescharacteristic
13C23×D4×C41C2211yescharacteristic
14C23×D4×C41C2211yescharacteristic, complemented
15C41×#546—22no—
16C41×#546—22no—
17D42×C41—22no—
18D42×C41—22no—
19C41×#535—21no—
20C41×#534—21no—
21C41×#534C2212yes—
22C41×#525—21no—
23C2×#121×C41—22no—
24C2×#120×C41—21no—
25C2×#120×C41—21no—
26C2×#120×C41C2211yescharacteristic
27C2×#120×C41C2212yes—
28C2×#120×C41C2212yescomplemented
29C2×#120×C41C2211yescharacteristic, complemented
30C41×#518C2211yescharacteristic
31C22×C22⋊C4×C41C2212yescomplemented
32C41×B(4,𝔽2)—24no—
33C2×#99×C41—24no—
34C2×#99×C41C2211yescharacteristic
35C2×#99×C41C2211yescharacteristic
36C2×#99×C41C2212yescomplemented
37C2×#99×C41C2212yescomplemented
38C2×#99×C41C2212yescomplemented
39C41×#394—22no—
40C41×#392—21no—
41C41×#392—21no—
42C41×#392—22no—
43C41×#386—21no—
44C41×#386—22no—
45C41×#386C2211yescharacteristic
46C41×#386C2211yescharacteristic, complemented
47C41×#386C2212yescomplemented
48C41×#385C2212yescomplemented
49C41×#379C2212yescomplemented
50C41×#379C2211yescharacteristic, complemented
51C41×#342C2212yescomplemented
52C41×#342C2212yescomplemented
53C25×C41D411yescharacteristic, complemented
54C25×C41C2311yescharacteristic
55C25×C41C2311yescharacteristic
56H(5,𝔽2)×C41—22no—
57H(5,𝔽2)×C41—22no—
58H(5,𝔽2)×C41—42no—
59C2×#41×C41—21no—
60C2×#41×C41—22no—
61C22×D4×C41—21no—
62C22×D4×C41—21no—
63C22×D4×C41—22no—
64C22×D4×C41—22no—
65C22×D4×C41—22no—
66C22×D4×C41—22no—
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C22×D4×C41—22no—
70C22×D4×C41—22no—
71C22×D4×C41—21no—
72C22×D4×C41—22no—
73C22×D4×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—22no—
76C22×D4×C41—44no—
77C22×D4×C41—42no—
78C22×D4×C41D411yescharacteristic, complemented
79C22×D4×C41D411yescharacteristic, complemented
80C22×D4×C41D412yescomplemented
81C22×D4×C41D412yescomplemented
82C22×D4×C41C2312yes—
83C22×D4×C41C2311yescharacteristic
84C22×D4×C41C2311yescharacteristic
85C23×C4×C41—22no—
86C23×C4×C41D411yescharacteristic, complemented
87C23×C4×C41C2311yescharacteristic
88#127×C41—22no—
89#124×C41—22no—
90#123×C41—22no—
91#123×C41—22no—
92#123×C41—22no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95#121×C41—21no—
96#121×C41—21no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—48no—
104#120×C41—22no—
105#120×C41—22no—
106#120×C41—22no—
107#120×C41—22no—
108#120×C41—22no—
109#120×C41—22no—
110#120×C41—22no—
111#120×C41—22no—
112#120×C41—22no—
113#120×C41—22no—
114#120×C41—22no—
115#120×C41—24no—
116#120×C41—42no—
117#120×C41—42no—
118#120×C41—44no—
119C4×D4×C41—22no—
120C4×D4×C41—22no—
121C4×D4×C41—22no—
122C4×D4×C41—22no—
123#117×C41—21no—
124C2×C4⋊C4×C41—22no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41—24no—
129C2×C22⋊C4×C41—22no—
130C2×C22⋊C4×C41—21no—
131C2×C22⋊C4×C41—21no—
132C2×C22⋊C4×C41—21no—
133C2×C22⋊C4×C41—22no—
134C2×C22⋊C4×C41—21no—
135C2×C22⋊C4×C41—21no—
136C2×C22⋊C4×C41—22no—
137C2×C22⋊C4×C41—22no—
138C2×C22⋊C4×C41—21no—
139C2×C22⋊C4×C41—22no—
140C2×C22⋊C4×C41—42no—
141C2×C22⋊C4×C41D412yescomplemented
142C2×C22⋊C4×C41D412yescomplemented
143C2×C22⋊C4×C41C2312yes—
144C2×C22⋊C4×C41C2311yescharacteristic
145C2×C22⋊C4×C41C2311yescharacteristic
146C2×C22⋊C4×C41C2312yes—
147C2×C22⋊C4×C41C2312yes—
148#99×C41—22no—
149#99×C41—24no—
150#99×C41—24no—
151#99×C41—42no—
152#99×C41D414yescomplemented
153#95×C41—22no—
154#95×C41—21no—
155#95×C41—21no—
156#95×C41—22no—
157C24×C41—21no—
158C24×C41—21no—
159C24×C41—22no—
160C24×C41—21no—
161C24×C41—22no—
162C24×C41—21no—
163C24×C41—21no—
164C24×C41—21no—
165C24×C41—22no—
166C24×C41—21no—
167C24×C41—21no—
168C24×C41—22no—
169C24×C41—41no—
170C24×C41—42no—
171C24×C41—42no—
172C24×C41—42no—
173C24×C41—81no—
174C24×C41—81no—
175C24×C41—81no—
176C24×C41C2×D411yescharacteristic
177C24×C41C2×D412yes—
178C24×C41C2×D411yescharacteristic
179C24×C41C2×D412yes—
180C24×C41C2×D412yes—
181C24×C41C2×D411yescharacteristic
182C24×C41C2×D411yescharacteristic
183C24×C41C2411yescharacteristic
184#41×C41—44no—
185#41×C41—44no—
186#41×C41—42no—
187#41×C41—42no—
188C2×Q8×C41—21no—
189C2×D4×C41—22no—
190C2×D4×C41—22no—
191C2×D4×C41—22no—
192C2×D4×C41—24no—
193C2×D4×C41—21no—
194C2×D4×C41—28no—
195C2×D4×C41—22no—
196C2×D4×C41—22no—
197C2×D4×C41—22no—
198C2×D4×C41—22no—
199C2×D4×C41—22no—
200C2×D4×C41—21no—
201C2×D4×C41—22no—
202C2×D4×C41—22no—
203C2×D4×C41—22no—
204C2×D4×C41—22no—
205C2×D4×C41—21no—
206C2×D4×C41—22no—
207C2×D4×C41—22no—
208C2×D4×C41—22no—
209C2×D4×C41—22no—
210C2×D4×C41—22no—
211C2×D4×C41—22no—
212C2×D4×C41—22no—
213C2×D4×C41—22no—
214C2×D4×C41—22no—
215C2×D4×C41—41no—
216C2×D4×C41—41no—
217C2×D4×C41—42no—
218C2×D4×C41—44no—
219C2×D4×C41—44no—
220C2×D4×C41—44no—
221C2×D4×C41—44no—
222C2×D4×C41—44no—
223C2×D4×C41—44no—
224C2×D4×C41—44no—
225C2×D4×C41—44no—
226C2×D4×C41—44no—
227C2×D4×C41—42no—
228C2×D4×C41—42no—
229C2×D4×C41—44no—
230C2×D4×C41—42no—
231C2×D4×C41—41no—
232C2×D4×C41—42no—
233C2×D4×C41—41no—
234C2×D4×C41—42no—
235C2×D4×C41—44no—
236C2×D4×C41—42no—
237C2×D4×C41—42no—
238C2×D4×C41—42no—
239C2×D4×C41—44no—
240C2×D4×C41—42no—
241C2×D4×C41—82no—
242C2×D4×C41—82no—
243C2×D4×C41—81no—
244C2×D4×C41—81no—
245C2×D4×C41—82no—
246C2×D4×C41—82no—
247C2×D4×C41C2×D412yes—
248C2×D4×C41#4112yes—
249C22×C4×C41—21no—
250C22×C4×C41—22no—
251C22×C4×C41—21no—
252C22×C4×C41—21no—
253C22×C4×C41—21no—
254C22×C4×C41—22no—
255C22×C4×C41—22no—
256C22×C4×C41—21no—
257C22×C4×C41—21no—
258C22×C4×C41—22no—
259C22×C4×C41—22no—
260C22×C4×C41—21no—
261C22×C4×C41—21no—
262C22×C4×C41—42no—
263C22×C4×C41—41no—
264C22×C4×C41—44no—
265C22×C4×C41—44no—
266C22×C4×C41—82no—
267C22×C4×C41C2×D412yes—
268C22×C4×C41C2×D411yescharacteristic
269C22×C4×C41C2×D411yescharacteristic
270C22×C4×C41C2×D412yes—
271C22×C4×C41C2×D412yes—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—22no—
275C4⋊C4×C41—22no—
276C4⋊C4×C41—44no—
277C22⋊C4×C41—22no—
278C22⋊C4×C41—22no—
279C22⋊C4×C41—22no—
280C22⋊C4×C41—22no—
281C22⋊C4×C41—22no—
282C22⋊C4×C41—22no—
283C22⋊C4×C41—22no—
284C22⋊C4×C41—22no—
285C22⋊C4×C41—22no—
286C22⋊C4×C41—22no—
287C22⋊C4×C41—22no—
288C22⋊C4×C41—22no—
289C22⋊C4×C41—22no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—21no—
292C22⋊C4×C41—22no—
293C22⋊C4×C41—22no—
294C22⋊C4×C41—44no—
295C22⋊C4×C41—44no—
296C22⋊C4×C41—42no—
297C22⋊C4×C41—42no—
298C22⋊C4×C41—42no—
299C22⋊C4×C41—44no—
300C22⋊C4×C41—42no—
301C22⋊C4×C41—44no—
302C22⋊C4×C41—42no—
303C22⋊C4×C41—82no—
304C22⋊C4×C41—81no—
305C22⋊C4×C41C2×D414yescomplemented
306C42×C41—22no—
307C23×C41—21no—
308C23×C41—21no—
309C23×C41—21no—
310C23×C41—22no—
311C23×C41—22no—
312C23×C41—22no—
313C23×C41—24no—
314C23×C41—21no—
315C23×C41—21no—
316C23×C41—21no—
317C23×C41—22no—
318C23×C41—22no—
319C23×C41—24no—
320C23×C41—22no—
321C23×C41—21no—
322C23×C41—22no—
323C23×C41—21no—
324C23×C41—21no—
325C23×C41—22no—
326C23×C41—22no—
327C23×C41—41no—
328C23×C41—42no—
329C23×C41—41no—
330C23×C41—41no—
331C23×C41—41no—
332C23×C41—42no—
333C23×C41—41no—
334C23×C41—42no—
335C23×C41—42no—
336C23×C41—42no—
337C23×C41—41no—
338C23×C41—41no—
339C23×C41—41no—
340C23×C41—41no—
341C23×C41—42no—
342C23×C41—42no—
343C23×C41—41no—
344C23×C41—42no—
345C23×C41—41no—
346C23×C41—41no—
347C23×C41—42no—
348C23×C41—42no—
349C23×C41—42no—
350C23×C41—42no—
351C23×C41—41no—
352C23×C41—41no—
353C23×C41—41no—
354C23×C41—42no—
355C23×C41—42no—
356C23×C41—42no—
357C23×C41—81no—
358C23×C41—81no—
359C23×C41—82no—
360C23×C41—82no—
361C23×C41—82no—
362C23×C41—82no—
363C23×C41—84no—
364C23×C41—84no—
365C23×C41—81no—
366C23×C41—81no—
367C23×C41—84no—
368C23×C41—84no—
369C23×C41#12011yescharacteristic
370C23×C41#12012yes—
371C23×C41#12011yescharacteristic
372C23×C41#12112yescomplemented
373C23×C41C22×D411yescharacteristic
374C23×C41C22×D412yes—
375C23×C41C22×D411yescharacteristic
376C23×C41C2×#4111yescharacteristic
377C23×C41H(5,𝔽2)12yes—
378Q8×C41—42no—
379D4×C41—24no—
380D4×C41—24no—
381D4×C41—44no—
382D4×C41—42no—
383D4×C41—44no—
384D4×C41—48no—
385D4×C41—44no—
386D4×C41—44no—
387D4×C41—44no—
388D4×C41—42no—
389D4×C41—42no—
390D4×C41—42no—
391D4×C41—42no—
392D4×C41—42no—
393D4×C41—42no—
394D4×C41—44no—
395D4×C41—44no—
396D4×C41—82no—
397D4×C41—82no—
398D4×C41—82no—
399D4×C41—82no—
400D4×C41—88no—
401D4×C41—84no—
402D4×C41—84no—
403C2×C4×C41—21no—
404C2×C4×C41—21no—
405C2×C4×C41—22no—
406C2×C4×C41—24no—
407C2×C4×C41—22no—
408C2×C4×C41—22no—
409C2×C4×C41—22no—
410C2×C4×C41—21no—
411C2×C4×C41—21no—
412C2×C4×C41—21no—
413C2×C4×C41—24no—
414C2×C4×C41—22no—
415C2×C4×C41—22no—
416C2×C4×C41—42no—
417C2×C4×C41—42no—
418C2×C4×C41—44no—
419C2×C4×C41—42no—
420C2×C4×C41—42no—
421C2×C4×C41—41no—
422C2×C4×C41—42no—
423C2×C4×C41—42no—
424C2×C4×C41—41no—
425C2×C4×C41—42no—
426C2×C4×C41—42no—
427C2×C4×C41—42no—
428C2×C4×C41—41no—
429C2×C4×C41—41no—
430C2×C4×C41—42no—
431C2×C4×C41—41no—
432C2×C4×C41—41no—
433C2×C4×C41—41no—
434C2×C4×C41—41no—
435C2×C4×C41—42no—
436C2×C4×C41—81no—
437C2×C4×C41—81no—
438C2×C4×C41—88no—
439C2×C4×C41#12112yescomplemented
440#24404C4111yesmaximal, characteristic, direct product factor, Sylow
441C22×C41—21no—
442C22×C41—22no—
443C22×C41—21no—
444C22×C41—22no—
445C22×C41—21no—
446C22×C41—21no—
447C22×C41—21no—
448C22×C41—22no—
449C22×C41—22no—
450C22×C41—22no—
451C22×C41—21no—
452C22×C41—21no—
453C22×C41—22no—
454C22×C41—41no—
455C22×C41—41no—
456C22×C41—42no—
457C22×C41—44no—
458C22×C41—44no—
459C22×C41—42no—
460C22×C41—42no—
461C22×C41—42no—
462C22×C41—44no—
463C22×C41—42no—
464C22×C41—42no—
465C22×C41—42no—
466C22×C41—44no—
467C22×C41—41no—
468C22×C41—41no—
469C22×C41—42no—
470C22×C41—41no—
471C22×C41—42no—
472C22×C41—42no—
473C22×C41—41no—
474C22×C41—42no—
475C22×C41—41no—
476C22×C41—82no—
477C22×C41—81no—
478C22×C41—81no—
479C22×C41—81no—
480C22×C41—82no—
481C22×C41—84no—
482C22×C41—82no—
483C22×C41—82no—
484C22×C41—81no—
485C22×C41—82no—
486C22×C41—81no—
487C22×C41—81no—
488C22×C41—82no—
489C22×C41—84no—
490C22×C41—81no—
491C22×C41—81no—
492C22×C41—162no—
493C22×C41B(4,𝔽2)12yescomplemented
494C22×C41C2×#12011yescharacteristic
495C22×C41C2×#12111yescharacteristic
496C22×C41#53411yescharacteristic
497C22×C41D4212yes—
498C22×C41#54612yes—
499C4×C41—22no—
500C4×C41—44no—
501C4×C41—41no—
502C4×C41—42no—
503C4×C41—42no—
504C4×C41—42no—
505C4×C41—42no—
506C4×C41—82no—
507C4×C41—81no—
508C4×C41—81no—
509#3484C2×C4111yescharacteristic, complemented
510C2×B(4,𝔽2)C2×C4111yescharacteristic, complemented
511C22×#99C2×C4111yescharacteristic, complemented
512#2410C2×C4112yescomplemented
513#2403C2×C4111yescharacteristic, complemented
514#2044C2×C4112yescomplemented
515#2021C2×C4112yescomplemented
516#1898C2×C4112yescomplemented
517#1889C2×C4111yescharacteristic, complemented
518#1867C2×C4111yescharacteristic, complemented
519#1790C2×C4111yescharacteristic, complemented
520C2×C41—22no—
521C2×C41—21no—
522C2×C41—21no—
523C2×C41—22no—
524C2×C41—22no—
525C2×C41—42no—
526C2×C41—41no—
527C2×C41—42no—
528C2×C41—82no—
529C2×C41—81no—
530C2×C41—82no—
531C2×C41#241011yescharacteristic
532C2×C41C2×B(4,𝔽2)11yescharacteristic
533C2×C41#302611yescharacteristic
534C2×H(5,𝔽2)C22×C4111yescharacteristic
535C23×D4C22×C4111yescharacteristic
536C23×D4C22×C4111yescharacteristic, complemented
537#546—22no—
538#546—22no—
539D42—22no—
540D42—22no—
541#535—21no—
542#534—21no—
543#534C22×C4112yes—
544#525—21no—
545C2×#121—22no—
546C2×#120—21no—
547C2×#120—21no—
548C2×#120C22×C4111yescharacteristic
549C2×#120C22×C4112yes—
550C2×#120C22×C4112yescomplemented
551C2×#120C22×C4111yescharacteristic, complemented
552#518C22×C4111yescharacteristic
553C22×C22⋊C4C22×C4112yescomplemented
554B(4,𝔽2)—24no—
555C2×#99—24no—
556C2×#99C22×C4111yescharacteristic
557C2×#99C22×C4111yescharacteristic
558C2×#99C22×C4112yescomplemented
559C2×#99C22×C4112yescomplemented
560C2×#99C22×C4112yescomplemented
561#394—22no—
562#392—21no—
563#392—21no—
564#392—22no—
565#386—21no—
566#386—22no—
567#386C22×C4111yescharacteristic
568#386C22×C4111yescharacteristic, complemented
569#386C22×C4112yescomplemented
570#385C22×C4112yescomplemented
571#379C22×C4112yescomplemented
572#379C22×C4111yescharacteristic, complemented
573#342C22×C4112yescomplemented
574#342C22×C4112yescomplemented
575C41#2440411yescharacteristic, direct product factor, Sylow
576C25D4×C4111yescharacteristic, complemented
577C25C23×C4111yescharacteristic
578C25C23×C4111yescharacteristic
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×C4111yescharacteristic, complemented
602C22×D4D4×C4111yescharacteristic, complemented
603C22×D4D4×C4112yescomplemented
604C22×D4D4×C4112yescomplemented
605C22×D4C23×C4112yes—
606C22×D4C23×C4111yescharacteristic
607C22×D4C23×C4111yescharacteristic
608C23×C4—22no—
609C23×C4D4×C4111yescharacteristic, complemented
610C23×C4C23×C4111yescharacteristic
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×C4112yescomplemented
665C2×C22⋊C4D4×C4112yescomplemented
666C2×C22⋊C4C23×C4112yes—
667C2×C22⋊C4C23×C4111yescharacteristic
668C2×C22⋊C4C23×C4111yescharacteristic
669C2×C22⋊C4C23×C4112yes—
670C2×C22⋊C4C23×C4112yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C4114yescomplemented
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×C4111yescharacteristic
700C24C2×D4×C4112yes—
701C24C2×D4×C4111yescharacteristic
702C24C2×D4×C4112yes—
703C24C2×D4×C4112yes—
704C24C2×D4×C4111yescharacteristic
705C24C2×D4×C4111yescharacteristic
706C24C24×C4111yescharacteristic
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×C4112yes—
771C2×D4#41×C4112yes—
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×C4112yes—
791C22×C4C2×D4×C4111yescharacteristic
792C22×C4C2×D4×C4111yescharacteristic
793C22×C4C2×D4×C4112yes—
794C22×C4C2×D4×C4112yes—
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×C4114yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
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—41no—
875C23—41no—
876C23—41no—
877C23—42no—
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×C4111yescharacteristic
893C23#120×C4112yes—
894C23#120×C4111yescharacteristic
895C23#121×C4112yescomplemented
896C23C22×D4×C4111yescharacteristic
897C23C22×D4×C4112yes—
898C23C22×D4×C4111yescharacteristic
899C23C2×#41×C4111yescharacteristic
900C23H(5,𝔽2)×C4112yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
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×C4112yescomplemented
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—
1015C22C41×B(4,𝔽2)12yescomplemented
1016C22C2×#120×C4111yescharacteristic
1017C22C2×#121×C4111yescharacteristic
1018C22C41×#53411yescharacteristic
1019C22D42×C4112yes—
1020C22C41×#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—
1042C2C41×#241011yescharacteristic
1043C2C2×C41×B(4,𝔽2)11yescharacteristic
1044C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC24C24×C41
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C25×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3484C2semidirect
2. C2×C41×B(4,𝔽2)C2semidirect
3. C22×#99×C41C2semidirect
4. C41×#2410C2semidirect
5. C41×#2403C2semidirect
6. C41×#2044C2semidirect
7. C41×#2021C2semidirect
8. C41×#1898C2semidirect
9. C41×#1889C2semidirect
10. C41×#1867C2semidirect
11. C41×#1790C2semidirect
14. C23×D4×C41C22semidirect
28. C2×#120×C41C22semidirect
29. C2×#120×C41C22semidirect
31. C22×C22⋊C4×C41C22semidirect
36. C2×#99×C41C22semidirect
37. C2×#99×C41C22semidirect
38. C2×#99×C41C22semidirect
46. C41×#386C22semidirect
47. C41×#386C22semidirect
48. C41×#385C22semidirect
49. C41×#379C22semidirect
50. C41×#379C22semidirect
51. C41×#342C22semidirect
52. C41×#342C22semidirect
53. C25×C41D4semidirect
78. C22×D4×C41D4semidirect
79. C22×D4×C41D4semidirect
80. C22×D4×C41D4semidirect
81. C22×D4×C41D4semidirect
86. C23×C4×C41D4semidirect
141. C2×C22⋊C4×C41D4semidirect
142. C2×C22⋊C4×C41D4semidirect
152. #99×C41D4semidirect
305. C22⋊C4×C41C2×D4semidirect
372. C23×C41#121semidirect
439. C2×C4×C41#121semidirect
440. #24404C41direct (N × H)
493. C22×C41B(4,𝔽2)semidirect
509. #3484C2×C41semidirect
510. C2×B(4,𝔽2)C2×C41semidirect
511. C22×#99C2×C41semidirect
512. #2410C2×C41semidirect
513. #2403C2×C41semidirect
514. #2044C2×C41semidirect
515. #2021C2×C41semidirect
516. #1898C2×C41semidirect
517. #1889C2×C41semidirect
518. #1867C2×C41semidirect
519. #1790C2×C41semidirect
536. C23×D4C22×C41semidirect
550. C2×#120C22×C41semidirect
551. C2×#120C22×C41semidirect
553. C22×C22⋊C4C22×C41semidirect
558. C2×#99C22×C41semidirect
559. C2×#99C22×C41semidirect
560. C2×#99C22×C41semidirect
568. #386C22×C41semidirect
569. #386C22×C41semidirect
570. #385C22×C41semidirect
571. #379C22×C41semidirect
572. #379C22×C41semidirect
573. #342C22×C41semidirect
574. #342C22×C41semidirect
575. C41#24404direct (N × H)
576. C25D4×C41semidirect
601. C22×D4D4×C41semidirect
602. C22×D4D4×C41semidirect
603. C22×D4D4×C41semidirect
604. C22×D4D4×C41semidirect
609. C23×C4D4×C41semidirect
664. C2×C22⋊C4D4×C41semidirect
665. C2×C22⋊C4D4×C41semidirect
675. #99D4×C41semidirect
828. C22⋊C4C2×D4×C41semidirect
895. C23#121×C41semidirect
962. C2×C4#121×C41semidirect
1015. C22C41×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C41×#34842
C2×C41×B(4,𝔽2)2
C22×#99×C412
C41×#24102
C41×#24032
C41×#20442
C41×#20212
C41×#18982
C41×#18892
C41×#18672
C41×#17902
#2440441