Finite Group Databasebeta

← C41×#18708 #23794909

Subgroups — C41×#18708 #23794909

Order 10496.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3554C211yesmaximal, characteristic, complemented
2C41×#3251C211yesmaximal, characteristic, complemented
3C41×#3216C211yesmaximal, characteristic, complemented
4C41×#3169C211yesmaximal, characteristic, complemented
5C41×#1649C211yesmaximal, characteristic, complemented
6C41×#1648C211yesmaximal, characteristic, complemented
7C41×#1641C211yesmaximal, characteristic, complemented
8C41×#1640C211yesmaximal, characteristic, complemented
9C41×#1627C211yesmaximal, characteristic, complemented
10C41×#1626C211yesmaximal, characteristic, complemented
11C41×#1621C211yesmaximal, characteristic, complemented
12C41×#1620C211yesmaximal, characteristic, complemented
13C41×#1557C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1493C211yesmaximal, characteristic, complemented
16C41×#562—22no—
17C41×#559—21no—
18C41×#559C2211yescharacteristic
19C41×#557C2211yescharacteristic
20C41×#554—21no—
21C41×#550C2211yescharacteristic
22D4×Q8×C41C2211yescharacteristic
23C41×#548—21no—
24C41×#547—21no—
25C41×#542—21no—
26C41×#542—21no—
27C41×#540—21no—
28C41×#539—22no—
29C41×#536—21no—
30C41×#533C2211yescharacteristic
31C41×#532C2211yescharacteristic
32C41×#532C2211yescharacteristic
33C41×#529C2211yescharacteristic
34C41×#500C2211yescharacteristic
35C41×#497—21no—
36C41×#493C2211yescharacteristic
37C41×#489—21no—
38C41×#486C2211yescharacteristic
39C41×#486C2211yescharacteristic
40C41×#478—21no—
41C41×#475C2211yescharacteristic
42C41×#474C2211yescharacteristic
43C41×#469—21no—
44C41×#468—21no—
45C41×#466—22no—
46C41×#463—21no—
47C41×#462C2211yescharacteristic
48C41×#462C2211yescharacteristic
49C41×#460C2211yescharacteristic
50C41×#460C2211yescharacteristic
51C41×#460C2211yescharacteristic
52C41×#459C2211yescharacteristic
53C41×#452—21no—
54C41×#452—21no—
55C4×D8×C41—22no—
56C41×#432C2211yescharacteristic
57C41×#423C2211yescharacteristic
58C2×C4×C8×C41C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×#331C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×Q8⋊C8C2211yescharacteristic
66C41×Q8⋊C8C2211yescharacteristic
67C41×Q8⋊C8C2211yescharacteristic
68C41×Q8⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic
70C41×D4⋊C8C2211yescharacteristic
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C22×Q8×C41—21no—
75C2×Q16×C41—21no—
76C2×Q16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×D8×C41—22no—
81C2×D8×C41—21no—
82C2×M16×C41—21no—
83C22×C8×C41—21no—
84C4⋊Q8×C41—21no—
85C4⋊Q8×C41—21no—
86C4⋊Q8×C41D411yescharacteristic
87C4⋊Q8×C41D411yescharacteristic
88C4⋊Q8×C41C2311yescharacteristic
89C4⋊Q8×C41C2311yescharacteristic
90#127×C41—21no—
91#127×C41C2311yescharacteristic
92#127×C41C2311yescharacteristic
93#126×C41—22no—
94#126×C41—21no—
95#125×C41—22no—
96#125×C41—21no—
97#125×C41—21no—
98#125×C41D411yescharacteristic
99#124×C41—22no—
100#124×C41—22no—
101#124×C41—21no—
102#124×C41—21no—
103#124×C41—21no—
104#124×C41—21no—
105#124×C41D411yescharacteristic
106#123×C41—22no—
107#123×C41—22no—
108#123×C41—22no—
109#123×C41—22no—
110#123×C41—22no—
111#123×C41—22no—
112#123×C41—21no—
113C22⋊Q8×C41—22no—
114C22⋊Q8×C41—22no—
115C22⋊Q8×C41—22no—
116C22⋊Q8×C41—22no—
117C22⋊Q8×C41—21no—
118C22⋊Q8×C41—22no—
119C22⋊Q8×C41—21no—
120C22⋊Q8×C41D411yescharacteristic
121C22⋊Q8×C41D411yescharacteristic
122C22⋊Q8×C41D411yescharacteristic
123#121×C41—22no—
124#121×C41—22no—
125#121×C41—22no—
126#121×C41—21no—
127#121×C41—21no—
128#121×C41—21no—
129#121×C41—21no—
130#121×C41D411yescharacteristic
131#121×C41D412yes—
132C4×Q8×C41—21no—
133C4×Q8×C41—21no—
134C4×Q8×C41—21no—
135C4×Q8×C41C2311yescharacteristic
136C4×Q8×C41C2311yescharacteristic
137C4×Q8×C41C2311yescharacteristic
138C4×D4×C41—22no—
139C4×D4×C41—21no—
140C4×D4×C41—21no—
141C4×D4×C41—21no—
142C4×D4×C41—21no—
143C4×D4×C41—21no—
144C4×D4×C41—21no—
145C4×D4×C41—21no—
146C4×D4×C41—21no—
147C4×D4×C41D412yes—
148C4×D4×C41C2311yescharacteristic
149#117×C41—21no—
150#117×C41—21no—
151C2×C4⋊C4×C41—22no—
152C2×C42×C41C2311yescharacteristic
153#107×C41—22no—
154#107×C41—21no—
155#106×C41—21no—
156C4⋊C8×C41—21no—
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159C4⋊C8×C41C2311yescharacteristic
160C4⋊C8×C41C2311yescharacteristic
161#103×C41—21no—
162#103×C41—21no—
163#103×C41—21no—
164#102×C41—22no—
165#102×C41—21no—
166#102×C41—22no—
167#102×C41—21no—
168#102×C41—21no—
169#102×C41—21no—
170#102×C41—21no—
171C22⋊C8×C41—21no—
172#97×C41—21no—
173C4×C8×C41—21no—
174C4×C8×C41C2311yescharacteristic
175C4×C8×C41C2311yescharacteristic
176#41×C41—81no—
177#41×C41—81no—
178#41×C41—81no—
179#41×C41—81no—
180#41×C41—81no—
181#41×C41—81no—
182C2×Q8×C41—22no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—21no—
186C2×Q8×C41—81no—
187C2×Q8×C41—81no—
188C2×Q8×C41C2×D411yescharacteristic
189C2×Q8×C41C2×D411yescharacteristic
190C2×Q8×C41C2×D411yescharacteristic
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—21no—
194C2×D4×C41—22no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—21no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—41no—
201C2×D4×C41C2×D411yescharacteristic
202C2×D4×C41C2×D412yes—
203C22×C4×C41—22no—
204C22×C4×C41—22no—
205C22×C4×C41—22no—
206C22×C4×C41—21no—
207C22×C4×C41—22no—
208C22×C4×C41—41no—
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212Q16×C41—81no—
213Q16×C41—81no—
214SD16×C41—81no—
215SD16×C41—81no—
216SD16×C41—81no—
217D8×C41—44no—
218D8×C41—81no—
219M16×C41—81no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—42no—
227C4⋊C4×C41—22no—
228C4⋊C4×C41—22no—
229C4⋊C4×C41—22no—
230C4⋊C4×C41—22no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—21no—
239C4⋊C4×C41—21no—
240C4⋊C4×C41—21no—
241C4⋊C4×C41—21no—
242C4⋊C4×C41—21no—
243C4⋊C4×C41—21no—
244C4⋊C4×C41—21no—
245C4⋊C4×C41C2×D411yescharacteristic
246C4⋊C4×C41C2×D411yescharacteristic
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D412yes—
250C22⋊C4×C41—22no—
251C22⋊C4×C41—22no—
252C22⋊C4×C41—22no—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—21no—
256C22⋊C4×C41—21no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—21no—
261C22⋊C4×C41—22no—
262C22⋊C4×C41—22no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—41no—
265C22⋊C4×C41—41no—
266C42×C41—22no—
267C42×C41—21no—
268C42×C41—21no—
269C42×C41—21no—
270C42×C41C2×D411yescharacteristic
271C42×C41C2×D411yescharacteristic
272C42×C41C2×D411yescharacteristic
273C42×C41C2411yescharacteristic
274C23×C41—21no—
275C23×C41—22no—
276C23×C41—41no—
277C23×C41#12011yescharacteristic
278Q8×C41—21no—
279Q8×C41—21no—
280Q8×C41—21no—
281Q8×C41—21no—
282Q8×C41—21no—
283Q8×C41—21no—
284Q8×C41—41no—
285Q8×C41—41no—
286Q8×C41—41no—
287Q8×C41—41no—
288Q8×C41—81no—
289Q8×C41—82no—
290D4×C41—21no—
291D4×C41—21no—
292D4×C41—42no—
293D4×C41—42no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—41no—
298D4×C41—41no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—81no—
303D4×C41—82no—
304D4×C41—82no—
305D4×C41—82no—
306D4×C41—82no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—22no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—82no—
324C2×C4×C41—82no—
325C2×C4×C41—82no—
326C2×C4×C41—82no—
327C2×C4×C41—82no—
328C2×C4×C41#12011yescharacteristic
329C2×C4×C41#12011yescharacteristic
330C2×C4×C41#12011yescharacteristic
331C2×C4×C41C22×D411yescharacteristic
332C2×C4×C41C22×D411yescharacteristic
333C2×C4×C41C22×D411yescharacteristic
334C8×C41—22no—
335C8×C41—41no—
336C8×C41—41no—
337C8×C41—41no—
338C8×C41—41no—
339C8×C41—41no—
340#18708C4111yesmaximal, characteristic, direct product factor, Sylow
341C22×C41—21no—
342C22×C41—21no—
343C22×C41—21no—
344C22×C41—41no—
345C22×C41—42no—
346C22×C41—41no—
347C22×C41—42no—
348C22×C41—42no—
349C22×C41—41no—
350C22×C41—81no—
351C22×C41—81no—
352C22×C41—81no—
353C22×C41C2×#12011yescharacteristic
354C4×C41—21no—
355C4×C41—21no—
356C4×C41—21no—
357C4×C41—21no—
358C4×C41—41no—
359C4×C41—41no—
360C4×C41—42no—
361C4×C41—41no—
362C4×C41—41no—
363C4×C41—41no—
364C4×C41—41no—
365C4×C41—41no—
366C4×C41—81no—
367C4×C41#57611yescharacteristic
368C4×C41#57611yescharacteristic
369C4×C41#57711yescharacteristic
370C4×C41#57811yescharacteristic
371#3554C2×C4111yescharacteristic, complemented
372#3251C2×C4111yescharacteristic, complemented
373#3216C2×C4111yescharacteristic, complemented
374#3169C2×C4111yescharacteristic, complemented
375#1649C2×C4111yescharacteristic, complemented
376#1648C2×C4111yescharacteristic, complemented
377#1641C2×C4111yescharacteristic, complemented
378#1640C2×C4111yescharacteristic, complemented
379#1627C2×C4111yescharacteristic, complemented
380#1626C2×C4111yescharacteristic, complemented
381#1621C2×C4111yescharacteristic, complemented
382#1620C2×C4111yescharacteristic, complemented
383#1557C2×C4111yescharacteristic, complemented
384#1494C2×C4111yescharacteristic, complemented
385#1493C2×C4111yescharacteristic, complemented
386C2×C41—41no—
387C2×C41—81no—
388C2×C41—82no—
389C2×C41—161no—
390C2×C41#300811yescharacteristic
391C2×C41#301311yescharacteristic
392C2×C41#301811yescharacteristic
393#562—22no—
394#559—21no—
395#559C22×C4111yescharacteristic
396#557C22×C4111yescharacteristic
397#554—21no—
398#550C22×C4111yescharacteristic
399D4×Q8C22×C4111yescharacteristic
400#548—21no—
401#547—21no—
402#542—21no—
403#542—21no—
404#540—21no—
405#539—22no—
406#536—21no—
407#533C22×C4111yescharacteristic
408#532C22×C4111yescharacteristic
409#532C22×C4111yescharacteristic
410#529C22×C4111yescharacteristic
411#500C22×C4111yescharacteristic
412#497—21no—
413#493C22×C4111yescharacteristic
414#489—21no—
415#486C22×C4111yescharacteristic
416#486C22×C4111yescharacteristic
417#478—21no—
418#475C22×C4111yescharacteristic
419#474C22×C4111yescharacteristic
420#469—21no—
421#468—21no—
422#466—22no—
423#463—21no—
424#462C22×C4111yescharacteristic
425#462C22×C4111yescharacteristic
426#460C22×C4111yescharacteristic
427#460C22×C4111yescharacteristic
428#460C22×C4111yescharacteristic
429#459C22×C4111yescharacteristic
430#452—21no—
431#452—21no—
432C4×D8—22no—
433#432C22×C4111yescharacteristic
434#423C22×C4111yescharacteristic
435C2×C4×C8C22×C4111yescharacteristic
436#332C22×C4111yescharacteristic
437#332C22×C4111yescharacteristic
438#331C22×C4111yescharacteristic
439#331C22×C4111yescharacteristic
440Q8⋊C8C22×C4111yescharacteristic
441Q8⋊C8C22×C4111yescharacteristic
442Q8⋊C8C22×C4111yescharacteristic
443Q8⋊C8C22×C4111yescharacteristic
444Q8⋊C8C22×C4111yescharacteristic
445Q8⋊C8C22×C4111yescharacteristic
446D4⋊C8C22×C4111yescharacteristic
447D4⋊C8C22×C4111yescharacteristic
448C41#1870811yescharacteristic, direct product factor, Sylow
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C4111yescharacteristic
465C4⋊Q8D4×C4111yescharacteristic
466C4⋊Q8C23×C4111yescharacteristic
467C4⋊Q8C23×C4111yescharacteristic
468#127—21no—
469#127C23×C4111yescharacteristic
470#127C23×C4111yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C4111yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C4111yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C4111yescharacteristic
499C22⋊Q8D4×C4111yescharacteristic
500C22⋊Q8D4×C4111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C4111yescharacteristic
509#121D4×C4112yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C4111yescharacteristic
514C4×Q8C23×C4111yescharacteristic
515C4×Q8C23×C4111yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C4112yes—
526C4×D4C23×C4111yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C4111yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C4111yescharacteristic
536C4⋊C8C23×C4111yescharacteristic
537C4⋊C8C23×C4111yescharacteristic
538C4⋊C8C23×C4111yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C4111yescharacteristic
553C4×C8C23×C4111yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C4111yescharacteristic
567C2×Q8C2×D4×C4111yescharacteristic
568C2×Q8C2×D4×C4111yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C4111yescharacteristic
580C2×D4C2×D4×C4112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4111yescharacteristic
589C22×C4C2×D4×C4111yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C4111yescharacteristic
624C4⋊C4C2×D4×C4111yescharacteristic
625C4⋊C4C2×D4×C4111yescharacteristic
626C4⋊C4C2×D4×C4111yescharacteristic
627C4⋊C4C2×D4×C4112yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C4111yescharacteristic
649C42C2×D4×C4111yescharacteristic
650C42C2×D4×C4111yescharacteristic
651C42C24×C4111yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C4111yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C4111yescharacteristic
707C2×C4#120×C4111yescharacteristic
708C2×C4#120×C4111yescharacteristic
709C2×C4C22×D4×C4111yescharacteristic
710C2×C4C22×D4×C4111yescharacteristic
711C2×C4C22×D4×C4111yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C4111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C41×#57611yescharacteristic
745C4C41×#57611yescharacteristic
746C4C41×#57711yescharacteristic
747C4C41×#57811yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C41×#300811yescharacteristic
753C2C41×#301311yescharacteristic
754C2C41×#301811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3554C2semidirect
2. C41×#3251C2semidirect
3. C41×#3216C2semidirect
4. C41×#3169C2semidirect
5. C41×#1649C2semidirect
6. C41×#1648C2semidirect
7. C41×#1641C2semidirect
8. C41×#1640C2semidirect
9. C41×#1627C2semidirect
10. C41×#1626C2semidirect
11. C41×#1621C2semidirect
12. C41×#1620C2semidirect
13. C41×#1557C2semidirect
14. C41×#1494C2semidirect
15. C41×#1493C2semidirect
340. #18708C41direct (N × H)
371. #3554C2×C41semidirect
372. #3251C2×C41semidirect
373. #3216C2×C41semidirect
374. #3169C2×C41semidirect
375. #1649C2×C41semidirect
376. #1648C2×C41semidirect
377. #1641C2×C41semidirect
378. #1640C2×C41semidirect
379. #1627C2×C41semidirect
380. #1626C2×C41semidirect
381. #1621C2×C41semidirect
382. #1620C2×C41semidirect
383. #1557C2×C41semidirect
384. #1494C2×C41semidirect
385. #1493C2×C41semidirect
448. C41#18708direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35542
C41×#32512
C41×#32162
C41×#31692
C41×#16492
C41×#16482
C41×#16412
C41×#16402
C41×#16272
C41×#16262
C41×#16212
C41×#16202
C41×#15572
C41×#14942
C41×#14932
#1870841