Finite Group Databasebeta

← C41×#19012 #23795213

Subgroups — C41×#19012 #23795213

Order 10496.

844 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3531C211yesmaximal, characteristic, complemented
2C41×#3235C211yesmaximal, characteristic, complemented
3C41×#3219C211yesmaximal, characteristic, complemented
4C41×#3180C211yesmaximal, characteristic, complemented
5C41×#1664C211yesmaximal, characteristic, complemented
6C41×#1663C211yesmaximal, characteristic, complemented
7C41×#1661C211yesmaximal, characteristic, complemented
8C41×#1660C211yesmaximal, characteristic, complemented
9C41×#1658C211yesmaximal, characteristic, complemented
10C41×#1657C211yesmaximal, characteristic, complemented
11C41×#1657C211yesmaximal, characteristic, complemented
12C41×#1656C211yesmaximal, characteristic, complemented
13C41×#1535C211yesmaximal, characteristic, complemented
14C41×#1532C211yesmaximal, characteristic, complemented
15C41×#1531C211yesmaximal, characteristic, complemented
16C41×#564C2211yescharacteristic
17C41×#563—21no—
18C41×#563—21no—
19C41×#563—21no—
20C41×#563—21no—
21C41×#563C2211yescharacteristic
22C41×#563C2211yescharacteristic
23C41×#562—21no—
24C41×#562—21no—
25C41×#562C2211yescharacteristic
26C41×#533—21no—
27C41×#533—21no—
28C41×#533C2211yescharacteristic
29C41×#532C2211yescharacteristic
30C41×#529—21no—
31C41×#529—21no—
32C41×#529—21no—
33C41×#529—21no—
34C41×#529C2211yescharacteristic
35C41×#529C2211yescharacteristic
36C41×#501C2211yescharacteristic
37C41×#501C2211yescharacteristic
38C41×#501C2211yescharacteristic
39C41×#497C2211yescharacteristic
40C41×#496C2211yescharacteristic
41C41×#496C2211yescharacteristic
42C41×#491C2211yescharacteristic
43C41×#490C2211yescharacteristic
44C41×#490C2211yescharacteristic
45C41×#490C2211yescharacteristic
46C41×#490C2211yescharacteristic
47C41×#489C2211yescharacteristic
48C41×#482—21no—
49C41×#482—21no—
50C41×#476—21no—
51C41×#474—21no—
52C41×#466—21no—
53C41×#465—21no—
54C41×#464—21no—
55C41×#463—21no—
56C41×#452—21no—
57C41×#449—21no—
58C41×#442—21no—
59C41×#440—21no—
60C41×#432C2211yescharacteristic
61C41×#432C2211yescharacteristic
62C2×#97×C41C2211yescharacteristic
63C41×#330C2211yescharacteristic
64C41×#330C2211yescharacteristic
65C41×#330C2211yescharacteristic
66C41×#330C2211yescharacteristic
67C41×#330C2211yescharacteristic
68C41×#330C2211yescharacteristic
69C41×#330C2211yescharacteristic
70C41×#330C2211yescharacteristic
71C41×#329C2211yescharacteristic
72C41×#329C2211yescharacteristic
73C41×#329C2211yescharacteristic
74C41×#329C2211yescharacteristic
75C2×#41×C41—21no—
76C2×Q16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×D8×C41—21no—
81C2×D8×C41—21no—
82C22×C8×C41—21no—
83C4⋊Q8×C41—21no—
84C4⋊Q8×C41—21no—
85C4⋊Q8×C41—21no—
86C4⋊Q8×C41—21no—
87C4⋊Q8×C41D411yescharacteristic
88C4⋊Q8×C41D411yescharacteristic
89C4⋊Q8×C41C2311yescharacteristic
90#127×C41C2311yescharacteristic
91#126×C41—21no—
92#126×C41—21no—
93#126×C41—21no—
94#126×C41—21no—
95#126×C41—21no—
96#126×C41—21no—
97#126×C41—21no—
98#126×C41—21no—
99#126×C41—21no—
100#126×C41—21no—
101#125×C41—21no—
102#125×C41—21no—
103#125×C41—21no—
104#125×C41—21no—
105#125×C41—21no—
106#125×C41—21no—
107#125×C41—21no—
108#125×C41—21no—
109#125×C41C2311yescharacteristic
110#125×C41C2311yescharacteristic
111#125×C41C2311yescharacteristic
112#125×C41C2311yescharacteristic
113#124×C41—21no—
114#124×C41—21no—
115#124×C41—21no—
116#124×C41—21no—
117#124×C41—21no—
118#124×C41C2311yescharacteristic
119#124×C41C2311yescharacteristic
120#123×C41—21no—
121#123×C41—21no—
122#123×C41—21no—
123#123×C41—21no—
124#123×C41—21no—
125#123×C41—21no—
126#123×C41—21no—
127#123×C41—21no—
128#123×C41—21no—
129#123×C41—21no—
130C22⋊Q8×C41—21no—
131C22⋊Q8×C41—21no—
132C22⋊Q8×C41—21no—
133C22⋊Q8×C41—21no—
134C22⋊Q8×C41—21no—
135C22⋊Q8×C41—21no—
136C22⋊Q8×C41—21no—
137C22⋊Q8×C41—21no—
138C22⋊Q8×C41—21no—
139C22⋊Q8×C41—21no—
140C22⋊Q8×C41—21no—
141C22⋊Q8×C41—21no—
142C22⋊Q8×C41—21no—
143C22⋊Q8×C41—21no—
144C22⋊Q8×C41D411yescharacteristic
145C22⋊Q8×C41D411yescharacteristic
146#121×C41—21no—
147#121×C41—21no—
148#121×C41—21no—
149#121×C41—21no—
150#121×C41—21no—
151#121×C41—21no—
152#121×C41D411yescharacteristic
153#121×C41D411yescharacteristic
154C4×Q8×C41—21no—
155C4×Q8×C41—21no—
156C4×Q8×C41—21no—
157C4×Q8×C41—21no—
158C4×Q8×C41D411yescharacteristic
159C4×Q8×C41D411yescharacteristic
160C4×D4×C41—21no—
161C4×D4×C41—21no—
162C4×D4×C41—21no—
163C4×D4×C41—21no—
164C4×D4×C41—21no—
165C4×D4×C41—21no—
166C4×D4×C41D411yescharacteristic
167C4×D4×C41D411yescharacteristic
168#117×C41—21no—
169#117×C41—21no—
170#117×C41—21no—
171#117×C41—21no—
172#117×C41D411yescharacteristic
173#117×C41D411yescharacteristic
174C2×C42×C41—21no—
175C2×C42×C41—21no—
176C2×C42×C41C2311yescharacteristic
177#107×C41—21no—
178#107×C41—21no—
179#107×C41—21no—
180#106×C41—21no—
181#106×C41—21no—
182#106×C41—21no—
183C4⋊C8×C41—21no—
184C4⋊C8×C41—21no—
185#103×C41—21no—
186#103×C41—21no—
187#103×C41—21no—
188#102×C41—21no—
189#102×C41—21no—
190#102×C41—21no—
191#102×C41—21no—
192#102×C41—21no—
193#102×C41—21no—
194#102×C41—21no—
195#102×C41—21no—
196#102×C41—21no—
197C22⋊C8×C41—21no—
198C22⋊C8×C41—21no—
199#97×C41—21no—
200#97×C41C2311yescharacteristic
201#97×C41C2311yescharacteristic
202#97×C41C2311yescharacteristic
203#97×C41C2311yescharacteristic
204#97×C41C2311yescharacteristic
205#97×C41C2311yescharacteristic
206#41×C41—81no—
207#41×C41—81no—
208C2×Q8×C41—21no—
209C2×Q8×C41—21no—
210C2×Q8×C41—21no—
211C2×Q8×C41—21no—
212C2×Q8×C41—21no—
213C2×Q8×C41C2×D411yescharacteristic
214C2×Q8×C41C2×D411yescharacteristic
215C2×D4×C41—21no—
216C2×D4×C41—21no—
217C2×D4×C41—21no—
218C2×D4×C41—21no—
219C2×D4×C41—21no—
220C2×D4×C41—21no—
221C2×D4×C41—21no—
222C2×D4×C41—41no—
223C2×D4×C41C2×D411yescharacteristic
224C2×D4×C41C2×D411yescharacteristic
225C22×C4×C41—21no—
226C22×C4×C41—21no—
227C22×C4×C41—21no—
228C22×C4×C41—21no—
229C22×C4×C41—21no—
230C22×C4×C41—21no—
231C22×C4×C41—41no—
232C22×C4×C41C2×D411yescharacteristic
233C22×C4×C41C2×D411yescharacteristic
234C22×C4×C41C2×D411yescharacteristic
235Q16×C41—81no—
236SD16×C41—42no—
237SD16×C41—81no—
238SD16×C41—81no—
239D8×C41—42no—
240D8×C41—81no—
241C2×C8×C41—21no—
242C2×C8×C41—21no—
243C2×C8×C41—21no—
244C2×C8×C41—21no—
245C2×C8×C41—21no—
246C2×C8×C41—21no—
247C2×C8×C41—42no—
248C4⋊C4×C41—21no—
249C4⋊C4×C41—21no—
250C4⋊C4×C41—21no—
251C4⋊C4×C41—21no—
252C4⋊C4×C41—21no—
253C4⋊C4×C41—21no—
254C4⋊C4×C41—21no—
255C4⋊C4×C41—21no—
256C4⋊C4×C41—21no—
257C4⋊C4×C41—21no—
258C4⋊C4×C41—21no—
259C4⋊C4×C41—21no—
260C4⋊C4×C41—21no—
261C4⋊C4×C41—21no—
262C4⋊C4×C41—21no—
263C4⋊C4×C41—21no—
264C4⋊C4×C41—21no—
265C4⋊C4×C41—21no—
266C4⋊C4×C41—21no—
267C4⋊C4×C41—21no—
268C4⋊C4×C41—21no—
269C4⋊C4×C41—21no—
270C4⋊C4×C41—21no—
271C4⋊C4×C41—21no—
272C4⋊C4×C41—21no—
273C4⋊C4×C41—21no—
274C4⋊C4×C41—21no—
275C4⋊C4×C41—21no—
276C4⋊C4×C41C2×D411yescharacteristic
277C4⋊C4×C41C2×D411yescharacteristic
278C4⋊C4×C41C2×D411yescharacteristic
279C4⋊C4×C41C2×D411yescharacteristic
280C4⋊C4×C41C2×D411yescharacteristic
281C4⋊C4×C41C2×D411yescharacteristic
282C4⋊C4×C41C2×D411yescharacteristic
283C4⋊C4×C41C2×D411yescharacteristic
284C22⋊C4×C41—21no—
285C22⋊C4×C41—21no—
286C22⋊C4×C41—21no—
287C22⋊C4×C41—21no—
288C22⋊C4×C41—21no—
289C22⋊C4×C41—21no—
290C22⋊C4×C41—21no—
291C22⋊C4×C41—21no—
292C22⋊C4×C41—21no—
293C22⋊C4×C41—21no—
294C22⋊C4×C41—21no—
295C22⋊C4×C41—21no—
296C22⋊C4×C41—21no—
297C22⋊C4×C41—21no—
298C22⋊C4×C41—21no—
299C22⋊C4×C41—21no—
300C22⋊C4×C41—21no—
301C22⋊C4×C41—21no—
302C22⋊C4×C41—21no—
303C22⋊C4×C41—21no—
304C22⋊C4×C41—41no—
305C22⋊C4×C41—41no—
306C42×C41—21no—
307C42×C41—21no—
308C42×C41—21no—
309C42×C41—21no—
310C42×C41—21no—
311C42×C41—21no—
312C42×C41—21no—
313C42×C41—21no—
314C42×C41C2×D411yescharacteristic
315C42×C41C2×D411yescharacteristic
316C42×C41C2×D411yescharacteristic
317C42×C41C2411yescharacteristic
318C23×C41—21no—
319C23×C41—21no—
320C23×C41—41no—
321C23×C41#12011yescharacteristic
322Q8×C41—41no—
323Q8×C41—41no—
324Q8×C41—41no—
325Q8×C41—41no—
326Q8×C41—81no—
327Q8×C41—81no—
328Q8×C41—81no—
329Q8×C41—81no—
330D4×C41—41no—
331D4×C41—41no—
332D4×C41—41no—
333D4×C41—41no—
334D4×C41—41no—
335D4×C41—41no—
336D4×C41—42no—
337D4×C41—81no—
338D4×C41—81no—
339D4×C41—81no—
340D4×C41—81no—
341D4×C41—82no—
342C2×C4×C41—21no—
343C2×C4×C41—21no—
344C2×C4×C41—21no—
345C2×C4×C41—21no—
346C2×C4×C41—21no—
347C2×C4×C41—21no—
348C2×C4×C41—21no—
349C2×C4×C41—21no—
350C2×C4×C41—21no—
351C2×C4×C41—21no—
352C2×C4×C41—41no—
353C2×C4×C41—41no—
354C2×C4×C41—41no—
355C2×C4×C41—42no—
356C2×C4×C41—42no—
357C2×C4×C41—41no—
358C2×C4×C41—82no—
359C2×C4×C41—81no—
360C2×C4×C41—81no—
361C2×C4×C41—81no—
362C2×C4×C41—81no—
363C2×C4×C41#12011yescharacteristic
364C2×C4×C41#12011yescharacteristic
365C2×C4×C41#12011yescharacteristic
366C2×C4×C41C22×D411yescharacteristic
367C2×C4×C41C22×D411yescharacteristic
368C2×C4×C41C22×D411yescharacteristic
369C8×C41—22no—
370C8×C41—41no—
371C8×C41—41no—
372C8×C41—41no—
373C8×C41—41no—
374C8×C41—41no—
375#19012C4111yesmaximal, characteristic, direct product factor, Sylow
376C22×C41—21no—
377C22×C41—21no—
378C22×C41—21no—
379C22×C41—41no—
380C22×C41—41no—
381C22×C41—41no—
382C22×C41—41no—
383C22×C41—41no—
384C22×C41—41no—
385C22×C41—81no—
386C22×C41—81no—
387C22×C41—81no—
388C22×C41C2×#12011yescharacteristic
389C4×C41—21no—
390C4×C41—21no—
391C4×C41—21no—
392C4×C41—21no—
393C4×C41—21no—
394C4×C41—21no—
395C4×C41—41no—
396C4×C41—41no—
397C4×C41—41no—
398C4×C41—41no—
399C4×C41—41no—
400C4×C41—41no—
401C4×C41—41no—
402C4×C41—41no—
403C4×C41—41no—
404C4×C41—41no—
405C4×C41—81no—
406#3531C2×C4111yescharacteristic, complemented
407#3235C2×C4111yescharacteristic, complemented
408#3219C2×C4111yescharacteristic, complemented
409#3180C2×C4111yescharacteristic, complemented
410#1664C2×C4111yescharacteristic, complemented
411#1663C2×C4111yescharacteristic, complemented
412#1661C2×C4111yescharacteristic, complemented
413#1660C2×C4111yescharacteristic, complemented
414#1658C2×C4111yescharacteristic, complemented
415#1657C2×C4111yescharacteristic, complemented
416#1657C2×C4111yescharacteristic, complemented
417#1656C2×C4111yescharacteristic, complemented
418#1535C2×C4111yescharacteristic, complemented
419#1532C2×C4111yescharacteristic, complemented
420#1531C2×C4111yescharacteristic, complemented
421C2×C41—41no—
422C2×C41—81no—
423C2×C41—81no—
424C2×C41—161no—
425C2×C41#301811yescharacteristic
426C2×C41#302011yescharacteristic
427C2×C41#302111yescharacteristic
428#564C22×C4111yescharacteristic
429#563—21no—
430#563—21no—
431#563—21no—
432#563—21no—
433#563C22×C4111yescharacteristic
434#563C22×C4111yescharacteristic
435#562—21no—
436#562—21no—
437#562C22×C4111yescharacteristic
438#533—21no—
439#533—21no—
440#533C22×C4111yescharacteristic
441#532C22×C4111yescharacteristic
442#529—21no—
443#529—21no—
444#529—21no—
445#529—21no—
446#529C22×C4111yescharacteristic
447#529C22×C4111yescharacteristic
448#501C22×C4111yescharacteristic
449#501C22×C4111yescharacteristic
450#501C22×C4111yescharacteristic
451#497C22×C4111yescharacteristic
452#496C22×C4111yescharacteristic
453#496C22×C4111yescharacteristic
454#491C22×C4111yescharacteristic
455#490C22×C4111yescharacteristic
456#490C22×C4111yescharacteristic
457#490C22×C4111yescharacteristic
458#490C22×C4111yescharacteristic
459#489C22×C4111yescharacteristic
460#482—21no—
461#482—21no—
462#476—21no—
463#474—21no—
464#466—21no—
465#465—21no—
466#464—21no—
467#463—21no—
468#452—21no—
469#449—21no—
470#442—21no—
471#440—21no—
472#432C22×C4111yescharacteristic
473#432C22×C4111yescharacteristic
474C2×#97C22×C4111yescharacteristic
475#330C22×C4111yescharacteristic
476#330C22×C4111yescharacteristic
477#330C22×C4111yescharacteristic
478#330C22×C4111yescharacteristic
479#330C22×C4111yescharacteristic
480#330C22×C4111yescharacteristic
481#330C22×C4111yescharacteristic
482#330C22×C4111yescharacteristic
483#329C22×C4111yescharacteristic
484#329C22×C4111yescharacteristic
485#329C22×C4111yescharacteristic
486#329C22×C4111yescharacteristic
487C41#1901211yescharacteristic, direct product factor, Sylow
488C2×#41—21no—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—21no—
494C2×D8—21no—
495C22×C8—21no—
496C4⋊Q8—21no—
497C4⋊Q8—21no—
498C4⋊Q8—21no—
499C4⋊Q8—21no—
500C4⋊Q8D4×C4111yescharacteristic
501C4⋊Q8D4×C4111yescharacteristic
502C4⋊Q8C23×C4111yescharacteristic
503#127C23×C4111yescharacteristic
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#126—21no—
512#126—21no—
513#126—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#125C23×C4111yescharacteristic
523#125C23×C4111yescharacteristic
524#125C23×C4111yescharacteristic
525#125C23×C4111yescharacteristic
526#124—21no—
527#124—21no—
528#124—21no—
529#124—21no—
530#124—21no—
531#124C23×C4111yescharacteristic
532#124C23×C4111yescharacteristic
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8D4×C4111yescharacteristic
558C22⋊Q8D4×C4111yescharacteristic
559#121—21no—
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121D4×C4111yescharacteristic
566#121D4×C4111yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8D4×C4111yescharacteristic
572C4×Q8D4×C4111yescharacteristic
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4D4×C4111yescharacteristic
580C4×D4D4×C4111yescharacteristic
581#117—21no—
582#117—21no—
583#117—21no—
584#117—21no—
585#117D4×C4111yescharacteristic
586#117D4×C4111yescharacteristic
587C2×C42—21no—
588C2×C42—21no—
589C2×C42C23×C4111yescharacteristic
590#107—21no—
591#107—21no—
592#107—21no—
593#106—21no—
594#106—21no—
595#106—21no—
596C4⋊C8—21no—
597C4⋊C8—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#102—21no—
602#102—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608#102—21no—
609#102—21no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612#97—21no—
613#97C23×C4111yescharacteristic
614#97C23×C4111yescharacteristic
615#97C23×C4111yescharacteristic
616#97C23×C4111yescharacteristic
617#97C23×C4111yescharacteristic
618#97C23×C4111yescharacteristic
619#41—81no—
620#41—81no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8C2×D4×C4111yescharacteristic
627C2×Q8C2×D4×C4111yescharacteristic
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—41no—
636C2×D4C2×D4×C4111yescharacteristic
637C2×D4C2×D4×C4111yescharacteristic
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—41no—
645C22×C4C2×D4×C4111yescharacteristic
646C22×C4C2×D4×C4111yescharacteristic
647C22×C4C2×D4×C4111yescharacteristic
648Q16—81no—
649SD16—42no—
650SD16—81no—
651SD16—81no—
652D8—42no—
653D8—81no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C4111yescharacteristic
690C4⋊C4C2×D4×C4111yescharacteristic
691C4⋊C4C2×D4×C4111yescharacteristic
692C4⋊C4C2×D4×C4111yescharacteristic
693C4⋊C4C2×D4×C4111yescharacteristic
694C4⋊C4C2×D4×C4111yescharacteristic
695C4⋊C4C2×D4×C4111yescharacteristic
696C4⋊C4C2×D4×C4111yescharacteristic
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—41no—
718C22⋊C4—41no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C4111yescharacteristic
728C42C2×D4×C4111yescharacteristic
729C42C2×D4×C4111yescharacteristic
730C42C24×C4111yescharacteristic
731C23—21no—
732C23—21no—
733C23—41no—
734C23#120×C4111yescharacteristic
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—81no—
740Q8—81no—
741Q8—81no—
742Q8—81no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—42no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754D4—82no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—82no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4#120×C4111yescharacteristic
777C2×C4#120×C4111yescharacteristic
778C2×C4#120×C4111yescharacteristic
779C2×C4C22×D4×C4111yescharacteristic
780C2×C4C22×D4×C4111yescharacteristic
781C2×C4C22×D4×C4111yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22C2×#120×C4111yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C2—41no—
819C2—81no—
820C2—81no—
821C2—161no—
822C2C41×#301811yescharacteristic
823C2C41×#302011yescharacteristic
824C2C41×#302111yescharacteristic
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×#3531C2semidirect
2. C41×#3235C2semidirect
3. C41×#3219C2semidirect
4. C41×#3180C2semidirect
5. C41×#1664C2semidirect
6. C41×#1663C2semidirect
7. C41×#1661C2semidirect
8. C41×#1660C2semidirect
9. C41×#1658C2semidirect
10. C41×#1657C2semidirect
11. C41×#1657C2semidirect
12. C41×#1656C2semidirect
13. C41×#1535C2semidirect
14. C41×#1532C2semidirect
15. C41×#1531C2semidirect
375. #19012C41direct (N × H)
406. #3531C2×C41semidirect
407. #3235C2×C41semidirect
408. #3219C2×C41semidirect
409. #3180C2×C41semidirect
410. #1664C2×C41semidirect
411. #1663C2×C41semidirect
412. #1661C2×C41semidirect
413. #1660C2×C41semidirect
414. #1658C2×C41semidirect
415. #1657C2×C41semidirect
416. #1657C2×C41semidirect
417. #1656C2×C41semidirect
418. #1535C2×C41semidirect
419. #1532C2×C41semidirect
420. #1531C2×C41semidirect
487. C41#19012direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35312
C41×#32352
C41×#32192
C41×#31802
C41×#16642
C41×#16632
C41×#16612
C41×#16602
C41×#16582
C41×#16572
C41×#16562
C41×#15352
C41×#15322
C41×#15312
#1901241