Finite Group Databasebeta

← C41×#19055 #23795256

Subgroups — C41×#19055 #23795256

Order 10496.

898 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3545C211yesmaximal, characteristic
2C41×#3239C211yesmaximal, characteristic, complemented
3C41×#3218C211yesmaximal, characteristic, complemented
4C2×C41×#489C211yesmaximal, characteristic, complemented
5C41×#1664C212yesmaximal, complemented
6C41×#1662C212yesmaximal, complemented
7C41×#1661C212yesmaximal, complemented
8C41×#1659C212yesmaximal, complemented
9C41×#1533C211yesmaximal, characteristic, complemented
10C41×#1532C211yesmaximal, characteristic, complemented
11C41×#1532C211yesmaximal, characteristic, complemented
12C41×#563C2211yescharacteristic
13C41×#562C2211yescharacteristic
14C41×#562C2211yescharacteristic
15C41×H(3,𝔽4)C2211yescharacteristic
16C41×#555—21no—
17C41×#551—21no—
18C41×#551—21no—
19C41×#551—21no—
20C41×#546—21no—
21C41×#546—21no—
22C41×#542—21no—
23C41×#542—21no—
24C41×#538—21no—
25C41×#538—21no—
26C41×#536—21no—
27C41×#534—21no—
28C2×C4⋊Q8×C41C2211yescharacteristic, complemented
29C41×#529C2211yescharacteristic
30C41×#529C2211yescharacteristic
31C2×#124×C41C2211yescharacteristic
32C41×#501C2212yescomplemented
33C41×#497C2212yescomplemented
34C41×#491C2212yescomplemented
35C41×#489—21no—
36C41×#489—21no—
37C41×#489C2212yes—
38C41×#489C2212yescomplemented
39C41×#489C2212yescomplemented
40C41×#484—21no—
41C41×#481—21no—
42C41×#475—21no—
43C41×#474—21no—
44C41×#462—21no—
45C41×#461—21no—
46C41×#451—21no—
47C41×#448—21no—
48C41×#432C2211yescharacteristic, complemented
49C41×#432C2211yescharacteristic, complemented
50C2×#103×C41—21no—
51C2×#102×C41—21no—
52C2×#97×C41C2211yescharacteristic, complemented
53C41×#330C2212yescomplemented
54C41×#330C2212yescomplemented
55C41×#329C2212yes—
56C41×#329C2212yescomplemented
57C41×#329C2212yescomplemented
58C41×#329C2212yescomplemented
59C2×#41×C41—21no—
60C22×Q8×C41—21no—
61C22×Q8×C41D411yescharacteristic
62C22×D4×C41—21no—
63C22×D4×C41D411yescharacteristic
64C2×Q16×C41—22no—
65C2×SD16×C41—22no—
66C22×C8×C41—21no—
67C4⋊Q8×C41—21no—
68C4⋊Q8×C41—21no—
69C4⋊Q8×C41—21no—
70C4⋊Q8×C41—21no—
71C4⋊Q8×C41—21no—
72C4⋊Q8×C41C2312yes—
73#126×C41—21no—
74#126×C41—21no—
75#126×C41—21no—
76#126×C41—21no—
77#126×C41—21no—
78#126×C41—21no—
79#125×C41C2311yescharacteristic
80#125×C41C2311yescharacteristic
81#124×C41—21no—
82#124×C41—21no—
83#124×C41—21no—
84#124×C41—21no—
85#124×C41—21no—
86#124×C41—21no—
87#124×C41—21no—
88#124×C41—21no—
89#124×C41D411yescharacteristic
90#124×C41D411yescharacteristic
91#124×C41C2311yescharacteristic
92#124×C41C2311yescharacteristic
93#124×C41C2311yescharacteristic
94#124×C41C2311yescharacteristic
95#123×C41—21no—
96#123×C41—21no—
97#123×C41—21no—
98#123×C41—21no—
99#123×C41—21no—
100#123×C41—21no—
101#123×C41—21no—
102#123×C41—21no—
103#123×C41—21no—
104#123×C41—21no—
105#123×C41—21no—
106#123×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41—21no—
109C22⋊Q8×C41—21no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41—21no—
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41—21no—
114C22⋊Q8×C41—21no—
115C22⋊Q8×C41D411yescharacteristic
116C22⋊Q8×C41D411yescharacteristic
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41—21no—
123#121×C41—21no—
124#121×C41—21no—
125#121×C41D411yescharacteristic
126#121×C41D411yescharacteristic
127#120×C41—21no—
128#120×C41—21no—
129#120×C41—21no—
130#120×C41—21no—
131#120×C41—21no—
132#120×C41—21no—
133C4×Q8×C41D411yescharacteristic
134C4×Q8×C41D411yescharacteristic
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41—21no—
141C4×D4×C41D411yescharacteristic
142C4×D4×C41D411yescharacteristic
143#117×C41—21no—
144#117×C41—21no—
145#117×C41—21no—
146#117×C41—21no—
147#117×C41—21no—
148C2×C4⋊C4×C41—21no—
149C2×C4⋊C4×C41—21no—
150C2×C22⋊C4×C41—21no—
151C2×C22⋊C4×C41—21no—
152C2×C22⋊C4×C41—21no—
153C2×C22⋊C4×C41—21no—
154C2×C22⋊C4×C41—21no—
155C2×C42×C41C2311yescharacteristic
156#107×C41—22no—
157#106×C41—22no—
158C4⋊C8×C41—21no—
159C4⋊C8×C41—21no—
160#103×C41—22no—
161#103×C41—22no—
162#103×C41—22no—
163#103×C41—22no—
164#103×C41—22no—
165#102×C41—22no—
166#102×C41—22no—
167#102×C41—22no—
168C22⋊C8×C41—21no—
169C22⋊C8×C41—21no—
170#97×C41—21no—
171#97×C41C2312yes—
172#97×C41C2312yes—
173#97×C41C2312yes—
174C24×C41—21no—
175C24×C41—21no—
176#41×C41—82no—
177C2×Q8×C41—21no—
178C2×Q8×C41—21no—
179C2×Q8×C41—22no—
180C2×Q8×C41—42no—
181C2×Q8×C41—41no—
182C2×Q8×C41—82no—
183C2×Q8×C41C2×D411yescharacteristic
184C2×Q8×C41C2×D411yescharacteristic
185C2×Q8×C41C2×D411yescharacteristic
186C2×Q8×C41C2×D411yescharacteristic
187C2×D4×C41—21no—
188C2×D4×C41—21no—
189C2×D4×C41—21no—
190C2×D4×C41—21no—
191C2×D4×C41—21no—
192C2×D4×C41—21no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—42no—
198C2×D4×C41—82no—
199C2×D4×C41C2×D411yescharacteristic
200C2×D4×C41C2×D411yescharacteristic
201C2×D4×C41C2×D411yescharacteristic
202C2×D4×C41C2×D411yescharacteristic
203C22×C4×C41—21no—
204C22×C4×C41—21no—
205C22×C4×C41—21no—
206C22×C4×C41—21no—
207C22×C4×C41—21no—
208C22×C4×C41—21no—
209C22×C4×C41—21no—
210C22×C4×C41—21no—
211C22×C4×C41—41no—
212C22×C4×C41C2×D411yescharacteristic
213C22×C4×C41C2×D411yescharacteristic
214C22×C4×C41C2×D411yescharacteristic
215Q16×C41—82no—
216SD16×C41—82no—
217C2×C8×C41—22no—
218C2×C8×C41—22no—
219C2×C8×C41—22no—
220C2×C8×C41—42no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—41no—
238C4⋊C4×C41—41no—
239C4⋊C4×C41C2×D411yescharacteristic
240C4⋊C4×C41C2×D411yescharacteristic
241C4⋊C4×C41C2×D411yescharacteristic
242C4⋊C4×C41C2×D411yescharacteristic
243C22⋊C4×C41—21no—
244C22⋊C4×C41—21no—
245C22⋊C4×C41—21no—
246C22⋊C4×C41—21no—
247C22⋊C4×C41—21no—
248C22⋊C4×C41—21no—
249C22⋊C4×C41—21no—
250C22⋊C4×C41—21no—
251C22⋊C4×C41—21no—
252C22⋊C4×C41—21no—
253C22⋊C4×C41—21no—
254C22⋊C4×C41—21no—
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—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—21no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—21no—
267C22⋊C4×C41—21no—
268C22⋊C4×C41—21no—
269C22⋊C4×C41—21no—
270C22⋊C4×C41—21no—
271C42×C41—21no—
272C42×C41—21no—
273C42×C41—21no—
274C42×C41—21no—
275C42×C41C2×D411yescharacteristic
276C42×C41C2×D411yescharacteristic
277C42×C41C2×D411yescharacteristic
278C42×C41C2411yescharacteristic
279C23×C41—21no—
280C23×C41—21no—
281C23×C41—21no—
282C23×C41—21no—
283C23×C41—42no—
284C23×C41—81no—
285C23×C41—81no—
286C23×C41—81no—
287C23×C41—81no—
288C23×C41—81no—
289C23×C41#12011yescharacteristic
290Q8×C41—41no—
291Q8×C41—41no—
292Q8×C41—41no—
293Q8×C41—41no—
294Q8×C41—42no—
295Q8×C41—42no—
296Q8×C41—81no—
297Q8×C41—82no—
298Q8×C41—81no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—42no—
304D4×C41—42no—
305D4×C41—81no—
306D4×C41—81no—
307D4×C41—81no—
308D4×C41—81no—
309D4×C41—81no—
310D4×C41—81no—
311D4×C41—81no—
312D4×C41—81no—
313C2×C4×C41—22no—
314C2×C4×C41—21no—
315C2×C4×C41—21no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—21no—
319C2×C4×C41—21no—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—42no—
325C2×C4×C41—42no—
326C2×C4×C41—81no—
327C2×C4×C41—81no—
328C2×C4×C41—81no—
329C2×C4×C41—81no—
330C2×C4×C41—81no—
331C2×C4×C41—81no—
332C2×C4×C41—81no—
333C2×C4×C41—82no—
334C2×C4×C41#12011yescharacteristic
335C2×C4×C41#12011yescharacteristic
336C2×C4×C41#12011yescharacteristic
337C2×C4×C41C22×D411yescharacteristic
338C2×C4×C41C22×D411yescharacteristic
339C2×C4×C41C22×D411yescharacteristic
340C8×C41—42no—
341C8×C41—42no—
342C8×C41—42no—
343#19055C4111yesmaximal, characteristic, direct product factor, Sylow
344C22×C41—21no—
345C22×C41—21no—
346C22×C41—41no—
347C22×C41—41no—
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—162no—
359C22×C41—162no—
360C22×C41#45512yes—
361C22×C41C2×#12011yescharacteristic
362C4×C41—21no—
363C4×C41—21no—
364C4×C41—21no—
365C4×C41—21no—
366C4×C41—21no—
367C4×C41—21no—
368C4×C41—41no—
369C4×C41—41no—
370C4×C41—41no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—41no—
375C4×C41—41no—
376C4×C41—82no—
377#3545C2×C4111yescharacteristic
378#3239C2×C4111yescharacteristic, complemented
379#3218C2×C4111yescharacteristic, complemented
380C2×#489C2×C4111yescharacteristic, complemented
381#1664C2×C4112yescomplemented
382#1662C2×C4112yescomplemented
383#1661C2×C4112yescomplemented
384#1659C2×C4112yescomplemented
385#1533C2×C4111yescharacteristic, complemented
386#1532C2×C4111yescharacteristic, complemented
387#1532C2×C4111yescharacteristic, complemented
388C2×C41—22no—
389C2×C41—81no—
390C2×C41—81no—
391C2×C41—81no—
392C2×C41—81no—
393C2×C41C2×#45511yescharacteristic
394C2×C41#302111yescharacteristic
395C2×C41#302211yescharacteristic
396#563C22×C4111yescharacteristic
397#562C22×C4111yescharacteristic
398#562C22×C4111yescharacteristic
399H(3,𝔽4)C22×C4111yescharacteristic
400#555—21no—
401#551—21no—
402#551—21no—
403#551—21no—
404#546—21no—
405#546—21no—
406#542—21no—
407#542—21no—
408#538—21no—
409#538—21no—
410#536—21no—
411#534—21no—
412C2×C4⋊Q8C22×C4111yescharacteristic, complemented
413#529C22×C4111yescharacteristic
414#529C22×C4111yescharacteristic
415C2×#124C22×C4111yescharacteristic
416#501C22×C4112yescomplemented
417#497C22×C4112yescomplemented
418#491C22×C4112yescomplemented
419#489—21no—
420#489—21no—
421#489C22×C4112yes—
422#489C22×C4112yescomplemented
423#489C22×C4112yescomplemented
424#484—21no—
425#481—21no—
426#475—21no—
427#474—21no—
428#462—21no—
429#461—21no—
430#451—21no—
431#448—21no—
432#432C22×C4111yescharacteristic, complemented
433#432C22×C4111yescharacteristic, complemented
434C2×#103—21no—
435C2×#102—21no—
436C2×#97C22×C4111yescharacteristic, complemented
437#330C22×C4112yescomplemented
438#330C22×C4112yescomplemented
439#329C22×C4112yes—
440#329C22×C4112yescomplemented
441#329C22×C4112yescomplemented
442#329C22×C4112yescomplemented
443C41#1905511yescharacteristic, direct product factor, Sylow
444C2×#41—21no—
445C22×Q8—21no—
446C22×Q8D4×C4111yescharacteristic
447C22×D4—21no—
448C22×D4D4×C4111yescharacteristic
449C2×Q16—22no—
450C2×SD16—22no—
451C22×C8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—21no—
457C4⋊Q8C23×C4112yes—
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#125C23×C4111yescharacteristic
465#125C23×C4111yescharacteristic
466#124—21no—
467#124—21no—
468#124—21no—
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124—21no—
474#124D4×C4111yescharacteristic
475#124D4×C4111yescharacteristic
476#124C23×C4111yescharacteristic
477#124C23×C4111yescharacteristic
478#124C23×C4111yescharacteristic
479#124C23×C4111yescharacteristic
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C4111yescharacteristic
501C22⋊Q8D4×C4111yescharacteristic
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C4111yescharacteristic
511#121D4×C4111yescharacteristic
512#120—21no—
513#120—21no—
514#120—21no—
515#120—21no—
516#120—21no—
517#120—21no—
518C4×Q8D4×C4111yescharacteristic
519C4×Q8D4×C4111yescharacteristic
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4D4×C4111yescharacteristic
527C4×D4D4×C4111yescharacteristic
528#117—21no—
529#117—21no—
530#117—21no—
531#117—21no—
532#117—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C42C23×C4111yescharacteristic
541#107—22no—
542#106—22no—
543C4⋊C8—21no—
544C4⋊C8—21no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555#97—21no—
556#97C23×C4112yes—
557#97C23×C4112yes—
558#97C23×C4112yes—
559C24—21no—
560C24—21no—
561#41—82no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—42no—
566C2×Q8—41no—
567C2×Q8—82no—
568C2×Q8C2×D4×C4111yescharacteristic
569C2×Q8C2×D4×C4111yescharacteristic
570C2×Q8C2×D4×C4111yescharacteristic
571C2×Q8C2×D4×C4111yescharacteristic
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—82no—
584C2×D4C2×D4×C4111yescharacteristic
585C2×D4C2×D4×C4111yescharacteristic
586C2×D4C2×D4×C4111yescharacteristic
587C2×D4C2×D4×C4111yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—41no—
597C22×C4C2×D4×C4111yescharacteristic
598C22×C4C2×D4×C4111yescharacteristic
599C22×C4C2×D4×C4111yescharacteristic
600Q16—82no—
601SD16—82no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—42no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
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—22no—
621C4⋊C4—22no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4C2×D4×C4111yescharacteristic
625C4⋊C4C2×D4×C4111yescharacteristic
626C4⋊C4C2×D4×C4111yescharacteristic
627C4⋊C4C2×D4×C4111yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×D4×C4111yescharacteristic
661C42C2×D4×C4111yescharacteristic
662C42C2×D4×C4111yescharacteristic
663C42C24×C4111yescharacteristic
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—42no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23#120×C4111yescharacteristic
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—42no—
681Q8—81no—
682Q8—82no—
683Q8—81no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—42no—
689D4—42no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4#120×C4111yescharacteristic
720C2×C4#120×C4111yescharacteristic
721C2×C4#120×C4111yescharacteristic
722C2×C4C22×D4×C4111yescharacteristic
723C2×C4C22×D4×C4111yescharacteristic
724C2×C4C22×D4×C4111yescharacteristic
725C8—42no—
726C8—42no—
727C8—42no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—162no—
743C22—162no—
744C22C41×#45512yes—
745C22C2×#120×C4111yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—82no—
761C2—22no—
762C2—81no—
763C2—81no—
764C2—81no—
765C2—81no—
766C2C2×C41×#45511yescharacteristic
767C2C41×#302111yescharacteristic
768C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3545C2
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
2. C41×#3239C2semidirect
3. C41×#3218C2semidirect
4. C2×C41×#489C2semidirect
5. C41×#1664C2semidirect
6. C41×#1662C2semidirect
7. C41×#1661C2semidirect
8. C41×#1659C2semidirect
9. C41×#1533C2semidirect
10. C41×#1532C2semidirect
11. C41×#1532C2semidirect
28. C2×C4⋊Q8×C41C22semidirect
32. C41×#501C22semidirect
33. C41×#497C22semidirect
34. C41×#491C22semidirect
38. C41×#489C22semidirect
39. C41×#489C22semidirect
48. C41×#432C22semidirect
49. C41×#432C22semidirect
52. C2×#97×C41C22semidirect
53. C41×#330C22semidirect
54. C41×#330C22semidirect
56. C41×#329C22semidirect
57. C41×#329C22semidirect
58. C41×#329C22semidirect
343. #19055C41direct (N × H)
378. #3239C2×C41semidirect
379. #3218C2×C41semidirect
380. C2×#489C2×C41semidirect
381. #1664C2×C41semidirect
382. #1662C2×C41semidirect
383. #1661C2×C41semidirect
384. #1659C2×C41semidirect
385. #1533C2×C41semidirect
386. #1532C2×C41semidirect
387. #1532C2×C41semidirect
412. C2×C4⋊Q8C22×C41semidirect
416. #501C22×C41semidirect
417. #497C22×C41semidirect
418. #491C22×C41semidirect
422. #489C22×C41semidirect
423. #489C22×C41semidirect
432. #432C22×C41semidirect
433. #432C22×C41semidirect
436. C2×#97C22×C41semidirect
437. #330C22×C41semidirect
438. #330C22×C41semidirect
440. #329C22×C41semidirect
441. #329C22×C41semidirect
442. #329C22×C41semidirect
443. C41#19055direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35452
C41×#32392
C41×#32182
C2×C41×#4892
C41×#16642
C41×#16622
C41×#16612
C41×#16592
C41×#15332
C41×#15322
#1905541