Finite Group Databasebeta

← C41×#18670 #23794871

Subgroups — C41×#18670 #23794871

Order 10496.

962 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3517C211yesmaximal, characteristic, complemented
2C41×#3212C211yesmaximal, characteristic, complemented
3C41×#3169C211yesmaximal, characteristic, complemented
4C41×#3115C211yesmaximal, characteristic, complemented
5C41×#1648C211yesmaximal, characteristic, complemented
6C41×#1647C211yesmaximal, characteristic, complemented
7C41×#1642C211yesmaximal, characteristic, complemented
8C41×#1641C211yesmaximal, characteristic, complemented
9C41×#1626C211yesmaximal, characteristic, complemented
10C41×#1625C211yesmaximal, characteristic, complemented
11C41×#1621C211yesmaximal, characteristic, complemented
12C41×#1621C211yesmaximal, characteristic, complemented
13C41×#1553C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1476C211yesmaximal, characteristic, complemented
16C41×#557C2211yescharacteristic
17C41×#553—22no—
18C41×#553—21no—
19C41×#550—21no—
20C41×#550—21no—
21C41×#550C2211yescharacteristic
22C41×#550C2211yescharacteristic
23C41×#547—21no—
24C41×#547C2211yescharacteristic
25C41×#540—22no—
26C41×#540—21no—
27C41×#532—21no—
28C41×#532C2211yescharacteristic
29C41×#532C2211yescharacteristic
30C41×#529—21no—
31C41×#529C2211yescharacteristic
32C41×#520—21no—
33C4×#41×C41C2211yescharacteristic
34C41×#500C2211yescharacteristic
35C41×#495—21no—
36C41×#493C2211yescharacteristic
37C41×#488—21no—
38C41×#486C2211yescharacteristic
39C41×#486C2211yescharacteristic
40C41×#482—21no—
41C41×#475C2211yescharacteristic
42C41×#474C2211yescharacteristic
43C41×#466—22no—
44C41×#462C2211yescharacteristic
45C41×#461C2211yescharacteristic
46C41×#460C2211yescharacteristic
47C41×#460C2211yescharacteristic
48C41×#459C2211yescharacteristic
49C41×#459C2211yescharacteristic
50C41×#452—21no—
51C41×#449—21no—
52C41×#449—21no—
53C41×#442—21no—
54C41×#440—21no—
55C4×D8×C41—22no—
56C41×#432C2211yescharacteristic
57C41×#431C2211yescharacteristic
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×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic
70C41×D4⋊C8C2211yescharacteristic
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C2×#41×C41—21no—
75C2×#41×C41—21no—
76C2×#41×C41D411yescharacteristic
77C2×Q16×C41—21no—
78C2×SD16×C41—21no—
79C2×SD16×C41—21no—
80C2×SD16×C41—21no—
81C2×D8×C41—22no—
82C2×D8×C41—21no—
83C2×D8×C41—21no—
84C22×C8×C41—21no—
85C4⋊Q8×C41—21no—
86C4⋊Q8×C41C2311yescharacteristic
87C4⋊Q8×C41C2311yescharacteristic
88#127×C41—22no—
89#127×C41—21no—
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×C41D411yescharacteristic
98#124×C41—21no—
99#124×C41—21no—
100#124×C41D411yescharacteristic
101#123×C41—22no—
102#123×C41—22no—
103#123×C41—22no—
104#123×C41—21no—
105#123×C41—22no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41D411yescharacteristic
108#121×C41—22no—
109#121×C41—22no—
110#121×C41—22no—
111#121×C41—22no—
112#121×C41—22no—
113#121×C41—21no—
114#121×C41—22no—
115#121×C41—22no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41D411yescharacteristic
122#121×C41D412yes—
123C4×Q8×C41—21no—
124C4×Q8×C41—21no—
125C4×Q8×C41D411yescharacteristic
126C4×Q8×C41C2311yescharacteristic
127C4×Q8×C41C2311yescharacteristic
128C4×D4×C41—22no—
129C4×D4×C41—22no—
130C4×D4×C41—22no—
131C4×D4×C41—22no—
132C4×D4×C41—21no—
133C4×D4×C41—21no—
134C4×D4×C41—21no—
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41—21no—
140C4×D4×C41D411yescharacteristic
141C4×D4×C41D412yes—
142C4×D4×C41C2311yescharacteristic
143C4×D4×C41C2311yescharacteristic
144#117×C41—22no—
145#117×C41—21no—
146#117×C41—21no—
147#117×C41D411yescharacteristic
148C2×C4⋊C4×C41—22no—
149C2×C4⋊C4×C41—21no—
150C2×C42×C41—21no—
151C2×C42×C41C2311yescharacteristic
152#107×C41—22no—
153#107×C41—21no—
154#106×C41—21no—
155C4⋊C8×C41C2311yescharacteristic
156C4⋊C8×C41C2311yescharacteristic
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159#103×C41—21no—
160#103×C41—21no—
161#103×C41—21no—
162#102×C41—22no—
163#102×C41—21no—
164#102×C41—22no—
165#102×C41—21no—
166#102×C41—21no—
167#102×C41—21no—
168#102×C41—21no—
169C22⋊C8×C41—21no—
170C22⋊C8×C41—21no—
171#97×C41—21no—
172C4×C8×C41—21no—
173C4×C8×C41—21no—
174C4×C8×C41C2311yescharacteristic
175C4×C8×C41C2311yescharacteristic
176#41×C41—22no—
177#41×C41—41no—
178#41×C41—42no—
179#41×C41—42no—
180#41×C41—81no—
181#41×C41—81no—
182#41×C41—81no—
183#41×C41—81no—
184#41×C41—81no—
185#41×C41—81no—
186#41×C41—81no—
187#41×C41—81no—
188C2×Q8×C41—21no—
189C2×Q8×C41—21no—
190C2×Q8×C41C2×D411yescharacteristic
191C2×Q8×C41C2×D411yescharacteristic
192C2×D4×C41—22no—
193C2×D4×C41—21no—
194C2×D4×C41—22no—
195C2×D4×C41—22no—
196C2×D4×C41—22no—
197C2×D4×C41—22no—
198C2×D4×C41—21no—
199C2×D4×C41—22no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—21no—
204C2×D4×C41—21no—
205C2×D4×C41—41no—
206C2×D4×C41C2×D411yescharacteristic
207C2×D4×C41C2×D411yescharacteristic
208C2×D4×C41C2×D412yes—
209C22×C4×C41—22no—
210C22×C4×C41—22no—
211C22×C4×C41—22no—
212C22×C4×C41—21no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—22no—
217C22×C4×C41—41no—
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220C22×C4×C41C2×D411yescharacteristic
221Q16×C41—81no—
222SD16×C41—42no—
223SD16×C41—81no—
224SD16×C41—81no—
225D8×C41—44no—
226D8×C41—42no—
227D8×C41—81no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—21no—
231C2×C8×C41—21no—
232C2×C8×C41—21no—
233C2×C8×C41—21no—
234C2×C8×C41—42no—
235C4⋊C4×C41—22no—
236C4⋊C4×C41—22no—
237C4⋊C4×C41—22no—
238C4⋊C4×C41—22no—
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×C41—21no—
246C4⋊C4×C41—21no—
247C4⋊C4×C41—21no—
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D411yescharacteristic
250C4⋊C4×C41C2×D411yescharacteristic
251C4⋊C4×C41C2×D411yescharacteristic
252C4⋊C4×C41C2×D412yes—
253C22⋊C4×C41—22no—
254C22⋊C4×C41—22no—
255C22⋊C4×C41—22no—
256C22⋊C4×C41—21no—
257C22⋊C4×C41—21no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—22no—
261C22⋊C4×C41—21no—
262C22⋊C4×C41—21no—
263C22⋊C4×C41—22no—
264C22⋊C4×C41—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—41no—
267C22⋊C4×C41—41no—
268C42×C41—22no—
269C42×C41—21no—
270C42×C41—21no—
271C42×C41—21no—
272C42×C41—21no—
273C42×C41C2×D411yescharacteristic
274C42×C41C2×D411yescharacteristic
275C42×C41C2×D411yescharacteristic
276C42×C41C2411yescharacteristic
277C23×C41—21no—
278C23×C41—21no—
279C23×C41—22no—
280C23×C41—41no—
281C23×C41#12011yescharacteristic
282Q8×C41—21no—
283Q8×C41—21no—
284Q8×C41—21no—
285Q8×C41—41no—
286Q8×C41—41no—
287Q8×C41—41no—
288Q8×C41—41no—
289Q8×C41#13512yes—
290D4×C41—21no—
291D4×C41—21no—
292D4×C41—21no—
293D4×C41—21no—
294D4×C41—42no—
295D4×C41—42no—
296D4×C41—44no—
297D4×C41—42no—
298D4×C41—41no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—41no—
304D4×C41—41no—
305D4×C41—41no—
306D4×C41—81no—
307D4×C41—82no—
308D4×C41—82no—
309D4×C41—82no—
310D4×C41—82no—
311D4×C41—82no—
312D4×C41—82no—
313C2×C4×C41—21no—
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—22no—
323C2×C4×C41—21no—
324C2×C4×C41—41no—
325C2×C4×C41—42no—
326C2×C4×C41—44no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—81no—
333C2×C4×C41—82no—
334C2×C4×C41—82no—
335C2×C4×C41—82no—
336C2×C4×C41—82no—
337C2×C4×C41#12011yescharacteristic
338C2×C4×C41#12011yescharacteristic
339C2×C4×C41#12011yescharacteristic
340C2×C4×C41C22×D411yescharacteristic
341C2×C4×C41C22×D411yescharacteristic
342C2×C4×C41C22×D411yescharacteristic
343C8×C41—22no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41—41no—
347C8×C41—41no—
348C8×C41—41no—
349#18670C4111yesmaximal, characteristic, direct product factor, Sylow
350C22×C41—21no—
351C22×C41—21no—
352C22×C41—21no—
353C22×C41—41no—
354C22×C41—42no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—42no—
359C22×C41—41no—
360C22×C41—42no—
361C22×C41—41no—
362C22×C41—81no—
363C22×C41—81no—
364C22×C41—81no—
365C22×C41C2×#12011yescharacteristic
366C4×C41—21no—
367C4×C41—22no—
368C4×C41—21no—
369C4×C41—21no—
370C4×C41—21no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—42no—
375C4×C41—41no—
376C4×C41—41no—
377C4×C41—81no—
378C4×C41C2×#13511yescharacteristic
379C4×C41#57511yescharacteristic
380C4×C41#57611yescharacteristic
381C4×C41#57611yescharacteristic
382#3517C2×C4111yescharacteristic, complemented
383#3212C2×C4111yescharacteristic, complemented
384#3169C2×C4111yescharacteristic, complemented
385#3115C2×C4111yescharacteristic, complemented
386#1648C2×C4111yescharacteristic, complemented
387#1647C2×C4111yescharacteristic, complemented
388#1642C2×C4111yescharacteristic, complemented
389#1641C2×C4111yescharacteristic, complemented
390#1626C2×C4111yescharacteristic, complemented
391#1625C2×C4111yescharacteristic, complemented
392#1621C2×C4111yescharacteristic, complemented
393#1621C2×C4111yescharacteristic, complemented
394#1553C2×C4111yescharacteristic, complemented
395#1494C2×C4111yescharacteristic, complemented
396#1476C2×C4111yescharacteristic, complemented
397C2×C41—41no—
398C2×C41—81no—
399C2×C41—81no—
400C2×C41—82no—
401C2×C41—161no—
402C2×C41#300211yescharacteristic
403C2×C41#300811yescharacteristic
404C2×C41#301811yescharacteristic
405#557C22×C4111yescharacteristic
406#553—22no—
407#553—21no—
408#550—21no—
409#550—21no—
410#550C22×C4111yescharacteristic
411#550C22×C4111yescharacteristic
412#547—21no—
413#547C22×C4111yescharacteristic
414#540—22no—
415#540—21no—
416#532—21no—
417#532C22×C4111yescharacteristic
418#532C22×C4111yescharacteristic
419#529—21no—
420#529C22×C4111yescharacteristic
421#520—21no—
422C4×#41C22×C4111yescharacteristic
423#500C22×C4111yescharacteristic
424#495—21no—
425#493C22×C4111yescharacteristic
426#488—21no—
427#486C22×C4111yescharacteristic
428#486C22×C4111yescharacteristic
429#482—21no—
430#475C22×C4111yescharacteristic
431#474C22×C4111yescharacteristic
432#466—22no—
433#462C22×C4111yescharacteristic
434#461C22×C4111yescharacteristic
435#460C22×C4111yescharacteristic
436#460C22×C4111yescharacteristic
437#459C22×C4111yescharacteristic
438#459C22×C4111yescharacteristic
439#452—21no—
440#449—21no—
441#449—21no—
442#442—21no—
443#440—21no—
444C4×D8—22no—
445#432C22×C4111yescharacteristic
446#431C22×C4111yescharacteristic
447C2×C4×C8C22×C4111yescharacteristic
448#332C22×C4111yescharacteristic
449#332C22×C4111yescharacteristic
450#331C22×C4111yescharacteristic
451#331C22×C4111yescharacteristic
452Q8⋊C8C22×C4111yescharacteristic
453Q8⋊C8C22×C4111yescharacteristic
454Q8⋊C8C22×C4111yescharacteristic
455Q8⋊C8C22×C4111yescharacteristic
456D4⋊C8C22×C4111yescharacteristic
457D4⋊C8C22×C4111yescharacteristic
458D4⋊C8C22×C4111yescharacteristic
459D4⋊C8C22×C4111yescharacteristic
460C41#1867011yescharacteristic, direct product factor, Sylow
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41D4×C4111yescharacteristic
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C22×C8—21no—
475C4⋊Q8—21no—
476C4⋊Q8C23×C4111yescharacteristic
477C4⋊Q8C23×C4111yescharacteristic
478#127—22no—
479#127—21no—
480#127—21no—
481#127C23×C4111yescharacteristic
482#127C23×C4111yescharacteristic
483#126—22no—
484#126—21no—
485#125—22no—
486#125—21no—
487#125D4×C4111yescharacteristic
488#124—21no—
489#124—21no—
490#124D4×C4111yescharacteristic
491#123—22no—
492#123—22no—
493#123—22no—
494#123—21no—
495#123—22no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C4111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121D4×C4111yescharacteristic
512#121D4×C4112yes—
513C4×Q8—21no—
514C4×Q8—21no—
515C4×Q8D4×C4111yescharacteristic
516C4×Q8C23×C4111yescharacteristic
517C4×Q8C23×C4111yescharacteristic
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C4111yescharacteristic
531C4×D4D4×C4112yes—
532C4×D4C23×C4111yescharacteristic
533C4×D4C23×C4111yescharacteristic
534#117—22no—
535#117—21no—
536#117—21no—
537#117D4×C4111yescharacteristic
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C42—21no—
541C2×C42C23×C4111yescharacteristic
542#107—22no—
543#107—21no—
544#106—21no—
545C4⋊C8C23×C4111yescharacteristic
546C4⋊C8C23×C4111yescharacteristic
547C4⋊C8C23×C4111yescharacteristic
548C4⋊C8C23×C4111yescharacteristic
549#103—21no—
550#103—21no—
551#103—21no—
552#102—22no—
553#102—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561#97—21no—
562C4×C8—21no—
563C4×C8—21no—
564C4×C8C23×C4111yescharacteristic
565C4×C8C23×C4111yescharacteristic
566#41—22no—
567#41—41no—
568#41—42no—
569#41—42no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576#41—81no—
577#41—81no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8C2×D4×C4111yescharacteristic
581C2×Q8C2×D4×C4111yescharacteristic
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—41no—
596C2×D4C2×D4×C4111yescharacteristic
597C2×D4C2×D4×C4111yescharacteristic
598C2×D4C2×D4×C4112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4C2×D4×C4111yescharacteristic
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611Q16—81no—
612SD16—42no—
613SD16—81no—
614SD16—81no—
615D8—44no—
616D8—42no—
617D8—81no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—42no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4C2×D4×C4111yescharacteristic
639C4⋊C4C2×D4×C4111yescharacteristic
640C4⋊C4C2×D4×C4111yescharacteristic
641C4⋊C4C2×D4×C4111yescharacteristic
642C4⋊C4C2×D4×C4112yes—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42C2×D4×C4111yescharacteristic
664C42C2×D4×C4111yescharacteristic
665C42C2×D4×C4111yescharacteristic
666C42C24×C4111yescharacteristic
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23#120×C4111yescharacteristic
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8#135×C4112yes—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—42no—
686D4—44no—
687D4—42no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—82no—
697D4—81no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—82no—
723C2×C4—81no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4#120×C4111yescharacteristic
728C2×C4#120×C4111yescharacteristic
729C2×C4#120×C4111yescharacteristic
730C2×C4C22×D4×C4111yescharacteristic
731C2×C4C22×D4×C4111yescharacteristic
732C2×C4C22×D4×C4111yescharacteristic
733C8—22no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22C2×#120×C4111yescharacteristic
755C4—21no—
756C4—22no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—81no—
767C4C2×#135×C4111yescharacteristic
768C4C41×#57511yescharacteristic
769C4C41×#57611yescharacteristic
770C4C41×#57611yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—161no—
776C2C41×#300211yescharacteristic
777C2C41×#300811yescharacteristic
778C2C41×#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×#3517C2semidirect
2. C41×#3212C2semidirect
3. C41×#3169C2semidirect
4. C41×#3115C2semidirect
5. C41×#1648C2semidirect
6. C41×#1647C2semidirect
7. C41×#1642C2semidirect
8. C41×#1641C2semidirect
9. C41×#1626C2semidirect
10. C41×#1625C2semidirect
11. C41×#1621C2semidirect
12. C41×#1621C2semidirect
13. C41×#1553C2semidirect
14. C41×#1494C2semidirect
15. C41×#1476C2semidirect
349. #18670C41direct (N × H)
382. #3517C2×C41semidirect
383. #3212C2×C41semidirect
384. #3169C2×C41semidirect
385. #3115C2×C41semidirect
386. #1648C2×C41semidirect
387. #1647C2×C41semidirect
388. #1642C2×C41semidirect
389. #1641C2×C41semidirect
390. #1626C2×C41semidirect
391. #1625C2×C41semidirect
392. #1621C2×C41semidirect
393. #1621C2×C41semidirect
394. #1553C2×C41semidirect
395. #1494C2×C41semidirect
396. #1476C2×C41semidirect
460. C41#18670direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35172
C41×#32122
C41×#31692
C41×#31152
C41×#16482
C41×#16472
C41×#16422
C41×#16412
C41×#16262
C41×#16252
C41×#16212
C41×#15532
C41×#14942
C41×#14762
#1867041