Finite Group Databasebeta

← C41×#18705 #23794906

Subgroups — C41×#18705 #23794906

Order 10496.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3546C211yesmaximal, characteristic
2C41×#3252C211yesmaximal, characteristic, complemented
3C41×#3235C211yesmaximal, characteristic, complemented
4C41×#3167C211yesmaximal, characteristic, complemented
5C41×#1654C211yesmaximal, characteristic, complemented
6C41×#1652C211yesmaximal, characteristic, complemented
7C41×#1641C211yesmaximal, characteristic, complemented
8C41×#1639C211yesmaximal, characteristic, complemented
9C41×#1638C211yesmaximal, characteristic, complemented
10C41×#1635C211yesmaximal, characteristic, complemented
11C41×#1631C211yesmaximal, characteristic, complemented
12C41×#1629C211yesmaximal, characteristic, complemented
13C41×#1557C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1492C211yesmaximal, characteristic, complemented
16C41×#560—22no—
17C41×#556C2211yescharacteristic
18C41×#553—21no—
19C41×#550—21no—
20C41×#550C2211yescharacteristic
21C41×#547C2211yescharacteristic
22C41×#546—21no—
23C41×#546—21no—
24D42×C41C2211yescharacteristic
25C41×#542—21no—
26C41×#538—22no—
27C41×#537—21no—
28C41×#535—21no—
29C41×#535—21no—
30C41×#533C2211yescharacteristic, complemented
31C41×#532C2211yescharacteristic
32C41×#532C2211yescharacteristic
33C41×#529C2211yescharacteristic
34C41×#501—21no—
35C41×#498C2211yescharacteristic, complemented
36C41×#492C2211yescharacteristic
37C41×#490—21no—
38C41×#487C2211yescharacteristic, complemented
39C41×#486C2211yescharacteristic
40C41×#482—21no—
41C41×#482—21no—
42C41×#479—21no—
43C41×#477C2211yescharacteristic, complemented
44C41×#476C2211yescharacteristic
45C41×#476C2211yescharacteristic
46C41×#476C2211yescharacteristic, complemented
47C41×#474C2211yescharacteristic
48C41×#474C2211yescharacteristic, complemented
49C41×#470—21no—
50C41×#468—21no—
51C41×#465—22no—
52C41×#464—21no—
53C41×#462C2211yescharacteristic, complemented
54C41×#461C2211yescharacteristic
55C4×SD16×C41—22no—
56C41×#432C2211yescharacteristic, complemented
57C41×#423C2211yescharacteristic, complemented
58C2×C4×C8×C41C2211yescharacteristic, complemented
59C41×#332C2211yescharacteristic, complemented
60C41×#332C2211yescharacteristic, complemented
61C41×#331C2211yescharacteristic
62C41×#331C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×Q8⋊C8C2211yescharacteristic, complemented
65C41×D4⋊C8C2211yescharacteristic
66C41×D4⋊C8C2211yescharacteristic
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic, complemented
70C41×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C41—21no—
72C2×#41×C41—21no—
73C2×#41×C41—21no—
74C2×#41×C41—21no—
75C22×D4×C41—21no—
76C22×D4×C41—21no—
77C2×Q16×C41—21no—
78C2×SD16×C41—22no—
79C2×SD16×C41—21no—
80C2×M16×C41—21no—
81C22×C8×C41—21no—
82C4⋊Q8×C41D411yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86#127×C41—22no—
87#127×C41—21no—
88#127×C41D411yescharacteristic
89#127×C41C2311yescharacteristic
90#126×C41—22no—
91#126×C41—22no—
92#126×C41—21no—
93#125×C41—21no—
94#125×C41D411yescharacteristic
95#124×C41—22no—
96#124×C41—21no—
97#124×C41—21no—
98#124×C41—21no—
99#124×C41D411yescharacteristic
100#123×C41—22no—
101#123×C41—22no—
102#123×C41—21no—
103#123×C41—22no—
104C22⋊Q8×C41—22no—
105C22⋊Q8×C41—21no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41—21no—
109C22⋊Q8×C41D411yescharacteristic
110#121×C41—22no—
111#121×C41—22no—
112#121×C41—22no—
113#121×C41—22no—
114#121×C41—22no—
115#121×C41—21no—
116#121×C41—22no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41—21no—
120#121×C41—21no—
121#121×C41—21no—
122#121×C41D411yescharacteristic
123#121×C41D411yescharacteristic
124#121×C41D411yescharacteristic
125#121×C41D412yes—
126#120×C41—22no—
127#120×C41—22no—
128#120×C41—22no—
129#120×C41—22no—
130C4×Q8×C41—21no—
131C4×Q8×C41—21no—
132C4×Q8×C41—21no—
133C4×Q8×C41C2311yescharacteristic
134C4×D4×C41—22no—
135C4×D4×C41—21no—
136C4×D4×C41—21no—
137C4×D4×C41—21no—
138C4×D4×C41—21no—
139C4×D4×C41D412yes—
140C4×D4×C41C2311yescharacteristic
141C4×D4×C41C2311yescharacteristic
142C4×D4×C41C2311yescharacteristic
143#117×C41—21no—
144#117×C41—21no—
145#117×C41—21no—
146C2×C4⋊C4×C41—21no—
147C2×C22⋊C4×C41—22no—
148C2×C42×C41C2311yescharacteristic
149#107×C41—21no—
150#107×C41—21no—
151#107×C41—21no—
152#106×C41—21no—
153#106×C41—21no—
154#106×C41—22no—
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—22no—
163#103×C41—21no—
164#103×C41—21no—
165#102×C41—22no—
166#102×C41—21no—
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
176C24×C41—22no—
177#41×C41—81no—
178#41×C41—81no—
179#41×C41—81no—
180#41×C41—81no—
181#41×C41—81no—
182#41×C41—81no—
183#41×C41—81no—
184#41×C41—81no—
185C2×Q8×C41—21no—
186C2×Q8×C41—21no—
187C2×Q8×C41—21no—
188C2×Q8×C41—21no—
189C2×Q8×C41C2×D411yescharacteristic
190C2×D4×C41—22no—
191C2×D4×C41—22no—
192C2×D4×C41—22no—
193C2×D4×C41—22no—
194C2×D4×C41—22no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—22no—
198C2×D4×C41—21no—
199C2×D4×C41—21no—
200C2×D4×C41—21no—
201C2×D4×C41—21no—
202C2×D4×C41—21no—
203C2×D4×C41—81no—
204C2×D4×C41—81no—
205C2×D4×C41—81no—
206C2×D4×C41—81no—
207C2×D4×C41C2×D411yescharacteristic
208C2×D4×C41C2×D411yescharacteristic
209C2×D4×C41C2×D411yescharacteristic
210C2×D4×C41C2×D412yes—
211C22×C4×C41—22no—
212C22×C4×C41—22no—
213C22×C4×C41—21no—
214C22×C4×C41—21no—
215C22×C4×C41—21no—
216C22×C4×C41—22no—
217C22×C4×C41C2×D411yescharacteristic
218C22×C4×C41C2×D411yescharacteristic
219C22×C4×C41C2×D411yescharacteristic
220Q16×C41—81no—
221SD16×C41—44no—
222SD16×C41—81no—
223M16×C41—81no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—21no—
228C2×C8×C41—21no—
229C2×C8×C41—21no—
230C2×C8×C41—42no—
231C4⋊C4×C41—22no—
232C4⋊C4×C41—22no—
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—41no—
244C4⋊C4×C41—41no—
245C4⋊C4×C41C2×D411yescharacteristic
246C4⋊C4×C41C2×D412yes—
247C4⋊C4×C41C2×D411yescharacteristic
248C4⋊C4×C41C2×D411yescharacteristic
249C4⋊C4×C41C2×D411yescharacteristic
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—21no—
265C22⋊C4×C41—21no—
266C22⋊C4×C41—41no—
267C42×C41—22no—
268C42×C41—21no—
269C42×C41—41no—
270C42×C41C2×D411yescharacteristic
271C42×C41C2×D411yescharacteristic
272C42×C41C2×D411yescharacteristic
273C42×C41C2411yescharacteristic
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—22no—
277C23×C41—21no—
278C23×C41—82no—
279C23×C41—82no—
280C23×C41—82no—
281C23×C41#12011yescharacteristic
282Q8×C41—21no—
283Q8×C41—21no—
284Q8×C41—42no—
285Q8×C41—41no—
286Q8×C41—41no—
287Q8×C41—41no—
288Q8×C41—41no—
289Q8×C41—81no—
290D4×C41—21no—
291D4×C41—21no—
292D4×C41—21no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—21no—
296D4×C41—42no—
297D4×C41—41no—
298D4×C41—41no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—81no—
302D4×C41—81no—
303D4×C41—81no—
304D4×C41—82no—
305D4×C41—81no—
306D4×C41—81no—
307D4×C41—82no—
308D4×C41—82no—
309D4×C41—82no—
310D4×C41—82no—
311D4×C41—82no—
312C2×C4×C41—21no—
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—22no—
320C2×C4×C41—21no—
321C2×C4×C41—21no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—82no—
332C2×C4×C41—82no—
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—22no—
341C8×C41—41no—
342C8×C41—41no—
343C8×C41—41no—
344C8×C41—41no—
345C8×C41—41no—
346#18705C4111yesmaximal, characteristic, direct product factor, Sylow
347C22×C41—21no—
348C22×C41—21no—
349C22×C41—21no—
350C22×C41—41no—
351C22×C41—41no—
352C22×C41—42no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—41no—
356C22×C41—42no—
357C22×C41—41no—
358C22×C41—42no—
359C22×C41—41no—
360C22×C41—41no—
361C22×C41—41no—
362C22×C41—164no—
363C22×C41C2×#12011yescharacteristic
364C4×C41—21no—
365C4×C41—21no—
366C4×C41—21no—
367C4×C41—21no—
368C4×C41—41no—
369C4×C41—42no—
370C4×C41—41no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—81no—
375C4×C41—81no—
376C4×C41#57611yescharacteristic
377C4×C41#57711yescharacteristic
378C4×C41#57711yescharacteristic
379C4×C41#57711yescharacteristic
380#3546C2×C4111yescharacteristic
381#3252C2×C4111yescharacteristic, complemented
382#3235C2×C4111yescharacteristic, complemented
383#3167C2×C4111yescharacteristic, complemented
384#1654C2×C4111yescharacteristic, complemented
385#1652C2×C4111yescharacteristic, complemented
386#1641C2×C4111yescharacteristic, complemented
387#1639C2×C4111yescharacteristic, complemented
388#1638C2×C4111yescharacteristic, complemented
389#1635C2×C4111yescharacteristic, complemented
390#1631C2×C4111yescharacteristic, complemented
391#1629C2×C4111yescharacteristic, complemented
392#1557C2×C4111yescharacteristic, complemented
393#1494C2×C4111yescharacteristic, complemented
394#1492C2×C4111yescharacteristic, complemented
395C2×C41—41no—
396C2×C41—81no—
397C2×C41—82no—
398C2×C41—81no—
399C2×C41—81no—
400C2×C41#300911yescharacteristic
401C2×C41#301211yescharacteristic
402C2×C41#301811yescharacteristic
403#560—22no—
404#556C22×C4111yescharacteristic
405#553—21no—
406#550—21no—
407#550C22×C4111yescharacteristic
408#547C22×C4111yescharacteristic
409#546—21no—
410#546—21no—
411D42C22×C4111yescharacteristic
412#542—21no—
413#538—22no—
414#537—21no—
415#535—21no—
416#535—21no—
417#533C22×C4111yescharacteristic, complemented
418#532C22×C4111yescharacteristic
419#532C22×C4111yescharacteristic
420#529C22×C4111yescharacteristic
421#501—21no—
422#498C22×C4111yescharacteristic, complemented
423#492C22×C4111yescharacteristic
424#490—21no—
425#487C22×C4111yescharacteristic, complemented
426#486C22×C4111yescharacteristic
427#482—21no—
428#482—21no—
429#479—21no—
430#477C22×C4111yescharacteristic, complemented
431#476C22×C4111yescharacteristic
432#476C22×C4111yescharacteristic
433#476C22×C4111yescharacteristic, complemented
434#474C22×C4111yescharacteristic
435#474C22×C4111yescharacteristic, complemented
436#470—21no—
437#468—21no—
438#465—22no—
439#464—21no—
440#462C22×C4111yescharacteristic, complemented
441#461C22×C4111yescharacteristic
442C4×SD16—22no—
443#432C22×C4111yescharacteristic, complemented
444#423C22×C4111yescharacteristic, complemented
445C2×C4×C8C22×C4111yescharacteristic, complemented
446#332C22×C4111yescharacteristic, complemented
447#332C22×C4111yescharacteristic, complemented
448#331C22×C4111yescharacteristic
449#331C22×C4111yescharacteristic
450Q8⋊C8C22×C4111yescharacteristic, complemented
451Q8⋊C8C22×C4111yescharacteristic, complemented
452D4⋊C8C22×C4111yescharacteristic
453D4⋊C8C22×C4111yescharacteristic
454D4⋊C8C22×C4111yescharacteristic
455D4⋊C8C22×C4111yescharacteristic
456D4⋊C8C22×C4111yescharacteristic, complemented
457D4⋊C8C22×C4111yescharacteristic, complemented
458C41#1870511yescharacteristic, direct product factor, Sylow
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C4111yescharacteristic
471C4⋊Q8C23×C4111yescharacteristic
472C4⋊Q8C23×C4111yescharacteristic
473C4⋊Q8C23×C4111yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C4111yescharacteristic
477#127C23×C4111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C4111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C4111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
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—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C4111yescharacteristic
511#121D4×C4111yescharacteristic
512#121D4×C4111yescharacteristic
513#121D4×C4112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C4111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C4112yes—
528C4×D4C23×C4111yescharacteristic
529C4×D4C23×C4111yescharacteristic
530C4×D4C23×C4111yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C4111yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C4111yescharacteristic
546C4⋊C8C23×C4111yescharacteristic
547C4⋊C8C23×C4111yescharacteristic
548C4⋊C8C23×C4111yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C4111yescharacteristic
563C4×C8C23×C4111yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C4111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C4111yescharacteristic
596C2×D4C2×D4×C4111yescharacteristic
597C2×D4C2×D4×C4111yescharacteristic
598C2×D4C2×D4×C4112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C4111yescharacteristic
606C22×C4C2×D4×C4111yescharacteristic
607C22×C4C2×D4×C4111yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C4111yescharacteristic
634C4⋊C4C2×D4×C4112yes—
635C4⋊C4C2×D4×C4111yescharacteristic
636C4⋊C4C2×D4×C4111yescharacteristic
637C4⋊C4C2×D4×C4111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C4111yescharacteristic
659C42C2×D4×C4111yescharacteristic
660C42C2×D4×C4111yescharacteristic
661C42C24×C4111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C4111yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C4111yescharacteristic
723C2×C4#120×C4111yescharacteristic
724C2×C4#120×C4111yescharacteristic
725C2×C4C22×D4×C4111yescharacteristic
726C2×C4C22×D4×C4111yescharacteristic
727C2×C4C22×D4×C4111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C4111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C41×#57611yescharacteristic
764C4C41×#57711yescharacteristic
765C4C41×#57711yescharacteristic
766C4C41×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C41×#300911yescharacteristic
773C2C41×#301211yescharacteristic
774C2C41×#301811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3546C2
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×#3252C2semidirect
3. C41×#3235C2semidirect
4. C41×#3167C2semidirect
5. C41×#1654C2semidirect
6. C41×#1652C2semidirect
7. C41×#1641C2semidirect
8. C41×#1639C2semidirect
9. C41×#1638C2semidirect
10. C41×#1635C2semidirect
11. C41×#1631C2semidirect
12. C41×#1629C2semidirect
13. C41×#1557C2semidirect
14. C41×#1494C2semidirect
15. C41×#1492C2semidirect
30. C41×#533C22semidirect
35. C41×#498C22semidirect
38. C41×#487C22semidirect
43. C41×#477C22semidirect
46. C41×#476C22semidirect
48. C41×#474C22semidirect
53. C41×#462C22semidirect
56. C41×#432C22semidirect
57. C41×#423C22semidirect
58. C2×C4×C8×C41C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
69. C41×D4⋊C8C22semidirect
70. C41×D4⋊C8C22semidirect
346. #18705C41direct (N × H)
381. #3252C2×C41semidirect
382. #3235C2×C41semidirect
383. #3167C2×C41semidirect
384. #1654C2×C41semidirect
385. #1652C2×C41semidirect
386. #1641C2×C41semidirect
387. #1639C2×C41semidirect
388. #1638C2×C41semidirect
389. #1635C2×C41semidirect
390. #1631C2×C41semidirect
391. #1629C2×C41semidirect
392. #1557C2×C41semidirect
393. #1494C2×C41semidirect
394. #1492C2×C41semidirect
417. #533C22×C41semidirect
422. #498C22×C41semidirect
425. #487C22×C41semidirect
430. #477C22×C41semidirect
433. #476C22×C41semidirect
435. #474C22×C41semidirect
440. #462C22×C41semidirect
443. #432C22×C41semidirect
444. #423C22×C41semidirect
445. C2×C4×C8C22×C41semidirect
446. #332C22×C41semidirect
447. #332C22×C41semidirect
450. Q8⋊C8C22×C41semidirect
451. Q8⋊C8C22×C41semidirect
456. D4⋊C8C22×C41semidirect
457. D4⋊C8C22×C41semidirect
458. C41#18705direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35462
C41×#32522
C41×#32352
C41×#31672
C41×#16542
C41×#16522
C41×#16412
C41×#16392
C41×#16382
C41×#16352
C41×#16312
C41×#16292
C41×#15572
C41×#14942
C41×#14922
#1870541