Finite Group Databasebeta

← C41×#18638 #23794839

Subgroups — C41×#18638 #23794839

Order 10496.

956 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3520C211yesmaximal, characteristic, complemented
2C41×#3247C211yesmaximal, characteristic, complemented
3C41×#3131C211yesmaximal, characteristic, complemented
4C41×#3109C211yesmaximal, characteristic, complemented
5C41×#1638C211yesmaximal, characteristic, complemented
6C41×#1637C211yesmaximal, characteristic, complemented
7C41×#1635C211yesmaximal, characteristic, complemented
8C41×#1635C211yesmaximal, characteristic, complemented
9C41×#1628C211yesmaximal, characteristic, complemented
10C41×#1627C211yesmaximal, characteristic, complemented
11C41×#1625C211yesmaximal, characteristic, complemented
12C41×#1625C211yesmaximal, characteristic, complemented
13C41×#1552C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C2×C41×D4⋊C8C211yesmaximal, characteristic, complemented
16C41×#556C2211yescharacteristic
17C41×#554—21no—
18C41×#552—21no—
19C41×#551—22no—
20D4×Q8×C41C2211yescharacteristic
21C41×#548—21no—
22C41×#547C2211yescharacteristic
23C41×#547C2211yescharacteristic
24C41×#546—21no—
25C41×#542—21no—
26C41×#539—22no—
27C41×#533C2211yescharacteristic
28C41×#532C2211yescharacteristic
29C41×#529C2211yescharacteristic
30C41×#525—21no—
31C2×C22⋊Q8×C41—21no—
32C41×#520—21no—
33C2×C4×D4×C41C2211yescharacteristic
34C41×#488—22no—
35C41×#487C2211yescharacteristic, complemented
36C41×#487C2211yescharacteristic, complemented
37C41×#486C2211yescharacteristic, complemented
38C41×#486C2211yescharacteristic, complemented
39C41×#481—21no—
40C41×#478—21no—
41C41×#477C2211yescharacteristic, complemented
42C41×#476C2211yescharacteristic
43C41×#476C2211yescharacteristic
44C41×#476C2211yescharacteristic, complemented
45C41×#466—21no—
46C41×#465—21no—
47C41×#463—21no—
48C41×#460C2211yescharacteristic, complemented
49C41×#459C2211yescharacteristic
50C41×#459C2211yescharacteristic
51C41×#459C2211yescharacteristic, complemented
52C41×#447—21no—
53C41×#442—21no—
54C41×#442—21no—
55C41×#432C2211yescharacteristic
56C2×C4⋊C8×C41C2211yescharacteristic
57C41×#416—22no—
58C2×C4×C8×C41C2211yescharacteristic
59C41×#332C2211yescharacteristic, complemented
60C41×#332C2211yescharacteristic, complemented
61C41×#332C2211yescharacteristic, complemented
62C41×#332C2211yescharacteristic, complemented
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—
74C22×Q8×C41—21no—
75C22×D4×C41D411yescharacteristic
76C23×C4×C41—21no—
77C2×SD16×C41—21no—
78C2×D8×C41—21no—
79C2×D8×C41—21no—
80C2×D8×C41—21no—
81C22×C8×C41—21no—
82C22×C8×C41—21no—
83C4⋊Q8×C41—21no—
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86C4⋊Q8×C41C2311yescharacteristic
87#127×C41C2311yescharacteristic
88#126×C41—22no—
89#126×C41—22no—
90#126×C41—21no—
91#125×C41—22no—
92#125×C41D411yescharacteristic
93#125×C41D412yes—
94#124×C41—22no—
95#124×C41—21no—
96#124×C41—21no—
97#124×C41D411yescharacteristic
98#123×C41—22no—
99#123×C41—22no—
100#123×C41—21no—
101#123×C41—22no—
102#123×C41—22no—
103C22⋊Q8×C41—22no—
104C22⋊Q8×C41—22no—
105C22⋊Q8×C41—22no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41—21no—
109C22⋊Q8×C41—21no—
110C22⋊Q8×C41—21no—
111C22⋊Q8×C41—22no—
112C22⋊Q8×C41—21no—
113C22⋊Q8×C41D411yescharacteristic
114#121×C41—22no—
115#121×C41—21no—
116#121×C41—21no—
117#121×C41—21no—
118#121×C41—21no—
119#121×C41D411yescharacteristic
120#120×C41—22no—
121C4×Q8×C41—21no—
122C4×Q8×C41—21no—
123C4×Q8×C41—21no—
124C4×Q8×C41C2311yescharacteristic
125C4×D4×C41—22no—
126C4×D4×C41—22no—
127C4×D4×C41—22no—
128C4×D4×C41—21no—
129C4×D4×C41—21no—
130C4×D4×C41—21no—
131C4×D4×C41—21no—
132C4×D4×C41—21no—
133C4×D4×C41—21no—
134C4×D4×C41D411yescharacteristic
135C4×D4×C41D411yescharacteristic
136C4×D4×C41C2311yescharacteristic
137C4×D4×C41C2311yescharacteristic
138C4×D4×C41C2311yescharacteristic
139#117×C41—22no—
140#117×C41—21no—
141#117×C41—21no—
142#117×C41D412yes—
143C2×C4⋊C4×C41—22no—
144C2×C4⋊C4×C41—21no—
145C2×C4⋊C4×C41—21no—
146C2×C4⋊C4×C41D411yescharacteristic
147C2×C22⋊C4×C41—22no—
148C2×C22⋊C4×C41—21no—
149C2×C42×C41C2311yescharacteristic
150#107×C41—21no—
151#106×C41—21no—
152#106×C41—21no—
153#106×C41—21no—
154C4⋊C8×C41—21no—
155C4⋊C8×C41C2311yescharacteristic
156C4⋊C8×C41C2311yescharacteristic
157C4⋊C8×C41C2311yescharacteristic
158C4⋊C8×C41C2311yescharacteristic
159#103×C41—21no—
160#103×C41—22no—
161#103×C41—22no—
162#102×C41—21no—
163#102×C41—21no—
164#102×C41—21no—
165#102×C41—22no—
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
176C24×C41—21no—
177#41×C41—44no—
178#41×C41—42no—
179#41×C41—42no—
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×D4×C41—22no—
190C2×D4×C41—22no—
191C2×D4×C41—21no—
192C2×D4×C41—22no—
193C2×D4×C41—21no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—21no—
197C2×D4×C41—41no—
198C2×D4×C41—41no—
199C2×D4×C41C2×D411yescharacteristic
200C2×D4×C41C2×D411yescharacteristic
201C2×D4×C41C2×D411yescharacteristic
202C22×C4×C41—22no—
203C22×C4×C41—22no—
204C22×C4×C41—22no—
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×C41—81no—
213C22×C4×C41—81no—
214C22×C4×C41C2×D411yescharacteristic
215C22×C4×C41C2×D411yescharacteristic
216C22×C4×C41C2×D411yescharacteristic
217SD16×C41—81no—
218D8×C41—42no—
219D8×C41—42no—
220D8×C41—81no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C2×C8×C41—21no—
227C2×C8×C41—42no—
228C2×C8×C41—81no—
229C4⋊C4×C41—22no—
230C4⋊C4×C41—22no—
231C4⋊C4×C41—22no—
232C4⋊C4×C41—22no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—22no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
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×C41C2×D412yes—
245C4⋊C4×C41C2×D412yes—
246C4⋊C4×C41C2×D411yescharacteristic
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—22no—
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—41no—
266C22⋊C4×C41—41no—
267C42×C41—22no—
268C42×C41—22no—
269C42×C41—21no—
270C42×C41C2×D411yescharacteristic
271C42×C41C2×D411yescharacteristic
272C42×C41C2×D411yescharacteristic
273C42×C41C2411yescharacteristic
274C23×C41—21no—
275C23×C41—21no—
276C23×C41—21no—
277C23×C41—42no—
278C23×C41—42no—
279C23×C41—41no—
280C23×C41—81no—
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—82no—
290D4×C41—21no—
291D4×C41—21no—
292D4×C41—21no—
293D4×C41—21no—
294D4×C41—21no—
295D4×C41—42no—
296D4×C41—42no—
297D4×C41—44no—
298D4×C41—42no—
299D4×C41—41no—
300D4×C41—41no—
301D4×C41—41no—
302D4×C41—41no—
303D4×C41—82no—
304D4×C41—82no—
305D4×C41#13512yes—
306C2×C4×C41—22no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—22no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—22no—
316C2×C4×C41—21no—
317C2×C4×C41—21no—
318C2×C4×C41—44no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—81no—
327C2×C4×C41—81no—
328C2×C4×C41—82no—
329C2×C4×C41—81no—
330C2×C4×C41—82no—
331C2×C4×C41—82no—
332C2×C4×C41#12011yescharacteristic
333C2×C4×C41#12011yescharacteristic
334C2×C4×C41#12011yescharacteristic
335C2×C4×C41C22×D411yescharacteristic
336C2×C4×C41C22×D411yescharacteristic
337C2×C4×C41C22×D411yescharacteristic
338C8×C41—41no—
339C8×C41—41no—
340C8×C41—41no—
341C8×C41—41no—
342C8×C41—41no—
343C8×C41—41no—
344#18638C4111yesmaximal, characteristic, direct product factor, Sylow
345C22×C41—21no—
346C22×C41—21no—
347C22×C41—22no—
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—84no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41#45412yes—
361C22×C41C2×#12011yescharacteristic
362C4×C41—21no—
363C4×C41—21no—
364C4×C41—21no—
365C4×C41—21no—
366C4×C41—41no—
367C4×C41—42no—
368C4×C41—41no—
369C4×C41—41no—
370C4×C41—42no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—81no—
374C4×C41C2×#13511yescharacteristic
375C4×C41#57511yescharacteristic
376C4×C41#57611yescharacteristic
377C4×C41#57711yescharacteristic
378#3520C2×C4111yescharacteristic, complemented
379#3247C2×C4111yescharacteristic, complemented
380#3131C2×C4111yescharacteristic, complemented
381#3109C2×C4111yescharacteristic, complemented
382#1638C2×C4111yescharacteristic, complemented
383#1637C2×C4111yescharacteristic, complemented
384#1635C2×C4111yescharacteristic, complemented
385#1635C2×C4111yescharacteristic, complemented
386#1628C2×C4111yescharacteristic, complemented
387#1627C2×C4111yescharacteristic, complemented
388#1625C2×C4111yescharacteristic, complemented
389#1625C2×C4111yescharacteristic, complemented
390#1552C2×C4111yescharacteristic, complemented
391#1494C2×C4111yescharacteristic, complemented
392C2×D4⋊C8C2×C4111yescharacteristic, complemented
393C2×C41—22no—
394C2×C41—42no—
395C2×C41—81no—
396C2×C41—81no—
397C2×C41—161no—
398C2×C41#300211yescharacteristic
399C2×C41#301211yescharacteristic
400C2×C41C2×#45411yescharacteristic
401#556C22×C4111yescharacteristic
402#554—21no—
403#552—21no—
404#551—22no—
405D4×Q8C22×C4111yescharacteristic
406#548—21no—
407#547C22×C4111yescharacteristic
408#547C22×C4111yescharacteristic
409#546—21no—
410#542—21no—
411#539—22no—
412#533C22×C4111yescharacteristic
413#532C22×C4111yescharacteristic
414#529C22×C4111yescharacteristic
415#525—21no—
416C2×C22⋊Q8—21no—
417#520—21no—
418C2×C4×D4C22×C4111yescharacteristic
419#488—22no—
420#487C22×C4111yescharacteristic, complemented
421#487C22×C4111yescharacteristic, complemented
422#486C22×C4111yescharacteristic, complemented
423#486C22×C4111yescharacteristic, complemented
424#481—21no—
425#478—21no—
426#477C22×C4111yescharacteristic, complemented
427#476C22×C4111yescharacteristic
428#476C22×C4111yescharacteristic
429#476C22×C4111yescharacteristic, complemented
430#466—21no—
431#465—21no—
432#463—21no—
433#460C22×C4111yescharacteristic, complemented
434#459C22×C4111yescharacteristic
435#459C22×C4111yescharacteristic
436#459C22×C4111yescharacteristic, complemented
437#447—21no—
438#442—21no—
439#442—21no—
440#432C22×C4111yescharacteristic
441C2×C4⋊C8C22×C4111yescharacteristic
442#416—22no—
443C2×C4×C8C22×C4111yescharacteristic
444#332C22×C4111yescharacteristic, complemented
445#332C22×C4111yescharacteristic, complemented
446#332C22×C4111yescharacteristic, complemented
447#332C22×C4111yescharacteristic, complemented
448Q8⋊C8C22×C4111yescharacteristic, complemented
449Q8⋊C8C22×C4111yescharacteristic, complemented
450D4⋊C8C22×C4111yescharacteristic
451D4⋊C8C22×C4111yescharacteristic
452D4⋊C8C22×C4111yescharacteristic
453D4⋊C8C22×C4111yescharacteristic
454D4⋊C8C22×C4111yescharacteristic, complemented
455D4⋊C8C22×C4111yescharacteristic, complemented
456C41#1863811yescharacteristic, direct product factor, Sylow
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C22×Q8—21no—
461C22×D4D4×C4111yescharacteristic
462C23×C4—21no—
463C2×SD16—21no—
464C2×D8—21no—
465C2×D8—21no—
466C2×D8—21no—
467C22×C8—21no—
468C22×C8—21no—
469C4⋊Q8—21no—
470C4⋊Q8C23×C4111yescharacteristic
471C4⋊Q8C23×C4111yescharacteristic
472C4⋊Q8C23×C4111yescharacteristic
473#127C23×C4111yescharacteristic
474#126—22no—
475#126—22no—
476#126—21no—
477#125—22no—
478#125D4×C4111yescharacteristic
479#125D4×C4112yes—
480#124—22no—
481#124—21no—
482#124—21no—
483#124D4×C4111yescharacteristic
484#123—22no—
485#123—22no—
486#123—21no—
487#123—22no—
488#123—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8—21no—
499C22⋊Q8D4×C4111yescharacteristic
500#121—22no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121D4×C4111yescharacteristic
506#120—22no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8C23×C4111yescharacteristic
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4D4×C4111yescharacteristic
521C4×D4D4×C4111yescharacteristic
522C4×D4C23×C4111yescharacteristic
523C4×D4C23×C4111yescharacteristic
524C4×D4C23×C4111yescharacteristic
525#117—22no—
526#117—21no—
527#117—21no—
528#117D4×C4112yes—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C4111yescharacteristic
533C2×C22⋊C4—22no—
534C2×C22⋊C4—21no—
535C2×C42C23×C4111yescharacteristic
536#107—21no—
537#106—21no—
538#106—21no—
539#106—21no—
540C4⋊C8—21no—
541C4⋊C8C23×C4111yescharacteristic
542C4⋊C8C23×C4111yescharacteristic
543C4⋊C8C23×C4111yescharacteristic
544C4⋊C8C23×C4111yescharacteristic
545#103—21no—
546#103—22no—
547#103—22no—
548#102—21no—
549#102—21no—
550#102—21no—
551#102—22no—
552#102—22no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557C22⋊C8—21no—
558#97—21no—
559C4×C8—21no—
560C4×C8C23×C4111yescharacteristic
561C4×C8C23×C4111yescharacteristic
562C24—21no—
563#41—44no—
564#41—42no—
565#41—42no—
566#41—81no—
567#41—81no—
568C2×Q8—22no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—81no—
573C2×Q8—81no—
574C2×Q8C2×D4×C4111yescharacteristic
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4C2×D4×C4111yescharacteristic
586C2×D4C2×D4×C4111yescharacteristic
587C2×D4C2×D4×C4111yescharacteristic
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—41no—
598C22×C4—81no—
599C22×C4—81no—
600C22×C4C2×D4×C4111yescharacteristic
601C22×C4C2×D4×C4111yescharacteristic
602C22×C4C2×D4×C4111yescharacteristic
603SD16—81no—
604D8—42no—
605D8—42no—
606D8—81no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—81no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4C2×D4×C4112yes—
631C4⋊C4C2×D4×C4112yes—
632C4⋊C4C2×D4×C4111yescharacteristic
633C4⋊C4C2×D4×C4111yescharacteristic
634C4⋊C4C2×D4×C4111yescharacteristic
635C4⋊C4C2×D4×C4111yescharacteristic
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—22no—
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—41no—
652C22⋊C4—41no—
653C42—22no—
654C42—22no—
655C42—21no—
656C42C2×D4×C4111yescharacteristic
657C42C2×D4×C4111yescharacteristic
658C42C2×D4×C4111yescharacteristic
659C42C24×C4111yescharacteristic
660C23—21no—
661C23—21no—
662C23—21no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—81no—
667C23#120×C4111yescharacteristic
668Q8—21no—
669Q8—21no—
670Q8—42no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—82no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—42no—
682D4—42no—
683D4—44no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690D4—82no—
691D4#135×C4112yes—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—44no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—82no—
715C2×C4—81no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4#120×C4111yescharacteristic
719C2×C4#120×C4111yescharacteristic
720C2×C4#120×C4111yescharacteristic
721C2×C4C22×D4×C4111yescharacteristic
722C2×C4C22×D4×C4111yescharacteristic
723C2×C4C22×D4×C4111yescharacteristic
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—41no—
729C8—41no—
730C22—21no—
731C22—21no—
732C22—22no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C41×#45412yes—
746C22C2×#120×C4111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—41no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—81no—
759C4C2×#135×C4111yescharacteristic
760C4C41×#57511yescharacteristic
761C4C41×#57611yescharacteristic
762C4C41×#57711yescharacteristic
763C2—22no—
764C2—42no—
765C2—81no—
766C2—81no—
767C2—161no—
768C2C41×#300211yescharacteristic
769C2C41×#301211yescharacteristic
770C2C2×C41×#45411yescharacteristic
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×#3520C2semidirect
2. C41×#3247C2semidirect
3. C41×#3131C2semidirect
4. C41×#3109C2semidirect
5. C41×#1638C2semidirect
6. C41×#1637C2semidirect
7. C41×#1635C2semidirect
8. C41×#1635C2semidirect
9. C41×#1628C2semidirect
10. C41×#1627C2semidirect
11. C41×#1625C2semidirect
12. C41×#1625C2semidirect
13. C41×#1552C2semidirect
14. C41×#1494C2semidirect
15. C2×C41×D4⋊C8C2semidirect
35. C41×#487C22semidirect
36. C41×#487C22semidirect
37. C41×#486C22semidirect
38. C41×#486C22semidirect
41. C41×#477C22semidirect
44. C41×#476C22semidirect
48. C41×#460C22semidirect
51. C41×#459C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
61. C41×#332C22semidirect
62. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
69. C41×D4⋊C8C22semidirect
70. C41×D4⋊C8C22semidirect
344. #18638C41direct (N × H)
378. #3520C2×C41semidirect
379. #3247C2×C41semidirect
380. #3131C2×C41semidirect
381. #3109C2×C41semidirect
382. #1638C2×C41semidirect
383. #1637C2×C41semidirect
384. #1635C2×C41semidirect
385. #1635C2×C41semidirect
386. #1628C2×C41semidirect
387. #1627C2×C41semidirect
388. #1625C2×C41semidirect
389. #1625C2×C41semidirect
390. #1552C2×C41semidirect
391. #1494C2×C41semidirect
392. C2×D4⋊C8C2×C41semidirect
420. #487C22×C41semidirect
421. #487C22×C41semidirect
422. #486C22×C41semidirect
423. #486C22×C41semidirect
426. #477C22×C41semidirect
429. #476C22×C41semidirect
433. #460C22×C41semidirect
436. #459C22×C41semidirect
444. #332C22×C41semidirect
445. #332C22×C41semidirect
446. #332C22×C41semidirect
447. #332C22×C41semidirect
448. Q8⋊C8C22×C41semidirect
449. Q8⋊C8C22×C41semidirect
454. D4⋊C8C22×C41semidirect
455. D4⋊C8C22×C41semidirect
456. C41#18638direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35202
C41×#32472
C41×#31312
C41×#31092
C41×#16382
C41×#16372
C41×#16352
C41×#16282
C41×#16272
C41×#16252
C41×#15522
C41×#14942
C2×C41×D4⋊C82
#1863841