Finite Group Databasebeta

← C41×#18659 #23794860

Subgroups — C41×#18659 #23794860

Order 10496.

938 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3514C211yesmaximal, characteristic
2C41×#3233C211yesmaximal, characteristic, complemented
3C41×#3167C211yesmaximal, characteristic, complemented
4C41×#3116C211yesmaximal, characteristic, complemented
5C41×#1652C211yesmaximal, characteristic, complemented
6C41×#1651C211yesmaximal, characteristic, complemented
7C41×#1640C211yesmaximal, characteristic, complemented
8C41×#1639C211yesmaximal, characteristic, complemented
9C41×#1638C211yesmaximal, characteristic, complemented
10C41×#1637C211yesmaximal, characteristic, complemented
11C41×#1630C211yesmaximal, characteristic, complemented
12C41×#1629C211yesmaximal, characteristic, complemented
13C41×#1553C211yesmaximal, characteristic, complemented
14C41×#1494C211yesmaximal, characteristic, complemented
15C41×#1476C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17C41×#556C2211yescharacteristic
18C41×#555—21no—
19C41×#551—22no—
20D4×Q8×C41C2211yescharacteristic
21C41×#548—21no—
22C41×#546—21no—
23C41×#546—21no—
24D42×C41C2211yescharacteristic
25C41×#542—21no—
26C41×#538—22no—
27C41×#533C2211yescharacteristic, complemented
28C41×#532C2211yescharacteristic
29C41×#529—21no—
30C41×#529C2211yescharacteristic
31C2×#124×C41—21no—
32C41×#518—21no—
33C4×#41×C41C2211yescharacteristic
34C41×#499—21no—
35C41×#498C2211yescharacteristic, complemented
36C41×#492C2211yescharacteristic
37C41×#488—21no—
38C41×#487C2211yescharacteristic, complemented
39C41×#486C2211yescharacteristic
40C41×#485—21no—
41C41×#485—21no—
42C41×#482—21no—
43C41×#477C2211yescharacteristic, complemented
44C41×#477C2211yescharacteristic, complemented
45C41×#476C2211yescharacteristic
46C41×#476C2211yescharacteristic
47C41×#475C2211yescharacteristic, complemented
48C41×#474C2211yescharacteristic
49C41×#465—22no—
50C41×#462C2211yescharacteristic, complemented
51C41×#461C2211yescharacteristic
52C41×#452—21no—
53C41×#441—21no—
54C41×#440—21no—
55C4×SD16×C41—22no—
56C41×#432C2211yescharacteristic, complemented
57C41×#431C2211yescharacteristic, 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×Q8⋊C8C2211yescharacteristic, complemented
66C41×Q8⋊C8C2211yescharacteristic, complemented
67C41×D4⋊C8C2211yescharacteristic
68C41×D4⋊C8C2211yescharacteristic
69C41×D4⋊C8C2211yescharacteristic
70C41×D4⋊C8C2211yescharacteristic
71C2×#41×C41—21no—
72C2×#41×C41D411yescharacteristic
73C22×Q8×C41—21no—
74C22×D4×C41—21no—
75C22×D4×C41—21no—
76C2×Q16×C41—21no—
77C2×SD16×C41—22no—
78C2×SD16×C41—21no—
79C22×C8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#127×C41C2311yescharacteristic
85#126×C41—22no—
86#126×C41—22no—
87#126×C41—21no—
88#125×C41—21no—
89#125×C41D411yescharacteristic
90#124×C41—22no—
91#124×C41—22no—
92#124×C41—22no—
93#124×C41—21no—
94#124×C41—21no—
95#124×C41—21no—
96#124×C41—21no—
97#124×C41D411yescharacteristic
98#123×C41—22no—
99#123×C41—22no—
100#123×C41—22no—
101#123×C41—21no—
102C22⋊Q8×C41—22no—
103C22⋊Q8×C41—21no—
104C22⋊Q8×C41—21no—
105C22⋊Q8×C41—22no—
106C22⋊Q8×C41—21no—
107C22⋊Q8×C41—21no—
108C22⋊Q8×C41D411yescharacteristic
109#121×C41—22no—
110#121×C41—22no—
111#121×C41—21no—
112#121×C41—21no—
113#121×C41—21no—
114#121×C41D411yescharacteristic
115#121×C41D412yes—
116#120×C41—22no—
117#120×C41—22no—
118C4×Q8×C41—21no—
119C4×Q8×C41—21no—
120C4×Q8×C41—21no—
121C4×Q8×C41D411yescharacteristic
122C4×Q8×C41C2311yescharacteristic
123C4×Q8×C41C2311yescharacteristic
124C4×D4×C41—22no—
125C4×D4×C41—22no—
126C4×D4×C41—21no—
127C4×D4×C41—21no—
128C4×D4×C41—21no—
129C4×D4×C41—21no—
130C4×D4×C41—21no—
131C4×D4×C41—21no—
132C4×D4×C41—21no—
133C4×D4×C41D411yescharacteristic
134C4×D4×C41D412yes—
135C4×D4×C41C2311yescharacteristic
136C4×D4×C41C2311yescharacteristic
137#117×C41—22no—
138#117×C41—21no—
139#117×C41—21no—
140#117×C41—21no—
141#117×C41—21no—
142#117×C41D411yescharacteristic
143C2×C22⋊C4×C41—22no—
144C2×C22⋊C4×C41—22no—
145C2×C22⋊C4×C41—22no—
146C2×C42×C41—21no—
147C2×C42×C41C2311yescharacteristic
148#107×C41—21no—
149#107×C41—21no—
150#107×C41—21no—
151#106×C41—22no—
152#106×C41—21no—
153#106×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#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—
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
176C24×C41—22no—
177#41×C41—22no—
178#41×C41—41no—
179#41×C41—81no—
180#41×C41—81no—
181C2×Q8×C41—22no—
182C2×Q8×C41—21no—
183C2×Q8×C41—21no—
184C2×Q8×C41—21no—
185C2×Q8×C41—81no—
186C2×Q8×C41—81no—
187C2×Q8×C41C2×D411yescharacteristic
188C2×Q8×C41C2×D411yescharacteristic
189C2×D4×C41—22no—
190C2×D4×C41—21no—
191C2×D4×C41—22no—
192C2×D4×C41—21no—
193C2×D4×C41—22no—
194C2×D4×C41—21no—
195C2×D4×C41—21no—
196C2×D4×C41—42no—
197C2×D4×C41—42no—
198C2×D4×C41—81no—
199C2×D4×C41—81no—
200C2×D4×C41C2×D411yescharacteristic
201C2×D4×C41C2×D411yescharacteristic
202C2×D4×C41C2×D412yes—
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—22no—
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2×D411yescharacteristic
213Q16×C41—42no—
214SD16×C41—44no—
215SD16×C41—42no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—42no—
223C4⋊C4×C41—22no—
224C4⋊C4×C41—22no—
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—21no—
236C4⋊C4×C41—41no—
237C4⋊C4×C41—41no—
238C4⋊C4×C41C2×D411yescharacteristic
239C4⋊C4×C41C2×D412yes—
240C4⋊C4×C41C2×D411yescharacteristic
241C4⋊C4×C41C2×D411yescharacteristic
242C4⋊C4×C41C2×D411yescharacteristic
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—22no—
246C22⋊C4×C41—22no—
247C22⋊C4×C41—22no—
248C22⋊C4×C41—22no—
249C22⋊C4×C41—22no—
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—22no—
257C22⋊C4×C41—22no—
258C22⋊C4×C41—21no—
259C22⋊C4×C41—21no—
260C22⋊C4×C41—41no—
261C42×C41—22no—
262C42×C41—21no—
263C42×C41—21no—
264C42×C41—21no—
265C42×C41—21no—
266C42×C41—41no—
267C42×C41C2×D411yescharacteristic
268C42×C41C2×D411yescharacteristic
269C42×C41C2×D411yescharacteristic
270C42×C41C2411yescharacteristic
271C23×C41—21no—
272C23×C41—21no—
273C23×C41—22no—
274C23×C41—44no—
275C23×C41—82no—
276C23×C41—82no—
277C23×C41#12011yescharacteristic
278Q8×C41—21no—
279Q8×C41—21no—
280Q8×C41—21no—
281Q8×C41—21no—
282Q8×C41—42no—
283Q8×C41—41no—
284Q8×C41—41no—
285Q8×C41—41no—
286Q8×C41—41no—
287Q8×C41—82no—
288D4×C41—21no—
289D4×C41—21no—
290D4×C41—21no—
291D4×C41—42no—
292D4×C41—42no—
293D4×C41—44no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—41no—
298D4×C41—81no—
299D4×C41—82no—
300D4×C41—82no—
301D4×C41#13512yes—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
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—41no—
314C2×C4×C41—42no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—81no—
322C2×C4×C41—82no—
323C2×C4×C41—82no—
324C2×C4×C41—82no—
325C2×C4×C41#12011yescharacteristic
326C2×C4×C41#12011yescharacteristic
327C2×C4×C41#12011yescharacteristic
328C2×C4×C41C22×D411yescharacteristic
329C2×C4×C41C22×D411yescharacteristic
330C2×C4×C41C22×D411yescharacteristic
331C8×C41—22no—
332C8×C41—41no—
333C8×C41—41no—
334C8×C41—41no—
335C8×C41—41no—
336C8×C41—41no—
337#18659C4111yesmaximal, characteristic, direct product factor, Sylow
338C22×C41—21no—
339C22×C41—22no—
340C22×C41—21no—
341C22×C41—21no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—42no—
346C22×C41—42no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—41no—
350C22×C41—164no—
351C22×C41C2×#12011yescharacteristic
352C4×C41—21no—
353C4×C41—21no—
354C4×C41—21no—
355C4×C41—21no—
356C4×C41—41no—
357C4×C41—41no—
358C4×C41—41no—
359C4×C41—42no—
360C4×C41—41no—
361C4×C41—41no—
362C4×C41—41no—
363C4×C41—81no—
364C4×C41—81no—
365C4×C41C2×#13511yescharacteristic
366C4×C41#57511yescharacteristic
367C4×C41#57711yescharacteristic
368C4×C41#57711yescharacteristic
369#3514C2×C4111yescharacteristic
370#3233C2×C4111yescharacteristic, complemented
371#3167C2×C4111yescharacteristic, complemented
372#3116C2×C4111yescharacteristic, complemented
373#1652C2×C4111yescharacteristic, complemented
374#1651C2×C4111yescharacteristic, complemented
375#1640C2×C4111yescharacteristic, complemented
376#1639C2×C4111yescharacteristic, complemented
377#1638C2×C4111yescharacteristic, complemented
378#1637C2×C4111yescharacteristic, complemented
379#1630C2×C4111yescharacteristic, complemented
380#1629C2×C4111yescharacteristic, complemented
381#1553C2×C4111yescharacteristic, complemented
382#1494C2×C4111yescharacteristic, complemented
383#1476C2×C4111yescharacteristic, complemented
384C2×C41—41no—
385C2×C41—42no—
386C2×C41—82no—
387C2×C41—81no—
388C2×C41#300211yescharacteristic
389C2×C41#300911yescharacteristic
390C2×C41#301811yescharacteristic
391#559C22×C4111yescharacteristic
392#556C22×C4111yescharacteristic
393#555—21no—
394#551—22no—
395D4×Q8C22×C4111yescharacteristic
396#548—21no—
397#546—21no—
398#546—21no—
399D42C22×C4111yescharacteristic
400#542—21no—
401#538—22no—
402#533C22×C4111yescharacteristic, complemented
403#532C22×C4111yescharacteristic
404#529—21no—
405#529C22×C4111yescharacteristic
406C2×#124—21no—
407#518—21no—
408C4×#41C22×C4111yescharacteristic
409#499—21no—
410#498C22×C4111yescharacteristic, complemented
411#492C22×C4111yescharacteristic
412#488—21no—
413#487C22×C4111yescharacteristic, complemented
414#486C22×C4111yescharacteristic
415#485—21no—
416#485—21no—
417#482—21no—
418#477C22×C4111yescharacteristic, complemented
419#477C22×C4111yescharacteristic, complemented
420#476C22×C4111yescharacteristic
421#476C22×C4111yescharacteristic
422#475C22×C4111yescharacteristic, complemented
423#474C22×C4111yescharacteristic
424#465—22no—
425#462C22×C4111yescharacteristic, complemented
426#461C22×C4111yescharacteristic
427#452—21no—
428#441—21no—
429#440—21no—
430C4×SD16—22no—
431#432C22×C4111yescharacteristic, complemented
432#431C22×C4111yescharacteristic, complemented
433C2×C4×C8C22×C4111yescharacteristic, complemented
434#332C22×C4111yescharacteristic, complemented
435#332C22×C4111yescharacteristic, complemented
436#331C22×C4111yescharacteristic
437#331C22×C4111yescharacteristic
438Q8⋊C8C22×C4111yescharacteristic, complemented
439Q8⋊C8C22×C4111yescharacteristic, complemented
440Q8⋊C8C22×C4111yescharacteristic, complemented
441Q8⋊C8C22×C4111yescharacteristic, complemented
442D4⋊C8C22×C4111yescharacteristic
443D4⋊C8C22×C4111yescharacteristic
444D4⋊C8C22×C4111yescharacteristic
445D4⋊C8C22×C4111yescharacteristic
446C41#1865911yescharacteristic, direct product factor, Sylow
447C2×#41—21no—
448C2×#41D4×C4111yescharacteristic
449C22×Q8—21no—
450C22×D4—21no—
451C22×D4—21no—
452C2×Q16—21no—
453C2×SD16—22no—
454C2×SD16—21no—
455C22×C8—21no—
456C4⋊Q8—21no—
457C4⋊Q8C23×C4111yescharacteristic
458C4⋊Q8C23×C4111yescharacteristic
459C4⋊Q8C23×C4111yescharacteristic
460#127C23×C4111yescharacteristic
461#126—22no—
462#126—22no—
463#126—21no—
464#125—21no—
465#125D4×C4111yescharacteristic
466#124—22no—
467#124—22no—
468#124—22no—
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124D4×C4111yescharacteristic
474#123—22no—
475#123—22no—
476#123—22no—
477#123—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8D4×C4111yescharacteristic
485#121—22no—
486#121—22no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121D4×C4111yescharacteristic
491#121D4×C4112yes—
492#120—22no—
493#120—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C4111yescharacteristic
498C4×Q8C23×C4111yescharacteristic
499C4×Q8C23×C4111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4D4×C4111yescharacteristic
510C4×D4D4×C4112yes—
511C4×D4C23×C4111yescharacteristic
512C4×D4C23×C4111yescharacteristic
513#117—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117D4×C4111yescharacteristic
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C42—21no—
523C2×C42C23×C4111yescharacteristic
524#107—21no—
525#107—21no—
526#107—21no—
527#106—22no—
528#106—21no—
529#106—21no—
530#106—21no—
531C4⋊C8C23×C4111yescharacteristic
532C4⋊C8C23×C4111yescharacteristic
533C4⋊C8C23×C4111yescharacteristic
534C4⋊C8C23×C4111yescharacteristic
535#103—21no—
536#103—21no—
537#103—21no—
538#103—22no—
539#103—21no—
540#103—21no—
541#102—22no—
542#102—21no—
543#102—21no—
544#102—21no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547#97—21no—
548C4×C8—21no—
549C4×C8—21no—
550C4×C8C23×C4111yescharacteristic
551C4×C8C23×C4111yescharacteristic
552C24—22no—
553#41—22no—
554#41—41no—
555#41—81no—
556#41—81no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8C2×D4×C4111yescharacteristic
564C2×Q8C2×D4×C4111yescharacteristic
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4C2×D4×C4111yescharacteristic
577C2×D4C2×D4×C4111yescharacteristic
578C2×D4C2×D4×C4112yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4C2×D4×C4111yescharacteristic
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4111yescharacteristic
589Q16—42no—
590SD16—44no—
591SD16—42no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—42no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4C2×D4×C4111yescharacteristic
615C4⋊C4C2×D4×C4112yes—
616C4⋊C4C2×D4×C4111yescharacteristic
617C4⋊C4C2×D4×C4111yescharacteristic
618C4⋊C4C2×D4×C4111yescharacteristic
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—41no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—41no—
643C42C2×D4×C4111yescharacteristic
644C42C2×D4×C4111yescharacteristic
645C42C2×D4×C4111yescharacteristic
646C42C24×C4111yescharacteristic
647C23—21no—
648C23—21no—
649C23—22no—
650C23—44no—
651C23—82no—
652C23—82no—
653C23#120×C4111yescharacteristic
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—21no—
658Q8—42no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—82no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—81no—
676D4—82no—
677D4#135×C4112yes—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—82no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4#120×C4111yescharacteristic
702C2×C4#120×C4111yescharacteristic
703C2×C4#120×C4111yescharacteristic
704C2×C4C22×D4×C4111yescharacteristic
705C2×C4C22×D4×C4111yescharacteristic
706C2×C4C22×D4×C4111yescharacteristic
707C8—22no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C8—41no—
713C22—21no—
714C22—22no—
715C22—21no—
716C22—21no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—42no—
724C22—41no—
725C22—164no—
726C22C2×#120×C4111yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4C2×#135×C4111yescharacteristic
741C4C41×#57511yescharacteristic
742C4C41×#57711yescharacteristic
743C4C41×#57711yescharacteristic
744C2—41no—
745C2—42no—
746C2—81no—
747C2—82no—
748C2C41×#300211yescharacteristic
749C2C41×#300911yescharacteristic
750C2C41×#301811yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3514C2
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×#3233C2semidirect
3. C41×#3167C2semidirect
4. C41×#3116C2semidirect
5. C41×#1652C2semidirect
6. C41×#1651C2semidirect
7. C41×#1640C2semidirect
8. C41×#1639C2semidirect
9. C41×#1638C2semidirect
10. C41×#1637C2semidirect
11. C41×#1630C2semidirect
12. C41×#1629C2semidirect
13. C41×#1553C2semidirect
14. C41×#1494C2semidirect
15. C41×#1476C2semidirect
27. C41×#533C22semidirect
35. C41×#498C22semidirect
38. C41×#487C22semidirect
43. C41×#477C22semidirect
44. C41×#477C22semidirect
47. C41×#475C22semidirect
50. C41×#462C22semidirect
56. C41×#432C22semidirect
57. C41×#431C22semidirect
58. C2×C4×C8×C41C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
63. C41×Q8⋊C8C22semidirect
64. C41×Q8⋊C8C22semidirect
65. C41×Q8⋊C8C22semidirect
66. C41×Q8⋊C8C22semidirect
337. #18659C41direct (N × H)
370. #3233C2×C41semidirect
371. #3167C2×C41semidirect
372. #3116C2×C41semidirect
373. #1652C2×C41semidirect
374. #1651C2×C41semidirect
375. #1640C2×C41semidirect
376. #1639C2×C41semidirect
377. #1638C2×C41semidirect
378. #1637C2×C41semidirect
379. #1630C2×C41semidirect
380. #1629C2×C41semidirect
381. #1553C2×C41semidirect
382. #1494C2×C41semidirect
383. #1476C2×C41semidirect
402. #533C22×C41semidirect
410. #498C22×C41semidirect
413. #487C22×C41semidirect
418. #477C22×C41semidirect
419. #477C22×C41semidirect
422. #475C22×C41semidirect
425. #462C22×C41semidirect
431. #432C22×C41semidirect
432. #431C22×C41semidirect
433. C2×C4×C8C22×C41semidirect
434. #332C22×C41semidirect
435. #332C22×C41semidirect
438. Q8⋊C8C22×C41semidirect
439. Q8⋊C8C22×C41semidirect
440. Q8⋊C8C22×C41semidirect
441. Q8⋊C8C22×C41semidirect
446. C41#18659direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35142
C41×#32332
C41×#31672
C41×#31162
C41×#16522
C41×#16512
C41×#16402
C41×#16392
C41×#16382
C41×#16372
C41×#16302
C41×#16292
C41×#15532
C41×#14942
C41×#14762
#1865941