Finite Group Databasebeta

← C41×#20298 #23796499

Subgroups — C41×#20298 #23796499

Order 10496.

662 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3399C211yesmaximal, characteristic, complemented
2C41×#3373C211yesmaximal, characteristic, complemented
3C41×#3332C211yesmaximal, characteristic, complemented
4C41×#3276C211yesmaximal, characteristic, complemented
5C41×#1709C211yesmaximal, characteristic, complemented
6C41×#1702C211yesmaximal, characteristic, complemented
7C41×#1701C211yesmaximal, characteristic, complemented
8C41×#1690C211yesmaximal, characteristic, complemented
9C41×#1687C211yesmaximal, characteristic, complemented
10C41×#1642C211yesmaximal, characteristic, complemented
11C41×#1640C211yesmaximal, characteristic, complemented
12C41×#1627C211yesmaximal, characteristic, complemented
13C41×#1625C211yesmaximal, characteristic, complemented
14C41×#1590C211yesmaximal, characteristic, complemented
15C41×#1590C211yesmaximal, characteristic, complemented
16C2×#137×C41—21no—
17C41×#559C2211yescharacteristic
18C41×#550C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#547C2211yescharacteristic
21C41×#496—21no—
22C41×#494C2211yescharacteristic
23C41×#493C2211yescharacteristic
24C41×#489—21no—
25C41×#486C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#481—21no—
30C41×#476—21no—
31C41×#475C2211yescharacteristic
32C41×#475C2211yescharacteristic
33C41×#470—21no—
34C41×#469—21no—
35C41×#463—21no—
36C41×#463—21no—
37C41×#462C2211yescharacteristic
38C41×#461C2211yescharacteristic
39C41×#460C2211yescharacteristic
40C41×#459—21no—
41C41×#459C2211yescharacteristic
42C41×#459C2211yescharacteristic
43C41×#459C2211yescharacteristic
44C41×#452—21no—
45C41×#451—21no—
46C41×#449—21no—
47C41×#446C2211yescharacteristic
48C41×#446C2211yescharacteristic
49C41×#442—21no—
50C41×#442—21no—
51C4×SD16×C41C2211yescharacteristic
52C4×SD16×C41C2211yescharacteristic
53C41×#436C2211yescharacteristic
54C41×#436C2211yescharacteristic
55C41×#417—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#332C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#331C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C2×#41×C41—21no—
69C22×Q8×C41—21no—
70#137×C41—44no—
71C2×Q16×C41—21no—
72C2×Q16×C41—21no—
73C2×Q16×C41—21no—
74C2×SD16×C41—21no—
75C2×SD16×C41—21no—
76C2×SD16×C41D411yescharacteristic
77C2×SD16×C41D411yescharacteristic
78C2×D8×C41—21no—
79C2×D8×C41—21no—
80C2×D8×C41—21no—
81C2×D8×C41—21no—
82C2×D8×C41—21no—
83C2×M16×C41—21no—
84C2×M16×C41—21no—
85C4⋊Q8×C41—21no—
86C4⋊Q8×C41C2311yescharacteristic
87C4⋊Q8×C41C2311yescharacteristic
88#127×C41—21no—
89#127×C41C2311yescharacteristic
90#127×C41C2311yescharacteristic
91#124×C41—21no—
92#124×C41—21no—
93#123×C41—41no—
94#123×C41—41no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—21no—
97C22⋊Q8×C41—41no—
98#121×C41—21no—
99#121×C41—21no—
100#121×C41—41no—
101C4×Q8×C41C2311yescharacteristic
102C4×Q8×C41C2311yescharacteristic
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41—21no—
106C4×D4×C41—21no—
107C4×D4×C41C2311yescharacteristic
108C4×D4×C41C2311yescharacteristic
109C2×C4⋊C4×C41—21no—
110#106×C41—21no—
111#106×C41—21no—
112#106×C41D411yescharacteristic
113#106×C41D411yescharacteristic
114C4⋊C8×C41—21no—
115C4⋊C8×C41—21no—
116C4⋊C8×C41C2311yescharacteristic
117C4⋊C8×C41C2311yescharacteristic
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120#103×C41—21no—
121#103×C41—21no—
122#103×C41—21no—
123#103×C41—21no—
124#103×C41D411yescharacteristic
125#103×C41D411yescharacteristic
126#102×C41—21no—
127#102×C41—21no—
128#102×C41—21no—
129#102×C41—21no—
130#102×C41—21no—
131#102×C41—21no—
132#102×C41—21no—
133#102×C41—21no—
134#102×C41—41no—
135#102×C41—41no—
136#102×C41D411yescharacteristic
137#102×C41D411yescharacteristic
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140#97×C41—21no—
141#97×C41—21no—
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C4×C8×C41C2311yescharacteristic
145#41×C41—42no—
146#41×C41—42no—
147#41×C41—81no—
148#41×C41—81no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
151C2×Q8×C41—41no—
152C2×Q8×C41—42no—
153C2×Q8×C41—81no—
154C2×Q8×C41C2×D411yescharacteristic
155C2×Q8×C41C2×D411yescharacteristic
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—41no—
163C2×D4×C41—41no—
164C2×D4×C41—41no—
165C2×D4×C41C2×D411yescharacteristic
166C2×D4×C41C2×D411yescharacteristic
167C22×C4×C41—21no—
168C22×C4×C41—21no—
169C22×C4×C41—41no—
170C22×C4×C41—41no—
171C22×C4×C41—41no—
172C22×C4×C41—41no—
173Q16×C41—42no—
174Q16×C41—42no—
175Q16×C41—81no—
176SD16×C41—22no—
177SD16×C41—41no—
178SD16×C41—42no—
179SD16×C41—81no—
180D8×C41—42no—
181D8×C41—42no—
182D8×C41—81no—
183D8×C41—81no—
184D8×C41—81no—
185M16×C41—42no—
186M16×C41—81no—
187C2×C8×C41—21no—
188C2×C8×C41—21no—
189C2×C8×C41—21no—
190C2×C8×C41—21no—
191C2×C8×C41—21no—
192C2×C8×C41C2×D411yescharacteristic
193C2×C8×C41C2×D411yescharacteristic
194C2×C8×C41C2×D411yescharacteristic
195C2×C8×C41C2×D411yescharacteristic
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—41no—
203C4⋊C4×C41—41no—
204C4⋊C4×C41C2×D411yescharacteristic
205C4⋊C4×C41C2×D411yescharacteristic
206C4⋊C4×C41C2×D411yescharacteristic
207C4⋊C4×C41C2×D411yescharacteristic
208C22⋊C4×C41—21no—
209C22⋊C4×C41—21no—
210C22⋊C4×C41—41no—
211C22⋊C4×C41—41no—
212C22⋊C4×C41—41no—
213C22⋊C4×C41—41no—
214C22⋊C4×C41—41no—
215C22⋊C4×C41—41no—
216C42×C41—21no—
217C42×C41—21no—
218C42×C41C2411yescharacteristic
219C23×C41—21no—
220C23×C41—21no—
221C23×C41—41no—
222C23×C41—41no—
223Q8×C41—21no—
224Q8×C41—21no—
225Q8×C41—21no—
226Q8×C41—21no—
227Q8×C41—41no—
228Q8×C41—41no—
229Q8×C41—41no—
230Q8×C41—41no—
231Q8×C41—82no—
232D4×C41—21no—
233D4×C41—21no—
234D4×C41—21no—
235D4×C41—21no—
236D4×C41—41no—
237D4×C41—41no—
238D4×C41—41no—
239D4×C41—41no—
240D4×C41—41no—
241D4×C41—41no—
242D4×C41—41no—
243D4×C41—41no—
244D4×C41—81no—
245D4×C41—81no—
246D4×C41—82no—
247D4×C41—82no—
248D4×C41—161no—
249C2×C4×C41—21no—
250C2×C4×C41—21no—
251C2×C4×C41—21no—
252C2×C4×C41—21no—
253C2×C4×C41—21no—
254C2×C4×C41—21no—
255C2×C4×C41—41no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—41no—
261C2×C4×C41—82no—
262C2×C4×C41—82no—
263C2×C4×C41—82no—
264C2×C4×C41—161no—
265C2×C4×C41C22×D411yescharacteristic
266C2×C4×C41C22×D411yescharacteristic
267C2×C4×C41H(5,𝔽2)11yescharacteristic
268C8×C41—21no—
269C8×C41—21no—
270C8×C41—21no—
271C8×C41—41no—
272C8×C41—41no—
273C8×C41—41no—
274C8×C41—41no—
275C8×C41—41no—
276C8×C41AGL(1,ℤ/8)12yes—
277#20298C4111yesmaximal, characteristic, direct product factor, Sylow
278C22×C41—41no—
279C22×C41—41no—
280C22×C41—41no—
281C22×C41—41no—
282C22×C41—41no—
283C22×C41—41no—
284C22×C41—81no—
285C22×C41—81no—
286C22×C41—81no—
287C22×C41—81no—
288C22×C41—81no—
289C22×C41—81no—
290C22×C41D4211yescharacteristic
291C4×C41—21no—
292C4×C41—41no—
293C4×C41—41no—
294C4×C41—41no—
295C4×C41—41no—
296C4×C41—41no—
297C4×C41—41no—
298C4×C41—81no—
299C4×C41—81no—
300C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C41#57511yescharacteristic
302C4×C41#57611yescharacteristic
303C4×C41#57711yescharacteristic
304#3399C2×C4111yescharacteristic, complemented
305#3373C2×C4111yescharacteristic, complemented
306#3332C2×C4111yescharacteristic, complemented
307#3276C2×C4111yescharacteristic, complemented
308#1709C2×C4111yescharacteristic, complemented
309#1702C2×C4111yescharacteristic, complemented
310#1701C2×C4111yescharacteristic, complemented
311#1690C2×C4111yescharacteristic, complemented
312#1687C2×C4111yescharacteristic, complemented
313#1642C2×C4111yescharacteristic, complemented
314#1640C2×C4111yescharacteristic, complemented
315#1627C2×C4111yescharacteristic, complemented
316#1625C2×C4111yescharacteristic, complemented
317#1590C2×C4111yescharacteristic, complemented
318#1590C2×C4111yescharacteristic, complemented
319C2×C41—81no—
320C2×C41—81no—
321C2×C41—161no—
322C2×C41—161no—
323C2×C41#327411yescharacteristic
324C2×C41#327511yescharacteristic
325C2×C41#329011yescharacteristic
326C2×#137—21no—
327#559C22×C4111yescharacteristic
328#550C22×C4111yescharacteristic
329D4×Q8C22×C4111yescharacteristic
330#547C22×C4111yescharacteristic
331#496—21no—
332#494C22×C4111yescharacteristic
333#493C22×C4111yescharacteristic
334#489—21no—
335#486C22×C4111yescharacteristic
336#486C22×C4111yescharacteristic
337#486C22×C4111yescharacteristic
338#486C22×C4111yescharacteristic
339#481—21no—
340#476—21no—
341#475C22×C4111yescharacteristic
342#475C22×C4111yescharacteristic
343#470—21no—
344#469—21no—
345#463—21no—
346#463—21no—
347#462C22×C4111yescharacteristic
348#461C22×C4111yescharacteristic
349#460C22×C4111yescharacteristic
350#459—21no—
351#459C22×C4111yescharacteristic
352#459C22×C4111yescharacteristic
353#459C22×C4111yescharacteristic
354#452—21no—
355#451—21no—
356#449—21no—
357#446C22×C4111yescharacteristic
358#446C22×C4111yescharacteristic
359#442—21no—
360#442—21no—
361C4×SD16C22×C4111yescharacteristic
362C4×SD16C22×C4111yescharacteristic
363#436C22×C4111yescharacteristic
364#436C22×C4111yescharacteristic
365#417—21no—
366#334C22×C4111yescharacteristic
367#334C22×C4111yescharacteristic
368#332C22×C4111yescharacteristic
369#332C22×C4111yescharacteristic
370#331C22×C4111yescharacteristic
371#331C22×C4111yescharacteristic
372Q8⋊C8C22×C4111yescharacteristic
373Q8⋊C8C22×C4111yescharacteristic
374D4⋊C8C22×C4111yescharacteristic
375D4⋊C8C22×C4111yescharacteristic
376C82C22×C4111yescharacteristic
377C41#2029811yescharacteristic, direct product factor, Sylow
378C2×#41—21no—
379C2×#41—21no—
380C22×Q8—21no—
381#137—44no—
382C2×Q16—21no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C4111yescharacteristic
388C2×SD16D4×C4111yescharacteristic
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×M16—21no—
395C2×M16—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C4111yescharacteristic
398C4⋊Q8C23×C4111yescharacteristic
399#127—21no—
400#127C23×C4111yescharacteristic
401#127C23×C4111yescharacteristic
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—41no—
409#121—21no—
410#121—21no—
411#121—41no—
412C4×Q8C23×C4111yescharacteristic
413C4×Q8C23×C4111yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4C23×C4111yescharacteristic
419C4×D4C23×C4111yescharacteristic
420C2×C4⋊C4—21no—
421#106—21no—
422#106—21no—
423#106D4×C4111yescharacteristic
424#106D4×C4111yescharacteristic
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8C23×C4111yescharacteristic
428C4⋊C8C23×C4111yescharacteristic
429C4⋊C8C23×C4111yescharacteristic
430C4⋊C8C23×C4111yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103D4×C4111yescharacteristic
436#103D4×C4111yescharacteristic
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—41no—
446#102—41no—
447#102D4×C4111yescharacteristic
448#102D4×C4111yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8C23×C4111yescharacteristic
454C4×C8C23×C4111yescharacteristic
455C4×C8C23×C4111yescharacteristic
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8C2×D4×C4111yescharacteristic
466C2×Q8C2×D4×C4111yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C4111yescharacteristic
477C2×D4C2×D4×C4111yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484Q16—42no—
485Q16—42no—
486Q16—81no—
487SD16—22no—
488SD16—41no—
489SD16—42no—
490SD16—81no—
491D8—42no—
492D8—42no—
493D8—81no—
494D8—81no—
495D8—81no—
496M16—42no—
497M16—81no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8C2×D4×C4111yescharacteristic
504C2×C8C2×D4×C4111yescharacteristic
505C2×C8C2×D4×C4111yescharacteristic
506C2×C8C2×D4×C4111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C4111yescharacteristic
516C4⋊C4C2×D4×C4111yescharacteristic
517C4⋊C4C2×D4×C4111yescharacteristic
518C4⋊C4C2×D4×C4111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42C24×C4111yescharacteristic
530C23—21no—
531C23—21no—
532C23—41no—
533C23—41no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—81no—
556D4—81no—
557D4—82no—
558D4—82no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C4111yescharacteristic
577C2×C4C22×D4×C4111yescharacteristic
578C2×C4H(5,𝔽2)×C4111yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8AGL(1,ℤ/8)×C4112yes—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22D42×C4111yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
611C4C41×#57511yescharacteristic
612C4C41×#57611yescharacteristic
613C4C41×#57711yescharacteristic
614C2—81no—
615C2—81no—
616C2—161no—
617C2—161no—
618C2C41×#327411yescharacteristic
619C2C41×#327511yescharacteristic
620C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C41×#3399C2semidirect
2. C41×#3373C2semidirect
3. C41×#3332C2semidirect
4. C41×#3276C2semidirect
5. C41×#1709C2semidirect
6. C41×#1702C2semidirect
7. C41×#1701C2semidirect
8. C41×#1690C2semidirect
9. C41×#1687C2semidirect
10. C41×#1642C2semidirect
11. C41×#1640C2semidirect
12. C41×#1627C2semidirect
13. C41×#1625C2semidirect
14. C41×#1590C2semidirect
15. C41×#1590C2semidirect
277. #20298C41direct (N × H)
304. #3399C2×C41semidirect
305. #3373C2×C41semidirect
306. #3332C2×C41semidirect
307. #3276C2×C41semidirect
308. #1709C2×C41semidirect
309. #1702C2×C41semidirect
310. #1701C2×C41semidirect
311. #1690C2×C41semidirect
312. #1687C2×C41semidirect
313. #1642C2×C41semidirect
314. #1640C2×C41semidirect
315. #1627C2×C41semidirect
316. #1625C2×C41semidirect
317. #1590C2×C41semidirect
318. #1590C2×C41semidirect
377. C41#20298direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33992
C41×#33732
C41×#33322
C41×#32762
C41×#17092
C41×#17022
C41×#17012
C41×#16902
C41×#16872
C41×#16422
C41×#16402
C41×#16272
C41×#16252
C41×#15902
#2029841