Finite Group Databasebeta

← C41×#19793 #23795994

Subgroups — C41×#19793 #23795994

Order 10496.

616 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3394C211yesmaximal, characteristic, complemented
2C41×#3373C211yesmaximal, characteristic, complemented
3C41×#3302C211yesmaximal, characteristic, complemented
4C41×#3298C211yesmaximal, characteristic, complemented
5C41×#1719C211yesmaximal, characteristic, complemented
6C41×#1700C211yesmaximal, characteristic, complemented
7C41×#1681C211yesmaximal, characteristic, complemented
8C41×#1680C211yesmaximal, characteristic, complemented
9C41×#1665C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1649C211yesmaximal, characteristic, complemented
12C41×#1640C211yesmaximal, characteristic, complemented
13C41×#1625C211yesmaximal, characteristic
14C41×#1582C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17C41×#556C2211yescharacteristic
18D4×Q8×C41C2211yescharacteristic
19C41×#547C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#495—21no—
22C41×#492C2211yescharacteristic
23C41×#489—21no—
24C41×#487C2211yescharacteristic
25C41×#487C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#485—21no—
29C41×#483—21no—
30C41×#476—21no—
31C41×#475C2211yescharacteristic
32C41×#475C2211yescharacteristic
33C41×#474C2211yescharacteristic
34C41×#467—21no—
35C41×#465—21no—
36C41×#464—21no—
37C41×#463—21no—
38C41×#463—21no—
39C41×#462C2211yescharacteristic
40C41×#462C2211yescharacteristic
41C41×#461C2211yescharacteristic
42C41×#459C2211yescharacteristic
43C41×#459C2211yescharacteristic
44C41×#452—21no—
45C41×#448—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C41×#442—21no—
49C4×SD16×C41—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C8×D4×C41C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#416—21no—
55C2×#103×C41—21no—
56C41×#335C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#332C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C2×#41×C41—21no—
68C22×Q8×C41—21no—
69C2×Q16×C41—21no—
70C2×Q16×C41—21no—
71C2×SD16×C41—21no—
72C2×SD16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41D411yescharacteristic
75C2×SD16×C41D411yescharacteristic
76C2×D8×C41—21no—
77C2×D8×C41—21no—
78C22×C8×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—41no—
86#124×C41—21no—
87#124×C41—21no—
88#124×C41—21no—
89#123×C41—41no—
90#123×C41—41no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—41no—
95#121×C41—21no—
96C4×Q8×C41—21no—
97C4×Q8×C41C2311yescharacteristic
98C4×Q8×C41C2311yescharacteristic
99C4×D4×C41—21no—
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41C2311yescharacteristic
103C4×D4×C41C2311yescharacteristic
104#117×C41—21no—
105C2×C4⋊C4×C41—21no—
106#107×C41—21no—
107#107×C41—41no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41D411yescharacteristic
111#106×C41D411yescharacteristic
112C4⋊C8×C41—21no—
113C4⋊C8×C41—21no—
114C4⋊C8×C41C2311yescharacteristic
115C4⋊C8×C41C2311yescharacteristic
116C4⋊C8×C41C2311yescharacteristic
117C4⋊C8×C41C2311yescharacteristic
118#103×C41—21no—
119#103×C41—21no—
120#103×C41—21no—
121#103×C41—21no—
122#103×C41—21no—
123#103×C41—21no—
124#103×C41—21no—
125#103×C41—21no—
126#103×C41—21no—
127#103×C41D411yescharacteristic
128#103×C41D411yescharacteristic
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×C41D411yescharacteristic
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139#97×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144#41×C41—42no—
145#41×C41—81no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—41no—
150C2×Q8×C41—42no—
151C2×Q8×C41—81no—
152C2×Q8×C41C2×D411yescharacteristic
153C2×Q8×C41C2×D411yescharacteristic
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—41no—
158C2×D4×C41C2×D411yescharacteristic
159C2×D4×C41C2×D411yescharacteristic
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—41no—
163C22×C4×C41—41no—
164C22×C4×C41—41no—
165Q16×C41—81no—
166Q16×C41—81no—
167SD16×C41—22no—
168SD16×C41—41no—
169SD16×C41—42no—
170SD16×C41—81no—
171SD16×C41—81no—
172D8×C41—42no—
173D8×C41—81no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—81no—
180C2×C8×C41—81no—
181C2×C8×C41C2×D411yescharacteristic
182C2×C8×C41C2×D411yescharacteristic
183C2×C8×C41C2×D411yescharacteristic
184C2×C8×C41C2×D411yescharacteristic
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41C2×D411yescharacteristic
197C4⋊C4×C41C2×D411yescharacteristic
198C4⋊C4×C41C2×D411yescharacteristic
199C4⋊C4×C41C2×D411yescharacteristic
200C22⋊C4×C41—21no—
201C22⋊C4×C41—21no—
202C22⋊C4×C41—41no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C22⋊C4×C41—41no—
208C22⋊C4×C41—41no—
209C42×C41—21no—
210C42×C41—21no—
211C42×C41—41no—
212C42×C41C2411yescharacteristic
213C23×C41—21no—
214C23×C41—21no—
215C23×C41—41no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—21no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—41no—
224Q8×C41—41no—
225Q8×C41—41no—
226Q8×C41—82no—
227D4×C41—21no—
228D4×C41—21no—
229D4×C41—21no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—41no—
233D4×C41—41no—
234D4×C41—81no—
235D4×C41—82no—
236D4×C41#13512yes—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—82no—
251C2×C4×C41—82no—
252C2×C4×C41—161no—
253C2×C4×C41C22×D411yescharacteristic
254C2×C4×C41C22×D411yescharacteristic
255C2×C4×C41H(5,𝔽2)11yescharacteristic
256C8×C41—21no—
257C8×C41—21no—
258C8×C41—21no—
259C8×C41—21no—
260C8×C41—41no—
261C8×C41—41no—
262C8×C41—41no—
263C8×C41—41no—
264C8×C41—41no—
265#19793C4111yesmaximal, characteristic, direct product factor, Sylow
266C22×C41—22no—
267C22×C41—41no—
268C22×C41—41no—
269C22×C41—41no—
270C22×C41—41no—
271C22×C41—41no—
272C22×C41—81no—
273C22×C41—81no—
274C22×C41—81no—
275C22×C41D4211yescharacteristic
276C4×C41—21no—
277C4×C41—41no—
278C4×C41—41no—
279C4×C41—41no—
280C4×C41—41no—
281C4×C41—41no—
282C4×C41—41no—
283C4×C41—81no—
284C4×C41—81no—
285C4×C41—81no—
286C4×C41C2×#13511yescharacteristic
287C4×C41#57511yescharacteristic
288C4×C41#57611yescharacteristic
289C4×C41#57711yescharacteristic
290#3394C2×C4111yescharacteristic, complemented
291#3373C2×C4111yescharacteristic, complemented
292#3302C2×C4111yescharacteristic, complemented
293#3298C2×C4111yescharacteristic, complemented
294#1719C2×C4111yescharacteristic, complemented
295#1700C2×C4111yescharacteristic, complemented
296#1681C2×C4111yescharacteristic, complemented
297#1680C2×C4111yescharacteristic, complemented
298#1665C2×C4111yescharacteristic, complemented
299#1650C2×C4111yescharacteristic, complemented
300#1649C2×C4111yescharacteristic, complemented
301#1640C2×C4111yescharacteristic, complemented
302#1625C2×C4111yescharacteristic
303#1582C2×C4111yescharacteristic, complemented
304SD16⋊C8C2×C4111yescharacteristic, complemented
305C2×C41—42no—
306C2×C41—81no—
307C2×C41—161no—
308C2×C41#326811yescharacteristic
309C2×C41#328211yescharacteristic
310C2×C41#328911yescharacteristic
311#559C22×C4111yescharacteristic
312#556C22×C4111yescharacteristic
313D4×Q8C22×C4111yescharacteristic
314#547C22×C4111yescharacteristic
315#500C22×C4111yescharacteristic
316#495—21no—
317#492C22×C4111yescharacteristic
318#489—21no—
319#487C22×C4111yescharacteristic
320#487C22×C4111yescharacteristic
321#486C22×C4111yescharacteristic
322#486C22×C4111yescharacteristic
323#485—21no—
324#483—21no—
325#476—21no—
326#475C22×C4111yescharacteristic
327#475C22×C4111yescharacteristic
328#474C22×C4111yescharacteristic
329#467—21no—
330#465—21no—
331#464—21no—
332#463—21no—
333#463—21no—
334#462C22×C4111yescharacteristic
335#462C22×C4111yescharacteristic
336#461C22×C4111yescharacteristic
337#459C22×C4111yescharacteristic
338#459C22×C4111yescharacteristic
339#452—21no—
340#448—21no—
341#446C22×C4111yescharacteristic
342C8×Q8C22×C4111yescharacteristic
343#442—21no—
344C4×SD16—21no—
345C4×SD16C22×C4111yescharacteristic
346C4×SD16C22×C4111yescharacteristic
347C8×D4C22×C4111yescharacteristic
348C8×D4C22×C4111yescharacteristic
349#416—21no—
350C2×#103—21no—
351#335C22×C4111yescharacteristic
352#334C22×C4111yescharacteristic
353#332C22×C4111yescharacteristic
354#332C22×C4111yescharacteristic
355#332C22×C4111yescharacteristic
356#331C22×C4111yescharacteristic
357Q8⋊C8C22×C4111yescharacteristic
358Q8⋊C8C22×C4111yescharacteristic
359D4⋊C8C22×C4111yescharacteristic
360D4⋊C8C22×C4111yescharacteristic
361#322C22×C4111yescharacteristic
362C41#1979311yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C22×Q8—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16D4×C4111yescharacteristic
371C2×SD16D4×C4111yescharacteristic
372C2×D8—21no—
373C2×D8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C4111yescharacteristic
378C4⋊Q8C23×C4111yescharacteristic
379C4⋊Q8C23×C4111yescharacteristic
380#127C23×C4111yescharacteristic
381#126—41no—
382#124—21no—
383#124—21no—
384#124—21no—
385#123—41no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—41no—
391#121—21no—
392C4×Q8—21no—
393C4×Q8C23×C4111yescharacteristic
394C4×Q8C23×C4111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C4111yescharacteristic
399C4×D4C23×C4111yescharacteristic
400#117—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—41no—
404#106—21no—
405#106—21no—
406#106D4×C4111yescharacteristic
407#106D4×C4111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C4111yescharacteristic
411C4⋊C8C23×C4111yescharacteristic
412C4⋊C8C23×C4111yescharacteristic
413C4⋊C8C23×C4111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103D4×C4111yescharacteristic
424#103D4×C4111yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—41no—
431#102D4×C4111yescharacteristic
432#102D4×C4111yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C4111yescharacteristic
438C4×C8C23×C4111yescharacteristic
439C4×C8C23×C4111yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—41no—
446C2×Q8—42no—
447C2×Q8—81no—
448C2×Q8C2×D4×C4111yescharacteristic
449C2×Q8C2×D4×C4111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C2×D4×C4111yescharacteristic
455C2×D4C2×D4×C4111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461Q16—81no—
462Q16—81no—
463SD16—22no—
464SD16—41no—
465SD16—42no—
466SD16—81no—
467SD16—81no—
468D8—42no—
469D8—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×D4×C4111yescharacteristic
478C2×C8C2×D4×C4111yescharacteristic
479C2×C8C2×D4×C4111yescharacteristic
480C2×C8C2×D4×C4111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C4111yescharacteristic
493C4⋊C4C2×D4×C4111yescharacteristic
494C4⋊C4C2×D4×C4111yescharacteristic
495C4⋊C4C2×D4×C4111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C4111yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—82no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4#135×C4112yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4C22×D4×C4111yescharacteristic
550C2×C4C22×D4×C4111yescharacteristic
551C2×C4H(5,𝔽2)×C4111yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—21no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C4111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×#135×C4111yescharacteristic
582C4C41×#57511yescharacteristic
583C4C41×#57611yescharacteristic
584C4C41×#57711yescharacteristic
585C2—42no—
586C2—81no—
587C2—161no—
588C2C41×#326811yescharacteristic
589C2C41×#328211yescharacteristic
590C2C41×#328911yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#1625C2
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×#3394C2semidirect
2. C41×#3373C2semidirect
3. C41×#3302C2semidirect
4. C41×#3298C2semidirect
5. C41×#1719C2semidirect
6. C41×#1700C2semidirect
7. C41×#1681C2semidirect
8. C41×#1680C2semidirect
9. C41×#1665C2semidirect
10. C41×#1650C2semidirect
11. C41×#1649C2semidirect
12. C41×#1640C2semidirect
14. C41×#1582C2semidirect
15. C41×SD16⋊C8C2semidirect
265. #19793C41direct (N × H)
290. #3394C2×C41semidirect
291. #3373C2×C41semidirect
292. #3302C2×C41semidirect
293. #3298C2×C41semidirect
294. #1719C2×C41semidirect
295. #1700C2×C41semidirect
296. #1681C2×C41semidirect
297. #1680C2×C41semidirect
298. #1665C2×C41semidirect
299. #1650C2×C41semidirect
300. #1649C2×C41semidirect
301. #1640C2×C41semidirect
303. #1582C2×C41semidirect
304. SD16⋊C8C2×C41semidirect
362. C41#19793direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33942
C41×#33732
C41×#33022
C41×#32982
C41×#17192
C41×#17002
C41×#16812
C41×#16802
C41×#16652
C41×#16502
C41×#16492
C41×#16402
C41×#16252
C41×#15822
C41×SD16⋊C82
#1979341