Finite Group Databasebeta

← C41×#19825 #23796026

Subgroups — C41×#19825 #23796026

Order 10496.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3394C211yesmaximal, characteristic, complemented
2C41×#3361C211yesmaximal, characteristic, complemented
3C41×#3324C211yesmaximal, characteristic, complemented
4C41×#3295C211yesmaximal, characteristic, complemented
5C41×#1717C211yesmaximal, characteristic, complemented
6C41×#1697C211yesmaximal, characteristic, complemented
7C41×#1682C211yesmaximal, characteristic, complemented
8C41×#1678C211yesmaximal, characteristic, complemented
9C41×#1665C211yesmaximal, characteristic, complemented
10C41×#1644C211yesmaximal, characteristic, complemented
11C41×#1638C211yesmaximal, characteristic, complemented
12C41×#1620C211yesmaximal, characteristic, complemented
13C41×#1619C211yesmaximal, characteristic
14C41×#1583C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic, complemented
17C41×#556C2211yescharacteristic
18C41×#554C2211yescharacteristic
19D42×C41C2211yescharacteristic
20C41×#495—21no—
21C41×#493C2211yescharacteristic
22C41×#492C2211yescharacteristic, complemented
23C41×#488—21no—
24C41×#487C2211yescharacteristic, complemented
25C41×#486C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic, complemented
28C41×#482—21no—
29C41×#481—21no—
30C41×#478—21no—
31C41×#477C2211yescharacteristic, complemented
32C41×#476C2211yescharacteristic
33C41×#474C2211yescharacteristic
34C41×#468—21no—
35C41×#465—21no—
36C41×#464—21no—
37C41×#463—21no—
38C41×#463—21no—
39C41×#462C2211yescharacteristic, complemented
40C41×#460C2211yescharacteristic
41C41×#460C2211yescharacteristic
42C41×#459C2211yescharacteristic
43C41×#459C2211yescharacteristic
44C41×#450—21no—
45C41×#450—21no—
46C8×Q8×C41C2211yescharacteristic, complemented
47C8×Q8×C41C2211yescharacteristic, complemented
48C4×SD16×C41—21no—
49C4×SD16×C41C2211yescharacteristic
50C4×SD16×C41C2211yescharacteristic
51C4×D8×C41—21no—
52C41×#436C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#418—21no—
55C2×#102×C41—21no—
56C41×#335C2211yescharacteristic, complemented
57C41×#334C2211yescharacteristic, complemented
58C41×#333C2211yescharacteristic, complemented
59C41×#332C2211yescharacteristic, complemented
60C41×#331C2211yescharacteristic
61C41×#331C2211yescharacteristic, complemented
62C41×Q8⋊C8C2211yescharacteristic, complemented
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic, complemented
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C2×Q16×C41—21no—
70C2×SD16×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—
78C2×D8×C41—41no—
79C2×M16×C41—21no—
80C22×C8×C41—21no—
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83#127×C41C2311yescharacteristic
84#127×C41C2311yescharacteristic
85#126×C41—41no—
86#125×C41—21no—
87#124×C41—21no—
88#124×C41—21no—
89#124×C41—21no—
90#123×C41—41no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—41no—
94#121×C41—21no—
95#121×C41—21no—
96#120×C41—41no—
97C4×Q8×C41—21no—
98C4×Q8×C41C2311yescharacteristic
99C4×Q8×C41C2311yescharacteristic
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41—21no—
103C4×D4×C41C2311yescharacteristic
104C4×D4×C41C2311yescharacteristic
105#117×C41—21no—
106C2×C4⋊C4×C41—21no—
107#107×C41—21no—
108#107×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—41no—
121#103×C41D411yescharacteristic
122#103×C41D411yescharacteristic
123#102×C41—21no—
124#102×C41—21no—
125#102×C41—21no—
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—21no—
135#102×C41D411yescharacteristic
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138C22⋊C8×C41—21no—
139C4×C8×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C24×C41—41no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41C2×D411yescharacteristic
148C2×Q8×C41C2×D411yescharacteristic
149C2×D4×C41—21no—
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—41no—
156C2×D4×C41—41no—
157C2×D4×C41—42no—
158C2×D4×C41—42no—
159C2×D4×C41—81no—
160C2×D4×C41—81no—
161C2×D4×C41C2×D411yescharacteristic
162C2×D4×C41C2×D411yescharacteristic
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—41no—
166C22×C4×C41—41no—
167Q16×C41—81no—
168SD16×C41—22no—
169SD16×C41—41no—
170SD16×C41—42no—
171SD16×C41—81no—
172SD16×C41—81no—
173SD16×C41—81no—
174D8×C41—42no—
175D8×C41—81no—
176D8×C41—82no—
177M16×C41—81no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—81no—
184C2×C8×C41C2×D411yescharacteristic
185C2×C8×C41C2×D411yescharacteristic
186C2×C8×C41C2×D411yescharacteristic
187C2×C8×C41C2×D411yescharacteristic
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41—41no—
197C4⋊C4×C41C2×D411yescharacteristic
198C4⋊C4×C41C2×D411yescharacteristic
199C4⋊C4×C41C2×D411yescharacteristic
200C4⋊C4×C41C2×D411yescharacteristic
201C22⋊C4×C41—21no—
202C22⋊C4×C41—21no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C22⋊C4×C41—41no—
208C22⋊C4×C41—41no—
209C22⋊C4×C41—41no—
210C42×C41—21no—
211C42×C41—21no—
212C42×C41—41no—
213C42×C41C2411yescharacteristic
214C23×C41—21no—
215C23×C41—21no—
216C23×C41—41no—
217C23×C41—41no—
218C23×C41—82no—
219C23×C41—82no—
220C23×C41—161no—
221Q8×C41—21no—
222Q8×C41—21no—
223Q8×C41—21no—
224Q8×C41—21no—
225Q8×C41—41no—
226Q8×C41—41no—
227Q8×C41—81no—
228D4×C41—21no—
229D4×C41—21no—
230D4×C41—21no—
231D4×C41—41no—
232D4×C41—41no—
233D4×C41—41no—
234D4×C41—41no—
235D4×C41—41no—
236D4×C41—41no—
237D4×C41—41no—
238D4×C41—41no—
239D4×C41—81no—
240D4×C41—81no—
241D4×C41—82no—
242D4×C41—82no—
243D4×C41#13512yes—
244C2×C4×C41—21no—
245C2×C4×C41—21no—
246C2×C4×C41—21no—
247C2×C4×C41—21no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—161no—
257C2×C4×C41—161no—
258C2×C4×C41C22×D411yescharacteristic
259C2×C4×C41C22×D411yescharacteristic
260C2×C4×C41H(5,𝔽2)11yescharacteristic
261C8×C41—21no—
262C8×C41—21no—
263C8×C41—21no—
264C8×C41—21no—
265C8×C41—41no—
266C8×C41—41no—
267C8×C41—41no—
268C8×C41—41no—
269C8×C41—41no—
270#19825C4111yesmaximal, characteristic, direct product factor, Sylow
271C22×C41—22no—
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—41no—
276C22×C41—41no—
277C22×C41—81no—
278C22×C41—81no—
279C22×C41—81no—
280C22×C41—81no—
281C22×C41—81no—
282C22×C41—81no—
283C22×C41—164no—
284C22×C41D4211yescharacteristic
285C4×C41—21no—
286C4×C41—41no—
287C4×C41—41no—
288C4×C41—41no—
289C4×C41—41no—
290C4×C41—41no—
291C4×C41—41no—
292C4×C41—81no—
293C4×C41—81no—
294C4×C41C2×#13511yescharacteristic
295C4×C41#57511yescharacteristic
296C4×C41#57611yescharacteristic
297C4×C41#57711yescharacteristic
298#3394C2×C4111yescharacteristic, complemented
299#3361C2×C4111yescharacteristic, complemented
300#3324C2×C4111yescharacteristic, complemented
301#3295C2×C4111yescharacteristic, complemented
302#1717C2×C4111yescharacteristic, complemented
303#1697C2×C4111yescharacteristic, complemented
304#1682C2×C4111yescharacteristic, complemented
305#1678C2×C4111yescharacteristic, complemented
306#1665C2×C4111yescharacteristic, complemented
307#1644C2×C4111yescharacteristic, complemented
308#1638C2×C4111yescharacteristic, complemented
309#1620C2×C4111yescharacteristic, complemented
310#1619C2×C4111yescharacteristic
311#1583C2×C4111yescharacteristic, complemented
312SD16⋊C8C2×C4111yescharacteristic, complemented
313C2×C41—42no—
314C2×C41—81no—
315C2×C41—161no—
316C2×C41—161no—
317C2×C41#326811yescharacteristic
318C2×C41#328211yescharacteristic
319C2×C41#328811yescharacteristic
320#559C22×C4111yescharacteristic, complemented
321#556C22×C4111yescharacteristic
322#554C22×C4111yescharacteristic
323D42C22×C4111yescharacteristic
324#495—21no—
325#493C22×C4111yescharacteristic
326#492C22×C4111yescharacteristic, complemented
327#488—21no—
328#487C22×C4111yescharacteristic, complemented
329#486C22×C4111yescharacteristic
330#486C22×C4111yescharacteristic
331#486C22×C4111yescharacteristic, complemented
332#482—21no—
333#481—21no—
334#478—21no—
335#477C22×C4111yescharacteristic, complemented
336#476C22×C4111yescharacteristic
337#474C22×C4111yescharacteristic
338#468—21no—
339#465—21no—
340#464—21no—
341#463—21no—
342#463—21no—
343#462C22×C4111yescharacteristic, complemented
344#460C22×C4111yescharacteristic
345#460C22×C4111yescharacteristic
346#459C22×C4111yescharacteristic
347#459C22×C4111yescharacteristic
348#450—21no—
349#450—21no—
350C8×Q8C22×C4111yescharacteristic, complemented
351C8×Q8C22×C4111yescharacteristic, complemented
352C4×SD16—21no—
353C4×SD16C22×C4111yescharacteristic
354C4×SD16C22×C4111yescharacteristic
355C4×D8—21no—
356#436C22×C4111yescharacteristic
357C8×D4C22×C4111yescharacteristic
358#418—21no—
359C2×#102—21no—
360#335C22×C4111yescharacteristic, complemented
361#334C22×C4111yescharacteristic, complemented
362#333C22×C4111yescharacteristic, complemented
363#332C22×C4111yescharacteristic, complemented
364#331C22×C4111yescharacteristic
365#331C22×C4111yescharacteristic, complemented
366Q8⋊C8C22×C4111yescharacteristic, complemented
367Q8⋊C8C22×C4111yescharacteristic, complemented
368D4⋊C8C22×C4111yescharacteristic
369D4⋊C8C22×C4111yescharacteristic
370#322C22×C4111yescharacteristic, complemented
371C41#1982511yescharacteristic, direct product factor, Sylow
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C4111yescharacteristic
380C2×SD16D4×C4111yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C4111yescharacteristic
387C4⋊Q8C23×C4111yescharacteristic
388#127C23×C4111yescharacteristic
389#127C23×C4111yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C4111yescharacteristic
404C4×Q8C23×C4111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C4111yescharacteristic
409C4×D4C23×C4111yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C4111yescharacteristic
416#106D4×C4111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C4111yescharacteristic
420C4⋊C8C23×C4111yescharacteristic
421C4⋊C8C23×C4111yescharacteristic
422C4⋊C8C23×C4111yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C4111yescharacteristic
427#103D4×C4111yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102D4×C4111yescharacteristic
441#102D4×C4111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C4111yescharacteristic
447C4×C8C23×C4111yescharacteristic
448C4×C8C23×C4111yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C4111yescharacteristic
453C2×Q8C2×D4×C4111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C4111yescharacteristic
467C2×D4C2×D4×C4111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C4111yescharacteristic
490C2×C8C2×D4×C4111yescharacteristic
491C2×C8C2×D4×C4111yescharacteristic
492C2×C8C2×D4×C4111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C4111yescharacteristic
503C4⋊C4C2×D4×C4111yescharacteristic
504C4⋊C4C2×D4×C4111yescharacteristic
505C4⋊C4C2×D4×C4111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C4111yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C4112yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C4111yescharacteristic
564C2×C4C22×D4×C4111yescharacteristic
565C2×C4H(5,𝔽2)×C4111yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C4111yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C4111yescharacteristic
599C4C41×#57511yescharacteristic
600C4C41×#57611yescharacteristic
601C4C41×#57711yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C41×#326811yescharacteristic
607C2C41×#328211yescharacteristic
608C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#1619C2
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×#3361C2semidirect
3. C41×#3324C2semidirect
4. C41×#3295C2semidirect
5. C41×#1717C2semidirect
6. C41×#1697C2semidirect
7. C41×#1682C2semidirect
8. C41×#1678C2semidirect
9. C41×#1665C2semidirect
10. C41×#1644C2semidirect
11. C41×#1638C2semidirect
12. C41×#1620C2semidirect
14. C41×#1583C2semidirect
15. C41×SD16⋊C8C2semidirect
16. C41×#559C22semidirect
22. C41×#492C22semidirect
24. C41×#487C22semidirect
27. C41×#486C22semidirect
31. C41×#477C22semidirect
39. C41×#462C22semidirect
46. C8×Q8×C41C22semidirect
47. C8×Q8×C41C22semidirect
56. C41×#335C22semidirect
57. C41×#334C22semidirect
58. C41×#333C22semidirect
59. C41×#332C22semidirect
61. C41×#331C22semidirect
62. C41×Q8⋊C8C22semidirect
63. C41×Q8⋊C8C22semidirect
66. C41×#322C22semidirect
270. #19825C41direct (N × H)
298. #3394C2×C41semidirect
299. #3361C2×C41semidirect
300. #3324C2×C41semidirect
301. #3295C2×C41semidirect
302. #1717C2×C41semidirect
303. #1697C2×C41semidirect
304. #1682C2×C41semidirect
305. #1678C2×C41semidirect
306. #1665C2×C41semidirect
307. #1644C2×C41semidirect
308. #1638C2×C41semidirect
309. #1620C2×C41semidirect
311. #1583C2×C41semidirect
312. SD16⋊C8C2×C41semidirect
320. #559C22×C41semidirect
326. #492C22×C41semidirect
328. #487C22×C41semidirect
331. #486C22×C41semidirect
335. #477C22×C41semidirect
343. #462C22×C41semidirect
350. C8×Q8C22×C41semidirect
351. C8×Q8C22×C41semidirect
360. #335C22×C41semidirect
361. #334C22×C41semidirect
362. #333C22×C41semidirect
363. #332C22×C41semidirect
365. #331C22×C41semidirect
366. Q8⋊C8C22×C41semidirect
367. Q8⋊C8C22×C41semidirect
370. #322C22×C41semidirect
371. C41#19825direct (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×#33612
C41×#33242
C41×#32952
C41×#17172
C41×#16972
C41×#16822
C41×#16782
C41×#16652
C41×#16442
C41×#16382
C41×#16202
C41×#16192
C41×#15832
C41×SD16⋊C82
#1982541