Finite Group Databasebeta

← C41×#19949 #23796150

Subgroups — C41×#19949 #23796150

Order 10496.

622 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3399C211yesmaximal, characteristic, complemented
2C41×#3361C211yesmaximal, characteristic, complemented
3C41×#3357C211yesmaximal, characteristic, complemented
4C41×#3305C211yesmaximal, characteristic, complemented
5C41×#1706C211yesmaximal, characteristic, complemented
6C41×#1696C211yesmaximal, characteristic, complemented
7C41×#1687C211yesmaximal, characteristic, complemented
8C41×#1678C211yesmaximal, characteristic, complemented
9C41×#1677C211yesmaximal, characteristic, complemented
10C41×#1631C211yesmaximal, characteristic, complemented
11C41×#1630C211yesmaximal, characteristic, complemented
12C41×#1624C211yesmaximal, characteristic, complemented
13C41×#1622C211yesmaximal, characteristic, complemented
14C41×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C41C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17C41×#555C2211yescharacteristic
18C41×#554C2211yescharacteristic
19C41×#550C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#496—21no—
22C41×#493C2211yescharacteristic
23C41×#492C2211yescharacteristic
24C41×#492C2211yescharacteristic
25C41×#488—21no—
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#485—21no—
29C41×#482—21no—
30C41×#480—21no—
31C41×#478—21no—
32C41×#477C2211yescharacteristic
33C41×#477C2211yescharacteristic
34C41×#477C2211yescharacteristic
35C41×#476C2211yescharacteristic
36C41×#468—21no—
37C41×#466—21no—
38C41×#463—21no—
39C41×#463—21no—
40C41×#460C2211yescharacteristic
41C41×#459—21no—
42C41×#459C2211yescharacteristic
43C41×#459C2211yescharacteristic
44C41×#459C2211yescharacteristic
45C41×#449—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C41×#442—21no—
49C4×SD16×C41C2211yescharacteristic
50C4×SD16×C41C2211yescharacteristic
51C4×D8×C41—21no—
52C41×#436C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#428—21no—
55C41×#416—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#331C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C2×SD16×C41—21no—
69C2×SD16×C41—41no—
70C2×SD16×C41—41no—
71C2×SD16×C41D411yescharacteristic
72C2×SD16×C41D411yescharacteristic
73C2×D8×C41—21no—
74C2×D8×C41—21no—
75C2×D8×C41—21no—
76C2×D8×C41—21no—
77C2×D8×C41—21no—
78C2×M16×C41—21no—
79C22×C8×C41—21no—
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82#127×C41—21no—
83#127×C41C2311yescharacteristic
84#127×C41C2311yescharacteristic
85#125×C41—21no—
86#124×C41—21no—
87#124×C41—21no—
88#124×C41—41no—
89#123×C41—41no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—41no—
92#121×C41—21no—
93#121×C41—21no—
94#121×C41—21no—
95#121×C41—41no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×D4×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41—21no—
101C4×D4×C41—21no—
102C4×D4×C41C2311yescharacteristic
103C4×D4×C41C2311yescharacteristic
104#117×C41—21no—
105#117×C41—21no—
106C2×C4⋊C4×C41—21no—
107#107×C41—21no—
108#107×C41—21no—
109#107×C41—21no—
110#107×C41—21no—
111#107×C41—21no—
112#106×C41—21no—
113#106×C41D411yescharacteristic
114#106×C41D411yescharacteristic
115C4⋊C8×C41—21no—
116C4⋊C8×C41—21no—
117C4⋊C8×C41C2311yescharacteristic
118C4⋊C8×C41C2311yescharacteristic
119C4⋊C8×C41C2311yescharacteristic
120C4⋊C8×C41C2311yescharacteristic
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—21no—
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×C41C2×D411yescharacteristic
149C2×Q8×C41C2×D411yescharacteristic
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—41no—
157C2×D4×C41—41no—
158C2×D4×C41—41no—
159C2×D4×C41C2×D411yescharacteristic
160C2×D4×C41C2×D411yescharacteristic
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—41no—
164C22×C4×C41—41no—
165C22×C4×C41—41no—
166SD16×C41—22no—
167SD16×C41—41no—
168SD16×C41—82no—
169SD16×C41—82no—
170SD16×C41—81no—
171D8×C41—42no—
172D8×C41—42no—
173D8×C41—81no—
174D8×C41—81no—
175D8×C41—81no—
176M16×C41—42no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—81no—
183C2×C8×C41C2×D411yescharacteristic
184C2×C8×C41C2×D411yescharacteristic
185C2×C8×C41C2×D411yescharacteristic
186C2×C8×C41C2×D411yescharacteristic
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×C41C2×D411yescharacteristic
196C4⋊C4×C41C2×D411yescharacteristic
197C4⋊C4×C41C2×D411yescharacteristic
198C4⋊C4×C41C2×D411yescharacteristic
199C22⋊C4×C41—21no—
200C22⋊C4×C41—21no—
201C22⋊C4×C41—41no—
202C22⋊C4×C41—41no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—41no—
206C22⋊C4×C41—41no—
207C22⋊C4×C41—41no—
208C42×C41—21no—
209C42×C41—21no—
210C42×C41—41no—
211C42×C41C2411yescharacteristic
212C23×C41—21no—
213C23×C41—21no—
214C23×C41—41no—
215C23×C41—41no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—21no—
220Q8×C41—81no—
221Q8×C41—81no—
222D4×C41—21no—
223D4×C41—21no—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—41no—
227D4×C41—41no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—41no—
233D4×C41—41no—
234D4×C41—81no—
235D4×C41—81no—
236D4×C41—82no—
237D4×C41—161no—
238D4×C41—161no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—21no—
244C2×C4×C41—21no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—41no—
251C2×C4×C41—82no—
252C2×C4×C41—161no—
253C2×C4×C41—161no—
254C2×C4×C41C22×D411yescharacteristic
255C2×C4×C41C22×D411yescharacteristic
256C2×C4×C41H(5,𝔽2)11yescharacteristic
257C8×C41—22no—
258C8×C41—21no—
259C8×C41—21no—
260C8×C41—21no—
261C8×C41—41no—
262C8×C41—41no—
263C8×C41—41no—
264C8×C41—41no—
265C8×C41#13512yes—
266#19949C4111yesmaximal, characteristic, direct product factor, Sylow
267C22×C41—41no—
268C22×C41—41no—
269C22×C41—41no—
270C22×C41—41no—
271C22×C41—41no—
272C22×C41—41no—
273C22×C41—81no—
274C22×C41—81no—
275C22×C41—81no—
276C22×C41—81no—
277C22×C41—81no—
278C22×C41—81no—
279C22×C41D4211yescharacteristic
280C4×C41—21no—
281C4×C41—41no—
282C4×C41—41no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—41no—
287C4×C41—81no—
288C4×C41—81no—
289C4×C41C2×#13511yescharacteristic
290C4×C41#57511yescharacteristic
291C4×C41#57711yescharacteristic
292C4×C41#57711yescharacteristic
293#3399C2×C4111yescharacteristic, complemented
294#3361C2×C4111yescharacteristic, complemented
295#3357C2×C4111yescharacteristic, complemented
296#3305C2×C4111yescharacteristic, complemented
297#1706C2×C4111yescharacteristic, complemented
298#1696C2×C4111yescharacteristic, complemented
299#1687C2×C4111yescharacteristic, complemented
300#1678C2×C4111yescharacteristic, complemented
301#1677C2×C4111yescharacteristic, complemented
302#1631C2×C4111yescharacteristic, complemented
303#1630C2×C4111yescharacteristic, complemented
304#1624C2×C4111yescharacteristic, complemented
305#1622C2×C4111yescharacteristic, complemented
306#1590C2×C4111yescharacteristic, complemented
307C8×SD16C2×C4111yescharacteristic, complemented
308C2×C41—81no—
309C2×C41—81no—
310C2×C41—161no—
311C2×C41—161no—
312C2×C41#327511yescharacteristic
313C2×C41#328411yescharacteristic
314C2×C41#329211yescharacteristic
315#559C22×C4111yescharacteristic
316#555C22×C4111yescharacteristic
317#554C22×C4111yescharacteristic
318#550C22×C4111yescharacteristic
319#500C22×C4111yescharacteristic
320#496—21no—
321#493C22×C4111yescharacteristic
322#492C22×C4111yescharacteristic
323#492C22×C4111yescharacteristic
324#488—21no—
325#486C22×C4111yescharacteristic
326#486C22×C4111yescharacteristic
327#485—21no—
328#482—21no—
329#480—21no—
330#478—21no—
331#477C22×C4111yescharacteristic
332#477C22×C4111yescharacteristic
333#477C22×C4111yescharacteristic
334#476C22×C4111yescharacteristic
335#468—21no—
336#466—21no—
337#463—21no—
338#463—21no—
339#460C22×C4111yescharacteristic
340#459—21no—
341#459C22×C4111yescharacteristic
342#459C22×C4111yescharacteristic
343#459C22×C4111yescharacteristic
344#449—21no—
345#446C22×C4111yescharacteristic
346C8×Q8C22×C4111yescharacteristic
347#442—21no—
348C4×SD16C22×C4111yescharacteristic
349C4×SD16C22×C4111yescharacteristic
350C4×D8—21no—
351#436C22×C4111yescharacteristic
352C8×D4C22×C4111yescharacteristic
353#428—21no—
354#416—21no—
355#334C22×C4111yescharacteristic
356#334C22×C4111yescharacteristic
357#333C22×C4111yescharacteristic
358#333C22×C4111yescharacteristic
359#331C22×C4111yescharacteristic
360#331C22×C4111yescharacteristic
361Q8⋊C8C22×C4111yescharacteristic
362Q8⋊C8C22×C4111yescharacteristic
363D4⋊C8C22×C4111yescharacteristic
364D4⋊C8C22×C4111yescharacteristic
365C82C22×C4111yescharacteristic
366C41#1994911yescharacteristic, direct product factor, Sylow
367C2×#41—21no—
368C2×SD16—21no—
369C2×SD16—41no—
370C2×SD16—41no—
371C2×SD16D4×C4111yescharacteristic
372C2×SD16D4×C4111yescharacteristic
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×M16—21no—
379C22×C8—21no—
380C4⋊Q8C23×C4111yescharacteristic
381C4⋊Q8C23×C4111yescharacteristic
382#127—21no—
383#127C23×C4111yescharacteristic
384#127C23×C4111yescharacteristic
385#125—21no—
386#124—21no—
387#124—21no—
388#124—41no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—41no—
392#121—21no—
393#121—21no—
394#121—21no—
395#121—41no—
396C4×Q8C23×C4111yescharacteristic
397C4×Q8C23×C4111yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C4111yescharacteristic
403C4×D4C23×C4111yescharacteristic
404#117—21no—
405#117—21no—
406C2×C4⋊C4—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—21no—
412#106—21no—
413#106D4×C4111yescharacteristic
414#106D4×C4111yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8C23×C4111yescharacteristic
418C4⋊C8C23×C4111yescharacteristic
419C4⋊C8C23×C4111yescharacteristic
420C4⋊C8C23×C4111yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103D4×C4111yescharacteristic
425#103D4×C4111yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102D4×C4111yescharacteristic
436#102D4×C4111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8—21no—
441C4×C8C23×C4111yescharacteristic
442C4×C8C23×C4111yescharacteristic
443C4×C8C23×C4111yescharacteristic
444#41—42no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C4111yescharacteristic
449C2×Q8C2×D4×C4111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C4111yescharacteristic
460C2×D4C2×D4×C4111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466SD16—22no—
467SD16—41no—
468SD16—82no—
469SD16—82no—
470SD16—81no—
471D8—42no—
472D8—42no—
473D8—81no—
474D8—81no—
475D8—81no—
476M16—42no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—81no—
483C2×C8C2×D4×C4111yescharacteristic
484C2×C8C2×D4×C4111yescharacteristic
485C2×C8C2×D4×C4111yescharacteristic
486C2×C8C2×D4×C4111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×D4×C4111yescharacteristic
496C4⋊C4C2×D4×C4111yescharacteristic
497C4⋊C4C2×D4×C4111yescharacteristic
498C4⋊C4C2×D4×C4111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—41no—
511C42C24×C4111yescharacteristic
512C23—21no—
513C23—21no—
514C23—41no—
515C23—41no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—81no—
521Q8—81no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—161no—
538D4—161no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4—161no—
553C2×C4—161no—
554C2×C4C22×D4×C4111yescharacteristic
555C2×C4C22×D4×C4111yescharacteristic
556C2×C4H(5,𝔽2)×C4111yescharacteristic
557C8—22no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8#135×C4112yes—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22D42×C4111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4C2×#135×C4111yescharacteristic
589C4C41×#57511yescharacteristic
590C4C41×#57711yescharacteristic
591C4C41×#57711yescharacteristic
592C2—81no—
593C2—81no—
594C2—161no—
595C2—161no—
596C2C41×#327511yescharacteristic
597C2C41×#328411yescharacteristic
598C2C41×#329211yescharacteristic
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×#3361C2semidirect
3. C41×#3357C2semidirect
4. C41×#3305C2semidirect
5. C41×#1706C2semidirect
6. C41×#1696C2semidirect
7. C41×#1687C2semidirect
8. C41×#1678C2semidirect
9. C41×#1677C2semidirect
10. C41×#1631C2semidirect
11. C41×#1630C2semidirect
12. C41×#1624C2semidirect
13. C41×#1622C2semidirect
14. C41×#1590C2semidirect
15. C8×SD16×C41C2semidirect
266. #19949C41direct (N × H)
293. #3399C2×C41semidirect
294. #3361C2×C41semidirect
295. #3357C2×C41semidirect
296. #3305C2×C41semidirect
297. #1706C2×C41semidirect
298. #1696C2×C41semidirect
299. #1687C2×C41semidirect
300. #1678C2×C41semidirect
301. #1677C2×C41semidirect
302. #1631C2×C41semidirect
303. #1630C2×C41semidirect
304. #1624C2×C41semidirect
305. #1622C2×C41semidirect
306. #1590C2×C41semidirect
307. C8×SD16C2×C41semidirect
366. C41#19949direct (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×#33612
C41×#33572
C41×#33052
C41×#17062
C41×#16962
C41×#16872
C41×#16782
C41×#16772
C41×#16312
C41×#16302
C41×#16242
C41×#16222
C41×#15902
C8×SD16×C412
#1994941