Finite Group Databasebeta

← C41×#19796 #23795997

Subgroups — C41×#19796 #23795997

Order 10496.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C41C211yesmaximal, characteristic, complemented
2C41×#3369C211yesmaximal, characteristic, complemented
3C41×#3302C211yesmaximal, characteristic
4C41×#3298C211yesmaximal, characteristic
5C41×#1718C211yesmaximal, characteristic, complemented
6C41×#1700C211yesmaximal, characteristic, complemented
7C41×#1683C211yesmaximal, characteristic, complemented
8C41×#1680C211yesmaximal, characteristic, complemented
9C41×#1671C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1649C211yesmaximal, characteristic, complemented
12C41×#1645C211yesmaximal, characteristic, complemented
13C41×#1635C211yesmaximal, characteristic
14C41×#1582C211yesmaximal, characteristic, complemented
15C41×SD16⋊C8C211yesmaximal, characteristic, complemented
16Q82×C41C2211yescharacteristic
17C41×#556C2211yescharacteristic
18D4×Q8×C41C2211yescharacteristic
19C41×#547C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#498—21no—
22C41×#498C2211yescharacteristic
23C41×#489—21no—
24C41×#487C2211yescharacteristic
25C41×#487C2211yescharacteristic
26C41×#487C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#485—21no—
29C41×#483—21no—
30C41×#476—21no—
31C41×#476C2211yescharacteristic
32C41×#476C2211yescharacteristic
33C41×#475—21no—
34C41×#475—21no—
35C41×#475C2211yescharacteristic
36C41×#475C2211yescharacteristic
37C41×#474C2211yescharacteristic
38C41×#467—21no—
39C41×#465—21no—
40C41×#464—21no—
41C41×#462C2211yescharacteristic
42C41×#462C2211yescharacteristic
43C41×#461C2211yescharacteristic
44C41×#452—21no—
45C41×#448—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C41×#441—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×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#332C2211yescharacteristic
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×C41D411yescharacteristic
73C2×SD16×C41D411yescharacteristic
74C22×C8×C41—21no—
75C22×C8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41—41no—
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82C4⋊Q8×C41C2311yescharacteristic
83C4⋊Q8×C41C2311yescharacteristic
84#126×C41—41no—
85#124×C41—21no—
86#123×C41—41no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—21no—
90C22⋊Q8×C41—41no—
91#121×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41C2311yescharacteristic
96C4×Q8×C41C2311yescharacteristic
97C4×D4×C41—21no—
98C4×D4×C41C2311yescharacteristic
99C4×D4×C41C2311yescharacteristic
100#117×C41—21no—
101C2×C4⋊C4×C41—21no—
102#107×C41—21no—
103#107×C41—41no—
104#106×C41—21no—
105#106×C41—21no—
106#106×C41—21no—
107#106×C41—21no—
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×C41—21no—
128#103×C41—21no—
129#103×C41—41no—
130#103×C41D411yescharacteristic
131#103×C41D411yescharacteristic
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×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—41no—
151C2×Q8×C41—41no—
152C2×Q8×C41—42no—
153C2×Q8×C41—81no—
154C2×Q8×C41C2×D411yescharacteristic
155C2×Q8×C41C2×D411yescharacteristic
156C2×D4×C41—41no—
157C2×D4×C41C2×D411yescharacteristic
158C2×D4×C41C2×D411yescharacteristic
159C22×C4×C41—21no—
160C22×C4×C41—21no—
161C22×C4×C41—41no—
162C22×C4×C41—41no—
163Q16×C41—42no—
164Q16×C41—81no—
165SD16×C41—22no—
166SD16×C41—22no—
167SD16×C41—81no—
168C2×C8×C41—21no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—81no—
174C2×C8×C41—81no—
175C2×C8×C41C2×D411yescharacteristic
176C2×C8×C41C2×D411yescharacteristic
177C2×C8×C41C2×D411yescharacteristic
178C2×C8×C41C2×D411yescharacteristic
179C4⋊C4×C41—21no—
180C4⋊C4×C41—21no—
181C4⋊C4×C41—21no—
182C4⋊C4×C41—21no—
183C4⋊C4×C41—21no—
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41—41no—
193C4⋊C4×C41—41no—
194C4⋊C4×C41C2×D411yescharacteristic
195C4⋊C4×C41C2×D411yescharacteristic
196C4⋊C4×C41C2×D411yescharacteristic
197C4⋊C4×C41C2×D411yescharacteristic
198C22⋊C4×C41—21no—
199C22⋊C4×C41—21no—
200C22⋊C4×C41—41no—
201C22⋊C4×C41—41no—
202C22⋊C4×C41—41no—
203C22⋊C4×C41—41no—
204C42×C41—21no—
205C42×C41—21no—
206C42×C41—41no—
207C42×C41—41no—
208C42×C41C2411yescharacteristic
209C23×C41—21no—
210C23×C41—21no—
211Q8×C41—21no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—41no—
215Q8×C41—41no—
216Q8×C41—41no—
217Q8×C41—41no—
218Q8×C41—41no—
219Q8×C41—41no—
220Q8×C41—82no—
221Q8×C41—81no—
222Q8×C41—161no—
223Q8×C41#13512yes—
224D4×C41—21no—
225D4×C41—21no—
226D4×C41—21no—
227D4×C41—82no—
228D4×C41#13712yes—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—21no—
235C2×C4×C41—41no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—82no—
244C2×C4×C41—82no—
245C2×C4×C41C22×D411yescharacteristic
246C2×C4×C41C22×D411yescharacteristic
247C2×C4×C41H(5,𝔽2)11yescharacteristic
248C8×C41—21no—
249C8×C41—21no—
250C8×C41—21no—
251C8×C41—21no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255C8×C41—41no—
256C8×C41—41no—
257#19796C4111yesmaximal, characteristic, direct product factor, Sylow
258C22×C41—22no—
259C22×C41—41no—
260C22×C41—41no—
261C22×C41—41no—
262C22×C41—41no—
263C22×C41—41no—
264C22×C41D4211yescharacteristic
265C4×C41—22no—
266C4×C41—21no—
267C4×C41—41no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—41no—
272C4×C41—81no—
273C4×C41—81no—
274C4×C41—81no—
275C4×C41—81no—
276C4×C41C2×#13511yescharacteristic
277C4×C41C2×#13711yescharacteristic
278C4×C41#57711yescharacteristic
279C4×C41#57711yescharacteristic
280Q8×SD16C2×C4111yescharacteristic, complemented
281#3369C2×C4111yescharacteristic, complemented
282#3302C2×C4111yescharacteristic
283#3298C2×C4111yescharacteristic
284#1718C2×C4111yescharacteristic, complemented
285#1700C2×C4111yescharacteristic, complemented
286#1683C2×C4111yescharacteristic, complemented
287#1680C2×C4111yescharacteristic, complemented
288#1671C2×C4111yescharacteristic, complemented
289#1650C2×C4111yescharacteristic, complemented
290#1649C2×C4111yescharacteristic, complemented
291#1645C2×C4111yescharacteristic, complemented
292#1635C2×C4111yescharacteristic
293#1582C2×C4111yescharacteristic, complemented
294SD16⋊C8C2×C4111yescharacteristic, complemented
295C2×C41—42no—
296C2×C41—81no—
297C2×C41#326611yescharacteristic
298C2×C41#328211yescharacteristic
299C2×C41#328911yescharacteristic
300Q82C22×C4111yescharacteristic
301#556C22×C4111yescharacteristic
302D4×Q8C22×C4111yescharacteristic
303#547C22×C4111yescharacteristic
304#500C22×C4111yescharacteristic
305#498—21no—
306#498C22×C4111yescharacteristic
307#489—21no—
308#487C22×C4111yescharacteristic
309#487C22×C4111yescharacteristic
310#487C22×C4111yescharacteristic
311#487C22×C4111yescharacteristic
312#485—21no—
313#483—21no—
314#476—21no—
315#476C22×C4111yescharacteristic
316#476C22×C4111yescharacteristic
317#475—21no—
318#475—21no—
319#475C22×C4111yescharacteristic
320#475C22×C4111yescharacteristic
321#474C22×C4111yescharacteristic
322#467—21no—
323#465—21no—
324#464—21no—
325#462C22×C4111yescharacteristic
326#462C22×C4111yescharacteristic
327#461C22×C4111yescharacteristic
328#452—21no—
329#448—21no—
330#446C22×C4111yescharacteristic
331C8×Q8C22×C4111yescharacteristic
332#441—21no—
333C4×SD16—21no—
334C4×SD16C22×C4111yescharacteristic
335C4×SD16C22×C4111yescharacteristic
336C8×D4C22×C4111yescharacteristic
337C8×D4C22×C4111yescharacteristic
338#416—21no—
339C2×#103—21no—
340#335C22×C4111yescharacteristic
341#334C22×C4111yescharacteristic
342#333C22×C4111yescharacteristic
343#332C22×C4111yescharacteristic
344#332C22×C4111yescharacteristic
345#332C22×C4111yescharacteristic
346Q8⋊C8C22×C4111yescharacteristic
347Q8⋊C8C22×C4111yescharacteristic
348D4⋊C8C22×C4111yescharacteristic
349D4⋊C8C22×C4111yescharacteristic
350#322C22×C4111yescharacteristic
351C41#1979611yescharacteristic, direct product factor, Sylow
352C2×#41—21no—
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×SD16—21no—
357C2×SD16D4×C4111yescharacteristic
358C2×SD16D4×C4111yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8C23×C4111yescharacteristic
366C4⋊Q8C23×C4111yescharacteristic
367C4⋊Q8C23×C4111yescharacteristic
368C4⋊Q8C23×C4111yescharacteristic
369#126—41no—
370#124—21no—
371#123—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C4111yescharacteristic
381C4×Q8C23×C4111yescharacteristic
382C4×D4—21no—
383C4×D4C23×C4111yescharacteristic
384C4×D4C23×C4111yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—41no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106D4×C4111yescharacteristic
396#106D4×C4111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C4111yescharacteristic
400C4⋊C8C23×C4111yescharacteristic
401C4⋊C8C23×C4111yescharacteristic
402C4⋊C8C23×C4111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C4111yescharacteristic
416#103D4×C4111yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C4111yescharacteristic
421#102D4×C4111yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425C4×C8—21no—
426C4×C8C23×C4111yescharacteristic
427C4×C8C23×C4111yescharacteristic
428C4×C8C23×C4111yescharacteristic
429#41—42no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—42no—
438C2×Q8—81no—
439C2×Q8C2×D4×C4111yescharacteristic
440C2×Q8C2×D4×C4111yescharacteristic
441C2×D4—41no—
442C2×D4C2×D4×C4111yescharacteristic
443C2×D4C2×D4×C4111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—42no—
449Q16—81no—
450SD16—22no—
451SD16—22no—
452SD16—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8C2×D4×C4111yescharacteristic
461C2×C8C2×D4×C4111yescharacteristic
462C2×C8C2×D4×C4111yescharacteristic
463C2×C8C2×D4×C4111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C4111yescharacteristic
480C4⋊C4C2×D4×C4111yescharacteristic
481C4⋊C4C2×D4×C4111yescharacteristic
482C4⋊C4C2×D4×C4111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—41no—
493C42C24×C4111yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—81no—
507Q8—161no—
508Q8#135×C4112yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—82no—
513D4#137×C4112yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4C22×D4×C4111yescharacteristic
531C2×C4C22×D4×C4111yescharacteristic
532C2×C4H(5,𝔽2)×C4111yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D42×C4111yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#135×C4111yescharacteristic
561C4C2×#137×C4111yescharacteristic
562C4C41×#57711yescharacteristic
563C4C41×#57711yescharacteristic
564C2—42no—
565C2—81no—
566C2C41×#326611yescharacteristic
567C2C41×#328211yescharacteristic
568C2C41×#328911yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#547C22
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. Q8×SD16×C41C2semidirect
2. C41×#3369C2semidirect
5. C41×#1718C2semidirect
6. C41×#1700C2semidirect
7. C41×#1683C2semidirect
8. C41×#1680C2semidirect
9. C41×#1671C2semidirect
10. C41×#1650C2semidirect
11. C41×#1649C2semidirect
12. C41×#1645C2semidirect
14. C41×#1582C2semidirect
15. C41×SD16⋊C8C2semidirect
257. #19796C41direct (N × H)
280. Q8×SD16C2×C41semidirect
281. #3369C2×C41semidirect
284. #1718C2×C41semidirect
285. #1700C2×C41semidirect
286. #1683C2×C41semidirect
287. #1680C2×C41semidirect
288. #1671C2×C41semidirect
289. #1650C2×C41semidirect
290. #1649C2×C41semidirect
291. #1645C2×C41semidirect
293. #1582C2×C41semidirect
294. SD16⋊C8C2×C41semidirect
351. C41#19796direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×SD16×C412
C41×#33692
C41×#33022
C41×#32982
C41×#17182
C41×#17002
C41×#16832
C41×#16802
C41×#16712
C41×#16502
C41×#16492
C41×#16452
C41×#16352
C41×#15822
C41×SD16⋊C82
#1979641