Finite Group Databasebeta

← C41×#19798 #23795999

Subgroups — C41×#19798 #23795999

Order 10496.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C41C211yesmaximal, characteristic, complemented
2C41×#3375C211yesmaximal, characteristic, complemented
3C41×#3361C211yesmaximal, characteristic
4C41×#3299C211yesmaximal, characteristic, complemented
5C41×#1720C211yesmaximal, characteristic, complemented
6C41×#1704C211yesmaximal, characteristic, complemented
7C41×#1678C211yesmaximal, characteristic, complemented
8C41×#1677C211yesmaximal, characteristic
9C41×#1672C211yesmaximal, characteristic, complemented
10C41×#1640C211yesmaximal, characteristic, complemented
11C41×#1633C211yesmaximal, characteristic, complemented
12C41×#1632C211yesmaximal, characteristic, complemented
13C41×#1627C211yesmaximal, characteristic
14C41×#1582C211yesmaximal, characteristic, complemented
15C41×#1579C211yesmaximal, characteristic, complemented
16C41×#559C2211yescharacteristic
17Q82×C41C2211yescharacteristic
18C41×#554C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#498—21no—
21C41×#498C2211yescharacteristic
22C41×#494C2211yescharacteristic
23C41×#489—21no—
24C41×#488—21no—
25C41×#487C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#486C2211yescharacteristic
29C41×#484—21no—
30C41×#478—21no—
31C41×#477C2211yescharacteristic
32C41×#477C2211yescharacteristic
33C41×#477C2211yescharacteristic
34C41×#476—21no—
35C41×#476C2211yescharacteristic
36C41×#475—21no—
37C41×#475C2211yescharacteristic
38C41×#474—21no—
39C41×#467—21no—
40C41×#464—21no—
41C41×#463—21no—
42C41×#462C2211yescharacteristic
43C41×#460C2211yescharacteristic
44C41×#459C2211yescharacteristic
45C41×#451—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C8×Q8×C41C2211yescharacteristic
49C41×#440—21no—
50C4×Q16×C41C2211yescharacteristic
51C4×SD16×C41—21no—
52C4×SD16×C41C2211yescharacteristic
53C4×D8×C41—21no—
54C8×D4×C41C2211yescharacteristic
55C2×#103×C41—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×Q8⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C41×#322C2211yescharacteristic
67C22×Q8×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41—41no—
70C2×Q16×C41D411yescharacteristic
71C2×SD16×C41—21no—
72C2×SD16×C41D411yescharacteristic
73C2×D8×C41—21no—
74C22×C8×C41—21no—
75C4⋊Q8×C41—21no—
76C4⋊Q8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41—41no—
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81C4⋊Q8×C41C2311yescharacteristic
82#127×C41C2311yescharacteristic
83#125×C41—21no—
84#124×C41—21no—
85#124×C41—21no—
86#123×C41—41no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—41no—
90C22⋊Q8×C41—41no—
91C4×Q8×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41C2311yescharacteristic
94C4×Q8×C41C2311yescharacteristic
95C4×Q8×C41C2311yescharacteristic
96C4×D4×C41—21no—
97C4×D4×C41—21no—
98C4×D4×C41—21no—
99C4×D4×C41—21no—
100C4×D4×C41C2311yescharacteristic
101C2×C4⋊C4×C41—21no—
102#107×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41D411yescharacteristic
106#106×C41—21no—
107#106×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41D411yescharacteristic
111C4⋊C8×C41—21no—
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×C41D411yescharacteristic
126#103×C41D411yescharacteristic
127#103×C41D411yescharacteristic
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×C41—41no—
136#102×C41D411yescharacteristic
137C22⋊C8×C41—21no—
138#97×C41—21no—
139C4×C8×C41—21no—
140C4×C8×C41—21no—
141C4×C8×C41C2311yescharacteristic
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—41no—
148C2×Q8×C41—41no—
149C2×Q8×C41—42no—
150C2×Q8×C41—81no—
151C2×Q8×C41C2×D411yescharacteristic
152C2×Q8×C41C2×D411yescharacteristic
153C2×Q8×C41C2×D411yescharacteristic
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41C2×D411yescharacteristic
158C22×C4×C41—21no—
159C22×C4×C41—41no—
160C22×C4×C41—41no—
161C22×C4×C41—41no—
162Q16×C41—22no—
163Q16×C41—81no—
164Q16×C41—82no—
165SD16×C41—22no—
166SD16×C41—42no—
167D8×C41—42no—
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×C41C2×D411yescharacteristic
175C2×C8×C41C2×D411yescharacteristic
176C2×C8×C41C2×D411yescharacteristic
177C2×C8×C41C2×D411yescharacteristic
178C4⋊C4×C41—21no—
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—41no—
188C4⋊C4×C41—41no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41—41no—
191C4⋊C4×C41—41no—
192C4⋊C4×C41C2×D411yescharacteristic
193C4⋊C4×C41C2×D411yescharacteristic
194C4⋊C4×C41C2×D411yescharacteristic
195C4⋊C4×C41C2×D411yescharacteristic
196C22⋊C4×C41—21no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C22⋊C4×C41—41no—
202C42×C41—21no—
203C42×C41—21no—
204C42×C41—21no—
205C42×C41—41no—
206C42×C41C2411yescharacteristic
207C23×C41—21no—
208C23×C41—41no—
209Q8×C41—21no—
210Q8×C41—21no—
211Q8×C41—21no—
212Q8×C41—21no—
213Q8×C41—21no—
214Q8×C41—41no—
215Q8×C41—41no—
216Q8×C41—82no—
217Q8×C41—81no—
218Q8×C41—81no—
219Q8×C41—161no—
220Q8×C41#13512yes—
221D4×C41—21no—
222D4×C41—41no—
223D4×C41—41no—
224D4×C41—41no—
225D4×C41—41no—
226D4×C41—81no—
227D4×C41#13712yes—
228C2×C4×C41—21no—
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—82no—
241C2×C4×C41—161no—
242C2×C4×C41—161no—
243C2×C4×C41C22×D411yescharacteristic
244C2×C4×C41C22×D411yescharacteristic
245C2×C4×C41H(5,𝔽2)11yescharacteristic
246C8×C41—21no—
247C8×C41—21no—
248C8×C41—21no—
249C8×C41—21no—
250C8×C41—41no—
251C8×C41—41no—
252C8×C41—41no—
253C8×C41—41no—
254C8×C41—41no—
255#19798C4111yesmaximal, characteristic, direct product factor, Sylow
256C22×C41—22no—
257C22×C41—41no—
258C22×C41—41no—
259C22×C41—81no—
260C22×C41—81no—
261C22×C41—81no—
262C22×C41D4211yescharacteristic
263C4×C41—22no—
264C4×C41—21no—
265C4×C41—41no—
266C4×C41—41no—
267C4×C41—41no—
268C4×C41—41no—
269C4×C41—41no—
270C4×C41—41no—
271C4×C41—81no—
272C4×C41—81no—
273C4×C41—81no—
274C4×C41C2×#13511yescharacteristic
275C4×C41C2×#13711yescharacteristic
276C4×C41#57711yescharacteristic
277C4×C41#57811yescharacteristic
278Q8×SD16C2×C4111yescharacteristic, complemented
279#3375C2×C4111yescharacteristic, complemented
280#3361C2×C4111yescharacteristic
281#3299C2×C4111yescharacteristic, complemented
282#1720C2×C4111yescharacteristic, complemented
283#1704C2×C4111yescharacteristic, complemented
284#1678C2×C4111yescharacteristic, complemented
285#1677C2×C4111yescharacteristic
286#1672C2×C4111yescharacteristic, complemented
287#1640C2×C4111yescharacteristic, complemented
288#1633C2×C4111yescharacteristic, complemented
289#1632C2×C4111yescharacteristic, complemented
290#1627C2×C4111yescharacteristic
291#1582C2×C4111yescharacteristic, complemented
292#1579C2×C4111yescharacteristic, complemented
293C2×C41—42no—
294C2×C41—161no—
295C2×C41#327011yescharacteristic
296C2×C41#328211yescharacteristic
297C2×C41#328811yescharacteristic
298#559C22×C4111yescharacteristic
299Q82C22×C4111yescharacteristic
300#554C22×C4111yescharacteristic
301D4×Q8C22×C4111yescharacteristic
302#498—21no—
303#498C22×C4111yescharacteristic
304#494C22×C4111yescharacteristic
305#489—21no—
306#488—21no—
307#487C22×C4111yescharacteristic
308#486C22×C4111yescharacteristic
309#486C22×C4111yescharacteristic
310#486C22×C4111yescharacteristic
311#484—21no—
312#478—21no—
313#477C22×C4111yescharacteristic
314#477C22×C4111yescharacteristic
315#477C22×C4111yescharacteristic
316#476—21no—
317#476C22×C4111yescharacteristic
318#475—21no—
319#475C22×C4111yescharacteristic
320#474—21no—
321#467—21no—
322#464—21no—
323#463—21no—
324#462C22×C4111yescharacteristic
325#460C22×C4111yescharacteristic
326#459C22×C4111yescharacteristic
327#451—21no—
328#446C22×C4111yescharacteristic
329C8×Q8C22×C4111yescharacteristic
330C8×Q8C22×C4111yescharacteristic
331#440—21no—
332C4×Q16C22×C4111yescharacteristic
333C4×SD16—21no—
334C4×SD16C22×C4111yescharacteristic
335C4×D8—21no—
336C8×D4C22×C4111yescharacteristic
337C2×#103—21no—
338#334C22×C4111yescharacteristic
339#334C22×C4111yescharacteristic
340#333C22×C4111yescharacteristic
341#333C22×C4111yescharacteristic
342#332C22×C4111yescharacteristic
343#331C22×C4111yescharacteristic
344Q8⋊C8C22×C4111yescharacteristic
345Q8⋊C8C22×C4111yescharacteristic
346Q8⋊C8C22×C4111yescharacteristic
347D4⋊C8C22×C4111yescharacteristic
348#322C22×C4111yescharacteristic
349C41#1979811yescharacteristic, direct product factor, Sylow
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—41no—
353C2×Q16D4×C4111yescharacteristic
354C2×SD16—21no—
355C2×SD16D4×C4111yescharacteristic
356C2×D8—21no—
357C22×C8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8C23×C4111yescharacteristic
363C4⋊Q8C23×C4111yescharacteristic
364C4⋊Q8C23×C4111yescharacteristic
365#127C23×C4111yescharacteristic
366#125—21no—
367#124—21no—
368#124—21no—
369#123—41no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C23×C4111yescharacteristic
377C4×Q8C23×C4111yescharacteristic
378C4×Q8C23×C4111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C4111yescharacteristic
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107D4×C4111yescharacteristic
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106D4×C4111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C4111yescharacteristic
398C4⋊C8C23×C4111yescharacteristic
399C4⋊C8C23×C4111yescharacteristic
400C4⋊C8C23×C4111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103D4×C4111yescharacteristic
409#103D4×C4111yescharacteristic
410#103D4×C4111yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—41no—
419#102D4×C4111yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8C23×C4111yescharacteristic
425C4×C8C23×C4111yescharacteristic
426C4×C8C23×C4111yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C4111yescharacteristic
435C2×Q8C2×D4×C4111yescharacteristic
436C2×Q8C2×D4×C4111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×D4×C4111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445Q16—22no—
446Q16—81no—
447Q16—82no—
448SD16—22no—
449SD16—42no—
450D8—42no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—81no—
457C2×C8C2×D4×C4111yescharacteristic
458C2×C8C2×D4×C4111yescharacteristic
459C2×C8C2×D4×C4111yescharacteristic
460C2×C8C2×D4×C4111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C4111yescharacteristic
476C4⋊C4C2×D4×C4111yescharacteristic
477C4⋊C4C2×D4×C4111yescharacteristic
478C4⋊C4C2×D4×C4111yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C24×C4111yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—81no—
501Q8—81no—
502Q8—161no—
503Q8#135×C4112yes—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4#137×C4112yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—161no—
525C2×C4—161no—
526C2×C4C22×D4×C4111yescharacteristic
527C2×C4C22×D4×C4111yescharacteristic
528C2×C4H(5,𝔽2)×C4111yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C4111yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#135×C4111yescharacteristic
557C4C2×#137×C4111yescharacteristic
558C4C41×#57711yescharacteristic
559C4C41×#57811yescharacteristic
560C2—42no—
561C2—161no—
562C2C41×#327011yescharacteristic
563C2C41×#328211yescharacteristic
564C2C41×#328811yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#459C22
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×#3375C2semidirect
4. C41×#3299C2semidirect
5. C41×#1720C2semidirect
6. C41×#1704C2semidirect
7. C41×#1678C2semidirect
9. C41×#1672C2semidirect
10. C41×#1640C2semidirect
11. C41×#1633C2semidirect
12. C41×#1632C2semidirect
14. C41×#1582C2semidirect
15. C41×#1579C2semidirect
255. #19798C41direct (N × H)
278. Q8×SD16C2×C41semidirect
279. #3375C2×C41semidirect
281. #3299C2×C41semidirect
282. #1720C2×C41semidirect
283. #1704C2×C41semidirect
284. #1678C2×C41semidirect
286. #1672C2×C41semidirect
287. #1640C2×C41semidirect
288. #1633C2×C41semidirect
289. #1632C2×C41semidirect
291. #1582C2×C41semidirect
292. #1579C2×C41semidirect
349. C41#19798direct (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×#33752
C41×#33612
C41×#32992
C41×#17202
C41×#17042
C41×#16782
C41×#16772
C41×#16722
C41×#16402
C41×#16332
C41×#16322
C41×#16272
C41×#15822
C41×#15792
#1979841