Finite Group Databasebeta

← C41×#19919 #23796120

Subgroups — C41×#19919 #23796120

Order 10496.

586 conjugacy classes of subgroups.

The subgroup lattice has 562 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×#3340C211yesmaximal, characteristic
4C41×#3329C211yesmaximal, characteristic
5C41×#1707C211yesmaximal, characteristic, complemented
6C41×#1704C211yesmaximal, characteristic, complemented
7C41×#1703C211yesmaximal, characteristic, complemented
8C41×#1672C211yesmaximal, characteristic, complemented
9C41×#1671C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1649C211yesmaximal, characteristic, complemented
12C41×#1634C211yesmaximal, characteristic
13C41×#1633C211yesmaximal, characteristic, complemented
14C41×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C41C211yesmaximal, characteristic, complemented
16Q82×C41C2211yescharacteristic
17C41×#556C2211yescharacteristic
18C41×#555C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#500C2211yescharacteristic
21C41×#498—21no—
22C41×#498C2211yescharacteristic
23C41×#498C2211yescharacteristic
24C41×#494C2211yescharacteristic
25C41×#489—21no—
26C41×#487C2211yescharacteristic
27C41×#487C2211yescharacteristic
28C41×#485—21no—
29C41×#485—21no—
30C41×#482—21no—
31C41×#477C2211yescharacteristic
32C41×#477C2211yescharacteristic
33C41×#476—21no—
34C41×#476C2211yescharacteristic
35C41×#476C2211yescharacteristic
36C41×#475—21no—
37C41×#475—21no—
38C41×#475C2211yescharacteristic
39C41×#474C2211yescharacteristic
40C41×#468—21no—
41C41×#465—21no—
42C41×#464—21no—
43C41×#462C2211yescharacteristic
44C41×#461C2211yescharacteristic
45C41×#448—21no—
46C41×#446C2211yescharacteristic
47C8×Q8×C41C2211yescharacteristic
48C41×#441—21no—
49C4×SD16×C41—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C41×#436C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#427—21no—
55C41×#419—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#333C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#332C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C22×Q8×C41—21no—
68C2×Q16×C41—21no—
69C2×Q16×C41—41no—
70C2×SD16×C41—21no—
71C2×SD16×C41D411yescharacteristic
72C2×SD16×C41D411yescharacteristic
73C2×M16×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
82C4⋊Q8×C41C2311yescharacteristic
83#126×C41—41no—
84#124×C41—21no—
85#124×C41—41no—
86C22⋊Q8×C41—21no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—41no—
89#121×C41—21no—
90#121×C41—21no—
91C4×Q8×C41—21no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41C2311yescharacteristic
95C4×Q8×C41C2311yescharacteristic
96C4×D4×C41—21no—
97C4×D4×C41C2311yescharacteristic
98C4×D4×C41C2311yescharacteristic
99#117×C41—21no—
100#117×C41—21no—
101#117×C41—21no—
102#107×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—41no—
106#106×C41—21no—
107#106×C41—21no—
108#106×C41—21no—
109#106×C41—21no—
110#106×C41—21no—
111#106×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×C41—21no—
125#103×C41—21no—
126#103×C41—21no—
127#103×C41—21no—
128#103×C41—21no—
129#103×C41—21no—
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
144C2×Q8×C41—21no—
145C2×Q8×C41—21no—
146C2×Q8×C41—21no—
147C2×Q8×C41—21no—
148C2×Q8×C41—41no—
149C2×Q8×C41—41no—
150C2×Q8×C41—42no—
151C2×Q8×C41—81no—
152C2×Q8×C41C2×D411yescharacteristic
153C2×Q8×C41C2×D411yescharacteristic
154C2×D4×C41—41no—
155C2×D4×C41C2×D411yescharacteristic
156C2×D4×C41C2×D411yescharacteristic
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41—41no—
160Q16×C41—42no—
161Q16×C41—82no—
162SD16×C41—22no—
163SD16×C41—22no—
164SD16×C41—81no—
165M16×C41—81no—
166C2×C8×C41—21no—
167C2×C8×C41—21no—
168C2×C8×C41—21no—
169C2×C8×C41—21no—
170C2×C8×C41—21no—
171C2×C8×C41—42no—
172C2×C8×C41C2×D411yescharacteristic
173C2×C8×C41C2×D411yescharacteristic
174C2×C8×C41C2×D411yescharacteristic
175C2×C8×C41C2×D411yescharacteristic
176C4⋊C4×C41—21no—
177C4⋊C4×C41—21no—
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—41no—
187C4⋊C4×C41—41no—
188C4⋊C4×C41—41no—
189C4⋊C4×C41—41no—
190C4⋊C4×C41C2×D411yescharacteristic
191C4⋊C4×C41C2×D411yescharacteristic
192C4⋊C4×C41C2×D411yescharacteristic
193C4⋊C4×C41C2×D411yescharacteristic
194C22⋊C4×C41—21no—
195C22⋊C4×C41—21no—
196C22⋊C4×C41—41no—
197C22⋊C4×C41—41no—
198C22⋊C4×C41—41no—
199C22⋊C4×C41—41no—
200C22⋊C4×C41—41no—
201C42×C41—21no—
202C42×C41—21no—
203C42×C41—41no—
204C42×C41—41no—
205C42×C41—41no—
206C42×C41C2411yescharacteristic
207C23×C41—21no—
208C23×C41—21no—
209Q8×C41—21no—
210Q8×C41—21no—
211Q8×C41—21no—
212Q8×C41—41no—
213Q8×C41—41no—
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—21no—
223D4×C41—21no—
224D4×C41—21no—
225D4×C41—161no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—41no—
233C2×C4×C41—41no—
234C2×C4×C41—41no—
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×C41C22×D411yescharacteristic
242C2×C4×C41C22×D411yescharacteristic
243C2×C4×C41H(5,𝔽2)11yescharacteristic
244C8×C41—22no—
245C8×C41—21no—
246C8×C41—21no—
247C8×C41—21no—
248C8×C41—41no—
249C8×C41—41no—
250C8×C41—41no—
251C8×C41—41no—
252C8×C41#13712yes—
253#19919C4111yesmaximal, characteristic, direct product factor, Sylow
254C22×C41—41no—
255C22×C41—41no—
256C22×C41—41no—
257C22×C41—41no—
258C22×C41—41no—
259C22×C41—41no—
260C22×C41D4211yescharacteristic
261C4×C41—22no—
262C4×C41—21no—
263C4×C41—41no—
264C4×C41—41no—
265C4×C41—41no—
266C4×C41—41no—
267C4×C41—41no—
268C4×C41—81no—
269C4×C41—81no—
270C4×C41—81no—
271C4×C41—81no—
272C4×C41C2×#13511yescharacteristic
273C4×C41C2×#13711yescharacteristic
274C4×C41#57711yescharacteristic
275C4×C41#57811yescharacteristic
276Q8×SD16C2×C4111yescharacteristic, complemented
277#3369C2×C4111yescharacteristic, complemented
278#3340C2×C4111yescharacteristic
279#3329C2×C4111yescharacteristic
280#1707C2×C4111yescharacteristic, complemented
281#1704C2×C4111yescharacteristic, complemented
282#1703C2×C4111yescharacteristic, complemented
283#1672C2×C4111yescharacteristic, complemented
284#1671C2×C4111yescharacteristic, complemented
285#1650C2×C4111yescharacteristic, complemented
286#1649C2×C4111yescharacteristic, complemented
287#1634C2×C4111yescharacteristic
288#1633C2×C4111yescharacteristic, complemented
289#1590C2×C4111yescharacteristic, complemented
290C8×SD16C2×C4111yescharacteristic, complemented
291C2×C41—81no—
292C2×C41—81no—
293C2×C41#327611yescharacteristic
294C2×C41#328211yescharacteristic
295C2×C41#329111yescharacteristic
296Q82C22×C4111yescharacteristic
297#556C22×C4111yescharacteristic
298#555C22×C4111yescharacteristic
299D4×Q8C22×C4111yescharacteristic
300#500C22×C4111yescharacteristic
301#498—21no—
302#498C22×C4111yescharacteristic
303#498C22×C4111yescharacteristic
304#494C22×C4111yescharacteristic
305#489—21no—
306#487C22×C4111yescharacteristic
307#487C22×C4111yescharacteristic
308#485—21no—
309#485—21no—
310#482—21no—
311#477C22×C4111yescharacteristic
312#477C22×C4111yescharacteristic
313#476—21no—
314#476C22×C4111yescharacteristic
315#476C22×C4111yescharacteristic
316#475—21no—
317#475—21no—
318#475C22×C4111yescharacteristic
319#474C22×C4111yescharacteristic
320#468—21no—
321#465—21no—
322#464—21no—
323#462C22×C4111yescharacteristic
324#461C22×C4111yescharacteristic
325#448—21no—
326#446C22×C4111yescharacteristic
327C8×Q8C22×C4111yescharacteristic
328#441—21no—
329C4×SD16—21no—
330C4×SD16C22×C4111yescharacteristic
331C4×SD16C22×C4111yescharacteristic
332#436C22×C4111yescharacteristic
333C8×D4C22×C4111yescharacteristic
334#427—21no—
335#419—21no—
336#334C22×C4111yescharacteristic
337#334C22×C4111yescharacteristic
338#333C22×C4111yescharacteristic
339#333C22×C4111yescharacteristic
340#332C22×C4111yescharacteristic
341#332C22×C4111yescharacteristic
342Q8⋊C8C22×C4111yescharacteristic
343Q8⋊C8C22×C4111yescharacteristic
344D4⋊C8C22×C4111yescharacteristic
345D4⋊C8C22×C4111yescharacteristic
346C82C22×C4111yescharacteristic
347C41#1991911yescharacteristic, direct product factor, Sylow
348C22×Q8—21no—
349C2×Q16—21no—
350C2×Q16—41no—
351C2×SD16—21no—
352C2×SD16D4×C4111yescharacteristic
353C2×SD16D4×C4111yescharacteristic
354C2×M16—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—41no—
360C4⋊Q8C23×C4111yescharacteristic
361C4⋊Q8C23×C4111yescharacteristic
362C4⋊Q8C23×C4111yescharacteristic
363C4⋊Q8C23×C4111yescharacteristic
364#126—41no—
365#124—21no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370#121—21no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C4111yescharacteristic
376C4×Q8C23×C4111yescharacteristic
377C4×D4—21no—
378C4×D4C23×C4111yescharacteristic
379C4×D4C23×C4111yescharacteristic
380#117—21no—
381#117—21no—
382#117—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394#106D4×C4111yescharacteristic
395#106D4×C4111yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C4111yescharacteristic
399C4⋊C8C23×C4111yescharacteristic
400C4⋊C8C23×C4111yescharacteristic
401C4⋊C8C23×C4111yescharacteristic
402#103—21no—
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#103D4×C4111yescharacteristic
412#103D4×C4111yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102D4×C4111yescharacteristic
417#102D4×C4111yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420#97—21no—
421C4×C8—21no—
422C4×C8C23×C4111yescharacteristic
423C4×C8C23×C4111yescharacteristic
424C4×C8C23×C4111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8C2×D4×C4111yescharacteristic
434C2×Q8C2×D4×C4111yescharacteristic
435C2×D4—41no—
436C2×D4C2×D4×C4111yescharacteristic
437C2×D4C2×D4×C4111yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441Q16—42no—
442Q16—82no—
443SD16—22no—
444SD16—22no—
445SD16—81no—
446M16—81no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8C2×D4×C4111yescharacteristic
454C2×C8C2×D4×C4111yescharacteristic
455C2×C8C2×D4×C4111yescharacteristic
456C2×C8C2×D4×C4111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C4111yescharacteristic
472C4⋊C4C2×D4×C4111yescharacteristic
473C4⋊C4C2×D4×C4111yescharacteristic
474C4⋊C4C2×D4×C4111yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42—41no—
487C42C24×C4111yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8—81no—
499Q8—81no—
500Q8—161no—
501Q8#135×C4112yes—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—161no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4C22×D4×C4111yescharacteristic
523C2×C4C22×D4×C4111yescharacteristic
524C2×C4H(5,𝔽2)×C4111yescharacteristic
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8#137×C4112yes—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C4111yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C4111yescharacteristic
553C4C2×#137×C4111yescharacteristic
554C4C41×#57711yescharacteristic
555C4C41×#57811yescharacteristic
556C2—81no—
557C2—81no—
558C2C41×#327611yescharacteristic
559C2C41×#328211yescharacteristic
560C2C41×#329111yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#555C22
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×#1707C2semidirect
6. C41×#1704C2semidirect
7. C41×#1703C2semidirect
8. C41×#1672C2semidirect
9. C41×#1671C2semidirect
10. C41×#1650C2semidirect
11. C41×#1649C2semidirect
13. C41×#1633C2semidirect
14. C41×#1590C2semidirect
15. C8×SD16×C41C2semidirect
253. #19919C41direct (N × H)
276. Q8×SD16C2×C41semidirect
277. #3369C2×C41semidirect
280. #1707C2×C41semidirect
281. #1704C2×C41semidirect
282. #1703C2×C41semidirect
283. #1672C2×C41semidirect
284. #1671C2×C41semidirect
285. #1650C2×C41semidirect
286. #1649C2×C41semidirect
288. #1633C2×C41semidirect
289. #1590C2×C41semidirect
290. C8×SD16C2×C41semidirect
347. C41#19919direct (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×#33402
C41×#33292
C41×#17072
C41×#17042
C41×#17032
C41×#16722
C41×#16712
C41×#16502
C41×#16492
C41×#16342
C41×#16332
C41×#15902
C8×SD16×C412
#1991941