Finite Group Databasebeta

← C41×#20311 #23796512

Subgroups — C41×#20311 #23796512

Order 10496.

622 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3398C211yesmaximal, characteristic, complemented
2C41×#3386C211yesmaximal, characteristic, complemented
3C41×#3353C211yesmaximal, characteristic
4C41×#3276C211yesmaximal, characteristic
5C41×#1713C211yesmaximal, characteristic, complemented
6C41×#1694C211yesmaximal, characteristic, complemented
7C41×#1693C211yesmaximal, characteristic, complemented
8C41×#1690C211yesmaximal, characteristic, complemented
9C41×#1689C211yesmaximal, characteristic, complemented
10C41×#1650C211yesmaximal, characteristic, complemented
11C41×#1649C211yesmaximal, characteristic, complemented
12C41×#1648C211yesmaximal, characteristic, complemented
13C41×#1647C211yesmaximal, characteristic
14C41×#1590C211yesmaximal, characteristic, complemented
15C41×#1590C211yesmaximal, characteristic, complemented
16C2×#137×C41—21no—
17C41×#557C2211yescharacteristic
18C41×#556C2211yescharacteristic
19D4×Q8×C41C2211yescharacteristic
20C41×#547C2211yescharacteristic
21C41×#501—21no—
22C41×#500C2211yescharacteristic
23C41×#500C2211yescharacteristic
24C41×#500C2211yescharacteristic
25C41×#500C2211yescharacteristic
26C41×#497—21no—
27C41×#494C2211yescharacteristic
28C41×#494C2211yescharacteristic
29C41×#484—21no—
30C41×#482—21no—
31C41×#478—21no—
32C41×#477—21no—
33C41×#475C2211yescharacteristic
34C41×#475C2211yescharacteristic
35C41×#474C2211yescharacteristic
36C41×#474C2211yescharacteristic
37C41×#470—21no—
38C41×#468—21no—
39C41×#464—21no—
40C41×#462—21no—
41C41×#462C2211yescharacteristic
42C41×#462C2211yescharacteristic
43C41×#461C2211yescharacteristic
44C41×#461C2211yescharacteristic
45C41×#452—21no—
46C41×#451—21no—
47C41×#446C2211yescharacteristic
48C41×#446C2211yescharacteristic
49C41×#441—21no—
50C41×#440—21no—
51C4×SD16×C41C2211yescharacteristic
52C4×SD16×C41C2211yescharacteristic
53C41×#436C2211yescharacteristic
54C41×#436C2211yescharacteristic
55C41×#428—21no—
56C41×#334C2211yescharacteristic
57C41×#334C2211yescharacteristic
58C41×#332C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#332C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic
63C41×Q8⋊C8C2211yescharacteristic
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic
67C2×#41×C41—21no—
68C22×Q8×C41—21no—
69#137×C41—44no—
70C2×Q16×C41—21no—
71C2×Q16×C41—21no—
72C2×Q16×C41—21no—
73C2×Q16×C41—21no—
74C2×Q16×C41—21no—
75C2×Q16×C41—21no—
76C2×SD16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41D411yescharacteristic
79C2×SD16×C41D411yescharacteristic
80C2×M16×C41—21no—
81C2×M16×C41—21no—
82C4⋊Q8×C41—21no—
83C4⋊Q8×C41—21no—
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86C4⋊Q8×C41C2311yescharacteristic
87C4⋊Q8×C41C2311yescharacteristic
88#126×C41—41no—
89#125×C41—21no—
90#125×C41—41no—
91#124×C41—21no—
92#123×C41—41no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—41no—
97#121×C41—21no—
98C4×Q8×C41—21no—
99C4×Q8×C41—21no—
100C4×Q8×C41—21no—
101C4×Q8×C41C2311yescharacteristic
102C4×Q8×C41C2311yescharacteristic
103C4×D4×C41—21no—
104C4×D4×C41C2311yescharacteristic
105C4×D4×C41C2311yescharacteristic
106#117×C41—21no—
107C2×C4⋊C4×C41—21no—
108#107×C41—21no—
109#107×C41—21no—
110#107×C41—21no—
111#107×C41—21no—
112#107×C41—21no—
113#107×C41—21no—
114#107×C41—41no—
115#107×C41—41no—
116#106×C41—21no—
117#106×C41—21no—
118#106×C41D411yescharacteristic
119#106×C41D411yescharacteristic
120C4⋊C8×C41—21no—
121C4⋊C8×C41—21no—
122C4⋊C8×C41C2311yescharacteristic
123C4⋊C8×C41C2311yescharacteristic
124C4⋊C8×C41C2311yescharacteristic
125C4⋊C8×C41C2311yescharacteristic
126#103×C41—21no—
127#103×C41—21no—
128#103×C41—21no—
129#103×C41—21no—
130#103×C41—21no—
131#103×C41—21no—
132#103×C41D411yescharacteristic
133#103×C41D411yescharacteristic
134#102×C41—21no—
135#102×C41—21no—
136#102×C41D411yescharacteristic
137#102×C41D411yescharacteristic
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140#97×C41—21no—
141#97×C41—21no—
142C4×C8×C41C2311yescharacteristic
143C4×C8×C41C2311yescharacteristic
144C4×C8×C41C2311yescharacteristic
145#41×C41—42no—
146#41×C41—81no—
147C2×Q8×C41—21no—
148C2×Q8×C41—21no—
149C2×Q8×C41—21no—
150C2×Q8×C41—21no—
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—42no—
165Q16×C41—42no—
166Q16×C41—81no—
167Q16×C41—81no—
168Q16×C41—81no—
169SD16×C41—22no—
170SD16×C41—22no—
171SD16×C41—42no—
172SD16×C41—81no—
173M16×C41—42no—
174M16×C41—42no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41C2×D411yescharacteristic
181C2×C8×C41C2×D411yescharacteristic
182C2×C8×C41C2×D411yescharacteristic
183C2×C8×C41C2×D411yescharacteristic
184C4⋊C4×C41—21no—
185C4⋊C4×C41—21no—
186C4⋊C4×C41—21no—
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—21no—
194C4⋊C4×C41—41no—
195C4⋊C4×C41—41no—
196C4⋊C4×C41—41no—
197C4⋊C4×C41—41no—
198C4⋊C4×C41—41no—
199C4⋊C4×C41—41no—
200C4⋊C4×C41C2×D411yescharacteristic
201C4⋊C4×C41C2×D411yescharacteristic
202C4⋊C4×C41C2×D411yescharacteristic
203C4⋊C4×C41C2×D411yescharacteristic
204C22⋊C4×C41—21no—
205C22⋊C4×C41—21no—
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×C41—41no—
214C42×C41C2411yescharacteristic
215C23×C41—21no—
216C23×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—21no—
220Q8×C41—21no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—41no—
224Q8×C41—41no—
225Q8×C41—41no—
226Q8×C41—41no—
227Q8×C41—41no—
228Q8×C41—41no—
229Q8×C41—82no—
230D4×C41—21no—
231D4×C41—21no—
232D4×C41—21no—
233D4×C41—21no—
234D4×C41—82no—
235C2×C4×C41—21no—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—82no—
250C2×C4×C41—82no—
251C2×C4×C41C22×D411yescharacteristic
252C2×C4×C41C22×D411yescharacteristic
253C2×C4×C41H(5,𝔽2)11yescharacteristic
254C8×C41—22no—
255C8×C41—21no—
256C8×C41—21no—
257C8×C41—41no—
258C8×C41—41no—
259C8×C41—41no—
260C8×C41—41no—
261C8×C41AGL(1,ℤ/8)12yes—
262C8×C41#13712yescomplemented
263#20311C4111yesmaximal, characteristic, direct product factor, Sylow
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—41no—
267C22×C41—41no—
268C22×C41—41no—
269C22×C41—41no—
270C22×C41D4211yescharacteristic
271C4×C41—21no—
272C4×C41—41no—
273C4×C41—41no—
274C4×C41—41no—
275C4×C41—41no—
276C4×C41—41no—
277C4×C41—41no—
278C4×C41—81no—
279C4×C41—81no—
280C4×C41—81no—
281C4×C41—81no—
282C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C41C2×#13711yescharacteristic
284C4×C41#57611yescharacteristic
285C4×C41#57811yescharacteristic
286#3398C2×C4111yescharacteristic, complemented
287#3386C2×C4111yescharacteristic, complemented
288#3353C2×C4111yescharacteristic
289#3276C2×C4111yescharacteristic
290#1713C2×C4111yescharacteristic, complemented
291#1694C2×C4111yescharacteristic, complemented
292#1693C2×C4111yescharacteristic, complemented
293#1690C2×C4111yescharacteristic, complemented
294#1689C2×C4111yescharacteristic, complemented
295#1650C2×C4111yescharacteristic, complemented
296#1649C2×C4111yescharacteristic, complemented
297#1648C2×C4111yescharacteristic, complemented
298#1647C2×C4111yescharacteristic
299#1590C2×C4111yescharacteristic, complemented
300#1590C2×C4111yescharacteristic, complemented
301C2×C41—81no—
302C2×C41—81no—
303C2×C41#327411yescharacteristic
304C2×C41#327611yescharacteristic
305C2×C41#329311yescharacteristic
306C2×#137—21no—
307#557C22×C4111yescharacteristic
308#556C22×C4111yescharacteristic
309D4×Q8C22×C4111yescharacteristic
310#547C22×C4111yescharacteristic
311#501—21no—
312#500C22×C4111yescharacteristic
313#500C22×C4111yescharacteristic
314#500C22×C4111yescharacteristic
315#500C22×C4111yescharacteristic
316#497—21no—
317#494C22×C4111yescharacteristic
318#494C22×C4111yescharacteristic
319#484—21no—
320#482—21no—
321#478—21no—
322#477—21no—
323#475C22×C4111yescharacteristic
324#475C22×C4111yescharacteristic
325#474C22×C4111yescharacteristic
326#474C22×C4111yescharacteristic
327#470—21no—
328#468—21no—
329#464—21no—
330#462—21no—
331#462C22×C4111yescharacteristic
332#462C22×C4111yescharacteristic
333#461C22×C4111yescharacteristic
334#461C22×C4111yescharacteristic
335#452—21no—
336#451—21no—
337#446C22×C4111yescharacteristic
338#446C22×C4111yescharacteristic
339#441—21no—
340#440—21no—
341C4×SD16C22×C4111yescharacteristic
342C4×SD16C22×C4111yescharacteristic
343#436C22×C4111yescharacteristic
344#436C22×C4111yescharacteristic
345#428—21no—
346#334C22×C4111yescharacteristic
347#334C22×C4111yescharacteristic
348#332C22×C4111yescharacteristic
349#332C22×C4111yescharacteristic
350#332C22×C4111yescharacteristic
351#332C22×C4111yescharacteristic
352Q8⋊C8C22×C4111yescharacteristic
353Q8⋊C8C22×C4111yescharacteristic
354D4⋊C8C22×C4111yescharacteristic
355D4⋊C8C22×C4111yescharacteristic
356C82C22×C4111yescharacteristic
357C41#2031111yescharacteristic, direct product factor, Sylow
358C2×#41—21no—
359C22×Q8—21no—
360#137—44no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16D4×C4111yescharacteristic
370C2×SD16D4×C4111yescharacteristic
371C2×M16—21no—
372C2×M16—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C4111yescharacteristic
376C4⋊Q8C23×C4111yescharacteristic
377C4⋊Q8C23×C4111yescharacteristic
378C4⋊Q8C23×C4111yescharacteristic
379#126—41no—
380#125—21no—
381#125—41no—
382#124—21no—
383#123—41no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388#121—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C4111yescharacteristic
393C4×Q8C23×C4111yescharacteristic
394C4×D4—21no—
395C4×D4C23×C4111yescharacteristic
396C4×D4C23×C4111yescharacteristic
397#117—21no—
398C2×C4⋊C4—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#107—41no—
406#107—41no—
407#106—21no—
408#106—21no—
409#106D4×C4111yescharacteristic
410#106D4×C4111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C4111yescharacteristic
414C4⋊C8C23×C4111yescharacteristic
415C4⋊C8C23×C4111yescharacteristic
416C4⋊C8C23×C4111yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103D4×C4111yescharacteristic
424#103D4×C4111yescharacteristic
425#102—21no—
426#102—21no—
427#102D4×C4111yescharacteristic
428#102D4×C4111yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432#97—21no—
433C4×C8C23×C4111yescharacteristic
434C4×C8C23×C4111yescharacteristic
435C4×C8C23×C4111yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8C2×D4×C4111yescharacteristic
446C2×Q8C2×D4×C4111yescharacteristic
447C2×D4—41no—
448C2×D4C2×D4×C4111yescharacteristic
449C2×D4C2×D4×C4111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—41no—
454Q16—42no—
455Q16—42no—
456Q16—42no—
457Q16—81no—
458Q16—81no—
459Q16—81no—
460SD16—22no—
461SD16—22no—
462SD16—42no—
463SD16—81no—
464M16—42no—
465M16—42no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×D4×C4111yescharacteristic
472C2×C8C2×D4×C4111yescharacteristic
473C2×C8C2×D4×C4111yescharacteristic
474C2×C8C2×D4×C4111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C4111yescharacteristic
492C4⋊C4C2×D4×C4111yescharacteristic
493C4⋊C4C2×D4×C4111yescharacteristic
494C4⋊C4C2×D4×C4111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42—41no—
505C42C24×C4111yescharacteristic
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—82no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—82no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4C22×D4×C4111yescharacteristic
543C2×C4C22×D4×C4111yescharacteristic
544C2×C4H(5,𝔽2)×C4111yescharacteristic
545C8—22no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8AGL(1,ℤ/8)×C4112yes—
553C8#137×C4112yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D42×C4111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
573C4C2×#137×C4111yescharacteristic
574C4C41×#57611yescharacteristic
575C4C41×#57811yescharacteristic
576C2—81no—
577C2—81no—
578C2C41×#327411yescharacteristic
579C2C41×#327611yescharacteristic
580C2C41×#329311yescharacteristic
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. C41×#3398C2semidirect
2. C41×#3386C2semidirect
5. C41×#1713C2semidirect
6. C41×#1694C2semidirect
7. C41×#1693C2semidirect
8. C41×#1690C2semidirect
9. C41×#1689C2semidirect
10. C41×#1650C2semidirect
11. C41×#1649C2semidirect
12. C41×#1648C2semidirect
14. C41×#1590C2semidirect
15. C41×#1590C2semidirect
262. C8×C41#137semidirect
263. #20311C41direct (N × H)
286. #3398C2×C41semidirect
287. #3386C2×C41semidirect
290. #1713C2×C41semidirect
291. #1694C2×C41semidirect
292. #1693C2×C41semidirect
293. #1690C2×C41semidirect
294. #1689C2×C41semidirect
295. #1650C2×C41semidirect
296. #1649C2×C41semidirect
297. #1648C2×C41semidirect
299. #1590C2×C41semidirect
300. #1590C2×C41semidirect
357. C41#20311direct (N × H)
553. C8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#33982
C41×#33862
C41×#33532
C41×#32762
C41×#17132
C41×#16942
C41×#16932
C41×#16902
C41×#16892
C41×#16502
C41×#16492
C41×#16482
C41×#16472
C41×#15902
#2031141