Finite Group Databasebeta

← C41×#19913 #23796114

Subgroups — C41×#19913 #23796114

Order 10496.

618 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3372C211yesmaximal, characteristic, complemented
2C41×#3364C211yesmaximal, characteristic, complemented
3C41×#3324C211yesmaximal, characteristic
4C41×#3295C211yesmaximal, characteristic
5C41×#1711C211yesmaximal, characteristic, complemented
6C41×#1703C211yesmaximal, characteristic, complemented
7C41×#1702C211yesmaximal, characteristic, complemented
8C41×#1679C211yesmaximal, characteristic, complemented
9C41×#1678C211yesmaximal, characteristic, complemented
10C41×#1644C211yesmaximal, characteristic, complemented
11C41×#1639C211yesmaximal, characteristic
12C41×#1638C211yesmaximal, characteristic, complemented
13C41×#1626C211yesmaximal, characteristic, complemented
14C41×#1590C211yesmaximal, characteristic, complemented
15C8×SD16×C41C211yesmaximal, characteristic, complemented
16C41×#557C2211yescharacteristic, complemented
17C41×#556C2211yescharacteristic
18C41×#554C2211yescharacteristic
19D42×C41C2211yescharacteristic
20C41×#491—21no—
21C41×#488—21no—
22C41×#487C2211yescharacteristic, complemented
23C41×#487C2211yescharacteristic, complemented
24C41×#487C2211yescharacteristic, complemented
25C41×#486C2211yescharacteristic
26C41×#486C2211yescharacteristic
27C41×#486C2211yescharacteristic
28C41×#482—21no—
29C41×#481—21no—
30C41×#479—21no—
31C41×#479—21no—
32C41×#477C2211yescharacteristic, complemented
33C41×#476C2211yescharacteristic
34C41×#474C2211yescharacteristic
35C41×#474C2211yescharacteristic
36C41×#468—21no—
37C41×#465—21no—
38C41×#464—21no—
39C41×#462C2211yescharacteristic, complemented
40C41×#461—21no—
41C41×#461C2211yescharacteristic
42C41×#460C2211yescharacteristic
43C41×#460C2211yescharacteristic
44C41×#450—21no—
45C41×#450—21no—
46C41×#446C2211yescharacteristic, complemented
47C8×Q8×C41C2211yescharacteristic, complemented
48C41×#440—21no—
49C4×Q16×C41—21no—
50C4×SD16×C41C2211yescharacteristic
51C4×SD16×C41C2211yescharacteristic
52C41×#436C2211yescharacteristic
53C8×D4×C41C2211yescharacteristic
54C41×#418—21no—
55C2×#102×C41—21no—
56C41×#334C2211yescharacteristic, complemented
57C41×#334C2211yescharacteristic, complemented
58C41×#333C2211yescharacteristic, complemented
59C41×#332C2211yescharacteristic, complemented
60C41×#332C2211yescharacteristic, complemented
61C41×#331C2211yescharacteristic
62C41×Q8⋊C8C2211yescharacteristic, complemented
63C41×Q8⋊C8C2211yescharacteristic, complemented
64C41×D4⋊C8C2211yescharacteristic
65C41×D4⋊C8C2211yescharacteristic
66C82×C41C2211yescharacteristic, complemented
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C2×Q16×C41—21no—
70C2×SD16×C41—21no—
71C2×SD16×C41—21no—
72C2×SD16×C41—21no—
73C2×SD16×C41D411yescharacteristic
74C2×SD16×C41D411yescharacteristic
75C2×M16×C41—21no—
76C22×C8×C41—21no—
77C4⋊Q8×C41—21no—
78C4⋊Q8×C41C2311yescharacteristic
79C4⋊Q8×C41C2311yescharacteristic
80C4⋊Q8×C41C2311yescharacteristic
81#127×C41C2311yescharacteristic
82#126×C41—41no—
83#125×C41—21no—
84#125×C41—21no—
85#125×C41—41no—
86#124×C41—21no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—41no—
90#121×C41—21no—
91#121×C41—21no—
92#120×C41—41no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41C2311yescharacteristic
97C4×Q8×C41C2311yescharacteristic
98C4×D4×C41—21no—
99C4×D4×C41C2311yescharacteristic
100C4×D4×C41C2311yescharacteristic
101#117×C41—21no—
102C2×C4⋊C4×C41—21no—
103#107×C41—21no—
104#107×C41—21no—
105#107×C41—21no—
106#106×C41—21no—
107#106×C41D411yescharacteristic
108#106×C41D411yescharacteristic
109C4⋊C8×C41—21no—
110C4⋊C8×C41—21no—
111C4⋊C8×C41C2311yescharacteristic
112C4⋊C8×C41C2311yescharacteristic
113C4⋊C8×C41C2311yescharacteristic
114C4⋊C8×C41C2311yescharacteristic
115#103×C41—21no—
116#103×C41—21no—
117#103×C41—21no—
118#103×C41—21no—
119#103×C41—21no—
120#103×C41—21no—
121#103×C41—21no—
122#103×C41—41no—
123#103×C41D411yescharacteristic
124#103×C41D411yescharacteristic
125#102×C41—21no—
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—41no—
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
144C24×C41—41no—
145C2×Q8×C41—21no—
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—41no—
154C2×D4×C41—41no—
155C2×D4×C41—42no—
156C2×D4×C41—42no—
157C2×D4×C41—81no—
158C2×D4×C41—81no—
159C2×D4×C41C2×D411yescharacteristic
160C2×D4×C41C2×D411yescharacteristic
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—41no—
164Q16×C41—42no—
165SD16×C41—22no—
166SD16×C41—41no—
167SD16×C41—42no—
168SD16×C41—81no—
169SD16×C41—81no—
170M16×C41—81no—
171C2×C8×C41—21no—
172C2×C8×C41—21no—
173C2×C8×C41—21no—
174C2×C8×C41—21no—
175C2×C8×C41—21no—
176C2×C8×C41—81no—
177C2×C8×C41C2×D411yescharacteristic
178C2×C8×C41C2×D411yescharacteristic
179C2×C8×C41C2×D411yescharacteristic
180C2×C8×C41C2×D411yescharacteristic
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×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—
205C42×C41—21no—
206C42×C41—21no—
207C42×C41—41no—
208C42×C41—41no—
209C42×C41C2411yescharacteristic
210C23×C41—21no—
211C23×C41—21no—
212C23×C41—41no—
213C23×C41—82no—
214C23×C41—82no—
215C23×C41—161no—
216Q8×C41—21no—
217Q8×C41—21no—
218Q8×C41—21no—
219Q8×C41—21no—
220Q8×C41—41no—
221Q8×C41—41no—
222Q8×C41—41no—
223Q8×C41—41no—
224Q8×C41—81no—
225D4×C41—21no—
226D4×C41—21no—
227D4×C41—21no—
228D4×C41—41no—
229D4×C41—41no—
230D4×C41—41no—
231D4×C41—41no—
232D4×C41—81no—
233D4×C41—82no—
234D4×C41—82no—
235D4×C41#13512yes—
236C2×C4×C41—21no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
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—161no—
250C2×C4×C41C22×D411yescharacteristic
251C2×C4×C41C22×D411yescharacteristic
252C2×C4×C41H(5,𝔽2)11yescharacteristic
253C8×C41—21no—
254C8×C41—21no—
255C8×C41—21no—
256C8×C41—21no—
257C8×C41—41no—
258C8×C41—41no—
259C8×C41—41no—
260C8×C41—41no—
261C8×C41—41no—
262#19913C4111yesmaximal, characteristic, direct product factor, Sylow
263C22×C41—22no—
264C22×C41—41no—
265C22×C41—41no—
266C22×C41—41no—
267C22×C41—41no—
268C22×C41—41no—
269C22×C41—81no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—164no—
273C22×C41D4211yescharacteristic
274C4×C41—21no—
275C4×C41—41no—
276C4×C41—41no—
277C4×C41—41no—
278C4×C41—41no—
279C4×C41—41no—
280C4×C41—41no—
281C4×C41—81no—
282C4×C41—81no—
283C4×C41—81no—
284C4×C41C2×#13511yescharacteristic
285C4×C41#57511yescharacteristic
286C4×C41#57711yescharacteristic
287C4×C41#57711yescharacteristic
288#3372C2×C4111yescharacteristic, complemented
289#3364C2×C4111yescharacteristic, complemented
290#3324C2×C4111yescharacteristic
291#3295C2×C4111yescharacteristic
292#1711C2×C4111yescharacteristic, complemented
293#1703C2×C4111yescharacteristic, complemented
294#1702C2×C4111yescharacteristic, complemented
295#1679C2×C4111yescharacteristic, complemented
296#1678C2×C4111yescharacteristic, complemented
297#1644C2×C4111yescharacteristic, complemented
298#1639C2×C4111yescharacteristic
299#1638C2×C4111yescharacteristic, complemented
300#1626C2×C4111yescharacteristic, complemented
301#1590C2×C4111yescharacteristic, complemented
302C8×SD16C2×C4111yescharacteristic, complemented
303C2×C41—42no—
304C2×C41—81no—
305C2×C41—161no—
306C2×C41#327511yescharacteristic
307C2×C41#328211yescharacteristic
308C2×C41#329011yescharacteristic
309#557C22×C4111yescharacteristic, complemented
310#556C22×C4111yescharacteristic
311#554C22×C4111yescharacteristic
312D42C22×C4111yescharacteristic
313#491—21no—
314#488—21no—
315#487C22×C4111yescharacteristic, complemented
316#487C22×C4111yescharacteristic, complemented
317#487C22×C4111yescharacteristic, complemented
318#486C22×C4111yescharacteristic
319#486C22×C4111yescharacteristic
320#486C22×C4111yescharacteristic
321#482—21no—
322#481—21no—
323#479—21no—
324#479—21no—
325#477C22×C4111yescharacteristic, complemented
326#476C22×C4111yescharacteristic
327#474C22×C4111yescharacteristic
328#474C22×C4111yescharacteristic
329#468—21no—
330#465—21no—
331#464—21no—
332#462C22×C4111yescharacteristic, complemented
333#461—21no—
334#461C22×C4111yescharacteristic
335#460C22×C4111yescharacteristic
336#460C22×C4111yescharacteristic
337#450—21no—
338#450—21no—
339#446C22×C4111yescharacteristic, complemented
340C8×Q8C22×C4111yescharacteristic, complemented
341#440—21no—
342C4×Q16—21no—
343C4×SD16C22×C4111yescharacteristic
344C4×SD16C22×C4111yescharacteristic
345#436C22×C4111yescharacteristic
346C8×D4C22×C4111yescharacteristic
347#418—21no—
348C2×#102—21no—
349#334C22×C4111yescharacteristic, complemented
350#334C22×C4111yescharacteristic, complemented
351#333C22×C4111yescharacteristic, complemented
352#332C22×C4111yescharacteristic, complemented
353#332C22×C4111yescharacteristic, complemented
354#331C22×C4111yescharacteristic
355Q8⋊C8C22×C4111yescharacteristic, complemented
356Q8⋊C8C22×C4111yescharacteristic, complemented
357D4⋊C8C22×C4111yescharacteristic
358D4⋊C8C22×C4111yescharacteristic
359C82C22×C4111yescharacteristic, complemented
360C41#1991311yescharacteristic, direct product factor, Sylow
361C22×D4—21no—
362C22×D4—21no—
363C2×Q16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16D4×C4111yescharacteristic
368C2×SD16D4×C4111yescharacteristic
369C2×M16—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8C23×C4111yescharacteristic
373C4⋊Q8C23×C4111yescharacteristic
374C4⋊Q8C23×C4111yescharacteristic
375#127C23×C4111yescharacteristic
376#126—41no—
377#125—21no—
378#125—21no—
379#125—41no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384#121—21no—
385#121—21no—
386#120—41no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8C23×C4111yescharacteristic
391C4×Q8C23×C4111yescharacteristic
392C4×D4—21no—
393C4×D4C23×C4111yescharacteristic
394C4×D4C23×C4111yescharacteristic
395#117—21no—
396C2×C4⋊C4—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#106—21no—
401#106D4×C4111yescharacteristic
402#106D4×C4111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8C23×C4111yescharacteristic
406C4⋊C8C23×C4111yescharacteristic
407C4⋊C8C23×C4111yescharacteristic
408C4⋊C8C23×C4111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—41no—
417#103D4×C4111yescharacteristic
418#103D4×C4111yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—41no—
429#102D4×C4111yescharacteristic
430#102D4×C4111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—21no—
433#97—21no—
434C4×C8—21no—
435C4×C8C23×C4111yescharacteristic
436C4×C8C23×C4111yescharacteristic
437C4×C8C23×C4111yescharacteristic
438C24—41no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C4111yescharacteristic
443C2×Q8C2×D4×C4111yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—81no—
452C2×D4—81no—
453C2×D4C2×D4×C4111yescharacteristic
454C2×D4C2×D4×C4111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458Q16—42no—
459SD16—22no—
460SD16—41no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464M16—81no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
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—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C4111yescharacteristic
490C4⋊C4C2×D4×C4111yescharacteristic
491C4⋊C4C2×D4×C4111yescharacteristic
492C4⋊C4C2×D4×C4111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42—41no—
503C42C24×C4111yescharacteristic
504C23—21no—
505C23—21no—
506C23—41no—
507C23—82no—
508C23—82no—
509C23—161no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—82no—
528D4—82no—
529D4#135×C4112yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—161no—
544C2×C4C22×D4×C4111yescharacteristic
545C2×C4C22×D4×C4111yescharacteristic
546C2×C4H(5,𝔽2)×C4111yescharacteristic
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—164no—
566C22D42×C4111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4C2×#135×C4111yescharacteristic
578C4C41×#57511yescharacteristic
579C4C41×#57711yescharacteristic
580C4C41×#57711yescharacteristic
581C2—42no—
582C2—81no—
583C2—161no—
584C2C41×#327511yescharacteristic
585C2C41×#328211yescharacteristic
586C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalD42×C41C22
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×#3372C2semidirect
2. C41×#3364C2semidirect
5. C41×#1711C2semidirect
6. C41×#1703C2semidirect
7. C41×#1702C2semidirect
8. C41×#1679C2semidirect
9. C41×#1678C2semidirect
10. C41×#1644C2semidirect
12. C41×#1638C2semidirect
13. C41×#1626C2semidirect
14. C41×#1590C2semidirect
15. C8×SD16×C41C2semidirect
16. C41×#557C22semidirect
22. C41×#487C22semidirect
23. C41×#487C22semidirect
24. C41×#487C22semidirect
32. C41×#477C22semidirect
39. C41×#462C22semidirect
46. C41×#446C22semidirect
47. C8×Q8×C41C22semidirect
56. C41×#334C22semidirect
57. C41×#334C22semidirect
58. C41×#333C22semidirect
59. C41×#332C22semidirect
60. C41×#332C22semidirect
62. C41×Q8⋊C8C22semidirect
63. C41×Q8⋊C8C22semidirect
66. C82×C41C22semidirect
262. #19913C41direct (N × H)
288. #3372C2×C41semidirect
289. #3364C2×C41semidirect
292. #1711C2×C41semidirect
293. #1703C2×C41semidirect
294. #1702C2×C41semidirect
295. #1679C2×C41semidirect
296. #1678C2×C41semidirect
297. #1644C2×C41semidirect
299. #1638C2×C41semidirect
300. #1626C2×C41semidirect
301. #1590C2×C41semidirect
302. C8×SD16C2×C41semidirect
309. #557C22×C41semidirect
315. #487C22×C41semidirect
316. #487C22×C41semidirect
317. #487C22×C41semidirect
325. #477C22×C41semidirect
332. #462C22×C41semidirect
339. #446C22×C41semidirect
340. C8×Q8C22×C41semidirect
349. #334C22×C41semidirect
350. #334C22×C41semidirect
351. #333C22×C41semidirect
352. #332C22×C41semidirect
353. #332C22×C41semidirect
355. Q8⋊C8C22×C41semidirect
356. Q8⋊C8C22×C41semidirect
359. C82C22×C41semidirect
360. C41#19913direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33722
C41×#33642
C41×#33242
C41×#32952
C41×#17112
C41×#17032
C41×#17022
C41×#16792
C41×#16782
C41×#16442
C41×#16392
C41×#16382
C41×#16262
C41×#15902
C8×SD16×C412
#1991341