Finite Group Databasebeta

← C41×#20317 #23796518

Subgroups — C41×#20317 #23796518

Order 10496.

640 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3397C211yesmaximal, characteristic
2C41×#3384C211yesmaximal, characteristic, complemented
3C41×#3356C211yesmaximal, characteristic, complemented
4C41×#3278C211yesmaximal, characteristic, complemented
5C41×#1705C211yesmaximal, characteristic, complemented
6C41×#1692C211yesmaximal, characteristic, complemented
7C41×#1691C211yesmaximal, characteristic, complemented
8C41×#1686C211yesmaximal, characteristic, complemented
9C41×#1685C211yesmaximal, characteristic, complemented
10C41×#1652C211yesmaximal, characteristic, complemented
11C41×#1651C211yesmaximal, characteristic, complemented
12C41×#1631C211yesmaximal, characteristic, complemented
13C41×#1622C211yesmaximal, characteristic, complemented
14C41×#1591C211yesmaximal, characteristic, complemented
15C41×#1589C211yesmaximal, characteristic, complemented
16C2×#137×C41—21no—
17C41×#556C2211yescharacteristic
18C41×#554C2211yescharacteristic
19C41×#550C2211yescharacteristic
20D4×Q8×C41C2211yescharacteristic
21C41×#501—21no—
22C41×#498C2211yescharacteristic
23C41×#498C2211yescharacteristic
24C41×#498C2211yescharacteristic
25C41×#496—21no—
26C41×#492C2211yescharacteristic
27C41×#492C2211yescharacteristic
28C41×#492C2211yescharacteristic
29C41×#485—21no—
30C41×#483—21no—
31C41×#478—21no—
32C41×#477C2211yescharacteristic
33C41×#476—21no—
34C41×#476C2211yescharacteristic
35C41×#475C2211yescharacteristic
36C41×#474C2211yescharacteristic
37C41×#470—21no—
38C41×#468—21no—
39C41×#463—21no—
40C41×#462C2211yescharacteristic
41C41×#461C2211yescharacteristic
42C41×#460—21no—
43C41×#460C2211yescharacteristic
44C41×#459C2211yescharacteristic
45C41×#452—21no—
46C41×#448—21no—
47C41×#446C2211yescharacteristic
48C41×#446C2211yescharacteristic
49C41×#442—21no—
50C41×#440—21no—
51C4×Q16×C41C2211yescharacteristic
52C4×D8×C41C2211yescharacteristic
53C41×#436C2211yescharacteristic
54C41×#436C2211yescharacteristic
55C41×#428—21no—
56C41×#335C2211yescharacteristic
57C41×#335C2211yescharacteristic
58C41×#333C2211yescharacteristic
59C41×#332C2211yescharacteristic
60C41×#332C2211yescharacteristic
61C41×#331C2211yescharacteristic
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×C41D411yescharacteristic
72C2×SD16×C41—21no—
73C2×SD16×C41—21no—
74C2×SD16×C41—21no—
75C2×SD16×C41—21no—
76C2×SD16×C41—21no—
77C2×SD16×C41—21no—
78C2×SD16×C41—41no—
79C2×D8×C41—21no—
80C2×D8×C41D411yescharacteristic
81C2×M16×C41—21no—
82C2×M16×C41—21no—
83C4⋊Q8×C41—21no—
84C4⋊Q8×C41C2311yescharacteristic
85C4⋊Q8×C41C2311yescharacteristic
86C4⋊Q8×C41C2311yescharacteristic
87#127×C41—21no—
88#127×C41C2311yescharacteristic
89#126×C41—41no—
90#125×C41—21no—
91#124×C41—21no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—41no—
96C22⋊Q8×C41—41no—
97#121×C41—21no—
98#121×C41—41no—
99C4×Q8×C41—21no—
100C4×Q8×C41C2311yescharacteristic
101C4×Q8×C41C2311yescharacteristic
102C4×D4×C41—21no—
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41C2311yescharacteristic
106C4×D4×C41C2311yescharacteristic
107#117×C41—21no—
108C2×C4⋊C4×C41—21no—
109#107×C41—21no—
110#107×C41—21no—
111#107×C41D411yescharacteristic
112#107×C41D411yescharacteristic
113#106×C41—21no—
114#106×C41—21no—
115#106×C41—21no—
116#106×C41—21no—
117#106×C41—21no—
118#106×C41—21no—
119#106×C41—41no—
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×C41D411yescharacteristic
131#103×C41D411yescharacteristic
132#102×C41—21no—
133#102×C41—21no—
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—41no—
151C2×Q8×C41—42no—
152C2×Q8×C41—81no—
153C2×Q8×C41C2×D411yescharacteristic
154C2×Q8×C41C2×D411yescharacteristic
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—41no—
159C2×D4×C41—41no—
160C2×D4×C41C2×D411yescharacteristic
161C2×D4×C41C2×D411yescharacteristic
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—41no—
165C22×C4×C41—41no—
166C22×C4×C41—41no—
167Q16×C41—22no—
168Q16×C41—42no—
169SD16×C41—42no—
170SD16×C41—42no—
171SD16×C41—42no—
172SD16×C41—81no—
173SD16×C41—81no—
174SD16×C41—82no—
175SD16×C41—81no—
176D8×C41—22no—
177D8×C41—81no—
178M16×C41—42no—
179M16×C41—42no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—21no—
184C2×C8×C41—21no—
185C2×C8×C41C2×D411yescharacteristic
186C2×C8×C41C2×D411yescharacteristic
187C2×C8×C41C2×D411yescharacteristic
188C2×C8×C41C2×D411yescharacteristic
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—41no—
198C4⋊C4×C41—41no—
199C4⋊C4×C41—41no—
200C4⋊C4×C41—41no—
201C4⋊C4×C41C2×D411yescharacteristic
202C4⋊C4×C41C2×D411yescharacteristic
203C4⋊C4×C41C2×D411yescharacteristic
204C4⋊C4×C41C2×D411yescharacteristic
205C22⋊C4×C41—21no—
206C22⋊C4×C41—21no—
207C22⋊C4×C41—41no—
208C22⋊C4×C41—41no—
209C22⋊C4×C41—41no—
210C22⋊C4×C41—41no—
211C22⋊C4×C41—41no—
212C42×C41—21no—
213C42×C41—21no—
214C42×C41—41no—
215C42×C41C2411yescharacteristic
216C23×C41—21no—
217C23×C41—21no—
218C23×C41—41no—
219Q8×C41—21no—
220Q8×C41—21no—
221Q8×C41—21no—
222Q8×C41—21no—
223Q8×C41—41no—
224Q8×C41—41no—
225Q8×C41—41no—
226Q8×C41—41no—
227Q8×C41—81no—
228Q8×C41—82no—
229D4×C41—21no—
230D4×C41—21no—
231D4×C41—21no—
232D4×C41—21no—
233D4×C41—41no—
234D4×C41—41no—
235D4×C41—41no—
236D4×C41—41no—
237D4×C41—81no—
238D4×C41—82no—
239D4×C41—161no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—21no—
244C2×C4×C41—21no—
245C2×C4×C41—21no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—82no—
254C2×C4×C41—82no—
255C2×C4×C41—161no—
256C2×C4×C41C22×D411yescharacteristic
257C2×C4×C41C22×D411yescharacteristic
258C2×C4×C41H(5,𝔽2)11yescharacteristic
259C8×C41—22no—
260C8×C41—21no—
261C8×C41—21no—
262C8×C41—41no—
263C8×C41—41no—
264C8×C41—41no—
265C8×C41—41no—
266C8×C41AGL(1,ℤ/8)12yes—
267C8×C41#13712yescomplemented
268#20317C4111yesmaximal, characteristic, direct product factor, Sylow
269C22×C41—41no—
270C22×C41—41no—
271C22×C41—41no—
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—81no—
276C22×C41—81no—
277C22×C41—81no—
278C22×C41D4211yescharacteristic
279C4×C41—21no—
280C4×C41—41no—
281C4×C41—41no—
282C4×C41—41no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—81no—
287C4×C41—81no—
288C4×C41—81no—
289C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C41C2×#13711yescharacteristic
291C4×C41#57711yescharacteristic
292C4×C41#57711yescharacteristic
293#3397C2×C4111yescharacteristic
294#3384C2×C4111yescharacteristic, complemented
295#3356C2×C4111yescharacteristic, complemented
296#3278C2×C4111yescharacteristic, complemented
297#1705C2×C4111yescharacteristic, complemented
298#1692C2×C4111yescharacteristic, complemented
299#1691C2×C4111yescharacteristic, complemented
300#1686C2×C4111yescharacteristic, complemented
301#1685C2×C4111yescharacteristic, complemented
302#1652C2×C4111yescharacteristic, complemented
303#1651C2×C4111yescharacteristic, complemented
304#1631C2×C4111yescharacteristic, complemented
305#1622C2×C4111yescharacteristic, complemented
306#1591C2×C4111yescharacteristic, complemented
307#1589C2×C4111yescharacteristic, complemented
308C2×C41—81no—
309C2×C41—81no—
310C2×C41—161no—
311C2×C41#327211yescharacteristic
312C2×C41#327811yescharacteristic
313C2×C41#329111yescharacteristic
314C2×#137—21no—
315#556C22×C4111yescharacteristic
316#554C22×C4111yescharacteristic
317#550C22×C4111yescharacteristic
318D4×Q8C22×C4111yescharacteristic
319#501—21no—
320#498C22×C4111yescharacteristic
321#498C22×C4111yescharacteristic
322#498C22×C4111yescharacteristic
323#496—21no—
324#492C22×C4111yescharacteristic
325#492C22×C4111yescharacteristic
326#492C22×C4111yescharacteristic
327#485—21no—
328#483—21no—
329#478—21no—
330#477C22×C4111yescharacteristic
331#476—21no—
332#476C22×C4111yescharacteristic
333#475C22×C4111yescharacteristic
334#474C22×C4111yescharacteristic
335#470—21no—
336#468—21no—
337#463—21no—
338#462C22×C4111yescharacteristic
339#461C22×C4111yescharacteristic
340#460—21no—
341#460C22×C4111yescharacteristic
342#459C22×C4111yescharacteristic
343#452—21no—
344#448—21no—
345#446C22×C4111yescharacteristic
346#446C22×C4111yescharacteristic
347#442—21no—
348#440—21no—
349C4×Q16C22×C4111yescharacteristic
350C4×D8C22×C4111yescharacteristic
351#436C22×C4111yescharacteristic
352#436C22×C4111yescharacteristic
353#428—21no—
354#335C22×C4111yescharacteristic
355#335C22×C4111yescharacteristic
356#333C22×C4111yescharacteristic
357#332C22×C4111yescharacteristic
358#332C22×C4111yescharacteristic
359#331C22×C4111yescharacteristic
360Q8⋊C8C22×C4111yescharacteristic
361Q8⋊C8C22×C4111yescharacteristic
362D4⋊C8C22×C4111yescharacteristic
363D4⋊C8C22×C4111yescharacteristic
364C82C22×C4111yescharacteristic
365C41#2031711yescharacteristic, direct product factor, Sylow
366C2×#41—21no—
367C22×Q8—21no—
368#137—44no—
369C2×Q16—21no—
370C2×Q16D4×C4111yescharacteristic
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—41no—
378C2×D8—21no—
379C2×D8D4×C4111yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C4⋊Q8—21no—
383C4⋊Q8C23×C4111yescharacteristic
384C4⋊Q8C23×C4111yescharacteristic
385C4⋊Q8C23×C4111yescharacteristic
386#127—21no—
387#127C23×C4111yescharacteristic
388#126—41no—
389#125—21no—
390#124—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395C22⋊Q8—41no—
396#121—21no—
397#121—41no—
398C4×Q8—21no—
399C4×Q8C23×C4111yescharacteristic
400C4×Q8C23×C4111yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4C23×C4111yescharacteristic
405C4×D4C23×C4111yescharacteristic
406#117—21no—
407C2×C4⋊C4—21no—
408#107—21no—
409#107—21no—
410#107D4×C4111yescharacteristic
411#107D4×C4111yescharacteristic
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—41no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8C23×C4111yescharacteristic
422C4⋊C8C23×C4111yescharacteristic
423C4⋊C8C23×C4111yescharacteristic
424C4⋊C8C23×C4111yescharacteristic
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103D4×C4111yescharacteristic
430#103D4×C4111yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102D4×C4111yescharacteristic
436#102D4×C4111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440#97—21no—
441C4×C8C23×C4111yescharacteristic
442C4×C8C23×C4111yescharacteristic
443C4×C8C23×C4111yescharacteristic
444#41—42no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—41no—
450C2×Q8—42no—
451C2×Q8—81no—
452C2×Q8C2×D4×C4111yescharacteristic
453C2×Q8C2×D4×C4111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4C2×D4×C4111yescharacteristic
460C2×D4C2×D4×C4111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466Q16—22no—
467Q16—42no—
468SD16—42no—
469SD16—42no—
470SD16—42no—
471SD16—81no—
472SD16—81no—
473SD16—82no—
474SD16—81no—
475D8—22no—
476D8—81no—
477M16—42no—
478M16—42no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×D4×C4111yescharacteristic
485C2×C8C2×D4×C4111yescharacteristic
486C2×C8C2×D4×C4111yescharacteristic
487C2×C8C2×D4×C4111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C4111yescharacteristic
501C4⋊C4C2×D4×C4111yescharacteristic
502C4⋊C4C2×D4×C4111yescharacteristic
503C4⋊C4C2×D4×C4111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42C24×C4111yescharacteristic
515C23—21no—
516C23—21no—
517C23—41no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—82no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—82no—
538D4—161no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—161no—
555C2×C4C22×D4×C4111yescharacteristic
556C2×C4C22×D4×C4111yescharacteristic
557C2×C4H(5,𝔽2)×C4111yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8AGL(1,ℤ/8)×C4112yes—
566C8#137×C4112yescomplemented
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C4111yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
588C4C2×#137×C4111yescharacteristic
589C4C41×#57711yescharacteristic
590C4C41×#57711yescharacteristic
591C2—81no—
592C2—81no—
593C2—161no—
594C2C41×#327211yescharacteristic
595C2C41×#327811yescharacteristic
596C2C41×#329111yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3397C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C41×#3384C2semidirect
3. C41×#3356C2semidirect
4. C41×#3278C2semidirect
5. C41×#1705C2semidirect
6. C41×#1692C2semidirect
7. C41×#1691C2semidirect
8. C41×#1686C2semidirect
9. C41×#1685C2semidirect
10. C41×#1652C2semidirect
11. C41×#1651C2semidirect
12. C41×#1631C2semidirect
13. C41×#1622C2semidirect
14. C41×#1591C2semidirect
15. C41×#1589C2semidirect
267. C8×C41#137semidirect
268. #20317C41direct (N × H)
294. #3384C2×C41semidirect
295. #3356C2×C41semidirect
296. #3278C2×C41semidirect
297. #1705C2×C41semidirect
298. #1692C2×C41semidirect
299. #1691C2×C41semidirect
300. #1686C2×C41semidirect
301. #1685C2×C41semidirect
302. #1652C2×C41semidirect
303. #1651C2×C41semidirect
304. #1631C2×C41semidirect
305. #1622C2×C41semidirect
306. #1591C2×C41semidirect
307. #1589C2×C41semidirect
365. C41#20317direct (N × H)
566. C8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#33972
C41×#33842
C41×#33562
C41×#32782
C41×#17052
C41×#16922
C41×#16912
C41×#16862
C41×#16852
C41×#16522
C41×#16512
C41×#16312
C41×#16222
C41×#15912
C41×#15892
#2031741