Finite Group Databasebeta

← C41×#26084 #23802285

Subgroups — C41×#26084 #23802285

Order 10496.

678 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3164C211yesmaximal, characteristic, complemented
2C41×#3084C211yesmaximal, characteristic
3C41×#3083C211yesmaximal, characteristic
4C41×#2912C211yesmaximal, characteristic
5C41×#2090C211yesmaximal, characteristic, complemented
6C41×#2089C211yesmaximal, characteristic, complemented
7C41×#2061C211yesmaximal, characteristic, complemented
8C41×#2060C211yesmaximal, characteristic, complemented
9C41×#1951C211yesmaximal, characteristic, complemented
10C41×#1946C211yesmaximal, characteristic, complemented
11C41×#1860C211yesmaximal, characteristic
12C41×#1859C211yesmaximal, characteristic
13C41×#1847C211yesmaximal, characteristic, complemented
14C41×#1816C211yesmaximal, characteristic
15C41×#1765C211yesmaximal, characteristic
16C2×#131×C41C2211yescharacteristic
17C41×#544C2211yescharacteristic
18C41×#544C2211yescharacteristic
19C41×#520C2211yescharacteristic
20C41×#520C2211yescharacteristic
21C41×#501—21no—
22C41×#501—21no—
23C41×#500—21no—
24C41×#499—21no—
25C41×#479—21no—
26C41×#479—21no—
27C41×#478—21no—
28C41×#478—21no—
29C41×#477—21no—
30C41×#476—21no—
31C41×#475—21no—
32C41×#474—21no—
33C2×#108×C41C2211yescharacteristic
34C41×#428—21no—
35C41×#428—21no—
36C41×#428C2211yescharacteristic
37C41×#428C2211yescharacteristic
38C41×#428C2211yescharacteristic
39C41×#428C2211yescharacteristic
40C41×#428C2211yescharacteristic
41C41×#428C2211yescharacteristic
42C41×#427—21no—
43C41×#427C2211yescharacteristic
44C2×#107×C41C2211yescharacteristic
45C2×#107×C41C2211yescharacteristic
46C2×#106×C41—21no—
47C2×#106×C41C2211yescharacteristic
48C2×#106×C41C2211yescharacteristic
49C41×#424C2211yescharacteristic
50C41×#424C2211yescharacteristic
51C2×#104×C41C2211yescharacteristic
52C41×#417C2211yescharacteristic
53C41×#417C2211yescharacteristic
54C41×#416C2211yescharacteristic
55C41×#405C2211yescharacteristic
56C2×#97×C41C2211yescharacteristic
57C41×#384C2211yescharacteristic
58C41×#382C2211yescharacteristic
59C41×#343C2211yescharacteristic
60C41×#343C2211yescharacteristic
61C41×#343C2211yescharacteristic
62C41×#343C2211yescharacteristic
63C41×#341C2211yescharacteristic
64C41×#339C2211yescharacteristic
65C41×#339C2211yescharacteristic
66C41×#339C2211yescharacteristic
67C2×#41×C41C2311yescharacteristic
68#131×C41—22no—
69#131×C41Q814yescomplemented
70C2×M16×C41—21no—
71C2×M16×C41C2311yescharacteristic
72C2×M16×C41C2311yescharacteristic
73C2×M16×C41C2311yescharacteristic
74C2×M16×C41C2311yescharacteristic
75C22×C8×C41—21no—
76C22×C8×C41C2311yescharacteristic
77C22×C8×C41C2311yescharacteristic
78C4⋊Q8×C41—21no—
79C4⋊Q8×C41—21no—
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41—21no—
82#125×C41—21no—
83#125×C41—21no—
84#125×C41—21no—
85#125×C41—21no—
86C22⋊Q8×C41—41no—
87C22⋊Q8×C41—41no—
88C4×Q8×C41—21no—
89C4×Q8×C41—21no—
90C4×D4×C41—21no—
91C4×D4×C41—21no—
92C4×D4×C41—41no—
93C4×D4×C41—41no—
94#117×C41—21no—
95#117×C41—21no—
96#117×C41C2311yescharacteristic
97#117×C41C2311yescharacteristic
98#117×C41C2311yescharacteristic
99C2×C4⋊C4×C41—21no—
100C2×C4⋊C4×C41—21no—
101C2×C4⋊C4×C41—41no—
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C4⋊C4×C41C2311yescharacteristic
104C2×C4⋊C4×C41C2311yescharacteristic
105C2×C4⋊C4×C41C2311yescharacteristic
106C2×C42×C41C2311yescharacteristic
107#108×C41—22no—
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—21no—
115#107×C41—21no—
116#107×C41—21no—
117#107×C41—21no—
118#107×C41D411yescharacteristic
119#107×C41D411yescharacteristic
120#106×C41—21no—
121#106×C41—21no—
122#106×C41—21no—
123#106×C41—21no—
124#106×C41—21no—
125#106×C41—21no—
126#106×C41—21no—
127#106×C41—21no—
128#106×C41—21no—
129#106×C41—21no—
130#106×C41D411yescharacteristic
131#106×C41D411yescharacteristic
132C4⋊C8×C41—21no—
133C4⋊C8×C41—21no—
134C4⋊C8×C41—21no—
135C4⋊C8×C41—21no—
136#104×C41Q814yescomplemented
137#103×C41—21no—
138#103×C41—21no—
139#103×C41D411yescharacteristic
140#103×C41D411yescharacteristic
141#102×C41—21no—
142#102×C41—21no—
143#102×C41D411yescharacteristic
144#102×C41D411yescharacteristic
145#97×C41—21no—
146#97×C41—22no—
147C4×C8×C41—21no—
148#95×C41—41no—
149#41×C41—21no—
150#41×C41—21no—
151#41×C41C2×Q812yes—
152#41×C41C2×Q812yes—
153C2×Q8×C41—41no—
154C2×Q8×C41—41no—
155C2×Q8×C41C2×D411yescharacteristic
156C2×D4×C41—21no—
157C2×D4×C41C2×D411yescharacteristic
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—41no—
165C22×C4×C41—41no—
166C22×C4×C41C2411yescharacteristic
167M16×C41—21no—
168M16×C41—21no—
169M16×C41—24no—
170M16×C41—21no—
171M16×C41—21no—
172M16×C41—21no—
173M16×C41—21no—
174M16×C41C2×Q812yes—
175M16×C41C2×Q812yes—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—24no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41C2×D411yescharacteristic
184C2×C8×C41C2×D411yescharacteristic
185C2×C8×C41C2×D411yescharacteristic
186C2×C8×C41C2×D411yescharacteristic
187C2×C8×C41C2×Q812yes—
188C2×C8×C41#4112yes—
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×C41—41no—
202C4⋊C4×C41—41no—
203C4⋊C4×C41—41no—
204C4⋊C4×C41—41no—
205C4⋊C4×C41—82no—
206C4⋊C4×C41C2×D411yescharacteristic
207C4⋊C4×C41C2×D411yescharacteristic
208C4⋊C4×C41C2×D411yescharacteristic
209C4⋊C4×C41C2×D411yescharacteristic
210C4⋊C4×C41C2×D411yescharacteristic
211C4⋊C4×C41C2×D411yescharacteristic
212C22⋊C4×C41—21no—
213C22⋊C4×C41—21no—
214C22⋊C4×C41—21no—
215C22⋊C4×C41—41no—
216C22⋊C4×C41—41no—
217C42×C41—21no—
218C42×C41—21no—
219C42×C41—21no—
220C42×C41—21no—
221C42×C41—41no—
222C42×C41—41no—
223C42×C41C2×Q812yes—
224C23×C41—21no—
225C23×C41H(5,𝔽2)11yescharacteristic
226Q8×C41—21no—
227Q8×C41—161no—
228Q8×C41—161no—
229Q8×C41C4⋊Q812yes—
230D4×C41—22no—
231D4×C41—22no—
232D4×C41—21no—
233D4×C41C4⋊Q812yes—
234C2×C4×C41—21no—
235C2×C4×C41—22no—
236C2×C4×C41—22no—
237C2×C4×C41—21no—
238C2×C4×C41—21no—
239C2×C4×C41—21no—
240C2×C4×C41—21no—
241C2×C4×C41—21no—
242C2×C4×C41—21no—
243C2×C4×C41—22no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—81no—
251C2×C4×C41—81no—
252C2×C4×C41—81no—
253C2×C4×C41—81no—
254C2×C4×C41—161no—
255C2×C4×C41—161no—
256C2×C4×C41C22×D411yescharacteristic
257C2×C4×C41C22×D411yescharacteristic
258C2×C4×C41C22×Q811yescharacteristic
259C2×C4×C41C22×Q811yescharacteristic
260C2×C4×C41C2×#4111yescharacteristic
261C2×C4×C412−1+411yescharacteristic
262C8×C41—22no—
263C8×C41—21no—
264C8×C41—21no—
265C8×C41—22no—
266C8×C41—41no—
267C8×C41—41no—
268C8×C41C22⋊Q812yes—
269C8×C41C22⋊Q812yes—
270#26084C4111yesmaximal, characteristic, direct product factor, Sylow
271C22×C41—21no—
272C22×C41—21no—
273C22×C41—22no—
274C22×C41—41no—
275C22×C41—41no—
276C22×C41#54411yescharacteristic
277C22×C41D4211yescharacteristic
278C22×C41#55411yescharacteristic
279C4×C41—22no—
280C4×C41—42no—
281C4×C41—41no—
282C4×C41—41no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—41no—
287C4×C41—81no—
288C4×C41—81no—
289C4×C41—81no—
290C4×C41—81no—
291C4×C41C2×C22⋊Q811yescharacteristic
292C4×C41C2×C4⋊Q811yescharacteristic
293C4×C41#54711yescharacteristic
294C4×C41D4×Q811yescharacteristic
295#3164C2×C4111yescharacteristic, complemented
296#3084C2×C4111yescharacteristic
297#3083C2×C4111yescharacteristic
298#2912C2×C4111yescharacteristic
299#2090C2×C4111yescharacteristic, complemented
300#2089C2×C4111yescharacteristic, complemented
301#2061C2×C4111yescharacteristic, complemented
302#2060C2×C4111yescharacteristic, complemented
303#1951C2×C4111yescharacteristic, complemented
304#1946C2×C4111yescharacteristic, complemented
305#1860C2×C4111yescharacteristic
306#1859C2×C4111yescharacteristic
307#1847C2×C4111yescharacteristic, complemented
308#1816C2×C4111yescharacteristic
309#1765C2×C4111yescharacteristic
310C2×C41—21no—
311C2×C41—21no—
312C2×C41—42no—
313C2×C41#244011yescharacteristic
314C2×C41#328811yescharacteristic
315C2×C41#328911yescharacteristic
316C2×#131C22×C4111yescharacteristic
317#544C22×C4111yescharacteristic
318#544C22×C4111yescharacteristic
319#520C22×C4111yescharacteristic
320#520C22×C4111yescharacteristic
321#501—21no—
322#501—21no—
323#500—21no—
324#499—21no—
325#479—21no—
326#479—21no—
327#478—21no—
328#478—21no—
329#477—21no—
330#476—21no—
331#475—21no—
332#474—21no—
333C2×#108C22×C4111yescharacteristic
334#428—21no—
335#428—21no—
336#428C22×C4111yescharacteristic
337#428C22×C4111yescharacteristic
338#428C22×C4111yescharacteristic
339#428C22×C4111yescharacteristic
340#428C22×C4111yescharacteristic
341#428C22×C4111yescharacteristic
342#427—21no—
343#427C22×C4111yescharacteristic
344C2×#107C22×C4111yescharacteristic
345C2×#107C22×C4111yescharacteristic
346C2×#106—21no—
347C2×#106C22×C4111yescharacteristic
348C2×#106C22×C4111yescharacteristic
349#424C22×C4111yescharacteristic
350#424C22×C4111yescharacteristic
351C2×#104C22×C4111yescharacteristic
352#417C22×C4111yescharacteristic
353#417C22×C4111yescharacteristic
354#416C22×C4111yescharacteristic
355#405C22×C4111yescharacteristic
356C2×#97C22×C4111yescharacteristic
357#384C22×C4111yescharacteristic
358#382C22×C4111yescharacteristic
359#343C22×C4111yescharacteristic
360#343C22×C4111yescharacteristic
361#343C22×C4111yescharacteristic
362#343C22×C4111yescharacteristic
363#341C22×C4111yescharacteristic
364#339C22×C4111yescharacteristic
365#339C22×C4111yescharacteristic
366#339C22×C4111yescharacteristic
367C41#2608411yescharacteristic, direct product factor, Sylow
368C2×#41C23×C4111yescharacteristic
369#131—22no—
370#131Q8×C4114yescomplemented
371C2×M16—21no—
372C2×M16C23×C4111yescharacteristic
373C2×M16C23×C4111yescharacteristic
374C2×M16C23×C4111yescharacteristic
375C2×M16C23×C4111yescharacteristic
376C22×C8—21no—
377C22×C8C23×C4111yescharacteristic
378C22×C8C23×C4111yescharacteristic
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—41no—
394C4×D4—41no—
395#117—21no—
396#117—21no—
397#117C23×C4111yescharacteristic
398#117C23×C4111yescharacteristic
399#117C23×C4111yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4C23×C4111yescharacteristic
404C2×C4⋊C4C23×C4111yescharacteristic
405C2×C4⋊C4C23×C4111yescharacteristic
406C2×C4⋊C4C23×C4111yescharacteristic
407C2×C42C23×C4111yescharacteristic
408#108—22no—
409#107—21no—
410#107—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107—21no—
417#107—21no—
418#107—21no—
419#107D4×C4111yescharacteristic
420#107D4×C4111yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431#106D4×C4111yescharacteristic
432#106D4×C4111yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437#104Q8×C4114yescomplemented
438#103—21no—
439#103—21no—
440#103D4×C4111yescharacteristic
441#103D4×C4111yescharacteristic
442#102—21no—
443#102—21no—
444#102D4×C4111yescharacteristic
445#102D4×C4111yescharacteristic
446#97—21no—
447#97—22no—
448C4×C8—21no—
449#95—41no—
450#41—21no—
451#41—21no—
452#41C2×Q8×C4112yes—
453#41C2×Q8×C4112yes—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8C2×D4×C4111yescharacteristic
457C2×D4—21no—
458C2×D4C2×D4×C4111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4C24×C4111yescharacteristic
468M16—21no—
469M16—21no—
470M16—24no—
471M16—21no—
472M16—21no—
473M16—21no—
474M16—21no—
475M16C2×Q8×C4112yes—
476M16C2×Q8×C4112yes—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—24no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×D4×C4111yescharacteristic
485C2×C8C2×D4×C4111yescharacteristic
486C2×C8C2×D4×C4111yescharacteristic
487C2×C8C2×D4×C4111yescharacteristic
488C2×C8C2×Q8×C4112yes—
489C2×C8#41×C4112yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—82no—
507C4⋊C4C2×D4×C4111yescharacteristic
508C4⋊C4C2×D4×C4111yescharacteristic
509C4⋊C4C2×D4×C4111yescharacteristic
510C4⋊C4C2×D4×C4111yescharacteristic
511C4⋊C4C2×D4×C4111yescharacteristic
512C4⋊C4C2×D4×C4111yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42—41no—
524C42C2×Q8×C4112yes—
525C23—21no—
526C23H(5,𝔽2)×C4111yescharacteristic
527Q8—21no—
528Q8—161no—
529Q8—161no—
530Q8C4⋊Q8×C4112yes—
531D4—22no—
532D4—22no—
533D4—21no—
534D4C4⋊Q8×C4112yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—161no—
556C2×C4—161no—
557C2×C4C22×D4×C4111yescharacteristic
558C2×C4C22×D4×C4111yescharacteristic
559C2×C4C22×Q8×C4111yescharacteristic
560C2×C4C22×Q8×C4111yescharacteristic
561C2×C4C2×#41×C4111yescharacteristic
562C2×C42−1+4×C4111yescharacteristic
563C8—22no—
564C8—21no—
565C8—21no—
566C8—22no—
567C8—41no—
568C8—41no—
569C8C22⋊Q8×C4112yes—
570C8C22⋊Q8×C4112yes—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22C41×#54411yescharacteristic
577C22D42×C4111yescharacteristic
578C22C41×#55411yescharacteristic
579C4—22no—
580C4—42no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×C22⋊Q8×C4111yescharacteristic
592C4C2×C4⋊Q8×C4111yescharacteristic
593C4C41×#54711yescharacteristic
594C4D4×Q8×C4111yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2C41×#244011yescharacteristic
599C2C41×#328811yescharacteristic
600C2C41×#328911yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#41×C41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3164C2semidirect
5. C41×#2090C2semidirect
6. C41×#2089C2semidirect
7. C41×#2061C2semidirect
8. C41×#2060C2semidirect
9. C41×#1951C2semidirect
10. C41×#1946C2semidirect
13. C41×#1847C2semidirect
69. #131×C41Q8semidirect
136. #104×C41Q8semidirect
270. #26084C41direct (N × H)
295. #3164C2×C41semidirect
299. #2090C2×C41semidirect
300. #2089C2×C41semidirect
301. #2061C2×C41semidirect
302. #2060C2×C41semidirect
303. #1951C2×C41semidirect
304. #1946C2×C41semidirect
307. #1847C2×C41semidirect
367. C41#26084direct (N × H)
370. #131Q8×C41semidirect
437. #104Q8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31642
C41×#30842
C41×#30832
C41×#29122
C41×#20902
C41×#20892
C41×#20612
C41×#20602
C41×#19512
C41×#19462
C41×#18602
C41×#18592
C41×#18472
C41×#18162
C41×#17652
#2608441