Finite Group Databasebeta

← C41×#26848 #23803049

Subgroups — C41×#26848 #23803049

Order 10496.

718 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3136C211yesmaximal, characteristic
2C41×#3096C211yesmaximal, characteristic
3C41×#3082C211yesmaximal, characteristic, complemented
4C41×#2947C211yesmaximal, characteristic, complemented
5C41×#2063C211yesmaximal, characteristic, complemented
6C41×#2061C211yesmaximal, characteristic, complemented
7C41×#2052C211yesmaximal, characteristic, complemented
8C41×#2004C211yesmaximal, characteristic
9C41×#1958C211yesmaximal, characteristic, complemented
10C41×#1937C211yesmaximal, characteristic, complemented
11C41×#1931C211yesmaximal, characteristic, complemented
12C41×#1930C211yesmaximal, characteristic, complemented
13C41×#1888C211yesmaximal, characteristic, complemented
14C41×#1860C211yesmaximal, characteristic, complemented
15C41×#1772C211yesmaximal, characteristic, complemented
16C2×#137×C41C2211yescharacteristic
17C41×#544C2211yescharacteristic
18C41×#535C2211yescharacteristic
19C2×#124×C41C2211yescharacteristic
20C41×#520C2211yescharacteristic
21C41×#519C2211yescharacteristic
22C41×#490—21no—
23C41×#489—21no—
24C41×#488—21no—
25C41×#486—21no—
26C41×#482—21no—
27C41×#482—21no—
28C41×#481—21no—
29C41×#480—21no—
30C41×#479—21no—
31C41×#479—21no—
32C41×#477—21no—
33C41×#475—21no—
34C41×#441—21no—
35C41×#440—21no—
36C4×Q16×C41—21no—
37C4×SD16×C41—21no—
38C2×#108×C41C2211yescharacteristic
39C41×#428C2211yescharacteristic
40C41×#428C2211yescharacteristic
41C41×#428C2211yescharacteristic
42C41×#427C2211yescharacteristic
43C41×#424C2211yescharacteristic
44C2×#104×C41C2211yescharacteristic
45C41×#419C2211yescharacteristic
46C41×#418C2211yescharacteristic
47C41×#418C2211yescharacteristic
48C41×#417C2211yescharacteristic
49C41×#416C2211yescharacteristic
50C2×#103×C41C2211yescharacteristic
51C2×#103×C41C2211yescharacteristic
52C2×#102×C41C2211yescharacteristic
53C2×#102×C41C2211yescharacteristic
54C2×#101×C41C2211yescharacteristic
55C2×#100×C41C2211yescharacteristic
56C41×#408C2211yescharacteristic
57C41×#405C2211yescharacteristic
58C41×#405C2211yescharacteristic
59C2×C4×C8×C41C2211yescharacteristic
60C41×#382C2211yescharacteristic
61C41×#343C2211yescharacteristic
62C41×#343C2211yescharacteristic
63C41×#341C2211yescharacteristic
64C41×#339C2211yescharacteristic
65C41×#339C2211yescharacteristic
66C41×#339C2211yescharacteristic
67C2×#41×C41C2311yescharacteristic
68C22×Q8×C41C2311yescharacteristic
69C22×D4×C41C2311yescharacteristic
70#137×C41—22no—
71#137×C41—22no—
72C2×Q16×C41—21no—
73C2×SD16×C41—21no—
74C2×M16×C41C2311yescharacteristic
75C2×M16×C41C2311yescharacteristic
76C2×M16×C41C2311yescharacteristic
77C2×M16×C41C2311yescharacteristic
78C22×C8×C41C2311yescharacteristic
79C22×C8×C41C2311yescharacteristic
80C4⋊Q8×C41—21no—
81C4⋊Q8×C41—21no—
82#127×C41—21no—
83#125×C41—21no—
84#125×C41—21no—
85#124×C41—21no—
86#124×C41—22no—
87#124×C41—22no—
88C22⋊Q8×C41—41no—
89#121×C41—21no—
90#121×C41—21no—
91#120×C41—41no—
92C4×Q8×C41—21no—
93C4×Q8×C41—21no—
94C4×Q8×C41—21no—
95C4×Q8×C41—21no—
96C4×Q8×C41—21no—
97C4×D4×C41—21no—
98C4×D4×C41—41no—
99#117×C41—21no—
100#117×C41—41no—
101#117×C41C2311yescharacteristic
102#117×C41C2311yescharacteristic
103#117×C41C2311yescharacteristic
104C2×C4⋊C4×C41—21no—
105C2×C4⋊C4×C41C2311yescharacteristic
106C2×C4⋊C4×C41C2311yescharacteristic
107C2×C22⋊C4×C41—41no—
108C2×C42×C41C2311yescharacteristic
109#108×C41—22no—
110#107×C41—21no—
111#107×C41—21no—
112#107×C41—21no—
113#107×C41D411yescharacteristic
114#107×C41D411yescharacteristic
115#106×C41—21no—
116#106×C41—21no—
117#106×C41—21no—
118#106×C41D411yescharacteristic
119#106×C41D411yescharacteristic
120C4⋊C8×C41—21no—
121C4⋊C8×C41—21no—
122#104×C41—22no—
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×C41—21no—
136#102×C41—21no—
137#102×C41—21no—
138#102×C41—21no—
139#102×C41—21no—
140#102×C41—21no—
141#102×C41D411yescharacteristic
142#102×C41D411yescharacteristic
143#101×C41—22no—
144#100×C41—22no—
145C22⋊C8×C41—21no—
146C22⋊C8×C41—21no—
147#97×C41—21no—
148#97×C41—21no—
149C4×C8×C41—21no—
150C4×C8×C41—21no—
151C4×C8×C41—22no—
152#95×C41—41no—
153C24×C41—21no—
154#41×C41—21no—
155#41×C41—21no—
156#41×C41—21no—
157#41×C41—21no—
158C2×Q8×C41—21no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—21no—
162C2×Q8×C41—21no—
163C2×Q8×C41—41no—
164C2×Q8×C41C2×D411yescharacteristic
165C2×Q8×C41#4112yes—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—41no—
174C2×D4×C41—41no—
175C2×D4×C41C2×D411yescharacteristic
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—41no—
182C22×C4×C41C2411yescharacteristic
183Q16×C41—24no—
184SD16×C41—24no—
185M16×C41—21no—
186M16×C41—21no—
187M16×C41—21no—
188M16×C41—21no—
189M16×C41—21no—
190M16×C41—21no—
191M16×C41—21no—
192M16×C41#4112yes—
193C2×C8×C41—21no—
194C2×C8×C41—21no—
195C2×C8×C41—21no—
196C2×C8×C41—21no—
197C2×C8×C41—21no—
198C2×C8×C41—21no—
199C2×C8×C41—21no—
200C2×C8×C41—21no—
201C2×C8×C41C2×D411yescharacteristic
202C2×C8×C41C2×D411yescharacteristic
203C2×C8×C41C2×D411yescharacteristic
204C2×C8×C41C2×D411yescharacteristic
205C4⋊C4×C41—21no—
206C4⋊C4×C41—21no—
207C4⋊C4×C41—21no—
208C4⋊C4×C41—21no—
209C4⋊C4×C41—41no—
210C4⋊C4×C41—41no—
211C4⋊C4×C41—41no—
212C4⋊C4×C41—41no—
213C4⋊C4×C41—41no—
214C4⋊C4×C41—41no—
215C4⋊C4×C41C2×D411yescharacteristic
216C4⋊C4×C41C2×D411yescharacteristic
217C4⋊C4×C41C2×D411yescharacteristic
218C4⋊C4×C41C2×D411yescharacteristic
219C4⋊C4×C41C2×D411yescharacteristic
220C4⋊C4×C41C2×D411yescharacteristic
221C22⋊C4×C41—21no—
222C22⋊C4×C41—21no—
223C22⋊C4×C41—21no—
224C22⋊C4×C41—44no—
225C22⋊C4×C41—41no—
226C22⋊C4×C41—41no—
227C22⋊C4×C41—41no—
228C42×C41—21no—
229C42×C41—21no—
230C42×C41—21no—
231C42×C41—21no—
232C42×C41—41no—
233C42×C41—41no—
234C42×C41—41no—
235C42×C41#4112yes—
236C23×C41—21no—
237C23×C41—41no—
238C23×C41—41no—
239C23×C41—41no—
240C23×C41—81no—
241C23×C41—81no—
242C23×C41H(5,𝔽2)11yescharacteristic
243Q8×C41—22no—
244Q8×C41—21no—
245Q8×C41—21no—
246Q8×C41—22no—
247Q8×C41—41no—
248Q8×C41—41no—
249Q8×C41—161no—
250D4×C41—21no—
251D4×C41—21no—
252D4×C41—41no—
253D4×C41—41no—
254D4×C41—41no—
255D4×C41—41no—
256D4×C41—41no—
257D4×C41—41no—
258D4×C41—161no—
259D4×C41—161no—
260C2×C4×C41—21no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—22no—
268C2×C4×C41—22no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—81no—
278C2×C4×C41—81no—
279C2×C4×C41—161no—
280C2×C4×C41C22×D411yescharacteristic
281C2×C4×C41C22×D411yescharacteristic
282C2×C4×C41C2×#4111yescharacteristic
283C2×C4×C41C2×#4111yescharacteristic
284C2×C4×C41C2×#4111yescharacteristic
285C2×C4×C412−1+411yescharacteristic
286C8×C41—22no—
287C8×C41—21no—
288C8×C41—21no—
289C8×C41—21no—
290C8×C41—21no—
291C8×C41—41no—
292C8×C41—41no—
293C8×C41—41no—
294#26848C4111yesmaximal, characteristic, direct product factor, Sylow
295C22×C41—21no—
296C22×C41—21no—
297C22×C41—41no—
298C22×C41—41no—
299C22×C41—41no—
300C22×C41—82no—
301C22×C41—81no—
302C22×C41—81no—
303C22×C41—81no—
304C22×C41—161no—
305C22×C41#54211yescharacteristic
306C22×C41D4211yescharacteristic
307C22×C41#55111yescharacteristic
308C4×C41—42no—
309C4×C41—41no—
310C4×C41—42no—
311C4×C41—41no—
312C4×C41—41no—
313C4×C41—41no—
314C4×C41—41no—
315C4×C41—41no—
316C4×C41—41no—
317C4×C41—81no—
318C4×C41—81no—
319C4×C41#52511yescharacteristic
320C4×C41#53211yescharacteristic
321C4×C41#54711yescharacteristic
322C4×C41#54811yescharacteristic
323#3136C2×C4111yescharacteristic
324#3096C2×C4111yescharacteristic
325#3082C2×C4111yescharacteristic, complemented
326#2947C2×C4111yescharacteristic, complemented
327#2063C2×C4111yescharacteristic, complemented
328#2061C2×C4111yescharacteristic, complemented
329#2052C2×C4111yescharacteristic, complemented
330#2004C2×C4111yescharacteristic
331#1958C2×C4111yescharacteristic, complemented
332#1937C2×C4111yescharacteristic, complemented
333#1931C2×C4111yescharacteristic, complemented
334#1930C2×C4111yescharacteristic, complemented
335#1888C2×C4111yescharacteristic, complemented
336#1860C2×C4111yescharacteristic, complemented
337#1772C2×C4111yescharacteristic, complemented
338C2×C41—21no—
339C2×C41—21no—
340C2×C41—81no—
341C2×C41—161no—
342C2×C41#246111yescharacteristic
343C2×C41#329011yescharacteristic
344C2×C41#329011yescharacteristic
345C2×#137C22×C4111yescharacteristic
346#544C22×C4111yescharacteristic
347#535C22×C4111yescharacteristic
348C2×#124C22×C4111yescharacteristic
349#520C22×C4111yescharacteristic
350#519C22×C4111yescharacteristic
351#490—21no—
352#489—21no—
353#488—21no—
354#486—21no—
355#482—21no—
356#482—21no—
357#481—21no—
358#480—21no—
359#479—21no—
360#479—21no—
361#477—21no—
362#475—21no—
363#441—21no—
364#440—21no—
365C4×Q16—21no—
366C4×SD16—21no—
367C2×#108C22×C4111yescharacteristic
368#428C22×C4111yescharacteristic
369#428C22×C4111yescharacteristic
370#428C22×C4111yescharacteristic
371#427C22×C4111yescharacteristic
372#424C22×C4111yescharacteristic
373C2×#104C22×C4111yescharacteristic
374#419C22×C4111yescharacteristic
375#418C22×C4111yescharacteristic
376#418C22×C4111yescharacteristic
377#417C22×C4111yescharacteristic
378#416C22×C4111yescharacteristic
379C2×#103C22×C4111yescharacteristic
380C2×#103C22×C4111yescharacteristic
381C2×#102C22×C4111yescharacteristic
382C2×#102C22×C4111yescharacteristic
383C2×#101C22×C4111yescharacteristic
384C2×#100C22×C4111yescharacteristic
385#408C22×C4111yescharacteristic
386#405C22×C4111yescharacteristic
387#405C22×C4111yescharacteristic
388C2×C4×C8C22×C4111yescharacteristic
389#382C22×C4111yescharacteristic
390#343C22×C4111yescharacteristic
391#343C22×C4111yescharacteristic
392#341C22×C4111yescharacteristic
393#339C22×C4111yescharacteristic
394#339C22×C4111yescharacteristic
395#339C22×C4111yescharacteristic
396C41#2684811yescharacteristic, direct product factor, Sylow
397C2×#41C23×C4111yescharacteristic
398C22×Q8C23×C4111yescharacteristic
399C22×D4C23×C4111yescharacteristic
400#137—22no—
401#137—22no—
402C2×Q16—21no—
403C2×SD16—21no—
404C2×M16C23×C4111yescharacteristic
405C2×M16C23×C4111yescharacteristic
406C2×M16C23×C4111yescharacteristic
407C2×M16C23×C4111yescharacteristic
408C22×C8C23×C4111yescharacteristic
409C22×C8C23×C4111yescharacteristic
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412#127—21no—
413#125—21no—
414#125—21no—
415#124—21no—
416#124—22no—
417#124—22no—
418C22⋊Q8—41no—
419#121—21no—
420#121—21no—
421#120—41no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×D4—21no—
428C4×D4—41no—
429#117—21no—
430#117—41no—
431#117C23×C4111yescharacteristic
432#117C23×C4111yescharacteristic
433#117C23×C4111yescharacteristic
434C2×C4⋊C4—21no—
435C2×C4⋊C4C23×C4111yescharacteristic
436C2×C4⋊C4C23×C4111yescharacteristic
437C2×C22⋊C4—41no—
438C2×C42C23×C4111yescharacteristic
439#108—22no—
440#107—21no—
441#107—21no—
442#107—21no—
443#107D4×C4111yescharacteristic
444#107D4×C4111yescharacteristic
445#106—21no—
446#106—21no—
447#106—21no—
448#106D4×C4111yescharacteristic
449#106D4×C4111yescharacteristic
450C4⋊C8—21no—
451C4⋊C8—21no—
452#104—22no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103D4×C4111yescharacteristic
461#103D4×C4111yescharacteristic
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102—21no—
468#102—21no—
469#102—21no—
470#102—21no—
471#102D4×C4111yescharacteristic
472#102D4×C4111yescharacteristic
473#101—22no—
474#100—22no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477#97—21no—
478#97—21no—
479C4×C8—21no—
480C4×C8—21no—
481C4×C8—22no—
482#95—41no—
483C24—21no—
484#41—21no—
485#41—21no—
486#41—21no—
487#41—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—41no—
494C2×Q8C2×D4×C4111yescharacteristic
495C2×Q8#41×C4112yes—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4C2×D4×C4111yescharacteristic
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—41no—
512C22×C4C24×C4111yescharacteristic
513Q16—24no—
514SD16—24no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16#41×C4112yes—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C2×D4×C4111yescharacteristic
532C2×C8C2×D4×C4111yescharacteristic
533C2×C8C2×D4×C4111yescharacteristic
534C2×C8C2×D4×C4111yescharacteristic
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4C2×D4×C4111yescharacteristic
546C4⋊C4C2×D4×C4111yescharacteristic
547C4⋊C4C2×D4×C4111yescharacteristic
548C4⋊C4C2×D4×C4111yescharacteristic
549C4⋊C4C2×D4×C4111yescharacteristic
550C4⋊C4C2×D4×C4111yescharacteristic
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—44no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42#41×C4112yes—
566C23—21no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—81no—
571C23—81no—
572C23H(5,𝔽2)×C4111yescharacteristic
573Q8—22no—
574Q8—21no—
575Q8—21no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—161no—
580D4—21no—
581D4—21no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—161no—
589D4—161no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—161no—
610C2×C4C22×D4×C4111yescharacteristic
611C2×C4C22×D4×C4111yescharacteristic
612C2×C4C2×#41×C4111yescharacteristic
613C2×C4C2×#41×C4111yescharacteristic
614C2×C4C2×#41×C4111yescharacteristic
615C2×C42−1+4×C4111yescharacteristic
616C8—22no—
617C8—21no—
618C8—21no—
619C8—21no—
620C8—21no—
621C8—41no—
622C8—41no—
623C8—41no—
624C22—21no—
625C22—21no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—82no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—161no—
634C22C41×#54211yescharacteristic
635C22D42×C4111yescharacteristic
636C22C41×#55111yescharacteristic
637C4—42no—
638C4—41no—
639C4—42no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—81no—
647C4—81no—
648C4C41×#52511yescharacteristic
649C4C41×#53211yescharacteristic
650C4C41×#54711yescharacteristic
651C4C41×#54811yescharacteristic
652C2—21no—
653C2—21no—
654C2—81no—
655C2—161no—
656C2C41×#246111yescharacteristic
657C2C41×#329011yescharacteristic
658C2C41×#329011yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#535C22
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
3. C41×#3082C2semidirect
4. C41×#2947C2semidirect
5. C41×#2063C2semidirect
6. C41×#2061C2semidirect
7. C41×#2052C2semidirect
9. C41×#1958C2semidirect
10. C41×#1937C2semidirect
11. C41×#1931C2semidirect
12. C41×#1930C2semidirect
13. C41×#1888C2semidirect
14. C41×#1860C2semidirect
15. C41×#1772C2semidirect
294. #26848C41direct (N × H)
325. #3082C2×C41semidirect
326. #2947C2×C41semidirect
327. #2063C2×C41semidirect
328. #2061C2×C41semidirect
329. #2052C2×C41semidirect
331. #1958C2×C41semidirect
332. #1937C2×C41semidirect
333. #1931C2×C41semidirect
334. #1930C2×C41semidirect
335. #1888C2×C41semidirect
336. #1860C2×C41semidirect
337. #1772C2×C41semidirect
396. C41#26848direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31362
C41×#30962
C41×#30822
C41×#29472
C41×#20632
C41×#20612
C41×#20522
C41×#20042
C41×#19582
C41×#19372
C41×#19312
C41×#19302
C41×#18882
C41×#18602
C41×#17722
#2684841