Finite Group Databasebeta

← C41×#19043 #23795244

Subgroups — C41×#19043 #23795244

Order 10496.

950 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3558C211yesmaximal, characteristic
2C41×#3215C211yesmaximal, characteristic, complemented
3C41×#3181C211yesmaximal, characteristic, complemented
4C41×#3135C211yesmaximal, characteristic, complemented
5C41×#1662C212yesmaximal, complemented
6C41×#1661C212yesmaximal, complemented
7C41×#1659C212yesmaximal, complemented
8C41×#1659C212yesmaximal, complemented
9C41×#1532C211yesmaximal, characteristic, complemented
10C41×#1530C211yesmaximal, characteristic, complemented
11C2×C41×#329C211yesmaximal, characteristic, complemented
12C41×#562C2212yes—
13C41×H(3,𝔽4)C2212yes—
14C41×#559—21no—
15C41×#548—21no—
16C41×#546—22no—
17C41×#546—21no—
18D42×C41—21no—
19C41×#542—21no—
20C41×#538—22no—
21C41×#538—21no—
22C41×#535—21no—
23C41×#534—21no—
24C41×#533C2211yescharacteristic, complemented
25C41×#532C2211yescharacteristic
26C41×#529C2211yescharacteristic
27C2×#124×C41C2211yescharacteristic
28C41×#501C2211yescharacteristic, complemented
29C41×#497C2211yescharacteristic, complemented
30C41×#497C2212yescomplemented
31C41×#491—21no—
32C41×#491C2211yescharacteristic, complemented
33C41×#490—21no—
34C41×#489C2212yescomplemented
35C41×#489C2212yescomplemented
36C41×#489C2211yescharacteristic, complemented
37C41×#489C2212yescomplemented
38C41×#467—21no—
39C41×#465—21no—
40C41×#464—22no—
41C41×#451—21no—
42C41×#450—21no—
43C41×#441—21no—
44C41×#440—21no—
45C41×#432C2211yescharacteristic, complemented
46C41×#416—22no—
47C2×#97×C41C2211yescharacteristic, complemented
48C2×#97×C41C2211yescharacteristic, complemented
49C41×#330C2212yescomplemented
50C41×#329C2212yescomplemented
51C41×#329C2212yescomplemented
52C41×#329C2212yescomplemented
53C41×#329C2212yescomplemented
54C41×#329C2212yescomplemented
55C2×#41×C41—21no—
56C2×#41×C41D412yes—
57C22×Q8×C41D411yescharacteristic
58C22×D4×C41—22no—
59C22×D4×C41—21no—
60C22×D4×C41D411yescharacteristic
61C2×Q16×C41—21no—
62C2×Q16×C41—22no—
63C2×SD16×C41—21no—
64C2×SD16×C41—22no—
65C22×C8×C41—21no—
66C22×C8×C41—21no—
67C4⋊Q8×C41D411yescharacteristic
68C4⋊Q8×C41C2311yescharacteristic
69C4⋊Q8×C41C2311yescharacteristic
70#127×C41—21no—
71#127×C41D411yescharacteristic
72#126×C41—22no—
73#126×C41—21no—
74#125×C41—21no—
75#125×C41C2311yescharacteristic
76#124×C41—21no—
77#124×C41—22no—
78#124×C41—22no—
79#124×C41—22no—
80#124×C41—21no—
81#124×C41—21no—
82#124×C41D412yes—
83#124×C41C2312yes—
84#124×C41C2311yescharacteristic
85#124×C41C2312yes—
86#123×C41—22no—
87#123×C41—22no—
88#123×C41—21no—
89#123×C41—22no—
90#123×C41—22no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—22no—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41D411yescharacteristic
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—21no—
101#121×C41—22no—
102#121×C41—22no—
103#121×C41—21no—
104#121×C41—21no—
105#121×C41D411yescharacteristic
106#120×C41—22no—
107#120×C41—22no—
108#120×C41—22no—
109#120×C41—22no—
110#120×C41—22no—
111C4×Q8×C41—21no—
112C4×Q8×C41—21no—
113C4×Q8×C41—21no—
114C4×Q8×C41D411yescharacteristic
115C4×D4×C41—22no—
116C4×D4×C41—22no—
117C4×D4×C41—21no—
118C4×D4×C41—21no—
119C4×D4×C41—21no—
120C4×D4×C41—21no—
121C4×D4×C41D411yescharacteristic
122#117×C41—21no—
123#117×C41—21no—
124C2×C22⋊C4×C41—22no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C42×C41C2311yescharacteristic
128#107×C41—21no—
129#106×C41—21no—
130C4⋊C8×C41—21no—
131#103×C41—22no—
132#103×C41—22no—
133#103×C41—21no—
134#103×C41—22no—
135#103×C41—21no—
136#103×C41—21no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—21no—
140#102×C41—22no—
141C22⋊C8×C41—21no—
142#97×C41—21no—
143#97×C41—21no—
144#97×C41C2311yescharacteristic
145#97×C41C2311yescharacteristic
146#97×C41C2312yes—
147#97×C41C2312yes—
148C24×C41—22no—
149C24×C41—21no—
150#41×C41—44no—
151#41×C41—82no—
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
154C2×Q8×C41—21no—
155C2×Q8×C41—81no—
156C2×Q8×C41C2×D412yes—
157C2×Q8×C41C2×D411yescharacteristic
158C2×Q8×C41C2×D412yes—
159C2×D4×C41—22no—
160C2×D4×C41—21no—
161C2×D4×C41—22no—
162C2×D4×C41—22no—
163C2×D4×C41—22no—
164C2×D4×C41—22no—
165C2×D4×C41—22no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—81no—
170C2×D4×C41—82no—
171C2×D4×C41—84no—
172C2×D4×C41C2×D412yes—
173C2×D4×C41C2×D411yescharacteristic
174C2×D4×C41C2×D412yes—
175C22×C4×C41—22no—
176C22×C4×C41—22no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—22no—
180C22×C4×C41C2×D411yescharacteristic
181C22×C4×C41C2×D411yescharacteristic
182C22×C4×C41C2×D411yescharacteristic
183Q16×C41—42no—
184Q16×C41—82no—
185SD16×C41—42no—
186SD16×C41—82no—
187C2×C8×C41—21no—
188C2×C8×C41—22no—
189C2×C8×C41—21no—
190C2×C8×C41—22no—
191C2×C8×C41—42no—
192C2×C8×C41—42no—
193C4⋊C4×C41—22no—
194C4⋊C4×C41—22no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—21no—
203C4⋊C4×C41—21no—
204C4⋊C4×C41—21no—
205C4⋊C4×C41—41no—
206C4⋊C4×C41—41no—
207C4⋊C4×C41C2×D411yescharacteristic
208C4⋊C4×C41C2×D411yescharacteristic
209C22⋊C4×C41—22no—
210C22⋊C4×C41—22no—
211C22⋊C4×C41—22no—
212C22⋊C4×C41—22no—
213C22⋊C4×C41—22no—
214C22⋊C4×C41—21no—
215C22⋊C4×C41—22no—
216C22⋊C4×C41—21no—
217C22⋊C4×C41—22no—
218C22⋊C4×C41—21no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—22no—
221C22⋊C4×C41—21no—
222C22⋊C4×C41—21no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—22no—
225C22⋊C4×C41—41no—
226C42×C41—22no—
227C42×C41—21no—
228C42×C41—41no—
229C42×C41C2×D411yescharacteristic
230C42×C41C2×D411yescharacteristic
231C42×C41C2×D411yescharacteristic
232C42×C41C2411yescharacteristic
233C23×C41—22no—
234C23×C41—21no—
235C23×C41—22no—
236C23×C41—42no—
237C23×C41—81no—
238C23×C41—81no—
239C23×C41—82no—
240C23×C41—82no—
241C23×C41—82no—
242C23×C41#12011yescharacteristic
243Q8×C41—41no—
244Q8×C41—42no—
245Q8×C41—42no—
246Q8×C41—42no—
247Q8×C41—41no—
248Q8×C41—42no—
249Q8×C41—41no—
250D4×C41—41no—
251D4×C41—42no—
252D4×C41—42no—
253D4×C41—42no—
254D4×C41—42no—
255D4×C41—42no—
256D4×C41—44no—
257D4×C41—81no—
258D4×C41—82no—
259D4×C41—82no—
260D4×C41—82no—
261D4×C41—82no—
262D4×C41—82no—
263C2×C4×C41—22no—
264C2×C4×C41—21no—
265C2×C4×C41—22no—
266C2×C4×C41—22no—
267C2×C4×C41—21no—
268C2×C4×C41—21no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—42no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—82no—
275C2×C4×C41—81no—
276C2×C4×C41—82no—
277C2×C4×C41—82no—
278C2×C4×C41#12011yescharacteristic
279C2×C4×C41#12011yescharacteristic
280C2×C4×C41#12011yescharacteristic
281C2×C4×C41C22×D411yescharacteristic
282C2×C4×C41C22×D411yescharacteristic
283C2×C4×C41C22×D411yescharacteristic
284C8×C41—22no—
285C8×C41—42no—
286C8×C41—41no—
287C8×C41—42no—
288#19043C4111yesmaximal, characteristic, direct product factor, Sylow
289C22×C41—21no—
290C22×C41—21no—
291C22×C41—42no—
292C22×C41—42no—
293C22×C41—41no—
294C22×C41—41no—
295C22×C41—42no—
296C22×C41—42no—
297C22×C41—41no—
298C22×C41—42no—
299C22×C41—42no—
300C22×C41—162no—
301C22×C41—164no—
302C22×C41#45512yes—
303C22×C41C2×#12011yescharacteristic
304C4×C41—21no—
305C4×C41—21no—
306C4×C41—21no—
307C4×C41—21no—
308C4×C41—21no—
309C4×C41—21no—
310C4×C41—41no—
311C4×C41—42no—
312C4×C41—41no—
313C4×C41—41no—
314C4×C41—42no—
315C4×C41—81no—
316C4×C41—81no—
317#3558C2×C4111yescharacteristic
318#3215C2×C4111yescharacteristic, complemented
319#3181C2×C4111yescharacteristic, complemented
320#3135C2×C4111yescharacteristic, complemented
321#1662C2×C4112yescomplemented
322#1661C2×C4112yescomplemented
323#1659C2×C4112yescomplemented
324#1659C2×C4112yescomplemented
325#1532C2×C4111yescharacteristic, complemented
326#1530C2×C4111yescharacteristic, complemented
327C2×#329C2×C4111yescharacteristic, complemented
328C2×C41—22no—
329C2×C41—82no—
330C2×C41—82no—
331C2×C41—81no—
332C2×C41C2×#45511yescharacteristic
333C2×C41#301811yescharacteristic
334C2×C41#301911yescharacteristic
335#562C22×C4112yes—
336H(3,𝔽4)C22×C4112yes—
337#559—21no—
338#548—21no—
339#546—22no—
340#546—21no—
341D42—21no—
342#542—21no—
343#538—22no—
344#538—21no—
345#535—21no—
346#534—21no—
347#533C22×C4111yescharacteristic, complemented
348#532C22×C4111yescharacteristic
349#529C22×C4111yescharacteristic
350C2×#124C22×C4111yescharacteristic
351#501C22×C4111yescharacteristic, complemented
352#497C22×C4111yescharacteristic, complemented
353#497C22×C4112yescomplemented
354#491—21no—
355#491C22×C4111yescharacteristic, complemented
356#490—21no—
357#489C22×C4112yescomplemented
358#489C22×C4112yescomplemented
359#489C22×C4111yescharacteristic, complemented
360#489C22×C4112yescomplemented
361#467—21no—
362#465—21no—
363#464—22no—
364#451—21no—
365#450—21no—
366#441—21no—
367#440—21no—
368#432C22×C4111yescharacteristic, complemented
369#416—22no—
370C2×#97C22×C4111yescharacteristic, complemented
371C2×#97C22×C4111yescharacteristic, complemented
372#330C22×C4112yescomplemented
373#329C22×C4112yescomplemented
374#329C22×C4112yescomplemented
375#329C22×C4112yescomplemented
376#329C22×C4112yescomplemented
377#329C22×C4112yescomplemented
378C41#1904311yescharacteristic, direct product factor, Sylow
379C2×#41—21no—
380C2×#41D4×C4112yes—
381C22×Q8D4×C4111yescharacteristic
382C22×D4—22no—
383C22×D4—21no—
384C22×D4D4×C4111yescharacteristic
385C2×Q16—21no—
386C2×Q16—22no—
387C2×SD16—21no—
388C2×SD16—22no—
389C22×C8—21no—
390C22×C8—21no—
391C4⋊Q8D4×C4111yescharacteristic
392C4⋊Q8C23×C4111yescharacteristic
393C4⋊Q8C23×C4111yescharacteristic
394#127—21no—
395#127D4×C4111yescharacteristic
396#126—22no—
397#126—21no—
398#125—21no—
399#125C23×C4111yescharacteristic
400#124—21no—
401#124—22no—
402#124—22no—
403#124—22no—
404#124—21no—
405#124—21no—
406#124D4×C4112yes—
407#124C23×C4112yes—
408#124C23×C4111yescharacteristic
409#124C23×C4112yes—
410#123—22no—
411#123—22no—
412#123—21no—
413#123—22no—
414#123—22no—
415C22⋊Q8—21no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8D4×C4111yescharacteristic
421#121—22no—
422#121—22no—
423#121—22no—
424#121—21no—
425#121—22no—
426#121—22no—
427#121—21no—
428#121—21no—
429#121D4×C4111yescharacteristic
430#120—22no—
431#120—22no—
432#120—22no—
433#120—22no—
434#120—22no—
435C4×Q8—21no—
436C4×Q8—21no—
437C4×Q8—21no—
438C4×Q8D4×C4111yescharacteristic
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—21no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—21no—
445C4×D4D4×C4111yescharacteristic
446#117—21no—
447#117—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C42C23×C4111yescharacteristic
452#107—21no—
453#106—21no—
454C4⋊C8—21no—
455#103—22no—
456#103—22no—
457#103—21no—
458#103—22no—
459#103—21no—
460#103—21no—
461#102—22no—
462#102—22no—
463#102—21no—
464#102—22no—
465C22⋊C8—21no—
466#97—21no—
467#97—21no—
468#97C23×C4111yescharacteristic
469#97C23×C4111yescharacteristic
470#97C23×C4112yes—
471#97C23×C4112yes—
472C24—22no—
473C24—21no—
474#41—44no—
475#41—82no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—81no—
480C2×Q8C2×D4×C4112yes—
481C2×Q8C2×D4×C4111yescharacteristic
482C2×Q8C2×D4×C4112yes—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—81no—
494C2×D4—82no—
495C2×D4—84no—
496C2×D4C2×D4×C4112yes—
497C2×D4C2×D4×C4111yescharacteristic
498C2×D4C2×D4×C4112yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4C2×D4×C4111yescharacteristic
505C22×C4C2×D4×C4111yescharacteristic
506C22×C4C2×D4×C4111yescharacteristic
507Q16—42no—
508Q16—82no—
509SD16—42no—
510SD16—82no—
511C2×C8—21no—
512C2×C8—22no—
513C2×C8—21no—
514C2×C8—22no—
515C2×C8—42no—
516C2×C8—42no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4C2×D4×C4111yescharacteristic
532C4⋊C4C2×D4×C4111yescharacteristic
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C42—22no—
551C42—21no—
552C42—41no—
553C42C2×D4×C4111yescharacteristic
554C42C2×D4×C4111yescharacteristic
555C42C2×D4×C4111yescharacteristic
556C42C24×C4111yescharacteristic
557C23—22no—
558C23—21no—
559C23—22no—
560C23—42no—
561C23—81no—
562C23—81no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23#120×C4111yescharacteristic
567Q8—41no—
568Q8—42no—
569Q8—42no—
570Q8—42no—
571Q8—41no—
572Q8—42no—
573Q8—41no—
574D4—41no—
575D4—42no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—44no—
581D4—81no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—82no—
599C2×C4—81no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4#120×C4111yescharacteristic
603C2×C4#120×C4111yescharacteristic
604C2×C4#120×C4111yescharacteristic
605C2×C4C22×D4×C4111yescharacteristic
606C2×C4C22×D4×C4111yescharacteristic
607C2×C4C22×D4×C4111yescharacteristic
608C8—22no—
609C8—42no—
610C8—41no—
611C8—42no—
612C22—21no—
613C22—21no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—42no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—162no—
624C22—164no—
625C22C41×#45512yes—
626C22C2×#120×C4111yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—42no—
638C4—81no—
639C4—81no—
640C2—22no—
641C2—82no—
642C2—81no—
643C2—82no—
644C2C2×C41×#45511yescharacteristic
645C2C41×#301811yescharacteristic
646C2C41×#301911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3558C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3215C2semidirect
3. C41×#3181C2semidirect
4. C41×#3135C2semidirect
5. C41×#1662C2semidirect
6. C41×#1661C2semidirect
7. C41×#1659C2semidirect
8. C41×#1659C2semidirect
9. C41×#1532C2semidirect
10. C41×#1530C2semidirect
11. C2×C41×#329C2semidirect
24. C41×#533C22semidirect
28. C41×#501C22semidirect
29. C41×#497C22semidirect
30. C41×#497C22semidirect
32. C41×#491C22semidirect
34. C41×#489C22semidirect
35. C41×#489C22semidirect
36. C41×#489C22semidirect
37. C41×#489C22semidirect
45. C41×#432C22semidirect
47. C2×#97×C41C22semidirect
48. C2×#97×C41C22semidirect
49. C41×#330C22semidirect
50. C41×#329C22semidirect
51. C41×#329C22semidirect
52. C41×#329C22semidirect
53. C41×#329C22semidirect
54. C41×#329C22semidirect
288. #19043C41direct (N × H)
318. #3215C2×C41semidirect
319. #3181C2×C41semidirect
320. #3135C2×C41semidirect
321. #1662C2×C41semidirect
322. #1661C2×C41semidirect
323. #1659C2×C41semidirect
324. #1659C2×C41semidirect
325. #1532C2×C41semidirect
326. #1530C2×C41semidirect
327. C2×#329C2×C41semidirect
347. #533C22×C41semidirect
351. #501C22×C41semidirect
352. #497C22×C41semidirect
353. #497C22×C41semidirect
355. #491C22×C41semidirect
357. #489C22×C41semidirect
358. #489C22×C41semidirect
359. #489C22×C41semidirect
360. #489C22×C41semidirect
368. #432C22×C41semidirect
370. C2×#97C22×C41semidirect
371. C2×#97C22×C41semidirect
372. #330C22×C41semidirect
373. #329C22×C41semidirect
374. #329C22×C41semidirect
375. #329C22×C41semidirect
376. #329C22×C41semidirect
377. #329C22×C41semidirect
378. C41#19043direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35582
C41×#32152
C41×#31812
C41×#31352
C41×#16622
C41×#16612
C41×#16592
C41×#15322
C41×#15302
C2×C41×#3292
#1904341