Finite Group Databasebeta

← C41×#25670 #23801871

Subgroups — C41×#25670 #23801871

Order 10496.

972 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3512C211yesmaximal, characteristic
2C41×#3141C211yesmaximal, characteristic, complemented
3C41×#3079C211yesmaximal, characteristic, complemented
4C41×#2660C211yesmaximal, characteristic, complemented
5C41×#2040C212yesmaximal, complemented
6C41×#2039C212yesmaximal, complemented
7C41×#1998C211yesmaximal, characteristic, complemented
8C41×#1963C211yesmaximal, characteristic, complemented
9C41×#1860C212yesmaximal, complemented
10C41×#1859C212yesmaximal, complemented
11C41×#1759C211yesmaximal, characteristic, complemented
12C41×#553—21no—
13C41×#553—21no—
14C41×#553—22no—
15C41×#553—22no—
16C41×#552—21no—
17C41×#552—21no—
18C41×#541—21no—
19C41×#540—21no—
20C41×#537C2211yescharacteristic
21C41×#537C2211yescharacteristic
22C41×#532C2211yescharacteristic
23C2×C4⋊Q8×C41C2211yescharacteristic
24C41×#529—21no—
25C41×#529—21no—
26C2×#125×C41C2211yescharacteristic
27C41×#520C2211yescharacteristic
28C41×#520C2211yescharacteristic
29C4×#41×C41C2211yescharacteristic
30C41×#489—21no—
31C41×#489—21no—
32C41×#487—21no—
33C41×#486—21no—
34C41×#477—21no—
35C41×#476—21no—
36C41×#475—21no—
37C41×#474—21no—
38C41×#428C2212yes—
39C41×#423C2211yescharacteristic
40C2×#104×C41C2212yes—
41C2×#104×C41C2212yes—
42C2×#104×C41C2212yes—
43C41×#417C2212yes—
44C41×#417C2212yes—
45C41×#417C2212yes—
46C4×M16×C41C2211yescharacteristic
47C41×#398—22no—
48C41×#395—22no—
49C41×#384C2212yes—
50C41×#382C2212yes—
51C41×#376C2211yescharacteristic
52C41×#343C2212yes—
53C41×#343C2212yes—
54C41×#339C2212yes—
55C2×#41×C41C2311yescharacteristic
56C2×#41×C41C2311yescharacteristic
57C2×#41×C41C2311yescharacteristic
58C22×Q8×C41—21no—
59C2×M16×C41C2312yes—
60C2×M16×C41C2312yes—
61C4⋊Q8×C41—21no—
62C4⋊Q8×C41—21no—
63C4⋊Q8×C41—21no—
64C4⋊Q8×C41—21no—
65C4⋊Q8×C41D411yescharacteristic
66#127×C41D411yescharacteristic
67#126×C41—22no—
68#126×C41—22no—
69#126×C41—22no—
70#126×C41—22no—
71#125×C41—22no—
72#125×C41—22no—
73#125×C41—21no—
74#125×C41—21no—
75#125×C41—21no—
76#125×C41—21no—
77#124×C41D411yescharacteristic
78#124×C41D411yescharacteristic
79#123×C41—22no—
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—22no—
83C22⋊Q8×C41—21no—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—21no—
87#121×C41—22no—
88#121×C41—22no—
89#121×C41—21no—
90#121×C41—21no—
91#121×C41—21no—
92#121×C41—21no—
93#121×C41—21no—
94#121×C41—21no—
95#121×C41—22no—
96#121×C41—22no—
97C4×Q8×C41—21no—
98C4×Q8×C41—21no—
99C4×Q8×C41D411yescharacteristic
100C4×Q8×C41D411yescharacteristic
101C4×D4×C41—22no—
102C4×D4×C41—22no—
103C4×D4×C41—21no—
104C4×D4×C41—21no—
105C4×D4×C41—21no—
106C4×D4×C41—21no—
107C4×D4×C41—22no—
108C4×D4×C41—22no—
109C4×D4×C41—21no—
110C4×D4×C41—21no—
111C4×D4×C41D411yescharacteristic
112C4×D4×C41D411yescharacteristic
113#117×C41—22no—
114#117×C41—22no—
115#117×C41—21no—
116#117×C41—21no—
117#117×C41—21no—
118#117×C41C2311yescharacteristic
119C2×C4⋊C4×C41—21no—
120C2×C4⋊C4×C41—21no—
121C2×C4⋊C4×C41—21no—
122C2×C4⋊C4×C41—24no—
123C2×C4⋊C4×C41D412yes—
124C2×C4⋊C4×C41D412yes—
125C2×C4⋊C4×C41C2312yes—
126C2×C4⋊C4×C41C2311yescharacteristic
127C2×C4⋊C4×C41C2311yescharacteristic
128C2×C42×C41—21no—
129C2×C42×C41C2312yes—
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#106×C41—22no—
133C4⋊C8×C41—21no—
134C4⋊C8×C41—21no—
135#104×C41—24no—
136#104×C41—24no—
137#104×C41—24no—
138#103×C41—22no—
139#103×C41—22no—
140#103×C41—22no—
141#102×C41—22no—
142#102×C41—22no—
143#102×C41—22no—
144#97×C41—21no—
145C4×C8×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—24no—
149#41×C41—22no—
150#41×C41—22no—
151#41×C41—22no—
152#41×C41—22no—
153#41×C41—22no—
154#41×C41—22no—
155C2×Q8×C41—41no—
156C2×Q8×C41—41no—
157C2×Q8×C41—82no—
158C2×Q8×C41C2×D411yescharacteristic
159C2×Q8×C41C2×D411yescharacteristic
160C2×Q8×C41C2×D411yescharacteristic
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—22no—
165C2×D4×C41—22no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41C2×D411yescharacteristic
169C2×D4×C41C2×D411yescharacteristic
170C2×D4×C41C2×D411yescharacteristic
171C22×C4×C41—22no—
172C22×C4×C41—22no—
173C22×C4×C41—22no—
174C22×C4×C41—21no—
175C22×C4×C41—21no—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—22no—
180C22×C4×C41C2×D412yes—
181C22×C4×C41C2×D412yes—
182C22×C4×C41C2×D411yescharacteristic
183C22×C4×C41C2×D411yescharacteristic
184C22×C4×C41C2411yescharacteristic
185M16×C41—22no—
186M16×C41—22no—
187M16×C41—22no—
188M16×C41—22no—
189C2×C8×C41—22no—
190C2×C8×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—22no—
193C4⋊C4×C41—22no—
194C4⋊C4×C41—22no—
195C4⋊C4×C41—22no—
196C4⋊C4×C41—22no—
197C4⋊C4×C41—22no—
198C4⋊C4×C41—22no—
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—21no—
206C4⋊C4×C41—21no—
207C4⋊C4×C41—22no—
208C4⋊C4×C41—22no—
209C4⋊C4×C41—41no—
210C4⋊C4×C41—41no—
211C4⋊C4×C41—84no—
212C4⋊C4×C41C2×D411yescharacteristic
213C4⋊C4×C41C2×D411yescharacteristic
214C22⋊C4×C41—22no—
215C22⋊C4×C41—22no—
216C22⋊C4×C41—22no—
217C22⋊C4×C41—22no—
218C22⋊C4×C41—22no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—21no—
221C22⋊C4×C41—21no—
222C22⋊C4×C41—21no—
223C22⋊C4×C41—21no—
224C22⋊C4×C41—21no—
225C22⋊C4×C41—21no—
226C22⋊C4×C41—21no—
227C42×C41—22no—
228C42×C41—22no—
229C42×C41—21no—
230C42×C41—21no—
231C42×C41—21no—
232C42×C41—22no—
233C42×C41C2×D411yescharacteristic
234C42×C41C2×D411yescharacteristic
235C42×C41C2×D411yescharacteristic
236C42×C41C2×D411yescharacteristic
237C42×C41#4114yes—
238C23×C41—21no—
239C23×C41—21no—
240C23×C41—21no—
241C23×C41C22×D411yescharacteristic
242Q8×C41—21no—
243Q8×C41—21no—
244Q8×C41—22no—
245Q8×C41—22no—
246Q8×C41—82no—
247Q8×C41—82no—
248D4×C41—21no—
249D4×C41—21no—
250D4×C41—22no—
251D4×C41—22no—
252D4×C41—42no—
253D4×C41—42no—
254D4×C41—42no—
255D4×C41—81no—
256D4×C41—81no—
257D4×C41—82no—
258D4×C41—82no—
259C2×C4×C41—21no—
260C2×C4×C41—21no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—22no—
265C2×C4×C41—22no—
266C2×C4×C41—24no—
267C2×C4×C41—41no—
268C2×C4×C41—41no—
269C2×C4×C41—42no—
270C2×C4×C41—42no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—42no—
276C2×C4×C41—42no—
277C2×C4×C41—42no—
278C2×C4×C41—44no—
279C2×C4×C41—42no—
280C2×C4×C41—81no—
281C2×C4×C41—81no—
282C2×C4×C41—82no—
283C2×C4×C41—82no—
284C2×C4×C41#12011yescharacteristic
285C2×C4×C41#12011yescharacteristic
286C2×C4×C41#12011yescharacteristic
287C2×C4×C41#12011yescharacteristic
288C2×C4×C41C22×D411yescharacteristic
289C2×C4×C41C22×D411yescharacteristic
290C2×C4×C41C2×#4112yes—
291C2×C4×C412−1+412yes—
292C8×C41—42no—
293C8×C41—42no—
294#25670C4111yesmaximal, characteristic, direct product factor, Sylow
295C22×C41—21no—
296C22×C41—21no—
297C22×C41—41no—
298C22×C41—41no—
299C22×C41—41no—
300C22×C41—41no—
301C22×C41—41no—
302C22×C41—41no—
303C22×C41—41no—
304C22×C41—41no—
305C22×C41—41no—
306C22×C41C2×#12011yescharacteristic
307C22×C41#54812yes—
308C4×C41—21no—
309C4×C41—21no—
310C4×C41—21no—
311C4×C41—21no—
312C4×C41—44no—
313C4×C41—41no—
314C4×C41—41no—
315C4×C41—41no—
316C4×C41—42no—
317C4×C41—41no—
318C4×C41—42no—
319C4×C41—41no—
320C4×C41—82no—
321C4×C41#53211yescharacteristic
322C4×C41#53611yescharacteristic
323C4×C41#54712yes—
324#3512C2×C4111yescharacteristic
325#3141C2×C4111yescharacteristic, complemented
326#3079C2×C4111yescharacteristic, complemented
327#2660C2×C4111yescharacteristic, complemented
328#2040C2×C4112yescomplemented
329#2039C2×C4112yescomplemented
330#1998C2×C4111yescharacteristic, complemented
331#1963C2×C4111yescharacteristic, complemented
332#1860C2×C4112yescomplemented
333#1859C2×C4112yescomplemented
334#1759C2×C4111yescharacteristic, complemented
335C2×C41—22no—
336C2×C41—81no—
337C2×C41—81no—
338C2×C41—81no—
339C2×C41#243211yescharacteristic
340C2×C41#302111yescharacteristic
341C2×C41#302211yescharacteristic
342#553—21no—
343#553—21no—
344#553—22no—
345#553—22no—
346#552—21no—
347#552—21no—
348#541—21no—
349#540—21no—
350#537C22×C4111yescharacteristic
351#537C22×C4111yescharacteristic
352#532C22×C4111yescharacteristic
353C2×C4⋊Q8C22×C4111yescharacteristic
354#529—21no—
355#529—21no—
356C2×#125C22×C4111yescharacteristic
357#520C22×C4111yescharacteristic
358#520C22×C4111yescharacteristic
359C4×#41C22×C4111yescharacteristic
360#489—21no—
361#489—21no—
362#487—21no—
363#486—21no—
364#477—21no—
365#476—21no—
366#475—21no—
367#474—21no—
368#428C22×C4112yes—
369#423C22×C4111yescharacteristic
370C2×#104C22×C4112yes—
371C2×#104C22×C4112yes—
372C2×#104C22×C4112yes—
373#417C22×C4112yes—
374#417C22×C4112yes—
375#417C22×C4112yes—
376C4×M16C22×C4111yescharacteristic
377#398—22no—
378#395—22no—
379#384C22×C4112yes—
380#382C22×C4112yes—
381#376C22×C4111yescharacteristic
382#343C22×C4112yes—
383#343C22×C4112yes—
384#339C22×C4112yes—
385C41#2567011yescharacteristic, direct product factor, Sylow
386C2×#41C23×C4111yescharacteristic
387C2×#41C23×C4111yescharacteristic
388C2×#41C23×C4111yescharacteristic
389C22×Q8—21no—
390C2×M16C23×C4112yes—
391C2×M16C23×C4112yes—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8D4×C4111yescharacteristic
397#127D4×C4111yescharacteristic
398#126—22no—
399#126—22no—
400#126—22no—
401#126—22no—
402#125—22no—
403#125—22no—
404#125—21no—
405#125—21no—
406#125—21no—
407#125—21no—
408#124D4×C4111yescharacteristic
409#124D4×C4111yescharacteristic
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418#121—22no—
419#121—22no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121—22no—
427#121—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8D4×C4111yescharacteristic
431C4×Q8D4×C4111yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4D4×C4111yescharacteristic
443C4×D4D4×C4111yescharacteristic
444#117—22no—
445#117—22no—
446#117—21no—
447#117—21no—
448#117—21no—
449#117C23×C4111yescharacteristic
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4D4×C4112yes—
455C2×C4⋊C4D4×C4112yes—
456C2×C4⋊C4C23×C4112yes—
457C2×C4⋊C4C23×C4111yescharacteristic
458C2×C4⋊C4C23×C4111yescharacteristic
459C2×C42—21no—
460C2×C42C23×C4112yes—
461C2×C42C23×C4111yescharacteristic
462#107—22no—
463#106—22no—
464C4⋊C8—21no—
465C4⋊C8—21no—
466#104—24no—
467#104—24no—
468#104—24no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#97—21no—
476C4×C8—21no—
477#95—21no—
478#95—21no—
479#95—24no—
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—22no—
486C2×Q8—41no—
487C2×Q8—41no—
488C2×Q8—82no—
489C2×Q8C2×D4×C4111yescharacteristic
490C2×Q8C2×D4×C4111yescharacteristic
491C2×Q8C2×D4×C4111yescharacteristic
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4C2×D4×C4111yescharacteristic
500C2×D4C2×D4×C4111yescharacteristic
501C2×D4C2×D4×C4111yescharacteristic
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4C2×D4×C4112yes—
512C22×C4C2×D4×C4112yes—
513C22×C4C2×D4×C4111yescharacteristic
514C22×C4C2×D4×C4111yescharacteristic
515C22×C4C24×C4111yescharacteristic
516M16—22no—
517M16—22no—
518M16—22no—
519M16—22no—
520C2×C8—22no—
521C2×C8—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—84no—
543C4⋊C4C2×D4×C4111yescharacteristic
544C4⋊C4C2×D4×C4111yescharacteristic
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C42—22no—
559C42—22no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—22no—
564C42C2×D4×C4111yescharacteristic
565C42C2×D4×C4111yescharacteristic
566C42C2×D4×C4111yescharacteristic
567C42C2×D4×C4111yescharacteristic
568C42#41×C4114yes—
569C23—21no—
570C23—21no—
571C23—21no—
572C23C22×D4×C4111yescharacteristic
573Q8—21no—
574Q8—21no—
575Q8—22no—
576Q8—22no—
577Q8—82no—
578Q8—82no—
579D4—21no—
580D4—21no—
581D4—22no—
582D4—22no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—81no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4#120×C4111yescharacteristic
616C2×C4#120×C4111yescharacteristic
617C2×C4#120×C4111yescharacteristic
618C2×C4#120×C4111yescharacteristic
619C2×C4C22×D4×C4111yescharacteristic
620C2×C4C22×D4×C4111yescharacteristic
621C2×C4C2×#41×C4112yes—
622C2×C42−1+4×C4112yes—
623C8—42no—
624C8—42no—
625C22—21no—
626C22—21no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22C2×#120×C4111yescharacteristic
637C22C41×#54812yes—
638C4—21no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—44no—
643C4—41no—
644C4—41no—
645C4—41no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—82no—
651C4C41×#53211yescharacteristic
652C4C41×#53611yescharacteristic
653C4C41×#54712yes—
654C2—22no—
655C2—81no—
656C2—81no—
657C2—81no—
658C2C41×#243211yescharacteristic
659C2C41×#302111yescharacteristic
660C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3512C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#3141C2semidirect
3. C41×#3079C2semidirect
4. C41×#2660C2semidirect
5. C41×#2040C2semidirect
6. C41×#2039C2semidirect
7. C41×#1998C2semidirect
8. C41×#1963C2semidirect
9. C41×#1860C2semidirect
10. C41×#1859C2semidirect
11. C41×#1759C2semidirect
294. #25670C41direct (N × H)
325. #3141C2×C41semidirect
326. #3079C2×C41semidirect
327. #2660C2×C41semidirect
328. #2040C2×C41semidirect
329. #2039C2×C41semidirect
330. #1998C2×C41semidirect
331. #1963C2×C41semidirect
332. #1860C2×C41semidirect
333. #1859C2×C41semidirect
334. #1759C2×C41semidirect
385. C41#25670direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35122
C41×#31412
C41×#30792
C41×#26602
C41×#20402
C41×#20392
C41×#19982
C41×#19632
C41×#18602
C41×#18592
C41×#17592
#2567041