Finite Group Databasebeta

← C41×#61469 #23837670

Subgroups — C41×#61469 #23837670

Order 10496.

1866 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3483C211yesmaximal, characteristic
2Q8×#41×C41C211yesmaximal, characteristic, complemented
3C41×#3392C211yesmaximal, characteristic, complemented
4Q8×Q16×C41C211yesmaximal, characteristic, complemented
5C41×#3363C211yesmaximal, characteristic, complemented
6C41×#3362C211yesmaximal, characteristic, complemented
7C41×#3357C213yesmaximal, complemented
8C41×#3333C213yesmaximal, complemented
9C41×#3329C213yesmaximal, complemented
10C41×#3278C213yesmaximal, complemented
11C41×#3182C213yesmaximal, complemented
12C41×#3116C213yesmaximal, complemented
13C41×#3112C213yesmaximal, complemented
14C41×#2971C211yesmaximal, characteristic, complemented
15C4×#137×C41C213yesmaximal, complemented
16C2×#137×C41C2213yes—
17Q82×C41C2211yescharacteristic
18Q82×C41C2211yescharacteristic
19C41×#557—21no—
20C41×#557C2211yescharacteristic
21C41×#555—23no—
22C41×#555C2213yes—
23C41×#554—23no—
24C41×#554C2213yes—
25C41×#550—21no—
26C41×#550C2213yes—
27C41×#550C2211yescharacteristic
28D4×Q8×C41C2213yes—
29C41×#533—23no—
30C41×#533C2213yes—
31C41×#532—23no—
32C41×#532C2213yes—
33C4×#41×C41—21no—
34C4×#41×C41—21no—
35C4×#41×C41C2213yes—
36C4×#41×C41C2211yescharacteristic
37C2×C4×Q8×C41C2213yes—
38C41×#500C2213yes—
39C41×#492C2213yes—
40C41×#487C2213yes—
41C41×#486C2213yes—
42C41×#485C2216yes—
43C41×#480C2216yes—
44C41×#477C2213yes—
45C41×#477C2213yes—
46C41×#477C2213yes—
47C41×#476C2213yes—
48C41×#468C2216yes—
49C41×#468C2216yes—
50C41×#462C2213yes—
51C41×#461C2213yes—
52C41×#460C2213yes—
53C41×#460C2213yes—
54C41×#452C2216yes—
55C41×#448C2216yes—
56C8×Q8×C41C2211yescharacteristic
57C8×Q8×C41C2211yescharacteristic
58C41×#441C2213yes—
59C41×#441C2211yescharacteristic
60C41×#440C2213yes—
61C41×#440C2216yes—
62C41×#440C2213yes—
63C4×Q16×C41C2213yes—
64C4×Q16×C41C2213yes—
65C4×SD16×C41C2213yes—
66C4×SD16×C41C2213yes—
67C41×#436C2213yes—
68C41×#436C2213yes—
69C41×#432C2213yes—
70C41×#428C2213yes—
71C41×#419C2213yes—
72C41×#417C2213yes—
73C4×M16×C41C2213yes—
74C2×#41×C41—21no—
75C2×#41×C41—23no—
76C2×#41×C41D411yescharacteristic
77C2×#41×C41C2313yes—
78C22×Q8×C41C2313yes—
79#137×C41—212no—
80C2×Q16×C41C2313yes—
81C2×Q16×C41C2311yescharacteristic
82C2×SD16×C41C2313yes—
83C2×SD16×C41C2313yes—
84C2×SD16×C41C2316yes—
85C2×M16×C41C2313yes—
86C2×M16×C41C2313yes—
87C4⋊Q8×C41—23no—
88C4⋊Q8×C41—23no—
89C4⋊Q8×C41—23no—
90C4⋊Q8×C41C2313yes—
91C4⋊Q8×C41C2313yes—
92C4⋊Q8×C41C2313yes—
93#127×C41—23no—
94#127×C41C2313yes—
95#125×C41—23no—
96#125×C41—23no—
97#125×C41—23no—
98#124×C41—26no—
99#124×C41—23no—
100C22⋊Q8×C41—23no—
101C22⋊Q8×C41—26no—
102C22⋊Q8×C41—26no—
103C22⋊Q8×C41C2316yes—
104#121×C41—23no—
105#121×C41—23no—
106#121×C41—23no—
107#121×C41—26no—
108#121×C41C2316yes—
109C4×Q8×C41—21no—
110C4×Q8×C41—21no—
111C4×Q8×C41—21no—
112C4×Q8×C41—23no—
113C4×Q8×C41—23no—
114C4×Q8×C41—23no—
115C4×Q8×C41D411yescharacteristic
116C4×Q8×C41C2311yescharacteristic
117C4×Q8×C41C2313yes—
118C4×Q8×C41C2313yes—
119C4×Q8×C41C2313yes—
120C4×Q8×C41C2311yescharacteristic
121C4×Q8×C41C2313yes—
122C4×Q8×C41C2311yescharacteristic
123C4×D4×C41—23no—
124C4×D4×C41—23no—
125C4×D4×C41—23no—
126C4×D4×C41—23no—
127C4×D4×C41—23no—
128C4×D4×C41—23no—
129C4×D4×C41D413yes—
130C4×D4×C41C2313yes—
131C4×D4×C41C2313yes—
132C4×D4×C41C2313yes—
133#117×C41—23no—
134#117×C41—23no—
135#117×C41—23no—
136#117×C41D413yes—
137#117×C41C2313yes—
138C2×C4⋊C4×C41—23no—
139C2×C4⋊C4×C41C2313yes—
140C2×C42×C41—23no—
141C2×C42×C41—23no—
142C2×C42×C41C2313yes—
143#107×C41C2313yes—
144#107×C41C2316yes—
145#107×C41C2313yes—
146#106×C41C2311yescharacteristic
147#106×C41C2313yes—
148C4⋊C8×C41C2313yes—
149C4⋊C8×C41C2313yes—
150#103×C41C2311yescharacteristic
151#103×C41C2313yes—
152#103×C41C2311yescharacteristic
153#103×C41C2313yes—
154#103×C41C2313yes—
155#103×C41C2313yes—
156#103×C41C2316yes—
157#102×C41C2313yes—
158#102×C41C2313yes—
159#102×C41C2316yes—
160C22⋊C8×C41C2316yes—
161#97×C41C2311yescharacteristic
162#97×C41C2313yes—
163C4×C8×C41C2313yes—
164C4×C8×C41C2313yes—
165#41×C41—24no—
166#41×C41—26no—
167#41×C41—43no—
168#41×C41—44no—
169#41×C41—86no—
170C2×Q8×C41—23no—
171C2×Q8×C41—23no—
172C2×Q8×C41—23no—
173C2×Q8×C41—26no—
174C2×Q8×C41—43no—
175C2×Q8×C41C2×D411yescharacteristic
176C2×Q8×C41C2413yes—
177C2×Q8×C41C2411yescharacteristic
178C2×Q8×C41C2411yescharacteristic
179C2×D4×C41—23no—
180C2×D4×C41—26no—
181C2×D4×C41—23no—
182C2×D4×C41—23no—
183C2×D4×C41C2×D413yes—
184C2×D4×C41C2413yes—
185C22×C4×C41—23no—
186C22×C4×C41—23no—
187C22×C4×C41—23no—
188C22×C4×C41—23no—
189C22×C4×C41—23no—
190C22×C4×C41C2×D413yes—
191C22×C4×C41C2×D413yes—
192C22×C4×C41C2413yes—
193Q16×C41—26no—
194Q16×C41#4114yescomplemented
195SD16×C41—26no—
196SD16×C41—26no—
197SD16×C41—46no—
198M16×C41—26no—
199M16×C41—43no—
200C2×C8×C41C2411yescharacteristic
201C2×C8×C41C2413yes—
202C2×C8×C41C2413yes—
203C2×C8×C41C2411yescharacteristic
204C4⋊C4×C41—21no—
205C4⋊C4×C41—23no—
206C4⋊C4×C41—23no—
207C4⋊C4×C41—23no—
208C4⋊C4×C41—23no—
209C4⋊C4×C41—21no—
210C4⋊C4×C41—23no—
211C4⋊C4×C41—23no—
212C4⋊C4×C41—23no—
213C4⋊C4×C41—23no—
214C4⋊C4×C41—23no—
215C4⋊C4×C41—26no—
216C4⋊C4×C41C2×D413yes—
217C4⋊C4×C41C2×D413yes—
218C4⋊C4×C41C2411yescharacteristic
219C4⋊C4×C41C2413yes—
220C4⋊C4×C41C2411yescharacteristic
221C4⋊C4×C41C2413yes—
222C22⋊C4×C41—26no—
223C22⋊C4×C41—23no—
224C22⋊C4×C41—26no—
225C22⋊C4×C41—23no—
226C22⋊C4×C41—23no—
227C22⋊C4×C41C2×D416yes—
228C42×C41—21no—
229C42×C41—21no—
230C42×C41—23no—
231C42×C41—23no—
232C42×C41—23no—
233C42×C41—23no—
234C42×C41—23no—
235C42×C41C2×D413yes—
236C42×C41C2×D413yes—
237C42×C41C2413yes—
238C42×C41C2411yescharacteristic
239C23×C41—23no—
240C23×C41C22×D413yes—
241Q8×C41—21no—
242Q8×C41—21no—
243Q8×C41—23no—
244Q8×C41—23no—
245Q8×C41—46no—
246Q8×C41—83no—
247Q8×C41—83no—
248Q8×C41#13714yescomplemented
249Q8×C41C2×#4112yes—
250Q8×C41C2×#4112yes—
251D4×C41—26no—
252D4×C41—23no—
253D4×C41—23no—
254D4×C41—46no—
255D4×C41—46no—
256D4×C41—83no—
257D4×C41—86no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—26no—
261C2×C4×C41—23no—
262C2×C4×C41—23no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—23no—
266C2×C4×C41—23no—
267C2×C4×C41—23no—
268C2×C4×C41—43no—
269C2×C4×C41—46no—
270C2×C4×C41—46no—
271C2×C4×C41—46no—
272C2×C4×C41—46no—
273C2×C4×C41—83no—
274C2×C4×C41C22×D411yescharacteristic
275C2×C4×C41C22×D411yescharacteristic
276C2×C4×C41C22×D413yes—
277C2×C4×C41C22×D413yes—
278C2×C4×C41C22×D413yes—
279C2×C4×C41C2511yescharacteristic
280C8×C41—23no—
281C8×C41—21no—
282C8×C41—23no—
283C8×C41C2×#4112yes—
284#61469C4111yesmaximal, characteristic, direct product factor, Sylow
285C22×C41—23no—
286C22×C41—23no—
287C22×C41—23no—
288C22×C41—43no—
289C22×C41—43no—
290C22×C41—43no—
291C22×C41C23×D411yescharacteristic
292C4×C41—21no—
293C4×C41—23no—
294C4×C41—23no—
295C4×C41—22no—
296C4×C41—22no—
297C4×C41—21no—
298C4×C41—43no—
299C4×C41—41no—
300C4×C41—43no—
301C4×C41—43no—
302C4×C41—41no—
303C4×C41C2×#13716yes—
304C4×C41C22×#4111yescharacteristic
305C4×C41#58511yescharacteristic
306#3483C2×C4111yescharacteristic
307Q8×#41C2×C4111yescharacteristic, complemented
308#3392C2×C4111yescharacteristic, complemented
309Q8×Q16C2×C4111yescharacteristic, complemented
310#3363C2×C4111yescharacteristic, complemented
311#3362C2×C4111yescharacteristic, complemented
312#3357C2×C4113yescomplemented
313#3333C2×C4113yescomplemented
314#3329C2×C4113yescomplemented
315#3278C2×C4113yescomplemented
316#3182C2×C4113yescomplemented
317#3116C2×C4113yescomplemented
318#3112C2×C4113yescomplemented
319#2971C2×C4111yescharacteristic, complemented
320C4×#137C2×C4113yescomplemented
321C2×C41—43no—
322C2×C41—83no—
323C2×C41D4×#4111yescharacteristic
324C2×C41C22×#13711yescharacteristic
325C2×C41#358511yescharacteristic
326C2×#137C22×C4113yes—
327Q82C22×C4111yescharacteristic
328Q82C22×C4111yescharacteristic
329#557—21no—
330#557C22×C4111yescharacteristic
331#555—23no—
332#555C22×C4113yes—
333#554—23no—
334#554C22×C4113yes—
335#550—21no—
336#550C22×C4113yes—
337#550C22×C4111yescharacteristic
338D4×Q8C22×C4113yes—
339#533—23no—
340#533C22×C4113yes—
341#532—23no—
342#532C22×C4113yes—
343C4×#41—21no—
344C4×#41—21no—
345C4×#41C22×C4113yes—
346C4×#41C22×C4111yescharacteristic
347C2×C4×Q8C22×C4113yes—
348#500C22×C4113yes—
349#492C22×C4113yes—
350#487C22×C4113yes—
351#486C22×C4113yes—
352#485C22×C4116yes—
353#480C22×C4116yes—
354#477C22×C4113yes—
355#477C22×C4113yes—
356#477C22×C4113yes—
357#476C22×C4113yes—
358#468C22×C4116yes—
359#468C22×C4116yes—
360#462C22×C4113yes—
361#461C22×C4113yes—
362#460C22×C4113yes—
363#460C22×C4113yes—
364#452C22×C4116yes—
365#448C22×C4116yes—
366C8×Q8C22×C4111yescharacteristic
367C8×Q8C22×C4111yescharacteristic
368#441C22×C4113yes—
369#441C22×C4111yescharacteristic
370#440C22×C4113yes—
371#440C22×C4116yes—
372#440C22×C4113yes—
373C4×Q16C22×C4113yes—
374C4×Q16C22×C4113yes—
375C4×SD16C22×C4113yes—
376C4×SD16C22×C4113yes—
377#436C22×C4113yes—
378#436C22×C4113yes—
379#432C22×C4113yes—
380#428C22×C4113yes—
381#419C22×C4113yes—
382#417C22×C4113yes—
383C4×M16C22×C4113yes—
384C41#6146911yescharacteristic, direct product factor, Sylow
385C2×#41—21no—
386C2×#41—23no—
387C2×#41D4×C4111yescharacteristic
388C2×#41C23×C4113yes—
389C22×Q8C23×C4113yes—
390#137—212no—
391C2×Q16C23×C4113yes—
392C2×Q16C23×C4111yescharacteristic
393C2×SD16C23×C4113yes—
394C2×SD16C23×C4113yes—
395C2×SD16C23×C4116yes—
396C2×M16C23×C4113yes—
397C2×M16C23×C4113yes—
398C4⋊Q8—23no—
399C4⋊Q8—23no—
400C4⋊Q8—23no—
401C4⋊Q8C23×C4113yes—
402C4⋊Q8C23×C4113yes—
403C4⋊Q8C23×C4113yes—
404#127—23no—
405#127C23×C4113yes—
406#125—23no—
407#125—23no—
408#125—23no—
409#124—26no—
410#124—23no—
411C22⋊Q8—23no—
412C22⋊Q8—26no—
413C22⋊Q8—26no—
414C22⋊Q8C23×C4116yes—
415#121—23no—
416#121—23no—
417#121—23no—
418#121—26no—
419#121C23×C4116yes—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8—23no—
424C4×Q8—23no—
425C4×Q8—23no—
426C4×Q8D4×C4111yescharacteristic
427C4×Q8C23×C4111yescharacteristic
428C4×Q8C23×C4113yes—
429C4×Q8C23×C4113yes—
430C4×Q8C23×C4113yes—
431C4×Q8C23×C4111yescharacteristic
432C4×Q8C23×C4113yes—
433C4×Q8C23×C4111yescharacteristic
434C4×D4—23no—
435C4×D4—23no—
436C4×D4—23no—
437C4×D4—23no—
438C4×D4—23no—
439C4×D4—23no—
440C4×D4D4×C4113yes—
441C4×D4C23×C4113yes—
442C4×D4C23×C4113yes—
443C4×D4C23×C4113yes—
444#117—23no—
445#117—23no—
446#117—23no—
447#117D4×C4113yes—
448#117C23×C4113yes—
449C2×C4⋊C4—23no—
450C2×C4⋊C4C23×C4113yes—
451C2×C42—23no—
452C2×C42—23no—
453C2×C42C23×C4113yes—
454#107C23×C4113yes—
455#107C23×C4113yes—
456#107C23×C4116yes—
457#106C23×C4111yescharacteristic
458#106C23×C4113yes—
459C4⋊C8C23×C4113yes—
460C4⋊C8C23×C4113yes—
461#103C23×C4111yescharacteristic
462#103C23×C4113yes—
463#103C23×C4111yescharacteristic
464#103C23×C4113yes—
465#103C23×C4113yes—
466#103C23×C4113yes—
467#103C23×C4116yes—
468#102C23×C4113yes—
469#102C23×C4113yes—
470#102C23×C4116yes—
471C22⋊C8C23×C4116yes—
472#97C23×C4111yescharacteristic
473#97C23×C4113yes—
474C4×C8C23×C4113yes—
475C4×C8C23×C4113yes—
476#41—24no—
477#41—26no—
478#41—43no—
479#41—44no—
480#41—86no—
481C2×Q8—23no—
482C2×Q8—23no—
483C2×Q8—23no—
484C2×Q8—26no—
485C2×Q8—43no—
486C2×Q8C2×D4×C4111yescharacteristic
487C2×Q8C24×C4113yes—
488C2×Q8C24×C4111yescharacteristic
489C2×Q8C24×C4111yescharacteristic
490C2×D4—23no—
491C2×D4—26no—
492C2×D4—23no—
493C2×D4—23no—
494C2×D4C2×D4×C4113yes—
495C2×D4C24×C4113yes—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4—23no—
499C22×C4—23no—
500C22×C4—23no—
501C22×C4C2×D4×C4113yes—
502C22×C4C2×D4×C4113yes—
503C22×C4C24×C4113yes—
504Q16—26no—
505Q16#41×C4114yescomplemented
506SD16—26no—
507SD16—26no—
508SD16—46no—
509M16—26no—
510M16—43no—
511C2×C8C24×C4111yescharacteristic
512C2×C8C24×C4113yes—
513C2×C8C24×C4113yes—
514C2×C8C24×C4111yescharacteristic
515C4⋊C4—21no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—23no—
520C4⋊C4—21no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4—23no—
524C4⋊C4—23no—
525C4⋊C4—23no—
526C4⋊C4—26no—
527C4⋊C4C2×D4×C4113yes—
528C4⋊C4C2×D4×C4113yes—
529C4⋊C4C24×C4111yescharacteristic
530C4⋊C4C24×C4113yes—
531C4⋊C4C24×C4111yescharacteristic
532C4⋊C4C24×C4113yes—
533C22⋊C4—26no—
534C22⋊C4—23no—
535C22⋊C4—26no—
536C22⋊C4—23no—
537C22⋊C4—23no—
538C22⋊C4C2×D4×C4116yes—
539C42—21no—
540C42—21no—
541C42—23no—
542C42—23no—
543C42—23no—
544C42—23no—
545C42—23no—
546C42C2×D4×C4113yes—
547C42C2×D4×C4113yes—
548C42C24×C4113yes—
549C42C24×C4111yescharacteristic
550C23—23no—
551C23C22×D4×C4113yes—
552Q8—21no—
553Q8—21no—
554Q8—23no—
555Q8—23no—
556Q8—46no—
557Q8—83no—
558Q8—83no—
559Q8#137×C4114yescomplemented
560Q8C2×#41×C4112yes—
561Q8C2×#41×C4112yes—
562D4—26no—
563D4—23no—
564D4—23no—
565D4—46no—
566D4—46no—
567D4—83no—
568D4—86no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—26no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—43no—
580C2×C4—46no—
581C2×C4—46no—
582C2×C4—46no—
583C2×C4—46no—
584C2×C4—83no—
585C2×C4C22×D4×C4111yescharacteristic
586C2×C4C22×D4×C4111yescharacteristic
587C2×C4C22×D4×C4113yes—
588C2×C4C22×D4×C4113yes—
589C2×C4C22×D4×C4113yes—
590C2×C4C25×C4111yescharacteristic
591C8—23no—
592C8—21no—
593C8—23no—
594C8C2×#41×C4112yes—
595C22—23no—
596C22—23no—
597C22—23no—
598C22—43no—
599C22—43no—
600C22—43no—
601C22C23×D4×C4111yescharacteristic
602C4—21no—
603C4—21no—
604C4—23no—
605C4—23no—
606C4—22no—
607C4—22no—
608C4—41no—
609C4—43no—
610C4—41no—
611C4—43no—
612C4—43no—
613C4C2×#137×C4116yes—
614C4C22×#41×C4111yescharacteristic
615C4C41×#58511yescharacteristic
616C2—43no—
617C2—83no—
618C2D4×#41×C4111yescharacteristic
619C2C22×#137×C4111yescharacteristic
620C2C41×#358511yescharacteristic
subgroupG/H
center, socleC22×C41C23×D4
commutator, Frattini, cosocleC2×C4C25×C41
prime radicalC41×#3483C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C4×#41×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×#41×C41C2semidirect
3. C41×#3392C2semidirect
4. Q8×Q16×C41C2semidirect
5. C41×#3363C2semidirect
6. C41×#3362C2semidirect
7. C41×#3357C2semidirect
8. C41×#3333C2semidirect
9. C41×#3329C2semidirect
10. C41×#3278C2semidirect
11. C41×#3182C2semidirect
12. C41×#3116C2semidirect
13. C41×#3112C2semidirect
14. C41×#2971C2semidirect
15. C4×#137×C41C2semidirect
194. Q16×C41#41semidirect
248. Q8×C41#137semidirect
284. #61469C41direct (N × H)
307. Q8×#41C2×C41semidirect
308. #3392C2×C41semidirect
309. Q8×Q16C2×C41semidirect
310. #3363C2×C41semidirect
311. #3362C2×C41semidirect
312. #3357C2×C41semidirect
313. #3333C2×C41semidirect
314. #3329C2×C41semidirect
315. #3278C2×C41semidirect
316. #3182C2×C41semidirect
317. #3116C2×C41semidirect
318. #3112C2×C41semidirect
319. #2971C2×C41semidirect
320. C4×#137C2×C41semidirect
384. C41#61469direct (N × H)
505. Q16#41×C41semidirect
559. Q8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34832
Q8×#41×C412
C41×#33922
Q8×Q16×C412
C41×#33632
C41×#33622
C41×#33572
C41×#33332
C41×#33292
C41×#32782
C41×#31822
C41×#31162
C41×#31122
C41×#29712
C4×#137×C412
#6146941