Finite Group Databasebeta

← C41×#61470 #23837671

Subgroups — C41×#61470 #23837671

Order 10496.

1812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3482C211yesmaximal, characteristic
2Q8×#41×C41C211yesmaximal, characteristic, complemented
3C41×#3395C211yesmaximal, characteristic, complemented
4Q8×SD16×C41C211yesmaximal, characteristic, complemented
5C41×#3363C211yesmaximal, characteristic, complemented
6C41×#3359C211yesmaximal, characteristic, complemented
7C41×#3356C213yesmaximal, complemented
8C41×#3331C213yesmaximal, complemented
9C41×#3328C213yesmaximal, complemented
10C41×#3276C213yesmaximal, complemented
11C41×#3185C213yesmaximal, complemented
12C41×#3116C213yesmaximal, complemented
13C41×#3113C213yesmaximal, complemented
14C41×#2971C211yesmaximal, characteristic, complemented
15C4×#137×C41C213yesmaximal, complemented
16C2×#137×C41C2213yes—
17Q82×C41C2211yescharacteristic
18C41×#557—21no—
19C41×#557C2211yescharacteristic
20C41×#557C2211yescharacteristic
21C41×#556C2213yes—
22C41×#554—23no—
23C41×#554C2213yes—
24C41×#552—23no—
25D4×Q8×C41C2213yes—
26D4×Q8×C41C2211yescharacteristic
27C41×#548—21no—
28C41×#547C2213yes—
29C41×#533—23no—
30C41×#533C2213yes—
31C41×#533C2213yes—
32C41×#529—23no—
33C4×#41×C41—21no—
34C4×#41×C41C2213yes—
35C4×#41×C41C2211yescharacteristic
36C2×C4×Q8×C41—21no—
37C2×C4×Q8×C41C2213yes—
38C41×#498C2213yes—
39C41×#494C2213yes—
40C41×#487C2213yes—
41C41×#487C2213yes—
42C41×#485C2216yes—
43C41×#483C2216yes—
44C41×#477C2213yes—
45C41×#476C2213yes—
46C41×#475C2213yes—
47C41×#475C2213yes—
48C41×#470C2216yes—
49C41×#470C2216yes—
50C41×#462C2213yes—
51C41×#462C2213yes—
52C41×#462C2213yes—
53C41×#461C2213yes—
54C41×#452C2216yes—
55C41×#451C2216yes—
56C8×Q8×C41C2211yescharacteristic
57C8×Q8×C41C2211yescharacteristic
58C41×#441C2213yes—
59C41×#441C2216yes—
60C41×#441C2213yes—
61C41×#440C2213yes—
62C41×#440C2211yescharacteristic
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×C41D411yescharacteristic
75C2×#41×C41C2313yes—
76C22×Q8×C41—21no—
77C22×Q8×C41C2313yes—
78#137×C41—212no—
79C2×Q16×C41C2313yes—
80C2×Q16×C41C2313yes—
81C2×Q16×C41C2316yes—
82C2×SD16×C41C2313yes—
83C2×SD16×C41C2311yescharacteristic
84C2×M16×C41C2313yes—
85C2×M16×C41C2313yes—
86C4⋊Q8×C41—23no—
87C4⋊Q8×C41—23no—
88C4⋊Q8×C41C2313yes—
89C4⋊Q8×C41C2313yes—
90C4⋊Q8×C41C2313yes—
91C4⋊Q8×C41C2313yes—
92#126×C41—26no—
93#125×C41—23no—
94#125×C41—23no—
95#125×C41—23no—
96#125×C41—23no—
97#125×C41—23no—
98#124×C41—23no—
99#123×C41—26no—
100C22⋊Q8×C41—23no—
101C22⋊Q8×C41—23no—
102C22⋊Q8×C41—23no—
103C22⋊Q8×C41—26no—
104C22⋊Q8×C41—26no—
105C22⋊Q8×C41C2316yes—
106C22⋊Q8×C41C2316yes—
107#121×C41—23no—
108C4×Q8×C41—21no—
109C4×Q8×C41—21no—
110C4×Q8×C41—21no—
111C4×Q8×C41—23no—
112C4×Q8×C41—23no—
113C4×Q8×C41—23no—
114C4×Q8×C41—23no—
115C4×Q8×C41—23no—
116C4×Q8×C41D411yescharacteristic
117C4×Q8×C41C2311yescharacteristic
118C4×Q8×C41C2313yes—
119C4×Q8×C41C2313yes—
120C4×Q8×C41C2313yes—
121C4×Q8×C41C2313yes—
122C4×Q8×C41C2313yes—
123C4×Q8×C41C2311yescharacteristic
124C4×D4×C41—23no—
125C4×D4×C41—23no—
126C4×D4×C41—23no—
127C4×D4×C41—23no—
128C4×D4×C41D413yes—
129C4×D4×C41C2311yescharacteristic
130C4×D4×C41C2313yes—
131C4×D4×C41C2313yes—
132#117×C41—23no—
133#117×C41—23no—
134#117×C41—23no—
135#117×C41D413yes—
136#117×C41C2313yes—
137C2×C4⋊C4×C41—23no—
138C2×C4⋊C4×C41—23no—
139C2×C4⋊C4×C41C2313yes—
140C2×C42×C41—23no—
141C2×C42×C41—23no—
142C2×C42×C41C2313yes—
143#107×C41C2311yescharacteristic
144#107×C41C2313yes—
145#106×C41C2313yes—
146#106×C41C2313yes—
147#106×C41C2316yes—
148C4⋊C8×C41C2313yes—
149C4⋊C8×C41C2313yes—
150#103×C41C2313yes—
151#103×C41C2313yes—
152#103×C41C2311yescharacteristic
153#103×C41C2313yes—
154#103×C41C2313yes—
155#103×C41C2313yes—
156#103×C41C2316yes—
157#103×C41C2316yes—
158#102×C41C2311yescharacteristic
159#102×C41C2313yes—
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—
168C2×Q8×C41—23no—
169C2×Q8×C41—23no—
170C2×Q8×C41—23no—
171C2×Q8×C41—26no—
172C2×Q8×C41—43no—
173C2×Q8×C41—44no—
174C2×Q8×C41C2×D411yescharacteristic
175C2×Q8×C41C2413yes—
176C2×Q8×C41C2413yes—
177C2×Q8×C41C2411yescharacteristic
178C2×D4×C41—23no—
179C2×D4×C41C2×D413yes—
180C2×D4×C41C2411yescharacteristic
181C22×C4×C41—23no—
182C22×C4×C41—23no—
183C22×C4×C41—21no—
184C22×C4×C41—23no—
185C22×C4×C41—23no—
186C22×C4×C41C2×D413yes—
187C22×C4×C41C2×D413yes—
188C22×C4×C41C2413yes—
189Q16×C41—26no—
190Q16×C41—26no—
191Q16×C41—46no—
192SD16×C41—26no—
193SD16×C41#4114yescomplemented
194M16×C41—26no—
195M16×C41—43no—
196C2×C8×C41C2411yescharacteristic
197C2×C8×C41C2413yes—
198C2×C8×C41C2413yes—
199C2×C8×C41C2411yescharacteristic
200C4⋊C4×C41—21no—
201C4⋊C4×C41—23no—
202C4⋊C4×C41—26no—
203C4⋊C4×C41—23no—
204C4⋊C4×C41—23no—
205C4⋊C4×C41—23no—
206C4⋊C4×C41—23no—
207C4⋊C4×C41—23no—
208C4⋊C4×C41—23no—
209C4⋊C4×C41—23no—
210C4⋊C4×C41—23no—
211C4⋊C4×C41—23no—
212C4⋊C4×C41—23no—
213C4⋊C4×C41—23no—
214C4⋊C4×C41—26no—
215C4⋊C4×C41C2×D413yes—
216C4⋊C4×C41C2×D413yes—
217C4⋊C4×C41C2411yescharacteristic
218C4⋊C4×C41C2413yes—
219C4⋊C4×C41C2413yes—
220C4⋊C4×C41C2411yescharacteristic
221C22⋊C4×C41—26no—
222C22⋊C4×C41—26no—
223C22⋊C4×C41—23no—
224C22⋊C4×C41—21no—
225C22⋊C4×C41—23no—
226C22⋊C4×C41C2×D416yes—
227C42×C41—21no—
228C42×C41—23no—
229C42×C41—23no—
230C42×C41—23no—
231C42×C41—23no—
232C42×C41—23no—
233C42×C41—23no—
234C42×C41C2×D413yes—
235C42×C41C2×D413yes—
236C42×C41C2413yes—
237C42×C41C2411yescharacteristic
238C23×C41—21no—
239C23×C41C22×D413yes—
240Q8×C41—21no—
241Q8×C41—23no—
242Q8×C41—23no—
243Q8×C41—23no—
244Q8×C41—23no—
245Q8×C41—46no—
246Q8×C41—46no—
247Q8×C41—83no—
248Q8×C41#13714yescomplemented
249Q8×C41C2×#4112yes—
250D4×C41—26no—
251D4×C41—21no—
252D4×C41—46no—
253D4×C41C2×#4112yes—
254C2×C4×C41—21no—
255C2×C4×C41—26no—
256C2×C4×C41—23no—
257C2×C4×C41—23no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—23no—
261C2×C4×C41—23no—
262C2×C4×C41—23no—
263C2×C4×C41—23no—
264C2×C4×C41—43no—
265C2×C4×C41—46no—
266C2×C4×C41—46no—
267C2×C4×C41—42no—
268C2×C4×C41—46no—
269C2×C4×C41—83no—
270C2×C4×C41C22×D411yescharacteristic
271C2×C4×C41C22×D411yescharacteristic
272C2×C4×C41C22×D413yes—
273C2×C4×C41C22×D413yes—
274C2×C4×C41C22×D413yes—
275C2×C4×C41C2511yescharacteristic
276C8×C41—23no—
277C8×C41—21no—
278C8×C41—23no—
279C8×C41C2×#4112yes—
280#61470C4111yesmaximal, characteristic, direct product factor, Sylow
281C22×C41—23no—
282C22×C41—23no—
283C22×C41—22no—
284C22×C41—23no—
285C22×C41—41no—
286C22×C41—41no—
287C22×C41C23×D411yescharacteristic
288C4×C41—21no—
289C4×C41—23no—
290C4×C41—23no—
291C4×C41—22no—
292C4×C41—21no—
293C4×C41—41no—
294C4×C41—41no—
295C4×C41—43no—
296C4×C41—43no—
297C4×C41—43no—
298C4×C41—43no—
299C4×C41C2×#13716yes—
300C4×C41C22×#4111yescharacteristic
301C4×C41#58511yescharacteristic
302#3482C2×C4111yescharacteristic
303Q8×#41C2×C4111yescharacteristic, complemented
304#3395C2×C4111yescharacteristic, complemented
305Q8×SD16C2×C4111yescharacteristic, complemented
306#3363C2×C4111yescharacteristic, complemented
307#3359C2×C4111yescharacteristic, complemented
308#3356C2×C4113yescomplemented
309#3331C2×C4113yescomplemented
310#3328C2×C4113yescomplemented
311#3276C2×C4113yescomplemented
312#3185C2×C4113yescomplemented
313#3116C2×C4113yescomplemented
314#3113C2×C4113yescomplemented
315#2971C2×C4111yescharacteristic, complemented
316C4×#137C2×C4113yescomplemented
317C2×C41—43no—
318C2×C41—42no—
319C2×C41D4×#4111yescharacteristic
320C2×C41C22×#13711yescharacteristic
321C2×C41#358611yescharacteristic
322C2×#137C22×C4113yes—
323Q82C22×C4111yescharacteristic
324#557—21no—
325#557C22×C4111yescharacteristic
326#557C22×C4111yescharacteristic
327#556C22×C4113yes—
328#554—23no—
329#554C22×C4113yes—
330#552—23no—
331D4×Q8C22×C4113yes—
332D4×Q8C22×C4111yescharacteristic
333#548—21no—
334#547C22×C4113yes—
335#533—23no—
336#533C22×C4113yes—
337#533C22×C4113yes—
338#529—23no—
339C4×#41—21no—
340C4×#41C22×C4113yes—
341C4×#41C22×C4111yescharacteristic
342C2×C4×Q8—21no—
343C2×C4×Q8C22×C4113yes—
344#498C22×C4113yes—
345#494C22×C4113yes—
346#487C22×C4113yes—
347#487C22×C4113yes—
348#485C22×C4116yes—
349#483C22×C4116yes—
350#477C22×C4113yes—
351#476C22×C4113yes—
352#475C22×C4113yes—
353#475C22×C4113yes—
354#470C22×C4116yes—
355#470C22×C4116yes—
356#462C22×C4113yes—
357#462C22×C4113yes—
358#462C22×C4113yes—
359#461C22×C4113yes—
360#452C22×C4116yes—
361#451C22×C4116yes—
362C8×Q8C22×C4111yescharacteristic
363C8×Q8C22×C4111yescharacteristic
364#441C22×C4113yes—
365#441C22×C4116yes—
366#441C22×C4113yes—
367#440C22×C4113yes—
368#440C22×C4111yescharacteristic
369C4×Q16C22×C4113yes—
370C4×Q16C22×C4113yes—
371C4×SD16C22×C4113yes—
372C4×SD16C22×C4113yes—
373#436C22×C4113yes—
374#436C22×C4113yes—
375#432C22×C4113yes—
376#428C22×C4113yes—
377#419C22×C4113yes—
378#417C22×C4113yes—
379C4×M16C22×C4113yes—
380C41#6147011yescharacteristic, direct product factor, Sylow
381C2×#41D4×C4111yescharacteristic
382C2×#41C23×C4113yes—
383C22×Q8—21no—
384C22×Q8C23×C4113yes—
385#137—212no—
386C2×Q16C23×C4113yes—
387C2×Q16C23×C4113yes—
388C2×Q16C23×C4116yes—
389C2×SD16C23×C4113yes—
390C2×SD16C23×C4111yescharacteristic
391C2×M16C23×C4113yes—
392C2×M16C23×C4113yes—
393C4⋊Q8—23no—
394C4⋊Q8—23no—
395C4⋊Q8C23×C4113yes—
396C4⋊Q8C23×C4113yes—
397C4⋊Q8C23×C4113yes—
398C4⋊Q8C23×C4113yes—
399#126—26no—
400#125—23no—
401#125—23no—
402#125—23no—
403#125—23no—
404#125—23no—
405#124—23no—
406#123—26no—
407C22⋊Q8—23no—
408C22⋊Q8—23no—
409C22⋊Q8—23no—
410C22⋊Q8—26no—
411C22⋊Q8—26no—
412C22⋊Q8C23×C4116yes—
413C22⋊Q8C23×C4116yes—
414#121—23no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—23no—
419C4×Q8—23no—
420C4×Q8—23no—
421C4×Q8—23no—
422C4×Q8—23no—
423C4×Q8D4×C4111yescharacteristic
424C4×Q8C23×C4111yescharacteristic
425C4×Q8C23×C4113yes—
426C4×Q8C23×C4113yes—
427C4×Q8C23×C4113yes—
428C4×Q8C23×C4113yes—
429C4×Q8C23×C4113yes—
430C4×Q8C23×C4111yescharacteristic
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4D4×C4113yes—
436C4×D4C23×C4111yescharacteristic
437C4×D4C23×C4113yes—
438C4×D4C23×C4113yes—
439#117—23no—
440#117—23no—
441#117—23no—
442#117D4×C4113yes—
443#117C23×C4113yes—
444C2×C4⋊C4—23no—
445C2×C4⋊C4—23no—
446C2×C4⋊C4C23×C4113yes—
447C2×C42—23no—
448C2×C42—23no—
449C2×C42C23×C4113yes—
450#107C23×C4111yescharacteristic
451#107C23×C4113yes—
452#106C23×C4113yes—
453#106C23×C4113yes—
454#106C23×C4116yes—
455C4⋊C8C23×C4113yes—
456C4⋊C8C23×C4113yes—
457#103C23×C4113yes—
458#103C23×C4113yes—
459#103C23×C4111yescharacteristic
460#103C23×C4113yes—
461#103C23×C4113yes—
462#103C23×C4113yes—
463#103C23×C4116yes—
464#103C23×C4116yes—
465#102C23×C4111yescharacteristic
466#102C23×C4113yes—
467C22⋊C8C23×C4116yes—
468#97C23×C4111yescharacteristic
469#97C23×C4113yes—
470C4×C8C23×C4113yes—
471C4×C8C23×C4113yes—
472#41—24no—
473#41—26no—
474#41—43no—
475C2×Q8—23no—
476C2×Q8—23no—
477C2×Q8—23no—
478C2×Q8—26no—
479C2×Q8—43no—
480C2×Q8—44no—
481C2×Q8C2×D4×C4111yescharacteristic
482C2×Q8C24×C4113yes—
483C2×Q8C24×C4113yes—
484C2×Q8C24×C4111yescharacteristic
485C2×D4—23no—
486C2×D4C2×D4×C4113yes—
487C2×D4C24×C4111yescharacteristic
488C22×C4—23no—
489C22×C4—23no—
490C22×C4—21no—
491C22×C4—23no—
492C22×C4—23no—
493C22×C4C2×D4×C4113yes—
494C22×C4C2×D4×C4113yes—
495C22×C4C24×C4113yes—
496Q16—26no—
497Q16—26no—
498Q16—46no—
499SD16—26no—
500SD16#41×C4114yescomplemented
501M16—26no—
502M16—43no—
503C2×C8C24×C4111yescharacteristic
504C2×C8C24×C4113yes—
505C2×C8C24×C4113yes—
506C2×C8C24×C4111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—23no—
509C4⋊C4—26no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—23no—
520C4⋊C4—23no—
521C4⋊C4—26no—
522C4⋊C4C2×D4×C4113yes—
523C4⋊C4C2×D4×C4113yes—
524C4⋊C4C24×C4111yescharacteristic
525C4⋊C4C24×C4113yes—
526C4⋊C4C24×C4113yes—
527C4⋊C4C24×C4111yescharacteristic
528C22⋊C4—26no—
529C22⋊C4—26no—
530C22⋊C4—23no—
531C22⋊C4—21no—
532C22⋊C4—23no—
533C22⋊C4C2×D4×C4116yes—
534C42—21no—
535C42—23no—
536C42—23no—
537C42—23no—
538C42—23no—
539C42—23no—
540C42—23no—
541C42C2×D4×C4113yes—
542C42C2×D4×C4113yes—
543C42C24×C4113yes—
544C42C24×C4111yescharacteristic
545C23—21no—
546C23C22×D4×C4113yes—
547Q8—21no—
548Q8—23no—
549Q8—23no—
550Q8—23no—
551Q8—23no—
552Q8—46no—
553Q8—46no—
554Q8—83no—
555Q8#137×C4114yescomplemented
556Q8C2×#41×C4112yes—
557D4—26no—
558D4—21no—
559D4—46no—
560D4C2×#41×C4112yes—
561C2×C4—21no—
562C2×C4—26no—
563C2×C4—23no—
564C2×C4—23no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—23no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—23no—
571C2×C4—43no—
572C2×C4—46no—
573C2×C4—46no—
574C2×C4—42no—
575C2×C4—46no—
576C2×C4—83no—
577C2×C4C22×D4×C4111yescharacteristic
578C2×C4C22×D4×C4111yescharacteristic
579C2×C4C22×D4×C4113yes—
580C2×C4C22×D4×C4113yes—
581C2×C4C22×D4×C4113yes—
582C2×C4C25×C4111yescharacteristic
583C8—23no—
584C8—21no—
585C8—23no—
586C8C2×#41×C4112yes—
587C22—23no—
588C22—23no—
589C22—23no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22C23×D4×C4111yescharacteristic
594C4—21no—
595C4—21no—
596C4—23no—
597C4—23no—
598C4—22no—
599C4—43no—
600C4—41no—
601C4—41no—
602C4—43no—
603C4—43no—
604C4—43no—
605C4C2×#137×C4116yes—
606C4C22×#41×C4111yescharacteristic
607C4C41×#58511yescharacteristic
608C2—43no—
609C2—42no—
610C2D4×#41×C4111yescharacteristic
611C2C22×#137×C4111yescharacteristic
612C2C41×#358611yescharacteristic
subgroupG/H
center, socleC22×C41C23×D4
commutator, Frattini, cosocleC2×C4C25×C41
prime radicalC41×#3482C2
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×#3395C2semidirect
4. Q8×SD16×C41C2semidirect
5. C41×#3363C2semidirect
6. C41×#3359C2semidirect
7. C41×#3356C2semidirect
8. C41×#3331C2semidirect
9. C41×#3328C2semidirect
10. C41×#3276C2semidirect
11. C41×#3185C2semidirect
12. C41×#3116C2semidirect
13. C41×#3113C2semidirect
14. C41×#2971C2semidirect
15. C4×#137×C41C2semidirect
193. SD16×C41#41semidirect
248. Q8×C41#137semidirect
280. #61470C41direct (N × H)
303. Q8×#41C2×C41semidirect
304. #3395C2×C41semidirect
305. Q8×SD16C2×C41semidirect
306. #3363C2×C41semidirect
307. #3359C2×C41semidirect
308. #3356C2×C41semidirect
309. #3331C2×C41semidirect
310. #3328C2×C41semidirect
311. #3276C2×C41semidirect
312. #3185C2×C41semidirect
313. #3116C2×C41semidirect
314. #3113C2×C41semidirect
315. #2971C2×C41semidirect
316. C4×#137C2×C41semidirect
380. C41#61470direct (N × H)
500. SD16#41×C41semidirect
555. Q8#137×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34822
Q8×#41×C412
C41×#33952
Q8×SD16×C412
C41×#33632
C41×#33592
C41×#33562
C41×#33312
C41×#33282
C41×#32762
C41×#31852
C41×#31162
C41×#31132
C41×#29712
C4×#137×C412
#6147041