Finite Group Databasebeta

← C41×#18955 #23795156

Subgroups — C41×#18955 #23795156

Order 10496.

938 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×#3546C211yesmaximal, characteristic
2C41×#3238C211yesmaximal, characteristic, complemented
3C41×#3227C211yesmaximal, characteristic, complemented
4C41×#3206C211yesmaximal, characteristic, complemented
5C41×#1638C212yesmaximal, complemented
6C41×#1635C212yesmaximal, complemented
7C41×#1631C212yesmaximal, complemented
8C41×#1629C212yesmaximal, complemented
9C41×#1553C211yesmaximal, characteristic, complemented
10C41×#1496C211yesmaximal, characteristic, complemented
11C41×#1482C211yesmaximal, characteristic, complemented
12C41×#560—22no—
13C41×#556C2211yescharacteristic
14C41×#553—21no—
15C41×#550—21no—
16C41×#550C2211yescharacteristic
17C41×#547C2211yescharacteristic
18C41×#546—21no—
19C41×#546—21no—
20D42×C41C2211yescharacteristic
21C41×#542—21no—
22C41×#538—22no—
23C41×#537—21no—
24C41×#535—21no—
25C41×#535—21no—
26C41×#532C2211yescharacteristic
27C41×#532C2211yescharacteristic
28C2×C4⋊Q8×C41C2211yescharacteristic, complemented
29C41×#529C2211yescharacteristic
30C41×#501—21no—
31C41×#498—21no—
32C41×#492C2212yes—
33C41×#489—21no—
34C41×#487C2212yescomplemented
35C41×#486—21no—
36C41×#483—21no—
37C41×#481—21no—
38C41×#481—21no—
39C41×#480—21no—
40C41×#477C2212yescomplemented
41C41×#476C2212yes—
42C41×#476C2212yes—
43C41×#476C2212yescomplemented
44C41×#461—22no—
45C41×#448—22no—
46C41×#432C2211yescharacteristic, complemented
47C41×#431C2211yescharacteristic, complemented
48C41×#431C2211yescharacteristic, complemented
49C41×#332C2212yescomplemented
50C41×#331C2212yes—
51C41×Q8⋊C8C2212yescomplemented
52C41×D4⋊C8C2212yes—
53C41×D4⋊C8C2212yes—
54C41×D4⋊C8C2212yescomplemented
55C2×#41×C41—21no—
56C2×#41×C41—21no—
57C2×#41×C41—21no—
58C2×#41×C41—21no—
59C22×Q8×C41—21no—
60C22×D4×C41—21no—
61C22×D4×C41—21no—
62C2×SD16×C41—24no—
63C4⋊Q8×C41—21no—
64C4⋊Q8×C41—21no—
65C4⋊Q8×C41—21no—
66C4⋊Q8×C41D411yescharacteristic
67C4⋊Q8×C41C2312yes—
68C4⋊Q8×C41C2311yescharacteristic
69#127×C41—22no—
70#127×C41—21no—
71#127×C41D411yescharacteristic
72#127×C41C2311yescharacteristic
73#126×C41—22no—
74#126×C41—22no—
75#126×C41—21no—
76#125×C41D411yescharacteristic
77#124×C41—22no—
78#124×C41—21no—
79#124×C41—21no—
80#124×C41—21no—
81#124×C41D411yescharacteristic
82#123×C41—22no—
83#123×C41—22no—
84#123×C41—21no—
85#123×C41—22no—
86C22⋊Q8×C41—22no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41D411yescharacteristic
90#121×C41—22no—
91#121×C41—22no—
92#121×C41—22no—
93#121×C41—22no—
94#121×C41—22no—
95#121×C41—21no—
96#121×C41—22no—
97#121×C41—21no—
98#121×C41—21no—
99#121×C41—21no—
100#121×C41—21no—
101#121×C41—21no—
102#121×C41D411yescharacteristic
103#121×C41D411yescharacteristic
104#121×C41D411yescharacteristic
105#121×C41D412yes—
106#120×C41—22no—
107#120×C41—22no—
108#120×C41—22no—
109#120×C41—22no—
110C4×Q8×C41—21no—
111C4×Q8×C41C2311yescharacteristic
112C4×D4×C41—22no—
113C4×D4×C41—21no—
114C4×D4×C41—21no—
115C4×D4×C41—21no—
116C4×D4×C41—21no—
117C4×D4×C41D412yes—
118C4×D4×C41C2311yescharacteristic
119C4×D4×C41C2311yescharacteristic
120C4×D4×C41C2311yescharacteristic
121#117×C41—21no—
122#117×C41—21no—
123C2×C4⋊C4×C41—21no—
124C2×C4⋊C4×C41—21no—
125C2×C4⋊C4×C41—21no—
126C2×C22⋊C4×C41—22no—
127C2×C42×C41C2311yescharacteristic
128#107×C41—22no—
129#106×C41—22no—
130#106×C41—22no—
131#106×C41—22no—
132C4⋊C8×C41—21no—
133C4⋊C8×C41C2312yes—
134C4⋊C8×C41C2312yes—
135#103×C41—22no—
136#103×C41—24no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140C22⋊C8×C41—21no—
141C22⋊C8×C41—21no—
142C22⋊C8×C41—21no—
143#97×C41—21no—
144C4×C8×C41—21no—
145C4×C8×C41C2312yes—
146C24×C41—22no—
147#41×C41—82no—
148#41×C41—82no—
149#41×C41—82no—
150#41×C41—82no—
151C2×Q8×C41—21no—
152C2×Q8×C41—21no—
153C2×Q8×C41—22no—
154C2×Q8×C41—41no—
155C2×Q8×C41—82no—
156C2×Q8×C41C2×D411yescharacteristic
157C2×D4×C41—22no—
158C2×D4×C41—22no—
159C2×D4×C41—22no—
160C2×D4×C41—22no—
161C2×D4×C41—22no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—22no—
165C2×D4×C41—21no—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—82no—
171C2×D4×C41—82no—
172C2×D4×C41C2×D411yescharacteristic
173C2×D4×C41C2×D411yescharacteristic
174C2×D4×C41C2×D411yescharacteristic
175C2×D4×C41C2×D412yes—
176C22×C4×C41—22no—
177C22×C4×C41—22no—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—22no—
182C22×C4×C41—41no—
183C22×C4×C41C2×D411yescharacteristic
184C22×C4×C41C2×D411yescharacteristic
185C22×C4×C41C2×D411yescharacteristic
186SD16×C41—84no—
187C2×C8×C41—22no—
188C2×C8×C41—22no—
189C2×C8×C41—22no—
190C4⋊C4×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—22no—
199C4⋊C4×C41—22no—
200C4⋊C4×C41—41no—
201C4⋊C4×C41—41no—
202C4⋊C4×C41C2×D412yes—
203C4⋊C4×C41C2×D411yescharacteristic
204C4⋊C4×C41C2×D411yescharacteristic
205C4⋊C4×C41C2×D411yescharacteristic
206C4⋊C4×C41C2×D411yescharacteristic
207C22⋊C4×C41—22no—
208C22⋊C4×C41—22no—
209C22⋊C4×C41—22no—
210C22⋊C4×C41—22no—
211C22⋊C4×C41—22no—
212C22⋊C4×C41—21no—
213C22⋊C4×C41—21no—
214C22⋊C4×C41—21no—
215C22⋊C4×C41—21no—
216C22⋊C4×C41—21no—
217C22⋊C4×C41—21no—
218C22⋊C4×C41—22no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—21no—
221C22⋊C4×C41—21no—
222C22⋊C4×C41—21no—
223C42×C41—22no—
224C42×C41—21no—
225C42×C41C2×D411yescharacteristic
226C42×C41C2×D411yescharacteristic
227C42×C41C2×D411yescharacteristic
228C42×C41C2411yescharacteristic
229C23×C41—21no—
230C23×C41—21no—
231C23×C41—22no—
232C23×C41—21no—
233C23×C41—82no—
234C23×C41—82no—
235C23×C41—82no—
236C23×C41#12011yescharacteristic
237Q8×C41—22no—
238Q8×C41—44no—
239Q8×C41—42no—
240Q8×C41—81no—
241Q8×C41—82no—
242D4×C41—22no—
243D4×C41—22no—
244D4×C41—22no—
245D4×C41—42no—
246D4×C41—42no—
247D4×C41—42no—
248D4×C41—81no—
249D4×C41—81no—
250D4×C41—81no—
251D4×C41—81no—
252D4×C41—81no—
253D4×C41—82no—
254D4×C41—82no—
255D4×C41—82no—
256D4×C41—82no—
257D4×C41—82no—
258D4×C41—82no—
259C2×C4×C41—22no—
260C2×C4×C41—22no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—22no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—41no—
268C2×C4×C41—42no—
269C2×C4×C41—42no—
270C2×C4×C41—42no—
271C2×C4×C41—42no—
272C2×C4×C41—82no—
273C2×C4×C41—82no—
274C2×C4×C41—82no—
275C2×C4×C41—82no—
276C2×C4×C41#12011yescharacteristic
277C2×C4×C41#12011yescharacteristic
278C2×C4×C41#12011yescharacteristic
279C2×C4×C41C22×D411yescharacteristic
280C2×C4×C41C22×D411yescharacteristic
281C2×C4×C41C22×D411yescharacteristic
282C8×C41—42no—
283C8×C41—42no—
284C8×C41—42no—
285#18955C4111yesmaximal, characteristic, direct product factor, Sylow
286C22×C41—21no—
287C22×C41—21no—
288C22×C41—21no—
289C22×C41—41no—
290C22×C41—41no—
291C22×C41—41no—
292C22×C41—41no—
293C22×C41—42no—
294C22×C41—42no—
295C22×C41—41no—
296C22×C41—41no—
297C22×C41—42no—
298C22×C41—41no—
299C22×C41—41no—
300C22×C41—41no—
301C22×C41—164no—
302C22×C41C2×#12011yescharacteristic
303C4×C41—21no—
304C4×C41—21no—
305C4×C41—21no—
306C4×C41—21no—
307C4×C41—41no—
308C4×C41—41no—
309C4×C41—41no—
310C4×C41—41no—
311C4×C41—42no—
312C4×C41—41no—
313C4×C41—82no—
314C4×C41#57712yes—
315C4×C41#57712yes—
316#3546C2×C4111yescharacteristic
317#3238C2×C4111yescharacteristic, complemented
318#3227C2×C4111yescharacteristic, complemented
319#3206C2×C4111yescharacteristic, complemented
320#1638C2×C4112yescomplemented
321#1635C2×C4112yescomplemented
322#1631C2×C4112yescomplemented
323#1629C2×C4112yescomplemented
324#1553C2×C4111yescharacteristic, complemented
325#1496C2×C4111yescharacteristic, complemented
326#1482C2×C4111yescharacteristic, complemented
327C2×C41—41no—
328C2×C41—81no—
329C2×C41—82no—
330C2×C41—81no—
331C2×C41—81no—
332C2×C41#300911yescharacteristic
333C2×C41#300911yescharacteristic
334C2×C41#302111yescharacteristic
335#560—22no—
336#556C22×C4111yescharacteristic
337#553—21no—
338#550—21no—
339#550C22×C4111yescharacteristic
340#547C22×C4111yescharacteristic
341#546—21no—
342#546—21no—
343D42C22×C4111yescharacteristic
344#542—21no—
345#538—22no—
346#537—21no—
347#535—21no—
348#535—21no—
349#532C22×C4111yescharacteristic
350#532C22×C4111yescharacteristic
351C2×C4⋊Q8C22×C4111yescharacteristic, complemented
352#529C22×C4111yescharacteristic
353#501—21no—
354#498—21no—
355#492C22×C4112yes—
356#489—21no—
357#487C22×C4112yescomplemented
358#486—21no—
359#483—21no—
360#481—21no—
361#481—21no—
362#480—21no—
363#477C22×C4112yescomplemented
364#476C22×C4112yes—
365#476C22×C4112yes—
366#476C22×C4112yescomplemented
367#461—22no—
368#448—22no—
369#432C22×C4111yescharacteristic, complemented
370#431C22×C4111yescharacteristic, complemented
371#431C22×C4111yescharacteristic, complemented
372#332C22×C4112yescomplemented
373#331C22×C4112yes—
374Q8⋊C8C22×C4112yescomplemented
375D4⋊C8C22×C4112yes—
376D4⋊C8C22×C4112yes—
377D4⋊C8C22×C4112yescomplemented
378C41#1895511yescharacteristic, direct product factor, Sylow
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C22×Q8—21no—
384C22×D4—21no—
385C22×D4—21no—
386C2×SD16—24no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C4111yescharacteristic
391C4⋊Q8C23×C4112yes—
392C4⋊Q8C23×C4111yescharacteristic
393#127—22no—
394#127—21no—
395#127D4×C4111yescharacteristic
396#127C23×C4111yescharacteristic
397#126—22no—
398#126—22no—
399#126—21no—
400#125D4×C4111yescharacteristic
401#124—22no—
402#124—21no—
403#124—21no—
404#124—21no—
405#124D4×C4111yescharacteristic
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8D4×C4111yescharacteristic
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—22no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121D4×C4111yescharacteristic
427#121D4×C4111yescharacteristic
428#121D4×C4111yescharacteristic
429#121D4×C4112yes—
430#120—22no—
431#120—22no—
432#120—22no—
433#120—22no—
434C4×Q8—21no—
435C4×Q8C23×C4111yescharacteristic
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4D4×C4112yes—
442C4×D4C23×C4111yescharacteristic
443C4×D4C23×C4111yescharacteristic
444C4×D4C23×C4111yescharacteristic
445#117—21no—
446#117—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C42C23×C4111yescharacteristic
452#107—22no—
453#106—22no—
454#106—22no—
455#106—22no—
456C4⋊C8—21no—
457C4⋊C8C23×C4112yes—
458C4⋊C8C23×C4112yes—
459#103—22no—
460#103—24no—
461#102—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—21no—
467#97—21no—
468C4×C8—21no—
469C4×C8C23×C4112yes—
470C24—22no—
471#41—82no—
472#41—82no—
473#41—82no—
474#41—82no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—41no—
479C2×Q8—82no—
480C2×Q8C2×D4×C4111yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4C2×D4×C4111yescharacteristic
497C2×D4C2×D4×C4111yescharacteristic
498C2×D4C2×D4×C4111yescharacteristic
499C2×D4C2×D4×C4112yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—41no—
507C22×C4C2×D4×C4111yescharacteristic
508C22×C4C2×D4×C4111yescharacteristic
509C22×C4C2×D4×C4111yescharacteristic
510SD16—84no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4C2×D4×C4112yes—
527C4⋊C4C2×D4×C4111yescharacteristic
528C4⋊C4C2×D4×C4111yescharacteristic
529C4⋊C4C2×D4×C4111yescharacteristic
530C4⋊C4C2×D4×C4111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C42—22no—
548C42—21no—
549C42C2×D4×C4111yescharacteristic
550C42C2×D4×C4111yescharacteristic
551C42C2×D4×C4111yescharacteristic
552C42C24×C4111yescharacteristic
553C23—21no—
554C23—21no—
555C23—22no—
556C23—21no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23#120×C4111yescharacteristic
561Q8—22no—
562Q8—44no—
563Q8—42no—
564Q8—81no—
565Q8—82no—
566D4—22no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—81no—
576D4—82no—
577D4—81no—
578D4—82no—
579D4—82no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4#120×C4111yescharacteristic
601C2×C4#120×C4111yescharacteristic
602C2×C4#120×C4111yescharacteristic
603C2×C4C22×D4×C4111yescharacteristic
604C2×C4C22×D4×C4111yescharacteristic
605C2×C4C22×D4×C4111yescharacteristic
606C8—42no—
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—164no—
625C22C2×#120×C4111yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—82no—
637C4C41×#57712yes—
638C4C41×#57712yes—
639C2—41no—
640C2—81no—
641C2—81no—
642C2—82no—
643C2—81no—
644C2C41×#300911yescharacteristic
645C2C41×#300911yescharacteristic
646C2C41×#302111yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#3546C2
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×#3238C2semidirect
3. C41×#3227C2semidirect
4. C41×#3206C2semidirect
5. C41×#1638C2semidirect
6. C41×#1635C2semidirect
7. C41×#1631C2semidirect
8. C41×#1629C2semidirect
9. C41×#1553C2semidirect
10. C41×#1496C2semidirect
11. C41×#1482C2semidirect
28. C2×C4⋊Q8×C41C22semidirect
34. C41×#487C22semidirect
40. C41×#477C22semidirect
43. C41×#476C22semidirect
46. C41×#432C22semidirect
47. C41×#431C22semidirect
48. C41×#431C22semidirect
49. C41×#332C22semidirect
51. C41×Q8⋊C8C22semidirect
54. C41×D4⋊C8C22semidirect
285. #18955C41direct (N × H)
317. #3238C2×C41semidirect
318. #3227C2×C41semidirect
319. #3206C2×C41semidirect
320. #1638C2×C41semidirect
321. #1635C2×C41semidirect
322. #1631C2×C41semidirect
323. #1629C2×C41semidirect
324. #1553C2×C41semidirect
325. #1496C2×C41semidirect
326. #1482C2×C41semidirect
351. C2×C4⋊Q8C22×C41semidirect
357. #487C22×C41semidirect
363. #477C22×C41semidirect
366. #476C22×C41semidirect
369. #432C22×C41semidirect
370. #431C22×C41semidirect
371. #431C22×C41semidirect
372. #332C22×C41semidirect
374. Q8⋊C8C22×C41semidirect
377. D4⋊C8C22×C41semidirect
378. C41#18955direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35462
C41×#32382
C41×#32272
C41×#32062
C41×#16382
C41×#16352
C41×#16312
C41×#16292
C41×#15532
C41×#14962
C41×#14822
#1895541