Finite Group Databasebeta

← C41×#18290 #23794491

Subgroups — C41×#18290 #23794491

Order 10496.

1034 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3459C211yesmaximal, characteristic, complemented
2C41×#3188C212yesmaximal, complemented
3C41×#2635C211yesmaximal, characteristic, complemented
4C41×#1615C212yesmaximal, complemented
5C41×#1614C211yesmaximal, characteristic, complemented
6C41×#1613C211yesmaximal, characteristic, complemented
7C41×#1597C212yesmaximal, complemented
8C41×#1596C211yesmaximal, characteristic, complemented
9C41×#1595C211yesmaximal, characteristic, complemented
10C41×#1516C212yesmaximal, complemented
11C41×#1459C211yesmaximal, characteristic, complemented
12C41×#543C2211yescharacteristic
13C41×#539—22no—
14C41×#539C2212yes—
15C41×#538—22no—
16C41×#538—21no—
17C41×#534—21no—
18C41×#534C2211yescharacteristic
19C41×#529—22no—
20C41×#529—21no—
21C41×#525—22no—
22C41×#525C2212yes—
23C2×#121×C41C2211yescharacteristic, complemented
24C2×C4×D4×C41—21no—
25C2×C4×D4×C41C2211yescharacteristic
26C41×#484C2212yescomplemented
27C41×#482—22no—
28C41×#481C2212yes—
29C41×#466—22no—
30C41×#465—22no—
31C41×#450C2212yescomplemented
32C41×#449—22no—
33C41×#447C2212yes—
34C2×C22⋊C8×C41C2212yescomplemented
35C41×#400C2211yescharacteristic, complemented
36C41×#399C2211yescharacteristic
37C41×#394—21no—
38C41×#394C2211yescharacteristic, complemented
39C41×#392—21no—
40C41×#392C2211yescharacteristic
41C41×#388—21no—
42C41×#386—21no—
43C41×#381C2211yescharacteristic, complemented
44C41×#328C2212yescomplemented
45C41×#328C2212yescomplemented
46C41×#327C2212yes—
47C41×#327C2212yes—
48C41×#324C2212yescomplemented
49C41×#323C2211yescharacteristic
50C41×#323C2211yescharacteristic
51C2×#41×C41D412yescomplemented
52C22×D4×C41—21no—
53C22×D4×C41—21no—
54C22×D4×C41—21no—
55C22×D4×C41D411yescharacteristic
56C22×D4×C41C2311yescharacteristic
57C23×C4×C41—21no—
58C23×C4×C41D411yescharacteristic
59C23×C4×C41C2311yescharacteristic
60C2×SD16×C41—22no—
61C2×D8×C41—22no—
62C22×C8×C41—22no—
63#126×C41—22no—
64#126×C41—22no—
65#126×C41—22no—
66#125×C41—21no—
67#125×C41—22no—
68#124×C41—22no—
69#124×C41—21no—
70#123×C41—22no—
71#123×C41—22no—
72#123×C41—22no—
73#123×C41—22no—
74#123×C41—22no—
75#123×C41—22no—
76C22⋊Q8×C41—22no—
77C22⋊Q8×C41—22no—
78C22⋊Q8×C41—21no—
79C22⋊Q8×C41—22no—
80C22⋊Q8×C41D412yescomplemented
81C22⋊Q8×C41C2312yes—
82#121×C41—22no—
83#121×C41—22no—
84#121×C41—22no—
85#121×C41—21no—
86#121×C41—22no—
87#121×C41—22no—
88#121×C41D412yescomplemented
89#121×C41C2312yes—
90#120×C41—22no—
91#120×C41—22no—
92#120×C41—22no—
93C4×Q8×C41—21no—
94C4×D4×C41—22no—
95C4×D4×C41—22no—
96C4×D4×C41—21no—
97C4×D4×C41—22no—
98C4×D4×C41—22no—
99C4×D4×C41—22no—
100C4×D4×C41—22no—
101C4×D4×C41—22no—
102#117×C41—22no—
103#117×C41D412yescomplemented
104C2×C4⋊C4×C41—21no—
105C2×C4⋊C4×C41—21no—
106C2×C4⋊C4×C41C2311yescharacteristic
107C2×C4⋊C4×C41C2311yescharacteristic
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41—21no—
110C2×C22⋊C4×C41—21no—
111C2×C22⋊C4×C41—21no—
112C2×C22⋊C4×C41—21no—
113C2×C22⋊C4×C41—21no—
114C2×C22⋊C4×C41—21no—
115C2×C22⋊C4×C41—21no—
116C2×C22⋊C4×C41D411yescharacteristic
117C2×C22⋊C4×C41C2311yescharacteristic
118C2×C42×C41—21no—
119C2×C42×C41D411yescharacteristic
120#107×C41—22no—
121#106×C41—22no—
122#103×C41—22no—
123#102×C41—22no—
124#102×C41—22no—
125#102×C41—22no—
126C22⋊C8×C41—22no—
127C22⋊C8×C41C2312yes—
128C22⋊C8×C41C2312yes—
129#95×C41—21no—
130#95×C41—21no—
131#95×C41—21no—
132#95×C41C2311yescharacteristic
133#95×C41C2311yescharacteristic
134C24×C41—21no—
135C24×C41—21no—
136C24×C41C2×D411yescharacteristic
137C24×C41C2×D411yescharacteristic
138#41×C41—82no—
139C2×Q8×C41—21no—
140C2×Q8×C41C2×D412yes—
141C2×D4×C41—22no—
142C2×D4×C41—22no—
143C2×D4×C41—22no—
144C2×D4×C41—22no—
145C2×D4×C41—21no—
146C2×D4×C41—22no—
147C2×D4×C41—22no—
148C2×D4×C41—22no—
149C2×D4×C41—41no—
150C2×D4×C41—42no—
151C2×D4×C41—42no—
152C2×D4×C41—42no—
153C2×D4×C41—42no—
154C2×D4×C41—81no—
155C2×D4×C41—81no—
156C2×D4×C41—81no—
157C2×D4×C41—81no—
158C2×D4×C41—81no—
159C2×D4×C41C2×D412yes—
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—22no—
164C22×C4×C41—21no—
165C22×C4×C41—22no—
166C22×C4×C41—21no—
167C22×C4×C41—21no—
168C22×C4×C41—21no—
169C22×C4×C41—21no—
170C22×C4×C41—81no—
171C22×C4×C41—81no—
172C22×C4×C41—82no—
173C22×C4×C41C2×D411yescharacteristic
174C22×C4×C41C2×D411yescharacteristic
175C22×C4×C41C2×D411yescharacteristic
176C22×C4×C41C2×D411yescharacteristic
177C22×C4×C41C2×D412yes—
178C22×C4×C41C2×D412yes—
179C22×C4×C41C2411yescharacteristic
180SD16×C41—82no—
181D8×C41—82no—
182C2×C8×C41—22no—
183C2×C8×C41—22no—
184C2×C8×C41—82no—
185C4⋊C4×C41—22no—
186C4⋊C4×C41—22no—
187C4⋊C4×C41—22no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—22no—
191C4⋊C4×C41—22no—
192C4⋊C4×C41—22no—
193C4⋊C4×C41—22no—
194C4⋊C4×C41—22no—
195C4⋊C4×C41—81no—
196C4⋊C4×C41C2×D412yes—
197C4⋊C4×C41C2×D412yes—
198C22⋊C4×C41—22no—
199C22⋊C4×C41—22no—
200C22⋊C4×C41—22no—
201C22⋊C4×C41—22no—
202C22⋊C4×C41—22no—
203C22⋊C4×C41—22no—
204C22⋊C4×C41—22no—
205C22⋊C4×C41—22no—
206C22⋊C4×C41—22no—
207C22⋊C4×C41—22no—
208C22⋊C4×C41—22no—
209C22⋊C4×C41—22no—
210C22⋊C4×C41—42no—
211C22⋊C4×C41—41no—
212C22⋊C4×C41—41no—
213C22⋊C4×C41—81no—
214C22⋊C4×C41—81no—
215C22⋊C4×C41—81no—
216C22⋊C4×C41—81no—
217C42×C41—22no—
218C42×C41—22no—
219C42×C41—21no—
220C42×C41—21no—
221C23×C41—21no—
222C23×C41—21no—
223C23×C41—21no—
224C23×C41—21no—
225C23×C41—22no—
226C23×C41—41no—
227C23×C41—41no—
228C23×C41—41no—
229C23×C41—41no—
230C23×C41—42no—
231C23×C41—41no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41—41no—
235C23×C41—41no—
236C23×C41—41no—
237C23×C41—41no—
238C23×C41—81no—
239C23×C41—81no—
240C23×C41#12012yes—
241C23×C41#13512yes—
242C23×C41C22×D411yescharacteristic
243Q8×C41—42no—
244Q8×C41—81no—
245D4×C41—42no—
246D4×C41—42no—
247D4×C41—42no—
248D4×C41—44no—
249D4×C41—44no—
250D4×C41—42no—
251D4×C41—42no—
252D4×C41—82no—
253D4×C41—82no—
254D4×C41—81no—
255D4×C41—84no—
256D4×C41—84no—
257C2×C4×C41—21no—
258C2×C4×C41—22no—
259C2×C4×C41—21no—
260C2×C4×C41—22no—
261C2×C4×C41—21no—
262C2×C4×C41—22no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—42no—
266C2×C4×C41—41no—
267C2×C4×C41—42no—
268C2×C4×C41—41no—
269C2×C4×C41—42no—
270C2×C4×C41—44no—
271C2×C4×C41—42no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41—41no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41—41no—
283C2×C4×C41—81no—
284C2×C4×C41—81no—
285C2×C4×C41—82no—
286C2×C4×C41—81no—
287C2×C4×C41#12011yescharacteristic
288C2×C4×C41#12011yescharacteristic
289C2×C4×C41C22×D412yes—
290C8×C41—42no—
291C8×C41—42no—
292#18290C4111yesmaximal, characteristic, direct product factor, Sylow
293C22×C41—21no—
294C22×C41—21no—
295C22×C41—22no—
296C22×C41—22no—
297C22×C41—22no—
298C22×C41—22no—
299C22×C41—42no—
300C22×C41—41no—
301C22×C41—41no—
302C22×C41—42no—
303C22×C41—42no—
304C22×C41—42no—
305C22×C41—81no—
306C22×C41—81no—
307C22×C41—81no—
308C22×C41—81no—
309C22×C41—81no—
310C22×C41—81no—
311C22×C41—81no—
312C22×C41—84no—
313C22×C41—81no—
314C22×C41—81no—
315C22×C41—81no—
316C22×C41C2×#12011yescharacteristic
317C22×C41C2×#13511yescharacteristic
318C22×C41#57511yescharacteristic
319C4×C41—22no—
320C4×C41—21no—
321C4×C41—21no—
322C4×C41—41no—
323C4×C41—42no—
324C4×C41—41no—
325C4×C41—42no—
326C4×C41—41no—
327C4×C41—42no—
328C4×C41—81no—
329C4×C41—81no—
330C4×C41—81no—
331#3459C2×C4111yescharacteristic, complemented
332#3188C2×C4112yescomplemented
333#2635C2×C4111yescharacteristic, complemented
334#1615C2×C4112yescomplemented
335#1614C2×C4111yescharacteristic, complemented
336#1613C2×C4111yescharacteristic, complemented
337#1597C2×C4112yescomplemented
338#1596C2×C4111yescharacteristic, complemented
339#1595C2×C4111yescharacteristic, complemented
340#1516C2×C4112yescomplemented
341#1459C2×C4111yescharacteristic, complemented
342C2×C41—21no—
343C2×C41—21no—
344C2×C41—42no—
345C2×C41—42no—
346C2×C41—82no—
347C2×C41—161no—
348C2×C41#300211yescharacteristic
349C2×C41#302111yescharacteristic
350C2×C41#302611yescharacteristic
351#543C22×C4111yescharacteristic
352#539—22no—
353#539C22×C4112yes—
354#538—22no—
355#538—21no—
356#534—21no—
357#534C22×C4111yescharacteristic
358#529—22no—
359#529—21no—
360#525—22no—
361#525C22×C4112yes—
362C2×#121C22×C4111yescharacteristic, complemented
363C2×C4×D4—21no—
364C2×C4×D4C22×C4111yescharacteristic
365#484C22×C4112yescomplemented
366#482—22no—
367#481C22×C4112yes—
368#466—22no—
369#465—22no—
370#450C22×C4112yescomplemented
371#449—22no—
372#447C22×C4112yes—
373C2×C22⋊C8C22×C4112yescomplemented
374#400C22×C4111yescharacteristic, complemented
375#399C22×C4111yescharacteristic
376#394—21no—
377#394C22×C4111yescharacteristic, complemented
378#392—21no—
379#392C22×C4111yescharacteristic
380#388—21no—
381#386—21no—
382#381C22×C4111yescharacteristic, complemented
383#328C22×C4112yescomplemented
384#328C22×C4112yescomplemented
385#327C22×C4112yes—
386#327C22×C4112yes—
387#324C22×C4112yescomplemented
388#323C22×C4111yescharacteristic
389#323C22×C4111yescharacteristic
390C41#1829011yescharacteristic, direct product factor, Sylow
391C2×#41D4×C4112yescomplemented
392C22×D4—21no—
393C22×D4—21no—
394C22×D4—21no—
395C22×D4D4×C4111yescharacteristic
396C22×D4C23×C4111yescharacteristic
397C23×C4—21no—
398C23×C4D4×C4111yescharacteristic
399C23×C4C23×C4111yescharacteristic
400C2×SD16—22no—
401C2×D8—22no—
402C22×C8—22no—
403#126—22no—
404#126—22no—
405#126—22no—
406#125—21no—
407#125—22no—
408#124—22no—
409#124—21no—
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8D4×C4112yescomplemented
421C22⋊Q8C23×C4112yes—
422#121—22no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—22no—
427#121—22no—
428#121D4×C4112yescomplemented
429#121C23×C4112yes—
430#120—22no—
431#120—22no—
432#120—22no—
433C4×Q8—21no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117D4×C4112yescomplemented
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C4111yescharacteristic
447C2×C4⋊C4C23×C4111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C4111yescharacteristic
457C2×C22⋊C4C23×C4111yescharacteristic
458C2×C42—21no—
459C2×C42D4×C4111yescharacteristic
460#107—22no—
461#106—22no—
462#103—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466C22⋊C8—22no—
467C22⋊C8C23×C4112yes—
468C22⋊C8C23×C4112yes—
469#95—21no—
470#95—21no—
471#95—21no—
472#95C23×C4111yescharacteristic
473#95C23×C4111yescharacteristic
474C24—21no—
475C24—21no—
476C24C2×D4×C4111yescharacteristic
477C24C2×D4×C4111yescharacteristic
478#41—82no—
479C2×Q8—21no—
480C2×Q8C2×D4×C4112yes—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—41no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C2×D4×C4112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—81no—
511C22×C4—81no—
512C22×C4—82no—
513C22×C4C2×D4×C4111yescharacteristic
514C22×C4C2×D4×C4111yescharacteristic
515C22×C4C2×D4×C4111yescharacteristic
516C22×C4C2×D4×C4111yescharacteristic
517C22×C4C2×D4×C4112yes—
518C22×C4C2×D4×C4112yes—
519C22×C4C24×C4111yescharacteristic
520SD16—82no—
521D8—82no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—82no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—81no—
536C4⋊C4C2×D4×C4112yes—
537C4⋊C4C2×D4×C4112yes—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—42no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—22no—
558C42—22no—
559C42—21no—
560C42—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—42no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—81no—
579C23—81no—
580C23#120×C4112yes—
581C23#135×C4112yes—
582C23C22×D4×C4111yescharacteristic
583Q8—42no—
584Q8—81no—
585D4—42no—
586D4—42no—
587D4—42no—
588D4—44no—
589D4—44no—
590D4—42no—
591D4—42no—
592D4—82no—
593D4—82no—
594D4—81no—
595D4—84no—
596D4—84no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—81no—
624C2×C4—82no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4#120×C4111yescharacteristic
628C2×C4#120×C4111yescharacteristic
629C2×C4C22×D4×C4112yes—
630C8—42no—
631C8—42no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—42no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—84no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×#120×C4111yescharacteristic
656C22C2×#135×C4111yescharacteristic
657C22C41×#57511yescharacteristic
658C4—22no—
659C4—21no—
660C4—21no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C2—21no—
671C2—21no—
672C2—42no—
673C2—42no—
674C2—82no—
675C2—161no—
676C2C41×#300211yescharacteristic
677C2C41×#302111yescharacteristic
678C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3459C2semidirect
2. C41×#3188C2semidirect
3. C41×#2635C2semidirect
4. C41×#1615C2semidirect
5. C41×#1614C2semidirect
6. C41×#1613C2semidirect
7. C41×#1597C2semidirect
8. C41×#1596C2semidirect
9. C41×#1595C2semidirect
10. C41×#1516C2semidirect
11. C41×#1459C2semidirect
23. C2×#121×C41C22semidirect
26. C41×#484C22semidirect
31. C41×#450C22semidirect
34. C2×C22⋊C8×C41C22semidirect
35. C41×#400C22semidirect
38. C41×#394C22semidirect
43. C41×#381C22semidirect
44. C41×#328C22semidirect
45. C41×#328C22semidirect
48. C41×#324C22semidirect
51. C2×#41×C41D4semidirect
80. C22⋊Q8×C41D4semidirect
88. #121×C41D4semidirect
103. #117×C41D4semidirect
292. #18290C41direct (N × H)
331. #3459C2×C41semidirect
332. #3188C2×C41semidirect
333. #2635C2×C41semidirect
334. #1615C2×C41semidirect
335. #1614C2×C41semidirect
336. #1613C2×C41semidirect
337. #1597C2×C41semidirect
338. #1596C2×C41semidirect
339. #1595C2×C41semidirect
340. #1516C2×C41semidirect
341. #1459C2×C41semidirect
362. C2×#121C22×C41semidirect
365. #484C22×C41semidirect
370. #450C22×C41semidirect
373. C2×C22⋊C8C22×C41semidirect
374. #400C22×C41semidirect
377. #394C22×C41semidirect
382. #381C22×C41semidirect
383. #328C22×C41semidirect
384. #328C22×C41semidirect
387. #324C22×C41semidirect
390. C41#18290direct (N × H)
391. C2×#41D4×C41semidirect
420. C22⋊Q8D4×C41semidirect
428. #121D4×C41semidirect
443. #117D4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34592
C41×#31882
C41×#26352
C41×#16152
C41×#16142
C41×#16132
C41×#15972
C41×#15962
C41×#15952
C41×#15162
C41×#14592
#1829041