Finite Group Databasebeta

← C41×#18455 #23794656

Subgroups — C41×#18455 #23794656

Order 10496.

894 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3538C211yesmaximal, characteristic
2C41×#3196C211yesmaximal, characteristic
3C41×#3189C211yesmaximal, characteristic, complemented
4C41×#2817C211yesmaximal, characteristic, complemented
5C41×#1617C212yesmaximal, complemented
6C41×#1615C212yesmaximal, complemented
7C41×#1605C212yesmaximal, complemented
8C41×#1603C212yesmaximal, complemented
9C41×#1516C211yesmaximal, characteristic
10C41×#1511C211yesmaximal, characteristic, complemented
11C41×#1472C211yesmaximal, characteristic, complemented
12C41×#563—22no—
13C41×#552—21no—
14C41×#552—21no—
15C41×#551—22no—
16D4×Q8×C41—21no—
17D4×Q8×C41—21no—
18C41×#544—21no—
19C41×#544C2212yes—
20C41×#541—21no—
21C41×#539—21no—
22C41×#539C2212yes—
23C41×#536—21no—
24C41×#525C2211yescharacteristic
25C2×C22⋊Q8×C41C2211yescharacteristic
26C2×C22⋊Q8×C41C2211yescharacteristic
27C2×C22⋊Q8×C41C2211yescharacteristic
28C41×#485—21no—
29C41×#484—21no—
30C41×#484C2212yes—
31C41×#484C2211yescharacteristic
32C41×#481C2211yescharacteristic
33C41×#470—21no—
34C41×#468—21no—
35C41×#467—22no—
36C41×#452—21no—
37C41×#451—21no—
38C41×#451C2212yes—
39C41×#451C2211yescharacteristic
40C41×#448C2211yescharacteristic
41C41×#407C2211yescharacteristic
42C2×C22⋊C8×C41C2211yescharacteristic
43C41×#400—21no—
44C41×#400C2212yes—
45C41×#397—22no—
46C41×#395—21no—
47C41×#395C2212yes—
48C41×#381C2211yescharacteristic
49C41×#328C2212yes—
50C41×#328C2212yes—
51C41×#328C2212yes—
52C41×#327C2212yes—
53C41×#324C2212yes—
54C41×#324C2212yes—
55C2×#41×C41D411yescharacteristic
56C22×Q8×C41—21no—
57C22×Q8×C41D411yescharacteristic
58C22×Q8×C41D411yescharacteristic
59C22×Q8×C41C2311yescharacteristic
60C23×C4×C41C2311yescharacteristic
61C2×Q16×C41—22no—
62C2×Q16×C41—21no—
63C2×SD16×C41—21no—
64C2×M16×C41—21no—
65C22×C8×C41—21no—
66C4⋊Q8×C41—21no—
67C4⋊Q8×C41—22no—
68C4⋊Q8×C41—22no—
69C4⋊Q8×C41—22no—
70#126×C41—22no—
71#126×C41—22no—
72#126×C41—22no—
73#126×C41—22no—
74#125×C41—21no—
75#125×C41—22no—
76#125×C41—22no—
77#125×C41—22no—
78#125×C41—22no—
79#124×C41—22no—
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—22no—
83#123×C41—21no—
84#123×C41—22no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—21no—
87C22⋊Q8×C41—22no—
88C22⋊Q8×C41—22no—
89C22⋊Q8×C41—22no—
90C22⋊Q8×C41—21no—
91C22⋊Q8×C41—21no—
92C22⋊Q8×C41—21no—
93C22⋊Q8×C41—21no—
94C22⋊Q8×C41—21no—
95C22⋊Q8×C41—21no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—21no—
98C22⋊Q8×C41—21no—
99C22⋊Q8×C41—21no—
100C22⋊Q8×C41—21no—
101C22⋊Q8×C41D412yes—
102C22⋊Q8×C41D411yescharacteristic
103C22⋊Q8×C41C2312yes—
104C22⋊Q8×C41C2311yescharacteristic
105#121×C41D411yescharacteristic
106#121×C41C2311yescharacteristic
107#120×C41—21no—
108C4×Q8×C41—21no—
109C4×Q8×C41—21no—
110C4×D4×C41—22no—
111C4×D4×C41—21no—
112C4×D4×C41—21no—
113C4×D4×C41—22no—
114#117×C41—21no—
115#117×C41—22no—
116#117×C41—22no—
117#117×C41D411yescharacteristic
118C2×C4⋊C4×C41—21no—
119C2×C4⋊C4×C41—21no—
120C2×C4⋊C4×C41—22no—
121C2×C4⋊C4×C41D411yescharacteristic
122C2×C4⋊C4×C41D411yescharacteristic
123C2×C4⋊C4×C41C2311yescharacteristic
124C2×C4⋊C4×C41C2312yes—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41—21no—
128C2×C22⋊C4×C41D412yes—
129#107×C41—22no—
130#107×C41—21no—
131#106×C41—21no—
132#103×C41—22no—
133#103×C41—21no—
134#103×C41—21no—
135#103×C41—22no—
136#103×C41—21no—
137#102×C41—21no—
138C22⋊C8×C41—21no—
139C22⋊C8×C41—21no—
140C22⋊C8×C41C2312yes—
141C22⋊C8×C41C2311yescharacteristic
142C22⋊C8×C41C2311yescharacteristic
143#95×C41—21no—
144#95×C41—22no—
145#95×C41—22no—
146#95×C41—22no—
147#95×C41C2312yes—
148C24×C41C2×D411yescharacteristic
149#41×C41—81no—
150C2×Q8×C41—22no—
151C2×Q8×C41—21no—
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
154C2×Q8×C41—21no—
155C2×Q8×C41—21no—
156C2×Q8×C41—81no—
157C2×Q8×C41—81no—
158C2×Q8×C41—82no—
159C2×Q8×C41—81no—
160C2×Q8×C41C2×D412yes—
161C2×Q8×C41C2×D411yescharacteristic
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41C2×D411yescharacteristic
166C22×C4×C41—21no—
167C22×C4×C41—22no—
168C22×C4×C41—21no—
169C22×C4×C41—21no—
170C22×C4×C41—22no—
171C22×C4×C41—21no—
172C22×C4×C41—21no—
173C22×C4×C41—81no—
174C22×C4×C41C2×D412yes—
175C22×C4×C41C2×D412yes—
176C22×C4×C41C2×D411yescharacteristic
177C22×C4×C41C2×D411yescharacteristic
178C22×C4×C41C2×D411yescharacteristic
179C22×C4×C41C2×D411yescharacteristic
180C22×C4×C41C2×D411yescharacteristic
181C22×C4×C41C2411yescharacteristic
182Q16×C41—82no—
183Q16×C41—81no—
184SD16×C41—81no—
185M16×C41—81no—
186C2×C8×C41—21no—
187C2×C8×C41—22no—
188C2×C8×C41—21no—
189C2×C8×C41—81no—
190C4⋊C4×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—22no—
204C4⋊C4×C41—22no—
205C4⋊C4×C41—22no—
206C4⋊C4×C41—21no—
207C4⋊C4×C41—21no—
208C4⋊C4×C41—21no—
209C4⋊C4×C41—41no—
210C4⋊C4×C41—41no—
211C4⋊C4×C41—82no—
212C4⋊C4×C41C2×D411yescharacteristic
213C4⋊C4×C41C2×D412yes—
214C4⋊C4×C41C2×D411yescharacteristic
215C22⋊C4×C41—22no—
216C22⋊C4×C41—22no—
217C22⋊C4×C41—22no—
218C22⋊C4×C41—22no—
219C22⋊C4×C41—22no—
220C22⋊C4×C41—22no—
221C22⋊C4×C41—21no—
222C22⋊C4×C41—21no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—21no—
225C22⋊C4×C41—21no—
226C22⋊C4×C41—21no—
227C22⋊C4×C41—41no—
228C22⋊C4×C41—41no—
229C22⋊C4×C41—81no—
230C42×C41—22no—
231C42×C41—22no—
232C42×C41—22no—
233C42×C41—21no—
234C23×C41—22no—
235C23×C41—21no—
236C23×C41—41no—
237C23×C41—41no—
238C23×C41#12011yescharacteristic
239C23×C41#12011yescharacteristic
240C23×C41C22×D411yescharacteristic
241Q8×C41—42no—
242Q8×C41—41no—
243Q8×C41—42no—
244Q8×C41—42no—
245Q8×C41—41no—
246Q8×C41—41no—
247Q8×C41—42no—
248Q8×C41—81no—
249Q8×C41—82no—
250D4×C41—41no—
251D4×C41—42no—
252D4×C41—42no—
253D4×C41—81no—
254C2×C4×C41—21no—
255C2×C4×C41—21no—
256C2×C4×C41—22no—
257C2×C4×C41—22no—
258C2×C4×C41—21no—
259C2×C4×C41—22no—
260C2×C4×C41—22no—
261C2×C4×C41—24no—
262C2×C4×C41—41no—
263C2×C4×C41—41no—
264C2×C4×C41—41no—
265C2×C4×C41—41no—
266C2×C4×C41—41no—
267C2×C4×C41—41no—
268C2×C4×C41—42no—
269C2×C4×C41—42no—
270C2×C4×C41—42no—
271C2×C4×C41—42no—
272C2×C4×C41—42no—
273C2×C4×C41—42no—
274C2×C4×C41—42no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—42no—
278C2×C4×C41—81no—
279C2×C4×C41—82no—
280C2×C4×C41#12011yescharacteristic
281C2×C4×C41#12011yescharacteristic
282C2×C4×C41C22×D411yescharacteristic
283C2×C4×C41C22×D411yescharacteristic
284C8×C41—42no—
285C8×C41—41no—
286C8×C41—41no—
287#18455C4111yesmaximal, characteristic, direct product factor, Sylow
288C22×C41—21no—
289C22×C41—21no—
290C22×C41—21no—
291C22×C41—21no—
292C22×C41—21no—
293C22×C41—21no—
294C22×C41—21no—
295C22×C41—21no—
296C22×C41—41no—
297C22×C41—41no—
298C22×C41—41no—
299C22×C41—82no—
300C22×C41C2×#12011yescharacteristic
301C22×C41#57812yes—
302C4×C41—21no—
303C4×C41—21no—
304C4×C41—21no—
305C4×C41—21no—
306C4×C41—42no—
307C4×C41—41no—
308C4×C41—42no—
309C4×C41—41no—
310C4×C41—41no—
311C4×C41—42no—
312C4×C41—42no—
313C4×C41—82no—
314C4×C41—81no—
315C4×C41—81no—
316#3538C2×C4111yescharacteristic
317#3196C2×C4111yescharacteristic
318#3189C2×C4111yescharacteristic, complemented
319#2817C2×C4111yescharacteristic, complemented
320#1617C2×C4112yescomplemented
321#1615C2×C4112yescomplemented
322#1605C2×C4112yescomplemented
323#1603C2×C4112yescomplemented
324#1516C2×C4111yescharacteristic
325#1511C2×C4111yescharacteristic, complemented
326#1472C2×C4111yescharacteristic, complemented
327C2×C41—22no—
328C2×C41—41no—
329C2×C41—41no—
330C2×C41—81no—
331C2×C41#301111yescharacteristic
332C2×C41#302011yescharacteristic
333C2×C41#302611yescharacteristic
334#563—22no—
335#552—21no—
336#552—21no—
337#551—22no—
338D4×Q8—21no—
339D4×Q8—21no—
340#544—21no—
341#544C22×C4112yes—
342#541—21no—
343#539—21no—
344#539C22×C4112yes—
345#536—21no—
346#525C22×C4111yescharacteristic
347C2×C22⋊Q8C22×C4111yescharacteristic
348C2×C22⋊Q8C22×C4111yescharacteristic
349C2×C22⋊Q8C22×C4111yescharacteristic
350#485—21no—
351#484—21no—
352#484C22×C4112yes—
353#484C22×C4111yescharacteristic
354#481C22×C4111yescharacteristic
355#470—21no—
356#468—21no—
357#467—22no—
358#452—21no—
359#451—21no—
360#451C22×C4112yes—
361#451C22×C4111yescharacteristic
362#448C22×C4111yescharacteristic
363#407C22×C4111yescharacteristic
364C2×C22⋊C8C22×C4111yescharacteristic
365#400—21no—
366#400C22×C4112yes—
367#397—22no—
368#395—21no—
369#395C22×C4112yes—
370#381C22×C4111yescharacteristic
371#328C22×C4112yes—
372#328C22×C4112yes—
373#328C22×C4112yes—
374#327C22×C4112yes—
375#324C22×C4112yes—
376#324C22×C4112yes—
377C41#1845511yescharacteristic, direct product factor, Sylow
378C2×#41D4×C4111yescharacteristic
379C22×Q8—21no—
380C22×Q8D4×C4111yescharacteristic
381C22×Q8D4×C4111yescharacteristic
382C22×Q8C23×C4111yescharacteristic
383C23×C4C23×C4111yescharacteristic
384C2×Q16—22no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×M16—21no—
388C22×C8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393#126—22no—
394#126—22no—
395#126—22no—
396#126—22no—
397#125—21no—
398#125—22no—
399#125—22no—
400#125—22no—
401#125—22no—
402#124—22no—
403#123—22no—
404#123—22no—
405#123—22no—
406#123—21no—
407#123—22no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8D4×C4112yes—
425C22⋊Q8D4×C4111yescharacteristic
426C22⋊Q8C23×C4112yes—
427C22⋊Q8C23×C4111yescharacteristic
428#121D4×C4111yescharacteristic
429#121C23×C4111yescharacteristic
430#120—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—22no—
437#117—21no—
438#117—22no—
439#117—22no—
440#117D4×C4111yescharacteristic
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4D4×C4111yescharacteristic
445C2×C4⋊C4D4×C4111yescharacteristic
446C2×C4⋊C4C23×C4111yescharacteristic
447C2×C4⋊C4C23×C4112yes—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4D4×C4112yes—
452#107—22no—
453#107—21no—
454#106—21no—
455#103—22no—
456#103—21no—
457#103—21no—
458#103—22no—
459#103—21no—
460#102—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463C22⋊C8C23×C4112yes—
464C22⋊C8C23×C4111yescharacteristic
465C22⋊C8C23×C4111yescharacteristic
466#95—21no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95C23×C4112yes—
471C24C2×D4×C4111yescharacteristic
472#41—81no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—81no—
480C2×Q8—81no—
481C2×Q8—82no—
482C2×Q8—81no—
483C2×Q8C2×D4×C4112yes—
484C2×Q8C2×D4×C4111yescharacteristic
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×D4×C4111yescharacteristic
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—81no—
497C22×C4C2×D4×C4112yes—
498C22×C4C2×D4×C4112yes—
499C22×C4C2×D4×C4111yescharacteristic
500C22×C4C2×D4×C4111yescharacteristic
501C22×C4C2×D4×C4111yescharacteristic
502C22×C4C2×D4×C4111yescharacteristic
503C22×C4C2×D4×C4111yescharacteristic
504C22×C4C24×C4111yescharacteristic
505Q16—82no—
506Q16—81no—
507SD16—81no—
508M16—81no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—21no—
512C2×C8—81no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—82no—
535C4⋊C4C2×D4×C4111yescharacteristic
536C4⋊C4C2×D4×C4112yes—
537C4⋊C4C2×D4×C4111yescharacteristic
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—81no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—21no—
557C23—22no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23#120×C4111yescharacteristic
562C23#120×C4111yescharacteristic
563C23C22×D4×C4111yescharacteristic
564Q8—42no—
565Q8—41no—
566Q8—42no—
567Q8—42no—
568Q8—41no—
569Q8—41no—
570Q8—42no—
571Q8—81no—
572Q8—82no—
573D4—41no—
574D4—42no—
575D4—42no—
576D4—81no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—81no—
602C2×C4—82no—
603C2×C4#120×C4111yescharacteristic
604C2×C4#120×C4111yescharacteristic
605C2×C4C22×D4×C4111yescharacteristic
606C2×C4C22×D4×C4111yescharacteristic
607C8—42no—
608C8—41no—
609C8—41no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—82no—
622C22C2×#120×C4111yescharacteristic
623C22C41×#57812yes—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—42no—
635C4—82no—
636C4—81no—
637C4—81no—
638C2—22no—
639C2—41no—
640C2—41no—
641C2—81no—
642C2C41×#301111yescharacteristic
643C2C41×#302011yescharacteristic
644C2C41×#302611yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#525C22
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
3. C41×#3189C2semidirect
4. C41×#2817C2semidirect
5. C41×#1617C2semidirect
6. C41×#1615C2semidirect
7. C41×#1605C2semidirect
8. C41×#1603C2semidirect
10. C41×#1511C2semidirect
11. C41×#1472C2semidirect
287. #18455C41direct (N × H)
318. #3189C2×C41semidirect
319. #2817C2×C41semidirect
320. #1617C2×C41semidirect
321. #1615C2×C41semidirect
322. #1605C2×C41semidirect
323. #1603C2×C41semidirect
325. #1511C2×C41semidirect
326. #1472C2×C41semidirect
377. C41#18455direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35382
C41×#31962
C41×#31892
C41×#28172
C41×#16172
C41×#16152
C41×#16052
C41×#16032
C41×#15162
C41×#15112
C41×#14722
#1845541