Finite Group Databasebeta

← C41×#8466 #23784667

Subgroups — C41×#8466 #23784667

Order 10496.

798 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3494C211yesmaximal, characteristic
2C41×#1964C211yesmaximal, characteristic, complemented
3C41×#1826C211yesmaximal, characteristic, complemented
4C41×#1825C211yesmaximal, characteristic, complemented
5C41×#1513C211yesmaximal, characteristic, complemented
6C41×#1501C211yesmaximal, characteristic, complemented
7C41×#1471C211yesmaximal, characteristic, complemented
8C41×#555—21no—
9C41×#553—21no—
10C41×#553—21no—
11C41×#551—22no—
12C41×#547—21no—
13C41×#546—22no—
14C41×#544C411yescharacteristic, complemented
15C41×#542—21no—
16C41×#540—21no—
17C41×#535C411yescharacteristic, complemented
18C41×#532—21no—
19C41×#529—21no—
20C41×#525C2211yescharacteristic
21C2×#121×C41C2211yescharacteristic
22C41×#520C411yescharacteristic, complemented
23C41×#518C411yescharacteristic, complemented
24C2×#117×C41C2211yescharacteristic
25C2×#99×C41—22no—
26C41×#407C2211yescharacteristic
27C2×C22⋊C8×C41C2211yescharacteristic
28C41×#380C2211yescharacteristic
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#340—21no—
31C41×#340—21no—
32C41×#339—21no—
33C41×#339—21no—
34C41×#328—21no—
35C41×#328—21no—
36C41×#327—21no—
37C41×#327—21no—
38C41×#323—22no—
39C2×#41×C41—22no—
40C2×#41×C41C2×C411yescharacteristic
41C22×D4×C41C2×C411yescharacteristic
42C22×D4×C41D412yes—
43C23×C4×C41C2311yescharacteristic
44C2×M16×C41—21no—
45C22×C8×C41—21no—
46C4⋊Q8×C41—21no—
47C4⋊Q8×C41—21no—
48#127×C41—21no—
49#126×C41—22no—
50#126×C41—22no—
51#125×C41—21no—
52#125×C41—21no—
53#124×C41—22no—
54#124×C41—22no—
55#124×C41—21no—
56#123×C41—22no—
57#123×C41—22no—
58#123×C41—22no—
59#123×C41—22no—
60#123×C41—21no—
61C22⋊Q8×C41—22no—
62C22⋊Q8×C41—22no—
63C22⋊Q8×C41D411yescharacteristic
64C22⋊Q8×C41D411yescharacteristic
65#121×C41—22no—
66#121×C41—22no—
67#121×C41—22no—
68#121×C41—21no—
69#121×C41—21no—
70#121×C41—21no—
71#121×C41—21no—
72#121×C41—21no—
73#121×C41—21no—
74#121×C41D411yescharacteristic
75#121×C41D411yescharacteristic
76#120×C41—22no—
77#120×C41—21no—
78C4×Q8×C41—21no—
79C4×D4×C41—22no—
80C4×D4×C41—22no—
81C4×D4×C41—21no—
82C4×D4×C41—22no—
83C4×D4×C41—21no—
84C4×D4×C41—21no—
85C4×D4×C41—21no—
86C4×D4×C41—21no—
87C4×D4×C41—21no—
88C4×D4×C41—21no—
89#117×C41—22no—
90#117×C41—21no—
91#117×C41—21no—
92#117×C41—21no—
93#117×C41C2×C411yescharacteristic
94#117×C41C2×C411yescharacteristic
95#117×C41C2×C411yescharacteristic
96#117×C41D411yescharacteristic
97#117×C41D411yescharacteristic
98C2×C4⋊C4×C41—21no—
99C2×C4⋊C4×C41—21no—
100C2×C4⋊C4×C41C2×C411yescharacteristic
101C2×C4⋊C4×C41D411yescharacteristic
102C2×C4⋊C4×C41D411yescharacteristic
103C2×C22⋊C4×C41—22no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41D412yes—
108C2×C42×C41—21no—
109C2×C42×C41—21no—
110#99×C41—44no—
111C22⋊C8×C41—21no—
112C22⋊C8×C41—21no—
113C22⋊C8×C41—21no—
114C22⋊C8×C41—21no—
115#95×C41—21no—
116#95×C41—21no—
117C24×C41C22⋊C412yes—
118C24×C41C2×D411yescharacteristic
119#41×C41—42no—
120#41×C41—82no—
121#41×C41—82no—
122C2×Q8×C41—22no—
123C2×Q8×C41C22⋊C411yescharacteristic
124C2×D4×C41—21no—
125C2×D4×C41—21no—
126C2×D4×C41—22no—
127C2×D4×C41—22no—
128C2×D4×C41—22no—
129C2×D4×C41—21no—
130C2×D4×C41—22no—
131C2×D4×C41—21no—
132C2×D4×C41—21no—
133C2×D4×C41—42no—
134C2×D4×C41—42no—
135C2×D4×C41—42no—
136C2×D4×C41C22⋊C411yescharacteristic
137C22×C4×C41—21no—
138C22×C4×C41—22no—
139C22×C4×C41—22no—
140C22×C4×C41—22no—
141C22×C4×C41—21no—
142C22×C4×C41—21no—
143C22×C4×C41—42no—
144C22×C4×C41—41no—
145C22×C4×C41—41no—
146C22×C4×C41C22⋊C412yes—
147C22×C4×C41C22×C411yescharacteristic
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153M16×C41—42no—
154C2×C8×C41—42no—
155C2×C8×C41—41no—
156C2×C8×C41—41no—
157C4⋊C4×C41—22no—
158C4⋊C4×C41—22no—
159C4⋊C4×C41—22no—
160C4⋊C4×C41—22no—
161C4⋊C4×C41—21no—
162C4⋊C4×C41—21no—
163C4⋊C4×C41—21no—
164C4⋊C4×C41—21no—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—42no—
168C4⋊C4×C41C22⋊C411yescharacteristic
169C4⋊C4×C41C22⋊C411yescharacteristic
170C4⋊C4×C41C22⋊C411yescharacteristic
171C4⋊C4×C41C22⋊C411yescharacteristic
172C4⋊C4×C41C22⋊C411yescharacteristic
173C4⋊C4×C41C22⋊C411yescharacteristic
174C22⋊C4×C41—22no—
175C22⋊C4×C41—22no—
176C22⋊C4×C41—22no—
177C22⋊C4×C41—22no—
178C22⋊C4×C41—22no—
179C22⋊C4×C41—21no—
180C22⋊C4×C41—21no—
181C22⋊C4×C41—21no—
182C22⋊C4×C41—21no—
183C22⋊C4×C41—21no—
184C22⋊C4×C41—21no—
185C22⋊C4×C41—21no—
186C22⋊C4×C41—22no—
187C22⋊C4×C41—22no—
188C22⋊C4×C41—21no—
189C22⋊C4×C41—21no—
190C22⋊C4×C41—22no—
191C22⋊C4×C41—41no—
192C22⋊C4×C41—42no—
193C42×C41—22no—
194C42×C41—21no—
195C42×C41—21no—
196C42×C41—21no—
197C42×C41—21no—
198C42×C41—21no—
199C42×C41—42no—
200C23×C41—21no—
201C23×C41—21no—
202C23×C41—22no—
203C23×C41—21no—
204C23×C41—41no—
205C23×C41—41no—
206C23×C41—42no—
207C23×C41—42no—
208C23×C41—42no—
209C23×C41C2×C22⋊C411yescharacteristic
210C23×C41#12011yescharacteristic
211C23×C41#12011yescharacteristic
212Q8×C41—41no—
213Q8×C41—82no—
214D4×C41—41no—
215D4×C41—42no—
216D4×C41—42no—
217D4×C41—42no—
218D4×C41—41no—
219D4×C41—42no—
220D4×C41—41no—
221D4×C41—42no—
222D4×C41—81no—
223D4×C41—82no—
224D4×C41—82no—
225D4×C41—82no—
226C2×C4×C41—22no—
227C2×C4×C41—22no—
228C2×C4×C41—22no—
229C2×C4×C41—21no—
230C2×C4×C41—21no—
231C2×C4×C41—21no—
232C2×C4×C41—21no—
233C2×C4×C41—21no—
234C2×C4×C41—21no—
235C2×C4×C41—21no—
236C2×C4×C41—22no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—42no—
243C2×C4×C41—42no—
244C2×C4×C41—42no—
245C2×C4×C41—81no—
246C2×C4×C41—82no—
247C2×C4×C41—82no—
248C2×C4×C41—82no—
249C2×C4×C41—81no—
250C2×C4×C41—81no—
251C2×C4×C41—81no—
252C2×C4×C41—81no—
253C2×C4×C41—81no—
254C2×C4×C41C2×C22⋊C411yescharacteristic
255C2×C4×C41C2×C22⋊C411yescharacteristic
256C2×C4×C41#12011yescharacteristic
257C2×C4×C41#12011yescharacteristic
258C8×C41—81no—
259C8×C41—81no—
260#8466C4111yesmaximal, characteristic, direct product factor, Sylow
261C22×C41—21no—
262C22×C41—21no—
263C22×C41—21no—
264C22×C41—21no—
265C22×C41—21no—
266C22×C41—21no—
267C22×C41—21no—
268C22×C41—21no—
269C22×C41—41no—
270C22×C41—42no—
271C22×C41—42no—
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—42no—
275C22×C41—81no—
276C22×C41—81no—
277C22×C41—162no—
278C22×C41#37911yescharacteristic
279C22×C41#45311yescharacteristic
280C22×C41#45511yescharacteristic
281C4×C41—21no—
282C4×C41—21no—
283C4×C41—21no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—42no—
287C4×C41—41no—
288C4×C41—41no—
289C4×C41—41no—
290C4×C41—41no—
291C4×C41—41no—
292C4×C41—82no—
293C4×C41—161no—
294C4×C41#41012yes—
295#3494C2×C4111yescharacteristic
296#1964C2×C4111yescharacteristic, complemented
297#1826C2×C4111yescharacteristic, complemented
298#1825C2×C4111yescharacteristic, complemented
299#1513C2×C4111yescharacteristic, complemented
300#1501C2×C4111yescharacteristic, complemented
301#1471C2×C4111yescharacteristic, complemented
302C2×C41—21no—
303C2×C41—21no—
304C2×C41—41no—
305C2×C41—41no—
306C2×C41—81no—
307C2×C41—82no—
308C2×C41#178211yescharacteristic
309C2×C41#179211yescharacteristic
310C2×C41#179411yescharacteristic
311#555—21no—
312#553—21no—
313#553—21no—
314#551—22no—
315#547—21no—
316#546—22no—
317#544C4×C4111yescharacteristic, complemented
318#542—21no—
319#540—21no—
320#535C4×C4111yescharacteristic, complemented
321#532—21no—
322#529—21no—
323#525C22×C4111yescharacteristic
324C2×#121C22×C4111yescharacteristic
325#520C4×C4111yescharacteristic, complemented
326#518C4×C4111yescharacteristic, complemented
327C2×#117C22×C4111yescharacteristic
328C2×#99—22no—
329#407C22×C4111yescharacteristic
330C2×C22⋊C8C22×C4111yescharacteristic
331#380C22×C4111yescharacteristic
332C4×C22⋊C4C22×C4111yescharacteristic
333#340—21no—
334#340—21no—
335#339—21no—
336#339—21no—
337#328—21no—
338#328—21no—
339#327—21no—
340#327—21no—
341#323—22no—
342C41#846611yescharacteristic, direct product factor, Sylow
343C2×#41—22no—
344C2×#41C2×C4×C4111yescharacteristic
345C22×D4C2×C4×C4111yescharacteristic
346C22×D4D4×C4112yes—
347C23×C4C23×C4111yescharacteristic
348C2×M16—21no—
349C22×C8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352#127—21no—
353#126—22no—
354#126—22no—
355#125—21no—
356#125—21no—
357#124—22no—
358#124—22no—
359#124—21no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8D4×C4111yescharacteristic
368C22⋊Q8D4×C4111yescharacteristic
369#121—22no—
370#121—22no—
371#121—22no—
372#121—21no—
373#121—21no—
374#121—21no—
375#121—21no—
376#121—21no—
377#121—21no—
378#121D4×C4111yescharacteristic
379#121D4×C4111yescharacteristic
380#120—22no—
381#120—21no—
382C4×Q8—21no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393#117—22no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117C2×C4×C4111yescharacteristic
398#117C2×C4×C4111yescharacteristic
399#117C2×C4×C4111yescharacteristic
400#117D4×C4111yescharacteristic
401#117D4×C4111yescharacteristic
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C2×C4×C4111yescharacteristic
405C2×C4⋊C4D4×C4111yescharacteristic
406C2×C4⋊C4D4×C4111yescharacteristic
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4D4×C4112yes—
412C2×C42—21no—
413C2×C42—21no—
414#99—44no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419#95—21no—
420#95—21no—
421C24C22⋊C4×C4112yes—
422C24C2×D4×C4111yescharacteristic
423#41—42no—
424#41—82no—
425#41—82no—
426C2×Q8—22no—
427C2×Q8C22⋊C4×C4111yescharacteristic
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4C22⋊C4×C4111yescharacteristic
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22⋊C4×C4112yes—
451C22×C4C22×C4×C4111yescharacteristic
452C22×C4C2×D4×C4111yescharacteristic
453C22×C4C2×D4×C4111yescharacteristic
454C22×C4C2×D4×C4111yescharacteristic
455C22×C4C2×D4×C4111yescharacteristic
456C22×C4C2×D4×C4111yescharacteristic
457M16—42no—
458C2×C8—42no—
459C2×C8—41no—
460C2×C8—41no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4C22⋊C4×C4111yescharacteristic
473C4⋊C4C22⋊C4×C4111yescharacteristic
474C4⋊C4C22⋊C4×C4111yescharacteristic
475C4⋊C4C22⋊C4×C4111yescharacteristic
476C4⋊C4C22⋊C4×C4111yescharacteristic
477C4⋊C4C22⋊C4×C4111yescharacteristic
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—42no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23C2×C22⋊C4×C4111yescharacteristic
514C23#120×C4111yescharacteristic
515C23#120×C4111yescharacteristic
516Q8—41no—
517Q8—82no—
518D4—41no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—82no—
527D4—81no—
528D4—82no—
529D4—82no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4C2×C22⋊C4×C4111yescharacteristic
559C2×C4C2×C22⋊C4×C4111yescharacteristic
560C2×C4#120×C4111yescharacteristic
561C2×C4#120×C4111yescharacteristic
562C8—81no—
563C8—81no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—42no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—162no—
581C22C41×#37911yescharacteristic
582C22C41×#45311yescharacteristic
583C22C41×#45511yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—82no—
596C4—161no—
597C4C41×#41012yes—
598C2—21no—
599C2—21no—
600C2—41no—
601C2—41no—
602C2—82no—
603C2—81no—
604C2C41×#178211yescharacteristic
605C2C41×#179211yescharacteristic
606C2C41×#179411yescharacteristic
subgroupG/H
center, socleC22×C41#379
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC41×#3494C2
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
2. C41×#1964C2semidirect
3. C41×#1826C2semidirect
4. C41×#1825C2semidirect
5. C41×#1513C2semidirect
6. C41×#1501C2semidirect
7. C41×#1471C2semidirect
14. C41×#544C4semidirect
17. C41×#535C4semidirect
22. C41×#520C4semidirect
23. C41×#518C4semidirect
260. #8466C41direct (N × H)
296. #1964C2×C41semidirect
297. #1826C2×C41semidirect
298. #1825C2×C41semidirect
299. #1513C2×C41semidirect
300. #1501C2×C41semidirect
301. #1471C2×C41semidirect
317. #544C4×C41semidirect
320. #535C4×C41semidirect
325. #520C4×C41semidirect
326. #518C4×C41semidirect
342. C41#8466direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#34942
C41×#19642
C41×#18262
C41×#18252
C41×#15132
C41×#15012
C41×#14712
#846641