Finite Group Databasebeta

← C41×#14808 #23791009

Subgroups — C41×#14808 #23791009

Order 10496.

1526 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#397C211yesmaximal, characteristic
2C2×C41×#389C211yesmaximal, characteristic, complemented
3C2×C41×#388C212yesmaximal
4C2×C41×#388C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
6C41×#1445C211yesmaximal, characteristic, complemented
7C41×#1442C211yesmaximal, characteristic, complemented
8C41×#1441C212yesmaximal, complemented
9C41×#1439C211yesmaximal, characteristic
10C41×#1439C212yesmaximal
11C41×#1436C212yesmaximal, complemented
12C22×C4⋊C4×C41C2212yes—
13C22×C4⋊C4×C41C2212yes—
14C22×C4⋊C4×C41C2211yescharacteristic
15C22×C4⋊C4×C41C2211yescharacteristic
16C22×C4⋊C4×C41C2211yescharacteristic
17C22×C22⋊C4×C41C2211yescharacteristic
18C22×C22⋊C4×C41C2212yes—
19C22×C22⋊C4×C41C2211yescharacteristic
20C22×C22⋊C4×C41C2212yes—
21C22×C22⋊C4×C41C2211yescharacteristic
22C22×C42×C41C2212yes—
23C22×C42×C41C2211yescharacteristic
24C41×#397—24no—
25C41×#389—24no—
26C41×#388—28no—
27C41×#388—24no—
28C4×C4⋊C4×C41—24no—
29C2×#95×C41C2211yescharacteristic
30C2×#95×C41C2211yescharacteristic
31C2×#95×C41C2212yes—
32C2×#95×C41C2212yes—
33C2×#95×C41C2211yescharacteristic
34C2×#95×C41C2212yes—
35C2×#95×C41C2212yes—
36C2×#95×C41C2212yes—
37C2×#95×C41C2212yes—
38C2×#95×C41C2212yes—
39C2×#95×C41C2211yescharacteristic
40C25×C41C2311yescharacteristic
41C23×C4×C41C2312yes—
42C23×C4×C41C2311yescharacteristic
43C23×C4×C41C2311yescharacteristic
44C23×C4×C41C2312yes—
45C23×C4×C41C2311yescharacteristic
46C23×C4×C41C2312yes—
47C23×C4×C41C2312yes—
48C23×C4×C41C2311yescharacteristic
49C23×C4×C41C2311yescharacteristic
50C23×C4×C41C2311yescharacteristic
51C2×C4⋊C4×C41—24no—
52C2×C4⋊C4×C41—22no—
53C2×C4⋊C4×C41—24no—
54C2×C4⋊C4×C41—24no—
55C2×C4⋊C4×C41—24no—
56C2×C4⋊C4×C41—24no—
57C2×C4⋊C4×C41—22no—
58C2×C4⋊C4×C41—24no—
59C2×C4⋊C4×C41—22no—
60C2×C4⋊C4×C41—22no—
61C2×C4⋊C4×C41—24no—
62C2×C4⋊C4×C41—22no—
63C2×C4⋊C4×C41—24no—
64C2×C22⋊C4×C41—24no—
65C2×C22⋊C4×C41—22no—
66C2×C22⋊C4×C41—24no—
67C2×C22⋊C4×C41—24no—
68C2×C22⋊C4×C41—22no—
69C2×C22⋊C4×C41—24no—
70C2×C22⋊C4×C41—22no—
71C2×C22⋊C4×C41—22no—
72C2×C22⋊C4×C41—24no—
73C2×C22⋊C4×C41—22no—
74C2×C22⋊C4×C41—22no—
75C2×C22⋊C4×C41—24no—
76C2×C22⋊C4×C41—42no—
77C2×C22⋊C4×C41D414yes—
78C2×C42×C41—22no—
79C2×C42×C41—22no—
80C2×C42×C41—24no—
81C2×C42×C41—24no—
82C2×C42×C41—42no—
83C2×C42×C41D414yes—
84#95×C41—22no—
85#95×C41—24no—
86#95×C41—24no—
87#95×C41—22no—
88#95×C41—22no—
89#95×C41—24no—
90#95×C41—24no—
91#95×C41—24no—
92#95×C41—24no—
93#95×C41—42no—
94#95×C41D414yes—
95C24×C41—21no—
96C24×C41—21no—
97C24×C41—21no—
98C24×C41—22no—
99C24×C41—22no—
100C24×C41—21no—
101C24×C41—22no—
102C24×C41—21no—
103C24×C41—22no—
104C24×C41—21no—
105C24×C41C2×D412yes—
106C24×C41C2411yescharacteristic
107C22×C4×C41—21no—
108C22×C4×C41—21no—
109C22×C4×C41—21no—
110C22×C4×C41—21no—
111C22×C4×C41—22no—
112C22×C4×C41—22no—
113C22×C4×C41—21no—
114C22×C4×C41—22no—
115C22×C4×C41—21no—
116C22×C4×C41—22no—
117C22×C4×C41—22no—
118C22×C4×C41—22no—
119C22×C4×C41—21no—
120C22×C4×C41—22no—
121C22×C4×C41—22no—
122C22×C4×C41—22no—
123C22×C4×C41—22no—
124C22×C4×C41—21no—
125C22×C4×C41—22no—
126C22×C4×C41—22no—
127C22×C4×C41—22no—
128C22×C4×C41—22no—
129C22×C4×C41—22no—
130C22×C4×C41—22no—
131C22×C4×C41—22no—
132C22×C4×C41—22no—
133C22×C4×C41—22no—
134C22×C4×C41—22no—
135C22×C4×C41—22no—
136C22×C4×C41—22no—
137C22×C4×C41—22no—
138C22×C4×C41—21no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—22no—
142C22×C4×C41—22no—
143C22×C4×C41—22no—
144C22×C4×C41—22no—
145C22×C4×C41—22no—
146C22×C4×C41—21no—
147C22×C4×C41—22no—
148C22×C4×C41—22no—
149C22×C4×C41—22no—
150C22×C4×C41—22no—
151C22×C4×C41—21no—
152C22×C4×C41—22no—
153C22×C4×C41—22no—
154C22×C4×C41—21no—
155C22×C4×C41C2×D412yes—
156C22×C4×C41C2×D414yes—
157C22×C4×C41C2×D412yes—
158C22×C4×C41C2×D412yes—
159C22×C4×C41C2×D412yes—
160C22×C4×C41C2×D412yes—
161C22×C4×C41C2×D412yes—
162C22×C4×C41#4114yes—
163C22×C4×C41#4114yes—
164C22×C4×C41#4112yes—
165C22×C4×C41#4112yes—
166C22×C4×C41#4114yes—
167C4⋊C4×C41—28no—
168C4⋊C4×C41—216no—
169C4⋊C4×C41—48no—
170C4⋊C4×C41—44no—
171C4⋊C4×C41—44no—
172C22⋊C4×C41—216no—
173C22⋊C4×C41—28no—
174C22⋊C4×C41—48no—
175C22⋊C4×C41—44no—
176C22⋊C4×C41—44no—
177C42×C41—28no—
178C42×C41—48no—
179C23×C41—22no—
180C23×C41—24no—
181C23×C41—22no—
182C23×C41—22no—
183C23×C41—24no—
184C23×C41—41no—
185C23×C41—41no—
186C23×C41—42no—
187C23×C41—41no—
188C23×C41—42no—
189C23×C41—42no—
190C23×C41—41no—
191C23×C41—41no—
192C23×C41—41no—
193C23×C41—42no—
194C23×C41—42no—
195C23×C41—42no—
196C23×C41—41no—
197C23×C41—42no—
198C23×C41—41no—
199C23×C41—42no—
200C23×C41—42no—
201C23×C41—42no—
202C23×C41C22×D411yescharacteristic
203C23×C41C22×D411yescharacteristic
204C23×C41C22×D411yescharacteristic
205C23×C41C2×#4111yescharacteristic
206C23×C41C2×#4111yescharacteristic
207C23×C41C2×#4112yes—
208C23×C41C2×#4112yes—
209C23×C41C2×#4112yes—
210C23×C41H(5,𝔽2)11yescharacteristic
211C23×C412−1+412yes—
212C23×C412−1+411yescharacteristic
213C2×C4×C41—22no—
214C2×C4×C41—22no—
215C2×C4×C41—22no—
216C2×C4×C41—24no—
217C2×C4×C41—24no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—22no—
222C2×C4×C41—24no—
223C2×C4×C41—22no—
224C2×C4×C41—22no—
225C2×C4×C41—24no—
226C2×C4×C41—22no—
227C2×C4×C41—22no—
228C2×C4×C41—24no—
229C2×C4×C41—24no—
230C2×C4×C41—24no—
231C2×C4×C41—24no—
232C2×C4×C41—24no—
233C2×C4×C41—24no—
234C2×C4×C41—24no—
235C2×C4×C41—24no—
236C2×C4×C41—24no—
237C2×C4×C41—24no—
238C2×C4×C41—42no—
239C2×C4×C41—42no—
240C2×C4×C41—42no—
241C2×C4×C41—41no—
242C2×C4×C41—42no—
243C2×C4×C41—42no—
244C2×C4×C41—41no—
245C2×C4×C41—42no—
246C2×C4×C41—42no—
247C2×C4×C41—42no—
248C2×C4×C41—42no—
249C2×C4×C41—42no—
250C2×C4×C41—42no—
251C2×C4×C41—42no—
252C2×C4×C41—42no—
253C2×C4×C41—41no—
254C2×C4×C41—42no—
255C2×C4×C41—42no—
256C2×C4×C41—41no—
257C2×C4×C41—42no—
258C2×C4×C41—41no—
259C2×C4×C41—41no—
260C2×C4×C41—42no—
261C2×C4×C41—41no—
262C2×C4×C41—41no—
263C2×C4×C41—42no—
264C2×C4×C41—42no—
265C2×C4×C41—42no—
266C2×C4×C41—42no—
267C2×C4×C41—42no—
268C2×C4×C41—42no—
269C2×C4×C41—42no—
270C2×C4×C41#12114yes—
271C2×C4×C41#12114yes—
272C2×C4×C41#12414yes—
273#14808C4111yesmaximal, characteristic, direct product factor, Sylow
274C22×C41—42no—
275C22×C41—42no—
276C22×C41—44no—
277C22×C41—44no—
278C22×C41—42no—
279C22×C41—81no—
280C22×C41—81no—
281C22×C41—82no—
282C22×C41—81no—
283C22×C41—81no—
284C22×C41—82no—
285C22×C41C2×#12111yescharacteristic
286C22×C41C2×#12111yescharacteristic
287C22×C41#52511yescharacteristic
288C22×C41#52512yes—
289C22×C41#52512yes—
290C22×C41C2×#12411yescharacteristic
291C22×C41#52912yes—
292C22×C41#52912yes—
293C22×C41#53211yescharacteristic
294C22×C41#53611yescharacteristic
295C22×C41#53711yescharacteristic
296C22×C41#53912yes—
297C22×C41#54112yes—
298C22×C41D4211yescharacteristic
299C22×C41#54712yes—
300C22×C41#54711yescharacteristic
301C22×C41#54712yes—
302C22×C41#54811yescharacteristic
303C22×C41#55212yes—
304C22×C41#55311yescharacteristic
305C22×C41#55612yes—
306C22×C41#55612yes—
307C22×C41#55912yes—
308C4×C41—24no—
309C4×C41—24no—
310C4×C41—24no—
311C4×C41—44no—
312C4×C41—44no—
313C4×C41—44no—
314C4×C41—42no—
315C4×C41—81no—
316C4×C41—81no—
317C4×C41—82no—
318C2×#397C2×C4111yescharacteristic
319C2×#389C2×C4111yescharacteristic, complemented
320C2×#388C2×C4111yescharacteristic
321C2×#388C2×C4112yes—
322C2×C4×C4⋊C4C2×C4111yescharacteristic, complemented
323#1445C2×C4111yescharacteristic, complemented
324#1442C2×C4111yescharacteristic, complemented
325#1441C2×C4112yescomplemented
326#1439C2×C4111yescharacteristic
327#1439C2×C4112yes—
328#1436C2×C4112yescomplemented
329C2×C41—82no—
330C2×C41#239211yescharacteristic
331C2×C41#241311yescharacteristic
332C2×C41#241611yescharacteristic
333C2×C41#245512yes—
334C2×C41#246912yes—
335C2×C41#247812yes—
336C2×C41#254711yescharacteristic
337C2×C41#259211yescharacteristic
338C2×C41#259612yes—
339C2×C41#266411yescharacteristic
340C2×C41#285011yescharacteristic
341C22×C4⋊C4C22×C4111yescharacteristic
342C22×C4⋊C4C22×C4112yes—
343C22×C4⋊C4C22×C4112yes—
344C22×C4⋊C4C22×C4111yescharacteristic
345C22×C4⋊C4C22×C4111yescharacteristic
346C22×C22⋊C4C22×C4111yescharacteristic
347C22×C22⋊C4C22×C4112yes—
348C22×C22⋊C4C22×C4111yescharacteristic
349C22×C22⋊C4C22×C4112yes—
350C22×C22⋊C4C22×C4111yescharacteristic
351C22×C42C22×C4112yes—
352C22×C42C22×C4111yescharacteristic
353#397—24no—
354#389—24no—
355#388—28no—
356#388—24no—
357C4×C4⋊C4—24no—
358C2×#95C22×C4112yes—
359C2×#95C22×C4111yescharacteristic
360C2×#95C22×C4112yes—
361C2×#95C22×C4112yes—
362C2×#95C22×C4112yes—
363C2×#95C22×C4111yescharacteristic
364C2×#95C22×C4112yes—
365C2×#95C22×C4112yes—
366C2×#95C22×C4111yescharacteristic
367C2×#95C22×C4112yes—
368C2×#95C22×C4111yescharacteristic
369C41#1480811yescharacteristic, direct product factor, Sylow
370C25C23×C4111yescharacteristic
371C23×C4C23×C4112yes—
372C23×C4C23×C4111yescharacteristic
373C23×C4C23×C4111yescharacteristic
374C23×C4C23×C4111yescharacteristic
375C23×C4C23×C4112yes—
376C23×C4C23×C4112yes—
377C23×C4C23×C4112yes—
378C23×C4C23×C4111yescharacteristic
379C23×C4C23×C4111yescharacteristic
380C23×C4C23×C4111yescharacteristic
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4D4×C4114yes—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—42no—
413C2×C42D4×C4114yes—
414#95—22no—
415#95—24no—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—42no—
424#95D4×C4114yes—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24C2×D4×C4112yes—
436C24C24×C4111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4C2×D4×C4112yes—
486C22×C4C2×D4×C4114yes—
487C22×C4C2×D4×C4112yes—
488C22×C4C2×D4×C4112yes—
489C22×C4C2×D4×C4112yes—
490C22×C4C2×D4×C4112yes—
491C22×C4C2×D4×C4112yes—
492C22×C4#41×C4114yes—
493C22×C4#41×C4114yes—
494C22×C4#41×C4112yes—
495C22×C4#41×C4112yes—
496C22×C4#41×C4114yes—
497C4⋊C4—28no—
498C4⋊C4—216no—
499C4⋊C4—48no—
500C4⋊C4—44no—
501C4⋊C4—44no—
502C22⋊C4—216no—
503C22⋊C4—28no—
504C22⋊C4—48no—
505C22⋊C4—44no—
506C22⋊C4—44no—
507C42—28no—
508C42—48no—
509C23—22no—
510C23—24no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23C22×D4×C4111yescharacteristic
533C23C22×D4×C4111yescharacteristic
534C23C22×D4×C4111yescharacteristic
535C23C2×#41×C4111yescharacteristic
536C23C2×#41×C4111yescharacteristic
537C23C2×#41×C4112yes—
538C23C2×#41×C4112yes—
539C23C2×#41×C4112yes—
540C23H(5,𝔽2)×C4111yescharacteristic
541C232−1+4×C4112yes—
542C232−1+4×C4111yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4#121×C4114yes—
601C2×C4#121×C4114yes—
602C2×C4#124×C4114yes—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22—81no—
609C22—81no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—82no—
614C22C2×#121×C4111yescharacteristic
615C22C2×#121×C4111yescharacteristic
616C22C41×#52511yescharacteristic
617C22C41×#52512yes—
618C22C41×#52512yes—
619C22C2×#124×C4111yescharacteristic
620C22C41×#52912yes—
621C22C41×#52912yes—
622C22C41×#53211yescharacteristic
623C22C41×#53611yescharacteristic
624C22C41×#53711yescharacteristic
625C22C41×#53912yes—
626C22C41×#54112yes—
627C22D42×C4111yescharacteristic
628C22C41×#54712yes—
629C22C41×#54712yes—
630C22C41×#54711yescharacteristic
631C22C41×#54811yescharacteristic
632C22C41×#55212yes—
633C22C41×#55311yescharacteristic
634C22C41×#55612yes—
635C22C41×#55612yes—
636C22C41×#55912yes—
637C4—24no—
638C4—24no—
639C4—24no—
640C4—42no—
641C4—44no—
642C4—44no—
643C4—44no—
644C4—81no—
645C4—81no—
646C4—82no—
647C2—82no—
648C2C41×#239211yescharacteristic
649C2C41×#241311yescharacteristic
650C2C41×#241611yescharacteristic
651C2C41×#245512yes—
652C2C41×#246912yes—
653C2C41×#247812yes—
654C2C41×#254711yescharacteristic
655C2C41×#259211yescharacteristic
656C2C41×#259612yes—
657C2C41×#266411yescharacteristic
658C2C41×#285011yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutator, Frattini, cosocleC24C24×C41
prime radicalC25×C41C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#389C2semidirect
5. C2×C4×C4⋊C4×C41C2semidirect
6. C41×#1445C2semidirect
7. C41×#1442C2semidirect
8. C41×#1441C2semidirect
11. C41×#1436C2semidirect
273. #14808C41direct (N × H)
319. C2×#389C2×C41semidirect
322. C2×C4×C4⋊C4C2×C41semidirect
323. #1445C2×C41semidirect
324. #1442C2×C41semidirect
325. #1441C2×C41semidirect
328. #1436C2×C41semidirect
369. C41#14808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#3972
C2×C41×#3892
C2×C41×#3882
C2×C4×C4⋊C4×C412
C41×#14452
C41×#14422
C41×#14412
C41×#14392
C41×#14362
#1480841