Finite Group Databasebeta

← C41×#14506 #23790707

Subgroups — C41×#14506 #23790707

Order 10496.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C41C211yesmaximal, characteristic
2C2×C41×#388C212yesmaximal, complemented
3C41×#1445C212yesmaximal, complemented
4C41×#1439C212yesmaximal, complemented
5C41×#1438C211yesmaximal, characteristic
6C41×#1438C211yesmaximal, characteristic
7C41×#1437C212yesmaximal, complemented
8C41×C4⋊#95C212yesmaximal, complemented
9C41×C22⋊#95C212yesmaximal, complemented
10C23×D4×C41C2211yescharacteristic
11C24×C4×C41C2211yescharacteristic
12C2×#123×C41—28no—
13C2×#123×C41C418yescomplemented
14C22×C4⋊C4×C41C2212yes—
15C22×C4⋊C4×C41C2212yes—
16C22×C22⋊C4×C41C2212yes—
17C22×C22⋊C4×C41C2212yes—
18C22×C22⋊C4×C41C2211yescharacteristic
19C22×C22⋊C4×C41C2212yes—
20C22×C22⋊C4×C41C2212yes—
21C22×C22⋊C4×C41C2211yescharacteristic
22C22×C22⋊C4×C41C2211yescharacteristic
23C22×C42×C41C2212yes—
24C41×#388—28no—
25C2×#95×C41C2212yes—
26C2×#95×C41C2212yes—
27C2×#95×C41C2212yes—
28C2×#95×C41C2212yes—
29C2×#95×C41C2212yes—
30C2×#95×C41C2212yes—
31C2×#95×C41C2211yescharacteristic
32C2×#95×C41C2212yes—
33C2×#95×C41C2211yescharacteristic
34C25×C41C2311yescharacteristic
35C25×C41C2311yescharacteristic
36C22×D4×C41—24no—
37C22×D4×C41—42no—
38C22×D4×C41—41no—
39C22×D4×C41—41no—
40C22×D4×C41C2×C414yes—
41C23×C4×C41—24no—
42C23×C4×C41—42no—
43C23×C4×C41—41no—
44C23×C4×C41—41no—
45C23×C4×C41C2×C414yes—
46C23×C4×C41C2312yes—
47C23×C4×C41C2312yes—
48C23×C4×C41C2312yes—
49C23×C4×C41C2311yescharacteristic
50C23×C4×C41C2312yes—
51C23×C4×C41C2312yes—
52C23×C4×C41C2312yes—
53#123×C41—232no—
54C2×C4⋊C4×C41—24no—
55C2×C4⋊C4×C41—24no—
56C2×C4⋊C4×C41—24no—
57C2×C4⋊C4×C41—24no—
58C2×C4⋊C4×C41—42no—
59C2×C4⋊C4×C41C2×C418yes—
60C2×C22⋊C4×C41—24no—
61C2×C22⋊C4×C41—24no—
62C2×C22⋊C4×C41—24no—
63C2×C22⋊C4×C41—24no—
64C2×C22⋊C4×C41—24no—
65C2×C22⋊C4×C41—24no—
66C2×C22⋊C4×C41—24no—
67C2×C22⋊C4×C41—24no—
68C2×C22⋊C4×C41—41no—
69C2×C22⋊C4×C41—42no—
70C2×C22⋊C4×C41—42no—
71C2×C22⋊C4×C41—42no—
72C2×C22⋊C4×C41—42no—
73C2×C22⋊C4×C41—41no—
74C2×C22⋊C4×C41—42no—
75C2×C22⋊C4×C41C2×C418yes—
76C2×C22⋊C4×C41C2×C414yes—
77C2×C22⋊C4×C41D418yes—
78C2×C42×C41—24no—
79C2×C42×C41—24no—
80C2×C42×C41—42no—
81#95×C41—24no—
82#95×C41—24no—
83#95×C41—41no—
84#95×C41—42no—
85#95×C41—42no—
86#95×C41—42no—
87#95×C41—42no—
88#95×C41—42no—
89#95×C41—41no—
90C24×C41—22no—
91C24×C41—22no—
92C24×C41—22no—
93C24×C41—22no—
94C24×C41—21no—
95C24×C41—21no—
96C24×C41—22no—
97C24×C41—22no—
98C24×C41—22no—
99C24×C41—22no—
100C24×C41—22no—
101C24×C41—22no—
102C24×C41—21no—
103C24×C41—21no—
104C24×C41—22no—
105C24×C41C22×C412yes—
106C24×C41C22×C412yes—
107C24×C41C2×D414yes—
108C24×C41C2411yescharacteristic
109C2×D4×C41—28no—
110C2×D4×C41—44no—
111C2×D4×C41—44no—
112C2×D4×C41—48no—
113C2×D4×C41—48no—
114C22×C4×C41—22no—
115C22×C4×C41—22no—
116C22×C4×C41—22no—
117C22×C4×C41—22no—
118C22×C4×C41—28no—
119C22×C4×C41—22no—
120C22×C4×C41—22no—
121C22×C4×C41—22no—
122C22×C4×C41—22no—
123C22×C4×C41—22no—
124C22×C4×C41—22no—
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—21no—
136C22×C4×C41—21no—
137C22×C4×C41—22no—
138C22×C4×C41—22no—
139C22×C4×C41—22no—
140C22×C4×C41—22no—
141C22×C4×C41—22no—
142C22×C4×C41—22no—
143C22×C4×C41—22no—
144C22×C4×C41—22no—
145C22×C4×C41—22no—
146C22×C4×C41—22no—
147C22×C4×C41—22no—
148C22×C4×C41—22no—
149C22×C4×C41—22no—
150C22×C4×C41—22no—
151C22×C4×C41—22no—
152C22×C4×C41—22no—
153C22×C4×C41—22no—
154C22×C4×C41—22no—
155C22×C4×C41—44no—
156C22×C4×C41—44no—
157C22×C4×C41—48no—
158C22×C4×C41—48no—
159C22×C4×C41C22×C414yes—
160C22×C4×C41C22×C412yes—
161C22×C4×C41C22×C414yes—
162C22×C4×C41C2×D414yes—
163C22×C4×C41C2×D414yes—
164C22×C4×C41#4114yes—
165C22×C4×C41#4114yes—
166C4⋊C4×C41—216no—
167C4⋊C4×C41—48no—
168C22⋊C4×C41—216no—
169C22⋊C4×C41—44no—
170C22⋊C4×C41—48no—
171C22⋊C4×C41—48no—
172C22⋊C4×C41—48no—
173C22⋊C4×C41—44no—
174C22⋊C4×C41C22⋊C4116yescomplemented
175C42×C41—48no—
176C23×C41—24no—
177C23×C41—22no—
178C23×C41—22no—
179C23×C41—24no—
180C23×C41—24no—
181C23×C41—24no—
182C23×C41—24no—
183C23×C41—24no—
184C23×C41—24no—
185C23×C41—24no—
186C23×C41—22no—
187C23×C41—24no—
188C23×C41—22no—
189C23×C41—22no—
190C23×C41—24no—
191C23×C41—42no—
192C23×C41—42no—
193C23×C41—42no—
194C23×C41—42no—
195C23×C41—41no—
196C23×C41—42no—
197C23×C41—41no—
198C23×C41—41no—
199C23×C41—42no—
200C23×C41—41no—
201C23×C41—42no—
202C23×C41—42no—
203C23×C41—42no—
204C23×C41—42no—
205C23×C41—42no—
206C23×C41—42no—
207C23×C41—42no—
208C23×C41—42no—
209C23×C41—42no—
210C23×C41—42no—
211C23×C41—41no—
212C23×C41—42no—
213C23×C41—41no—
214C23×C41—41no—
215C23×C41—42no—
216C23×C41—41no—
217C23×C41C2×C22⋊C414yes—
218C23×C41C23×C411yescharacteristic
219C23×C41C22×D412yes—
220C23×C41C2×#4112yes—
221C23×C41C2×#4112yes—
222C23×C41H(5,𝔽2)12yes—
223C23×C41H(5,𝔽2)11yescharacteristic
224C23×C41H(5,𝔽2)11yescharacteristic
225C23×C41H(5,𝔽2)12yes—
226C23×C412−1+412yes—
227D4×C41—416no—
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—22no—
236C2×C4×C41—24no—
237C2×C4×C41—24no—
238C2×C4×C41—22no—
239C2×C4×C41—22no—
240C2×C4×C41—24no—
241C2×C4×C41—24no—
242C2×C4×C41—24no—
243C2×C4×C41—24no—
244C2×C4×C41—24no—
245C2×C4×C41—24no—
246C2×C4×C41—416no—
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—42no—
254C2×C4×C41—42no—
255C2×C4×C41—42no—
256C2×C4×C41—42no—
257C2×C4×C41—42no—
258C2×C4×C41—42no—
259C2×C4×C41—42no—
260C2×C4×C41—42no—
261C2×C4×C41—42no—
262C2×C4×C41—42no—
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—42no—
271C2×C4×C41—42no—
272C2×C4×C41—42no—
273C2×C4×C41—42no—
274C2×C4×C41—42no—
275C2×C4×C41C2×C22⋊C418yes—
276#14506C4111yesmaximal, characteristic, direct product factor, Sylow
277C22×C41—24no—
278C22×C41—28no—
279C22×C41—44no—
280C22×C41—42no—
281C22×C41—42no—
282C22×C41—44no—
283C22×C41—44no—
284C22×C41—44no—
285C22×C41—44no—
286C22×C41—42no—
287C22×C41—44no—
288C22×C41—44no—
289C22×C41—42no—
290C22×C41—42no—
291C22×C41—82no—
292C22×C41—82no—
293C22×C41—82no—
294C22×C41—82no—
295C22×C41C22×C22⋊C411yescharacteristic
296C22×C41C4×#4112yes—
297C22×C41#51811yescharacteristic
298C22×C41#51811yescharacteristic
299C22×C41#52012yes—
300C22×C41#53512yes—
301C22×C41#53512yes—
302C22×C41#53812yes—
303C22×C41#53912yes—
304C22×C41#54012yes—
305C22×C41#54212yes—
306C22×C41#54612yes—
307C22×C41#54612yes—
308C22×C41#54712yes—
309C22×C41#54712yes—
310C22×C41#55111yescharacteristic
311C22×C41#55312yes—
312C22×C41#55911yescharacteristic
313C22×C41#56011yescharacteristic
314C22×C41#56212yes—
315C22×C41#56311yescharacteristic
316C4×C41—28no—
317C4×C41—44no—
318C4×C41—42no—
319C4×C41—44no—
320C4×C41—44no—
321C4×C41—82no—
322C4×C41—82no—
323C22×#123C2×C4111yescharacteristic
324C2×#388C2×C4112yescomplemented
325#1445C2×C4112yescomplemented
326#1439C2×C4112yescomplemented
327#1438C2×C4111yescharacteristic
328#1438C2×C4111yescharacteristic
329#1437C2×C4112yescomplemented
330C4⋊#95C2×C4112yescomplemented
331C22⋊#95C2×C4112yescomplemented
332C2×C41—44no—
333C2×C41—82no—
334C2×C41#230911yescharacteristic
335C2×C41#233512yes—
336C2×C41#233912yes—
337C2×C41#237411yescharacteristic
338C2×C41#237611yescharacteristic
339C2×C41#270312yes—
340C2×C41#270612yes—
341C2×C41#271012yes—
342C2×C41#271812yes—
343C23×D4C22×C4111yescharacteristic
344C24×C4C22×C4111yescharacteristic
345C2×#123—28no—
346C2×#123C4×C4118yescomplemented
347C22×C4⋊C4C22×C4112yes—
348C22×C4⋊C4C22×C4112yes—
349C22×C22⋊C4C22×C4112yes—
350C22×C22⋊C4C22×C4112yes—
351C22×C22⋊C4C22×C4111yescharacteristic
352C22×C22⋊C4C22×C4112yes—
353C22×C22⋊C4C22×C4112yes—
354C22×C22⋊C4C22×C4111yescharacteristic
355C22×C22⋊C4C22×C4111yescharacteristic
356C22×C42C22×C4112yes—
357#388—28no—
358C2×#95C22×C4112yes—
359C2×#95C22×C4112yes—
360C2×#95C22×C4112yes—
361C2×#95C22×C4112yes—
362C2×#95C22×C4112yes—
363C2×#95C22×C4112yes—
364C2×#95C22×C4111yescharacteristic
365C2×#95C22×C4112yes—
366C2×#95C22×C4111yescharacteristic
367C41#1450611yescharacteristic, direct product factor, Sylow
368C25C23×C4111yescharacteristic
369C25C23×C4111yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C4114yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C4114yes—
380C23×C4C23×C4112yes—
381C23×C4C23×C4112yes—
382C23×C4C23×C4112yes—
383C23×C4C23×C4111yescharacteristic
384C23×C4C23×C4112yes—
385C23×C4C23×C4112yes—
386C23×C4C23×C4112yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C4118yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C4118yes—
410C2×C22⋊C4C2×C4×C4114yes—
411C2×C22⋊C4D4×C4118yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C4112yes—
440C24C22×C4×C4112yes—
441C24C2×D4×C4114yes—
442C24C24×C4111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
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—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C4114yes—
494C22×C4C22×C4×C4112yes—
495C22×C4C22×C4×C4114yes—
496C22×C4C2×D4×C4114yes—
497C22×C4C2×D4×C4114yes—
498C22×C4#41×C4114yes—
499C22×C4#41×C4114yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C41116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C4114yes—
552C23C23×C4×C4111yescharacteristic
553C23C22×D4×C4112yes—
554C23C2×#41×C4112yes—
555C23C2×#41×C4112yes—
556C23H(5,𝔽2)×C4112yes—
557C23H(5,𝔽2)×C4111yescharacteristic
558C23H(5,𝔽2)×C4111yescharacteristic
559C23H(5,𝔽2)×C4112yes—
560C232−1+4×C4112yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C4118yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C4111yescharacteristic
629C22C4×#41×C4112yes—
630C22C41×#51811yescharacteristic
631C22C41×#51811yescharacteristic
632C22C41×#52012yes—
633C22C41×#53512yes—
634C22C41×#53512yes—
635C22C41×#53812yes—
636C22C41×#53912yes—
637C22C41×#54012yes—
638C22C41×#54212yes—
639C22C41×#54612yes—
640C22C41×#54612yes—
641C22C41×#54712yes—
642C22C41×#54712yes—
643C22C41×#55111yescharacteristic
644C22C41×#55312yes—
645C22C41×#55911yescharacteristic
646C22C41×#56011yescharacteristic
647C22C41×#56212yes—
648C22C41×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C41×#230911yescharacteristic
659C2C41×#233512yes—
660C2C41×#233912yes—
661C2C41×#237411yescharacteristic
662C2C41×#237611yescharacteristic
663C2C41×#270312yes—
664C2C41×#270612yes—
665C2C41×#271012yes—
666C2C41×#271812yes—
subgroupG/H
center, socleC24×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC24C24×C41
prime radicalC23×D4×C41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#388C2semidirect
3. C41×#1445C2semidirect
4. C41×#1439C2semidirect
7. C41×#1437C2semidirect
8. C41×C4⋊#95C2semidirect
9. C41×C22⋊#95C2semidirect
13. C2×#123×C41C4semidirect
174. C22⋊C4×C41C22⋊C4semidirect
276. #14506C41direct (N × H)
324. C2×#388C2×C41semidirect
325. #1445C2×C41semidirect
326. #1439C2×C41semidirect
329. #1437C2×C41semidirect
330. C4⋊#95C2×C41semidirect
331. C22⋊#95C2×C41semidirect
346. C2×#123C4×C41semidirect
367. C41#14506direct (N × H)
508. C22⋊C4C22⋊C4×C41semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C412
C2×C41×#3882
C41×#14452
C41×#14392
C41×#14382
C41×#14372
C41×C4⋊#952
C41×C22⋊#952
#1450641