Finite Group Databasebeta

← C41×#27041 #23803242

Subgroups — C41×#27041 #23803242

Order 10496.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2497C211yesmaximal, characteristic, complemented
2C41×#2363C211yesmaximal, characteristic
3C41×#2071C211yesmaximal, characteristic, complemented
4C41×#2067C211yesmaximal, characteristic, complemented
5C41×#2033C211yesmaximal, characteristic
6C41×#2033C211yesmaximal, characteristic
7C41×#1947C211yesmaximal, characteristic, complemented
8C41×#1942C211yesmaximal, characteristic, complemented
9C41×#1923C211yesmaximal, characteristic, complemented
10C41×#1921C211yesmaximal, characteristic, complemented
11C41×#1919C211yesmaximal, characteristic, complemented
12C41×#1864C211yesmaximal, characteristic, complemented
13C41×#1854C211yesmaximal, characteristic, complemented
14C41×#1825C211yesmaximal, characteristic, complemented
15C4×#102×C41C211yesmaximal, characteristic, complemented
16C2×#121×C41C2211yescharacteristic
17C2×C4×D4×C41C2211yescharacteristic
18C2×#117×C41C2211yescharacteristic
19C2×#107×C41C2211yescharacteristic
20C2×#107×C41C2211yescharacteristic
21C2×#107×C41C2211yescharacteristic
22C2×#106×C41C2211yescharacteristic
23C2×C4⋊C8×C41C2211yescharacteristic
24C2×#102×C41C2211yescharacteristic
25C2×#102×C41C2211yescharacteristic
26C2×#102×C41C2211yescharacteristic
27C2×#102×C41C2211yescharacteristic
28C2×C22⋊C8×C41C2211yescharacteristic
29C2×C22⋊C8×C41C2211yescharacteristic
30C2×C4×C8×C41C2211yescharacteristic
31C41×#400—21no—
32C41×#396—21no—
33C41×#390—21no—
34C41×#390C2211yescharacteristic
35C41×#389C2211yescharacteristic
36C41×#389C2211yescharacteristic
37C41×#389C2211yescharacteristic
38C41×#388—21no—
39C41×#388—21no—
40C41×#387—21no—
41C41×#386—21no—
42C41×#384C2211yescharacteristic
43C41×#380C2211yescharacteristic
44C41×#380C2211yescharacteristic
45C4×C4⋊C4×C41C2211yescharacteristic
46C4×C4⋊C4×C41C2211yescharacteristic
47C4×C22⋊C4×C41—21no—
48C4×C22⋊C4×C41C2211yescharacteristic
49C41×#340C2211yescharacteristic
50C41×#340C2211yescharacteristic
51C41×#340C2211yescharacteristic
52C41×#340C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#336C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C22×D4×C41—21no—
60C22×D4×C41C2311yescharacteristic
61C23×C4×C41—21no—
62C23×C4×C41C2311yescharacteristic
63C22×C8×C41C2311yescharacteristic
64C22×C8×C41C2311yescharacteristic
65C22×C8×C41C2311yescharacteristic
66C22×C8×C41C2311yescharacteristic
67#121×C41—22no—
68#121×C41—22no—
69C4×D4×C41—22no—
70C4×D4×C41—41no—
71#117×C41—22no—
72#117×C41—41no—
73C2×C4⋊C4×C41—21no—
74C2×C4⋊C4×C41—21no—
75C2×C4⋊C4×C41—21no—
76C2×C4⋊C4×C41—21no—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41C2311yescharacteristic
79C2×C4⋊C4×C41C2311yescharacteristic
80C2×C4⋊C4×C41C2311yescharacteristic
81C2×C4⋊C4×C41C2311yescharacteristic
82C2×C4⋊C4×C41C2311yescharacteristic
83C2×C4⋊C4×C41C2311yescharacteristic
84C2×C4⋊C4×C41C2311yescharacteristic
85C2×C22⋊C4×C41—21no—
86C2×C22⋊C4×C41—21no—
87C2×C22⋊C4×C41—21no—
88C2×C22⋊C4×C41—21no—
89C2×C22⋊C4×C41—21no—
90C2×C22⋊C4×C41—21no—
91C2×C22⋊C4×C41—21no—
92C2×C22⋊C4×C41D411yescharacteristic
93C2×C22⋊C4×C41D411yescharacteristic
94C2×C42×C41—21no—
95C2×C42×C41—21no—
96C2×C42×C41—21no—
97C2×C42×C41C2311yescharacteristic
98C2×C42×C41C2311yescharacteristic
99#107×C41—22no—
100#107×C41—22no—
101#107×C41—41no—
102#106×C41—22no—
103C4⋊C8×C41—22no—
104#102×C41—22no—
105#102×C41—22no—
106#102×C41—22no—
107#102×C41—41no—
108C22⋊C8×C41—22no—
109C22⋊C8×C41—41no—
110C4×C8×C41—41no—
111#95×C41—21no—
112#95×C41—21no—
113#95×C41—21no—
114#95×C41—21no—
115#95×C41—21no—
116#95×C41—21no—
117#95×C41—21no—
118#95×C41D411yescharacteristic
119#95×C41D411yescharacteristic
120C24×C41—21no—
121C24×C41C2×D411yescharacteristic
122C2×D4×C41—24no—
123C2×D4×C41—21no—
124C2×D4×C41—21no—
125C2×D4×C41—21no—
126C2×D4×C41—21no—
127C2×D4×C41—21no—
128C2×D4×C41—81no—
129C2×D4×C41—81no—
130C2×D4×C41#4112yes—
131C22×C4×C41—21no—
132C22×C4×C41—21no—
133C22×C4×C41—21no—
134C22×C4×C41—21no—
135C22×C4×C41—21no—
136C22×C4×C41—21no—
137C22×C4×C41—21no—
138C22×C4×C41—21no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—21no—
142C22×C4×C41—21no—
143C22×C4×C41—21no—
144C22×C4×C41—42no—
145C22×C4×C41—42no—
146C22×C4×C41—81no—
147C22×C4×C41C2×D411yescharacteristic
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2411yescharacteristic
153C2×C8×C41—21no—
154C2×C8×C41—21no—
155C2×C8×C41—21no—
156C2×C8×C41—21no—
157C2×C8×C41—21no—
158C2×C8×C41—21no—
159C2×C8×C41—21no—
160C2×C8×C41—21no—
161C2×C8×C41—21no—
162C2×C8×C41—21no—
163C2×C8×C41—21no—
164C2×C8×C41#4112yes—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—21no—
168C4⋊C4×C41—21no—
169C4⋊C4×C41—21no—
170C4⋊C4×C41—21no—
171C4⋊C4×C41—21no—
172C4⋊C4×C41—21no—
173C4⋊C4×C41—21no—
174C4⋊C4×C41—21no—
175C4⋊C4×C41—21no—
176C4⋊C4×C41—21no—
177C4⋊C4×C41—42no—
178C4⋊C4×C41—81no—
179C4⋊C4×C41—81no—
180C4⋊C4×C41—81no—
181C4⋊C4×C41—81no—
182C4⋊C4×C41#4112yes—
183C4⋊C4×C41#4112yes—
184C22⋊C4×C41—24no—
185C22⋊C4×C41—22no—
186C22⋊C4×C41—22no—
187C22⋊C4×C41—42no—
188C22⋊C4×C41—42no—
189C22⋊C4×C41—42no—
190C22⋊C4×C41—81no—
191C22⋊C4×C41—81no—
192C22⋊C4×C41—81no—
193C42×C41—21no—
194C42×C41—21no—
195C42×C41—21no—
196C42×C41—21no—
197C42×C41—42no—
198C42×C41—81no—
199C42×C41—81no—
200C23×C41—22no—
201C23×C41—21no—
202C23×C41—21no—
203C23×C41—21no—
204C23×C41—21no—
205C23×C41—21no—
206C23×C41—21no—
207C23×C41—21no—
208C23×C41—41no—
209C23×C41—41no—
210C23×C41—41no—
211C23×C41—41no—
212C23×C41—41no—
213C23×C41—41no—
214C23×C41C22×D411yescharacteristic
215D4×C41—22no—
216D4×C41—22no—
217D4×C41—41no—
218D4×C41—41no—
219D4×C41—84no—
220C2×C4×C41—21no—
221C2×C4×C41—21no—
222C2×C4×C41—21no—
223C2×C4×C41—21no—
224C2×C4×C41—21no—
225C2×C4×C41—22no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
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—41no—
236C2×C4×C41—41no—
237C2×C4×C41—41no—
238C2×C4×C41—41no—
239C2×C4×C41—41no—
240C2×C4×C41—41no—
241C2×C4×C41—41no—
242C2×C4×C41—41no—
243C2×C4×C41—41no—
244C2×C4×C41—41no—
245C2×C4×C41—41no—
246C2×C4×C41—41no—
247C2×C4×C41—41no—
248C2×C4×C41—41no—
249C2×C4×C41—41no—
250C2×C4×C41—41no—
251C2×C4×C41—41no—
252C2×C4×C41—41no—
253C2×C4×C41—41no—
254C2×C4×C41—41no—
255C2×C4×C41—41no—
256C2×C4×C41—41no—
257C2×C4×C41—41no—
258C2×C4×C41—84no—
259C2×C4×C41#13512yes—
260C2×C4×C41#13712yes—
261C2×C4×C41C2×#4111yescharacteristic
262C2×C4×C41C2×#4111yescharacteristic
263C2×C4×C41C2×#4111yescharacteristic
264C2×C4×C41C2×#4111yescharacteristic
265C2×C4×C41H(5,𝔽2)11yescharacteristic
266C2×C4×C412−1+411yescharacteristic
267C8×C41—22no—
268C8×C41—41no—
269C8×C41—41no—
270C8×C41—41no—
271#27041C4111yesmaximal, characteristic, direct product factor, Sylow
272C22×C41—41no—
273C22×C41—41no—
274C22×C41—41no—
275C22×C41—42no—
276C22×C41—41no—
277C22×C41—42no—
278C22×C41—41no—
279C22×C41—42no—
280C22×C41—41no—
281C22×C41—41no—
282C22×C41—81no—
283C22×C41—81no—
284C22×C41—81no—
285C22×C41—81no—
286C22×C41#52511yescharacteristic
287C22×C41#54611yescharacteristic
288C22×C41#54711yescharacteristic
289C22×C41C2×#13511yescharacteristic
290C22×C41C2×#13711yescharacteristic
291C22×C41#57611yescharacteristic
292C22×C41#57611yescharacteristic
293C4×C41—22no—
294C4×C41—22no—
295C4×C41—41no—
296C4×C41—42no—
297C4×C41—41no—
298C4×C41—41no—
299C4×C41—42no—
300C4×C41—81no—
301C4×C41—81no—
302C4×C41—81no—
303C4×C41—81no—
304C4×C41—81no—
305C4×C41#52911yescharacteristic
306C4×C41#53911yescharacteristic
307C4×C41#55311yescharacteristic
308C4×C41#55611yescharacteristic
309#2497C2×C4111yescharacteristic, complemented
310#2363C2×C4111yescharacteristic
311#2071C2×C4111yescharacteristic, complemented
312#2067C2×C4111yescharacteristic, complemented
313#2033C2×C4111yescharacteristic
314#2033C2×C4111yescharacteristic
315#1947C2×C4111yescharacteristic, complemented
316#1942C2×C4111yescharacteristic, complemented
317#1923C2×C4111yescharacteristic, complemented
318#1921C2×C4111yescharacteristic, complemented
319#1919C2×C4111yescharacteristic, complemented
320#1864C2×C4111yescharacteristic, complemented
321#1854C2×C4111yescharacteristic, complemented
322#1825C2×C4111yescharacteristic, complemented
323C4×#102C2×C4111yescharacteristic, complemented
324C2×C41—81no—
325C2×C41—82no—
326C2×C41#246611yescharacteristic
327C2×C41#310711yescharacteristic
328C2×C41#312211yescharacteristic
329C2×C41#330511yescharacteristic
330C2×C41#331411yescharacteristic
331C2×C41#333911yescharacteristic
332C2×C41#335711yescharacteristic
333C2×#121C22×C4111yescharacteristic
334C2×C4×D4C22×C4111yescharacteristic
335C2×#117C22×C4111yescharacteristic
336C2×#107C22×C4111yescharacteristic
337C2×#107C22×C4111yescharacteristic
338C2×#107C22×C4111yescharacteristic
339C2×#106C22×C4111yescharacteristic
340C2×C4⋊C8C22×C4111yescharacteristic
341C2×#102C22×C4111yescharacteristic
342C2×#102C22×C4111yescharacteristic
343C2×#102C22×C4111yescharacteristic
344C2×#102C22×C4111yescharacteristic
345C2×C22⋊C8C22×C4111yescharacteristic
346C2×C22⋊C8C22×C4111yescharacteristic
347C2×C4×C8C22×C4111yescharacteristic
348#400—21no—
349#396—21no—
350#390—21no—
351#390C22×C4111yescharacteristic
352#389C22×C4111yescharacteristic
353#389C22×C4111yescharacteristic
354#389C22×C4111yescharacteristic
355#388—21no—
356#388—21no—
357#387—21no—
358#386—21no—
359#384C22×C4111yescharacteristic
360#380C22×C4111yescharacteristic
361#380C22×C4111yescharacteristic
362C4×C4⋊C4C22×C4111yescharacteristic
363C4×C4⋊C4C22×C4111yescharacteristic
364C4×C22⋊C4—21no—
365C4×C22⋊C4C22×C4111yescharacteristic
366#340C22×C4111yescharacteristic
367#340C22×C4111yescharacteristic
368#340C22×C4111yescharacteristic
369#340C22×C4111yescharacteristic
370#340C22×C4111yescharacteristic
371#340C22×C4111yescharacteristic
372#340C22×C4111yescharacteristic
373#340C22×C4111yescharacteristic
374#336C22×C4111yescharacteristic
375#336C22×C4111yescharacteristic
376C41#2704111yescharacteristic, direct product factor, Sylow
377C22×D4—21no—
378C22×D4C23×C4111yescharacteristic
379C23×C4—21no—
380C23×C4C23×C4111yescharacteristic
381C22×C8C23×C4111yescharacteristic
382C22×C8C23×C4111yescharacteristic
383C22×C8C23×C4111yescharacteristic
384C22×C8C23×C4111yescharacteristic
385#121—22no—
386#121—22no—
387C4×D4—22no—
388C4×D4—41no—
389#117—22no—
390#117—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4C23×C4111yescharacteristic
397C2×C4⋊C4C23×C4111yescharacteristic
398C2×C4⋊C4C23×C4111yescharacteristic
399C2×C4⋊C4C23×C4111yescharacteristic
400C2×C4⋊C4C23×C4111yescharacteristic
401C2×C4⋊C4C23×C4111yescharacteristic
402C2×C4⋊C4C23×C4111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4D4×C4111yescharacteristic
411C2×C22⋊C4D4×C4111yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C4111yescharacteristic
416C2×C42C23×C4111yescharacteristic
417#107—22no—
418#107—22no—
419#107—41no—
420#106—22no—
421C4⋊C8—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425#102—41no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428C4×C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95D4×C4111yescharacteristic
437#95D4×C4111yescharacteristic
438C24—21no—
439C24C2×D4×C4111yescharacteristic
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4#41×C4112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4C2×D4×C4111yescharacteristic
466C22×C4C2×D4×C4111yescharacteristic
467C22×C4C2×D4×C4111yescharacteristic
468C22×C4C2×D4×C4111yescharacteristic
469C22×C4C2×D4×C4111yescharacteristic
470C22×C4C24×C4111yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8#41×C4112yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—81no—
497C4⋊C4—81no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4#41×C4112yes—
501C4⋊C4#41×C4112yes—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—81no—
517C42—81no—
518C23—22no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C4111yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4#135×C4112yes—
578C2×C4#137×C4112yes—
579C2×C4C2×#41×C4111yescharacteristic
580C2×C4C2×#41×C4111yescharacteristic
581C2×C4C2×#41×C4111yescharacteristic
582C2×C4C2×#41×C4111yescharacteristic
583C2×C4H(5,𝔽2)×C4111yescharacteristic
584C2×C42−1+4×C4111yescharacteristic
585C8—22no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—42no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C41×#52511yescharacteristic
604C22C41×#54611yescharacteristic
605C22C41×#54711yescharacteristic
606C22C2×#135×C4111yescharacteristic
607C22C2×#137×C4111yescharacteristic
608C22C41×#57611yescharacteristic
609C22C41×#57611yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C41×#52911yescharacteristic
623C4C41×#53911yescharacteristic
624C4C41×#55311yescharacteristic
625C4C41×#55611yescharacteristic
626C2—81no—
627C2—82no—
628C2C41×#246611yescharacteristic
629C2C41×#310711yescharacteristic
630C2C41×#312211yescharacteristic
631C2C41×#330511yescharacteristic
632C2C41×#331411yescharacteristic
633C2C41×#333911yescharacteristic
634C2C41×#335711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#121×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#2497C2semidirect
3. C41×#2071C2semidirect
4. C41×#2067C2semidirect
7. C41×#1947C2semidirect
8. C41×#1942C2semidirect
9. C41×#1923C2semidirect
10. C41×#1921C2semidirect
11. C41×#1919C2semidirect
12. C41×#1864C2semidirect
13. C41×#1854C2semidirect
14. C41×#1825C2semidirect
15. C4×#102×C41C2semidirect
271. #27041C41direct (N × H)
309. #2497C2×C41semidirect
311. #2071C2×C41semidirect
312. #2067C2×C41semidirect
315. #1947C2×C41semidirect
316. #1942C2×C41semidirect
317. #1923C2×C41semidirect
318. #1921C2×C41semidirect
319. #1919C2×C41semidirect
320. #1864C2×C41semidirect
321. #1854C2×C41semidirect
322. #1825C2×C41semidirect
323. C4×#102C2×C41semidirect
376. C41#27041direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#24972
C41×#23632
C41×#20712
C41×#20672
C41×#20332
C41×#19472
C41×#19422
C41×#19232
C41×#19212
C41×#19192
C41×#18642
C41×#18542
C41×#18252
C4×#102×C412
#2704141