Finite Group Databasebeta

← C41×#32638 #23808839

Subgroups — C41×#32638 #23808839

Order 10496.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2592C211yesmaximal, characteristic
2C41×#2567C211yesmaximal, characteristic, complemented
3C41×#2067C211yesmaximal, characteristic
4C41×#2066C211yesmaximal, characteristic, complemented
5C41×#2042C211yesmaximal, characteristic
6C41×#2042C211yesmaximal, characteristic
7C41×#2024C211yesmaximal, characteristic, complemented
8C41×#2023C211yesmaximal, characteristic
9C41×#1985C211yesmaximal, characteristic, complemented
10C41×#1936C211yesmaximal, characteristic
11C41×#1935C211yesmaximal, characteristic, complemented
12C41×#1928C211yesmaximal, characteristic, complemented
13C41×#1926C211yesmaximal, characteristic
14C41×#1919C211yesmaximal, characteristic, complemented
15C41×#1918C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C41C2211yescharacteristic
17C2×#124×C41C2211yescharacteristic
18C2×C4×Q8×C41C2211yescharacteristic
19C2×#107×C41C2211yescharacteristic
20C2×#106×C41C2211yescharacteristic
21C2×C4⋊C8×C41C2211yescharacteristic
22C2×#103×C41C2211yescharacteristic
23C2×#103×C41C2211yescharacteristic
24C2×#103×C41C2211yescharacteristic
25C2×#103×C41C2211yescharacteristic
26C2×#102×C41C2211yescharacteristic
27C2×#102×C41C2211yescharacteristic
28C2×#102×C41C2211yescharacteristic
29C2×#102×C41C2211yescharacteristic
30C2×#97×C41C2211yescharacteristic
31C41×#397—21no—
32C41×#395—21no—
33C41×#395—21no—
34C41×#393—21no—
35C41×#391—21no—
36C41×#391C2211yescharacteristic
37C41×#391C2211yescharacteristic
38C41×#390C2211yescharacteristic
39C41×#390C2211yescharacteristic
40C41×#389C2211yescharacteristic
41C41×#389C2211yescharacteristic
42C41×#389C2211yescharacteristic
43C41×#389C2211yescharacteristic
44C41×#388—21no—
45C41×#388—21no—
46C41×#384—21no—
47C4×C4⋊C4×C41C2211yescharacteristic
48C4×C4⋊C4×C41C2211yescharacteristic
49C41×#340C2211yescharacteristic
50C41×#340C2211yescharacteristic
51C41×#340C2211yescharacteristic
52C41×#340C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#336C2211yescharacteristic
56C41×#336C2211yescharacteristic
57C41×#336C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C22×Q8×C41—21no—
60C22×Q8×C41D411yescharacteristic
61C22×Q8×C41C2311yescharacteristic
62C22×D4×C41C2311yescharacteristic
63C22×C8×C41C2311yescharacteristic
64C22×C8×C41C2311yescharacteristic
65C22×C8×C41C2311yescharacteristic
66C22×C8×C41C2311yescharacteristic
67C4⋊Q8×C41—41no—
68C4⋊Q8×C41—41no—
69#124×C41—41no—
70#124×C41—41no—
71C4×Q8×C41—41no—
72C4×Q8×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×C41D411yescharacteristic
79C2×C4⋊C4×C41D411yescharacteristic
80C2×C4⋊C4×C41D411yescharacteristic
81C2×C4⋊C4×C41C2311yescharacteristic
82C2×C4⋊C4×C41C2311yescharacteristic
83C2×C4⋊C4×C41C2311yescharacteristic
84C2×C4⋊C4×C41C2311yescharacteristic
85C2×C4⋊C4×C41C2311yescharacteristic
86C2×C4⋊C4×C41C2311yescharacteristic
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×C41—21no—
93C2×C42×C41—21no—
94C2×C42×C41—21no—
95C2×C42×C41C2311yescharacteristic
96C2×C42×C41C2311yescharacteristic
97C2×C42×C41C2311yescharacteristic
98#107×C41—22no—
99#106×C41—22no—
100C4⋊C8×C41—41no—
101#103×C41—22no—
102#103×C41—22no—
103#103×C41—41no—
104#103×C41—41no—
105#102×C41—22no—
106#102×C41—22no—
107#102×C41—41no—
108#102×C41—41no—
109#97×C41—41no—
110#95×C41—21no—
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×C41—21no—
119#95×C41—21no—
120C24×C41—21no—
121C2×Q8×C41—22no—
122C2×Q8×C41—21no—
123C2×Q8×C41—21no—
124C2×Q8×C41—21no—
125C2×Q8×C41—21no—
126C2×Q8×C41—21no—
127C2×Q8×C41—21no—
128C2×Q8×C41—41no—
129C2×Q8×C41—41no—
130C2×Q8×C41—42no—
131C2×Q8×C41—81no—
132C2×Q8×C41—81no—
133C2×D4×C41—21no—
134C2×D4×C41—21no—
135C2×D4×C41—21no—
136C2×D4×C41—21no—
137C2×D4×C41—21no—
138C2×D4×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—21no—
145C22×C4×C41—21no—
146C22×C4×C41C2×D411yescharacteristic
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—21no—
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—41no—
176C4⋊C4×C41—41no—
177C4⋊C4×C41—41no—
178C4⋊C4×C41—42no—
179C4⋊C4×C41—81no—
180C4⋊C4×C41—81no—
181C4⋊C4×C41—81no—
182C4⋊C4×C41—81no—
183C4⋊C4×C41#4112yes—
184C4⋊C4×C41#4112yes—
185C22⋊C4×C41—42no—
186C22⋊C4×C41—42no—
187C22⋊C4×C41—42no—
188C22⋊C4×C41—42no—
189C22⋊C4×C41—81no—
190C22⋊C4×C41—81no—
191C42×C41—21no—
192C42×C41—21no—
193C42×C41—21no—
194C42×C41—21no—
195C42×C41—21no—
196C42×C41—21no—
197C42×C41—42no—
198C42×C41—81no—
199C23×C41—41no—
200C23×C41—41no—
201C23×C41—41no—
202C23×C41—41no—
203C23×C41—41no—
204C23×C41—41no—
205C23×C41—41no—
206C23×C41C22×D411yescharacteristic
207Q8×C41—44no—
208Q8×C41—41no—
209Q8×C41—41no—
210Q8×C41—41no—
211Q8×C41—41no—
212Q8×C41—84no—
213D4×C41—41no—
214D4×C41—41no—
215D4×C41—41no—
216D4×C41—41no—
217C2×C4×C41—21no—
218C2×C4×C41—21no—
219C2×C4×C41—21no—
220C2×C4×C41—21no—
221C2×C4×C41—21no—
222C2×C4×C41—21no—
223C2×C4×C41—21no—
224C2×C4×C41—22no—
225C2×C4×C41—22no—
226C2×C4×C41—21no—
227C2×C4×C41—21no—
228C2×C4×C41—21no—
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—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#13712yes—
256C2×C4×C41C2×#4111yescharacteristic
257C2×C4×C41C2×#4111yescharacteristic
258C2×C4×C41H(5,𝔽2)11yescharacteristic
259C2×C4×C41H(5,𝔽2)11yescharacteristic
260C2×C4×C412−1+411yescharacteristic
261C2×C4×C412−1+411yescharacteristic
262C8×C41—41no—
263C8×C41—41no—
264C8×C41—41no—
265C8×C41—41no—
266#32638C4111yesmaximal, characteristic, direct product factor, Sylow
267C22×C41—81no—
268C22×C41—81no—
269C22×C41—81no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—81no—
273C22×C41—81no—
274C22×C41#53411yescharacteristic
275C22×C41#54811yescharacteristic
276C22×C41#54811yescharacteristic
277C22×C41C2×#13711yescharacteristic
278C22×C41#57511yescharacteristic
279C22×C41#57611yescharacteristic
280C22×C41#57711yescharacteristic
281C4×C41—22no—
282C4×C41—42no—
283C4×C41—42no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—41no—
287C4×C41—41no—
288C4×C41—41no—
289C4×C41—81no—
290C4×C41—81no—
291C4×C41—81no—
292C4×C41—81no—
293C4×C41—81no—
294C4×C41#54211yescharacteristic
295C4×C41#54211yescharacteristic
296C4×C41#55511yescharacteristic
297C4×C41#56311yescharacteristic
298#2592C2×C4111yescharacteristic
299#2567C2×C4111yescharacteristic, complemented
300#2067C2×C4111yescharacteristic
301#2066C2×C4111yescharacteristic, complemented
302#2042C2×C4111yescharacteristic
303#2042C2×C4111yescharacteristic
304#2024C2×C4111yescharacteristic, complemented
305#2023C2×C4111yescharacteristic
306#1985C2×C4111yescharacteristic, complemented
307#1936C2×C4111yescharacteristic
308#1935C2×C4111yescharacteristic, complemented
309#1928C2×C4111yescharacteristic, complemented
310#1926C2×C4111yescharacteristic
311#1919C2×C4111yescharacteristic, complemented
312#1918C2×C4111yescharacteristic, complemented
313C2×C41—161no—
314C2×C41#273111yescharacteristic
315C2×C41#319611yescharacteristic
316C2×C41#319811yescharacteristic
317C2×C41#336911yescharacteristic
318C2×C41#337011yescharacteristic
319C2×C41#337511yescharacteristic
320C2×C41#337611yescharacteristic
321C2×C4⋊Q8C22×C4111yescharacteristic
322C2×#124C22×C4111yescharacteristic
323C2×C4×Q8C22×C4111yescharacteristic
324C2×#107C22×C4111yescharacteristic
325C2×#106C22×C4111yescharacteristic
326C2×C4⋊C8C22×C4111yescharacteristic
327C2×#103C22×C4111yescharacteristic
328C2×#103C22×C4111yescharacteristic
329C2×#103C22×C4111yescharacteristic
330C2×#103C22×C4111yescharacteristic
331C2×#102C22×C4111yescharacteristic
332C2×#102C22×C4111yescharacteristic
333C2×#102C22×C4111yescharacteristic
334C2×#102C22×C4111yescharacteristic
335C2×#97C22×C4111yescharacteristic
336#397—21no—
337#395—21no—
338#395—21no—
339#393—21no—
340#391—21no—
341#391C22×C4111yescharacteristic
342#391C22×C4111yescharacteristic
343#390C22×C4111yescharacteristic
344#390C22×C4111yescharacteristic
345#389C22×C4111yescharacteristic
346#389C22×C4111yescharacteristic
347#389C22×C4111yescharacteristic
348#389C22×C4111yescharacteristic
349#388—21no—
350#388—21no—
351#384—21no—
352C4×C4⋊C4C22×C4111yescharacteristic
353C4×C4⋊C4C22×C4111yescharacteristic
354#340C22×C4111yescharacteristic
355#340C22×C4111yescharacteristic
356#340C22×C4111yescharacteristic
357#340C22×C4111yescharacteristic
358#340C22×C4111yescharacteristic
359#340C22×C4111yescharacteristic
360#336C22×C4111yescharacteristic
361#336C22×C4111yescharacteristic
362#336C22×C4111yescharacteristic
363#336C22×C4111yescharacteristic
364C41#3263811yescharacteristic, direct product factor, Sylow
365C22×Q8—21no—
366C22×Q8D4×C4111yescharacteristic
367C22×Q8C23×C4111yescharacteristic
368C22×D4C23×C4111yescharacteristic
369C22×C8C23×C4111yescharacteristic
370C22×C8C23×C4111yescharacteristic
371C22×C8C23×C4111yescharacteristic
372C22×C8C23×C4111yescharacteristic
373C4⋊Q8—41no—
374C4⋊Q8—41no—
375#124—41no—
376#124—41no—
377C4×Q8—41no—
378C4×Q8—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4D4×C4111yescharacteristic
385C2×C4⋊C4D4×C4111yescharacteristic
386C2×C4⋊C4D4×C4111yescharacteristic
387C2×C4⋊C4C23×C4111yescharacteristic
388C2×C4⋊C4C23×C4111yescharacteristic
389C2×C4⋊C4C23×C4111yescharacteristic
390C2×C4⋊C4C23×C4111yescharacteristic
391C2×C4⋊C4C23×C4111yescharacteristic
392C2×C4⋊C4C23×C4111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42C23×C4111yescharacteristic
402C2×C42C23×C4111yescharacteristic
403C2×C42C23×C4111yescharacteristic
404#107—22no—
405#106—22no—
406C4⋊C8—41no—
407#103—22no—
408#103—22no—
409#103—41no—
410#103—41no—
411#102—22no—
412#102—22no—
413#102—41no—
414#102—41no—
415#97—41no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426C24—21no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8—81no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4C2×D4×C4111yescharacteristic
453C22×C4C2×D4×C4111yescharacteristic
454C22×C4C2×D4×C4111yescharacteristic
455C22×C4C2×D4×C4111yescharacteristic
456C22×C4C2×D4×C4111yescharacteristic
457C22×C4C2×D4×C4111yescharacteristic
458C22×C4C24×C4111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4#41×C4112yes—
490C4⋊C4#41×C4112yes—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C42—81no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23C22×D4×C4111yescharacteristic
513Q8—44no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—84no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
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#137×C4112yes—
562C2×C4C2×#41×C4111yescharacteristic
563C2×C4C2×#41×C4111yescharacteristic
564C2×C4H(5,𝔽2)×C4111yescharacteristic
565C2×C4H(5,𝔽2)×C4111yescharacteristic
566C2×C42−1+4×C4111yescharacteristic
567C2×C42−1+4×C4111yescharacteristic
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C41×#53411yescharacteristic
580C22C41×#54811yescharacteristic
581C22C41×#54811yescharacteristic
582C22C2×#137×C4111yescharacteristic
583C22C41×#57511yescharacteristic
584C22C41×#57611yescharacteristic
585C22C41×#57711yescharacteristic
586C4—22no—
587C4—42no—
588C4—42no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4C41×#54211yescharacteristic
600C4C41×#54211yescharacteristic
601C4C41×#55511yescharacteristic
602C4C41×#56311yescharacteristic
603C2—161no—
604C2C41×#273111yescharacteristic
605C2C41×#319611yescharacteristic
606C2C41×#319811yescharacteristic
607C2C41×#336911yescharacteristic
608C2C41×#337011yescharacteristic
609C2C41×#337511yescharacteristic
610C2C41×#337611yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×D4×C41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×Q8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2567C2semidirect
4. C41×#2066C2semidirect
7. C41×#2024C2semidirect
9. C41×#1985C2semidirect
11. C41×#1935C2semidirect
12. C41×#1928C2semidirect
14. C41×#1919C2semidirect
15. C41×#1918C2semidirect
266. #32638C41direct (N × H)
299. #2567C2×C41semidirect
301. #2066C2×C41semidirect
304. #2024C2×C41semidirect
306. #1985C2×C41semidirect
308. #1935C2×C41semidirect
309. #1928C2×C41semidirect
311. #1919C2×C41semidirect
312. #1918C2×C41semidirect
364. C41#32638direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#25922
C41×#25672
C41×#20672
C41×#20662
C41×#20422
C41×#20242
C41×#20232
C41×#19852
C41×#19362
C41×#19352
C41×#19282
C41×#19262
C41×#19192
C41×#19182
#3263841