Finite Group Databasebeta

← C41×#32709 #23808910

Subgroups — C41×#32709 #23808910

Order 10496.

1062 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2848C211yesmaximal, characteristic, complemented
2C41×#2847C211yesmaximal, characteristic
3C41×#2077C211yesmaximal, characteristic, complemented
4C41×#2076C211yesmaximal, characteristic, complemented
5C41×#2075C211yesmaximal, characteristic, complemented
6C41×#2036C211yesmaximal, characteristic, complemented
7C41×#2036C211yesmaximal, characteristic, complemented
8C41×#2035C211yesmaximal, characteristic, complemented
9C41×#2034C211yesmaximal, characteristic, complemented
10C41×#2033C211yesmaximal, characteristic, complemented
11C41×#2033C211yesmaximal, characteristic, complemented
12C41×#2000C211yesmaximal, characteristic, complemented
13C41×#2000C211yesmaximal, characteristic, complemented
14C41×#2000C211yesmaximal, characteristic, complemented
15C41×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic, complemented
18C2×C22⋊Q8×C41C2211yescharacteristic
19C2×C22⋊Q8×C41C2211yescharacteristic
20C2×C22⋊Q8×C41C2211yescharacteristic
21C2×#121×C41C2211yescharacteristic
22C2×#121×C41C2211yescharacteristic
23C2×#121×C41C2211yescharacteristic
24C2×#120×C41—21no—
25C2×#107×C41C2211yescharacteristic, complemented
26C2×#107×C41C2211yescharacteristic, complemented
27C2×#106×C41C2211yescharacteristic, complemented
28C2×#103×C41C2211yescharacteristic, complemented
29C2×#103×C41C2211yescharacteristic, complemented
30C2×#103×C41C2211yescharacteristic, complemented
31C2×#102×C41C2211yescharacteristic, complemented
32C2×#102×C41C2211yescharacteristic, complemented
33C2×#102×C41C2211yescharacteristic, complemented
34C2×C22⋊C8×C41C2211yescharacteristic
35C2×C22⋊C8×C41C2211yescharacteristic
36C2×C22⋊C8×C41C2211yescharacteristic
37C2×C22⋊C8×C41C2211yescharacteristic
38C2×C22⋊C8×C41C2211yescharacteristic
39C2×C22⋊C8×C41C2211yescharacteristic
40C41×#386—21no—
41C41×#386—21no—
42C41×#386—21no—
43C41×#385—21no—
44C41×#385—21no—
45C41×#385—21no—
46C41×#380C2211yescharacteristic
47C41×#380C2211yescharacteristic
48C41×#380C2211yescharacteristic
49C41×#380C2211yescharacteristic
50C41×#380C2211yescharacteristic
51C41×#380C2211yescharacteristic
52C41×#379—21no—
53C41×#340C2211yescharacteristic, complemented
54C41×#340C2211yescharacteristic, complemented
55C41×#340C2211yescharacteristic, complemented
56C41×#340C2211yescharacteristic, complemented
57C41×#340C2211yescharacteristic, complemented
58C41×#340C2211yescharacteristic, complemented
59C25×C41D411yescharacteristic
60C22×Q8×C41C2311yescharacteristic
61C22×D4×C41—21no—
62C22×D4×C41—21no—
63C22×D4×C41—21no—
64C22×D4×C41C2311yescharacteristic
65C23×C4×C41—41no—
66C23×C4×C41—41no—
67C23×C4×C41—41no—
68C23×C4×C41—41no—
69C23×C4×C41—41no—
70C23×C4×C41—41no—
71C23×C4×C41D411yescharacteristic
72C23×C4×C41D411yescharacteristic
73C23×C4×C41D411yescharacteristic
74C23×C4×C41C2311yescharacteristic
75C23×C4×C41C2311yescharacteristic
76C23×C4×C41C2311yescharacteristic
77C2×SD16×C41—41no—
78C2×SD16×C41—41no—
79C2×SD16×C41—41no—
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84C22⋊Q8×C41—41no—
85C22⋊Q8×C41—41no—
86C22⋊Q8×C41—41no—
87C22⋊Q8×C41—41no—
88C22⋊Q8×C41—41no—
89C22⋊Q8×C41—41no—
90#121×C41—41no—
91#121×C41—41no—
92#121×C41—41no—
93#121×C41—41no—
94#121×C41—41no—
95#121×C41—41no—
96#120×C41—44no—
97C2×C4⋊C4×C41—21no—
98C2×C4⋊C4×C41—21no—
99C2×C4⋊C4×C41—21no—
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C4⋊C4×C41C2311yescharacteristic
102C2×C4⋊C4×C41C2311yescharacteristic
103C2×C4⋊C4×C41C2311yescharacteristic
104C2×C4⋊C4×C41C2311yescharacteristic
105C2×C4⋊C4×C41C2311yescharacteristic
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41—21no—
110C2×C22⋊C4×C41—21no—
111C2×C22⋊C4×C41—21no—
112C2×C22⋊C4×C41—21no—
113C2×C22⋊C4×C41—21no—
114C2×C22⋊C4×C41—21no—
115C2×C22⋊C4×C41—21no—
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—21no—
118#107×C41—41no—
119#107×C41—41no—
120#106×C41—41no—
121#103×C41—41no—
122#103×C41—41no—
123#103×C41—41no—
124#102×C41—41no—
125#102×C41—41no—
126#102×C41—41no—
127C22⋊C8×C41—41no—
128C22⋊C8×C41—41no—
129C22⋊C8×C41—41no—
130C22⋊C8×C41—41no—
131C22⋊C8×C41—41no—
132C22⋊C8×C41—41no—
133#95×C41—21no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41—21no—
138#95×C41—21no—
139C24×C41—22no—
140C24×C41—22no—
141C24×C41—22no—
142C24×C41—21no—
143C24×C41—41no—
144C24×C41—41no—
145C24×C41—41no—
146C24×C41—41no—
147C24×C41C2×D411yescharacteristic
148C24×C41C2×D411yescharacteristic
149C24×C41C2×D411yescharacteristic
150C2×Q8×C41—21no—
151C2×Q8×C41—21no—
152C2×Q8×C41—21no—
153C2×Q8×C41—21no—
154C2×Q8×C41—21no—
155C2×Q8×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—42no—
163C2×D4×C41—42no—
164C2×D4×C41—42no—
165C2×D4×C41—42no—
166C2×D4×C41—42no—
167C2×D4×C41—42no—
168C2×D4×C41—42no—
169C2×D4×C41—42no—
170C2×D4×C41—42no—
171C22×C4×C41—21no—
172C22×C4×C41—21no—
173C22×C4×C41—21no—
174C22×C4×C41—21no—
175C22×C4×C41—21no—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
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—21no—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—41no—
197C22×C4×C41—41no—
198C22×C4×C41—41no—
199C22×C4×C41—41no—
200C22×C4×C41—41no—
201C22×C4×C41—41no—
202C22×C4×C41—41no—
203C22×C4×C41—41no—
204C22×C4×C41—41no—
205C22×C4×C41—44no—
206C22×C4×C41—44no—
207C22×C4×C41—44no—
208C22×C4×C41—44no—
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2×D411yescharacteristic
211C22×C4×C41C2×D411yescharacteristic
212C22×C4×C41C2411yescharacteristic
213SD16×C41—44no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41—21no—
225C2×C8×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—21no—
235C4⋊C4×C41—21no—
236C4⋊C4×C41—21no—
237C4⋊C4×C41—21no—
238C4⋊C4×C41—42no—
239C4⋊C4×C41—42no—
240C4⋊C4×C41—42no—
241C22⋊C4×C41—42no—
242C22⋊C4×C41—42no—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—42no—
252C22⋊C4×C41—42no—
253C23×C41—21no—
254C23×C41—21no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—21no—
267C23×C41—21no—
268C23×C41—21no—
269C23×C41—21no—
270C23×C41—21no—
271C23×C41—44no—
272C23×C41—44no—
273C23×C41—44no—
274C23×C41—44no—
275C23×C41—44no—
276C23×C41—44no—
277C23×C41—44no—
278C23×C41—41no—
279C23×C41—41no—
280C23×C41—41no—
281C23×C41—41no—
282C23×C41—41no—
283C23×C41—41no—
284C23×C41—41no—
285C23×C41#13512yes—
286C23×C41AGL(1,ℤ/8)12yes—
287C23×C41#13712yes—
288C23×C41C22×D411yescharacteristic
289Q8×C41—41no—
290Q8×C41—41no—
291Q8×C41—41no—
292Q8×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—41no—
296D4×C41—41no—
297D4×C41—84no—
298D4×C41—84no—
299D4×C41—84no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—44no—
310C2×C4×C41—44no—
311C2×C4×C41—44no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—41no—
335C2×C4×C41—41no—
336C2×C4×C41—41no—
337C2×C4×C41—41no—
338C2×C4×C41—41no—
339C2×C4×C41—41no—
340C2×C4×C41—41no—
341C2×C4×C41—41no—
342C2×C4×C41—41no—
343C2×C4×C41—41no—
344C2×C4×C41—41no—
345C2×C4×C41H(5,𝔽2)11yescharacteristic
346C2×C4×C41H(5,𝔽2)11yescharacteristic
347C2×C4×C41H(5,𝔽2)11yescharacteristic
348C2×C4×C41H(5,𝔽2)11yescharacteristic
349C2×C4×C41H(5,𝔽2)11yescharacteristic
350C2×C4×C41H(5,𝔽2)11yescharacteristic
351C8×C41—41no—
352C8×C41—41no—
353C8×C41—41no—
354C8×C41—41no—
355#32709C4111yesmaximal, characteristic, direct product factor, Sylow
356C22×C41—22no—
357C22×C41—22no—
358C22×C41—22no—
359C22×C41—22no—
360C22×C41—22no—
361C22×C41—22no—
362C22×C41—22no—
363C22×C41—22no—
364C22×C41—22no—
365C22×C41—416no—
366C22×C41—41no—
367C22×C41—41no—
368C22×C41—41no—
369C22×C41—41no—
370C22×C41—41no—
371C22×C41—41no—
372C22×C41—41no—
373C22×C41—41no—
374C22×C41—41no—
375C22×C41—41no—
376C22×C41—41no—
377C22×C41—41no—
378C22×C41—81no—
379C22×C41—81no—
380C22×C41—81no—
381C22×C41—81no—
382C22×C41—81no—
383C22×C41—81no—
384C22×C41—81no—
385C22×C41#53411yescharacteristic
386C22×C41#53411yescharacteristic
387C22×C41#53411yescharacteristic
388C22×C41C2×#13511yescharacteristic
389C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C41C2×#13711yescharacteristic
391C22×C41#57511yescharacteristic
392C4×C41—41no—
393C4×C41—41no—
394C4×C41—41no—
395C4×C41—81no—
396C4×C41—81no—
397C4×C41—81no—
398C4×C41—81no—
399C4×C41—81no—
400C4×C41—81no—
401C4×C41—81no—
402C4×C41#56011yescharacteristic
403C4×C41#56011yescharacteristic
404C4×C41#56011yescharacteristic
405C4×C41H(3,𝔽4)11yescharacteristic
406#2848C2×C4111yescharacteristic, complemented
407#2847C2×C4111yescharacteristic
408#2077C2×C4111yescharacteristic, complemented
409#2076C2×C4111yescharacteristic, complemented
410#2075C2×C4111yescharacteristic, complemented
411#2036C2×C4111yescharacteristic, complemented
412#2036C2×C4111yescharacteristic, complemented
413#2035C2×C4111yescharacteristic, complemented
414#2034C2×C4111yescharacteristic, complemented
415#2033C2×C4111yescharacteristic, complemented
416#2033C2×C4111yescharacteristic, complemented
417#2000C2×C4111yescharacteristic, complemented
418#2000C2×C4111yescharacteristic, complemented
419#2000C2×C4111yescharacteristic, complemented
420#1779C2×C4111yescharacteristic, complemented
421C2×C41—42no—
422C2×C41—42no—
423C2×C41—42no—
424C2×C41—161no—
425C2×C41#281211yescharacteristic
426C2×C41#318811yescharacteristic
427C2×C41#319011yescharacteristic
428C2×C41#319111yescharacteristic
429C2×C41#319311yescharacteristic
430C2×C41#319411yescharacteristic
431C2×C41#319611yescharacteristic
432C24×C4C22×C4111yescharacteristic
433C22×SD16C22×C4111yescharacteristic, complemented
434C2×C22⋊Q8C22×C4111yescharacteristic
435C2×C22⋊Q8C22×C4111yescharacteristic
436C2×C22⋊Q8C22×C4111yescharacteristic
437C2×#121C22×C4111yescharacteristic
438C2×#121C22×C4111yescharacteristic
439C2×#121C22×C4111yescharacteristic
440C2×#120—21no—
441C2×#107C22×C4111yescharacteristic, complemented
442C2×#107C22×C4111yescharacteristic, complemented
443C2×#106C22×C4111yescharacteristic, complemented
444C2×#103C22×C4111yescharacteristic, complemented
445C2×#103C22×C4111yescharacteristic, complemented
446C2×#103C22×C4111yescharacteristic, complemented
447C2×#102C22×C4111yescharacteristic, complemented
448C2×#102C22×C4111yescharacteristic, complemented
449C2×#102C22×C4111yescharacteristic, complemented
450C2×C22⋊C8C22×C4111yescharacteristic
451C2×C22⋊C8C22×C4111yescharacteristic
452C2×C22⋊C8C22×C4111yescharacteristic
453C2×C22⋊C8C22×C4111yescharacteristic
454C2×C22⋊C8C22×C4111yescharacteristic
455C2×C22⋊C8C22×C4111yescharacteristic
456#386—21no—
457#386—21no—
458#386—21no—
459#385—21no—
460#385—21no—
461#385—21no—
462#380C22×C4111yescharacteristic
463#380C22×C4111yescharacteristic
464#380C22×C4111yescharacteristic
465#380C22×C4111yescharacteristic
466#380C22×C4111yescharacteristic
467#380C22×C4111yescharacteristic
468#379—21no—
469#340C22×C4111yescharacteristic, complemented
470#340C22×C4111yescharacteristic, complemented
471#340C22×C4111yescharacteristic, complemented
472#340C22×C4111yescharacteristic, complemented
473#340C22×C4111yescharacteristic, complemented
474#340C22×C4111yescharacteristic, complemented
475C41#3270911yescharacteristic, direct product factor, Sylow
476C25D4×C4111yescharacteristic
477C22×Q8C23×C4111yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4C23×C4111yescharacteristic
482C23×C4—41no—
483C23×C4—41no—
484C23×C4—41no—
485C23×C4—41no—
486C23×C4—41no—
487C23×C4—41no—
488C23×C4D4×C4111yescharacteristic
489C23×C4D4×C4111yescharacteristic
490C23×C4D4×C4111yescharacteristic
491C23×C4C23×C4111yescharacteristic
492C23×C4C23×C4111yescharacteristic
493C23×C4C23×C4111yescharacteristic
494C2×SD16—41no—
495C2×SD16—41no—
496C2×SD16—41no—
497C22×C8C23×C4111yescharacteristic
498C22×C8C23×C4111yescharacteristic
499C22×C8C23×C4111yescharacteristic
500C22×C8C23×C4111yescharacteristic
501C22⋊Q8—41no—
502C22⋊Q8—41no—
503C22⋊Q8—41no—
504C22⋊Q8—41no—
505C22⋊Q8—41no—
506C22⋊Q8—41no—
507#121—41no—
508#121—41no—
509#121—41no—
510#121—41no—
511#121—41no—
512#121—41no—
513#120—44no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C4111yescharacteristic
518C2×C4⋊C4C23×C4111yescharacteristic
519C2×C4⋊C4C23×C4111yescharacteristic
520C2×C4⋊C4C23×C4111yescharacteristic
521C2×C4⋊C4C23×C4111yescharacteristic
522C2×C4⋊C4C23×C4111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535#107—41no—
536#107—41no—
537#106—41no—
538#103—41no—
539#103—41no—
540#103—41no—
541#102—41no—
542#102—41no—
543#102—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24C2×D4×C4111yescharacteristic
565C24C2×D4×C4111yescharacteristic
566C24C2×D4×C4111yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C2×D4×C4111yescharacteristic
627C22×C4C2×D4×C4111yescharacteristic
628C22×C4C2×D4×C4111yescharacteristic
629C22×C4C24×C4111yescharacteristic
630SD16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23#135×C4112yes—
703C23AGL(1,ℤ/8)×C4112yes—
704C23#137×C4112yes—
705C23C22×D4×C4111yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4H(5,𝔽2)×C4111yescharacteristic
763C2×C4H(5,𝔽2)×C4111yescharacteristic
764C2×C4H(5,𝔽2)×C4111yescharacteristic
765C2×C4H(5,𝔽2)×C4111yescharacteristic
766C2×C4H(5,𝔽2)×C4111yescharacteristic
767C2×C4H(5,𝔽2)×C4111yescharacteristic
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—416no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C41×#53411yescharacteristic
802C22C41×#53411yescharacteristic
803C22C41×#53411yescharacteristic
804C22C2×#135×C4111yescharacteristic
805C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
806C22C2×#137×C4111yescharacteristic
807C22C41×#57511yescharacteristic
808C4—41no—
809C4—41no—
810C4—41no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4C41×#56011yescharacteristic
819C4C41×#56011yescharacteristic
820C4C41×#56011yescharacteristic
821C4C41×H(3,𝔽4)11yescharacteristic
822C2—42no—
823C2—42no—
824C2—42no—
825C2—161no—
826C2C41×#281211yescharacteristic
827C2C41×#318811yescharacteristic
828C2C41×#319011yescharacteristic
829C2C41×#319111yescharacteristic
830C2C41×#319311yescharacteristic
831C2C41×#319411yescharacteristic
832C2C41×#319611yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C24×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#2848C2semidirect
3. C41×#2077C2semidirect
4. C41×#2076C2semidirect
5. C41×#2075C2semidirect
6. C41×#2036C2semidirect
7. C41×#2036C2semidirect
8. C41×#2035C2semidirect
9. C41×#2034C2semidirect
10. C41×#2033C2semidirect
11. C41×#2033C2semidirect
12. C41×#2000C2semidirect
13. C41×#2000C2semidirect
14. C41×#2000C2semidirect
15. C41×#1779C2semidirect
17. C22×SD16×C41C22semidirect
25. C2×#107×C41C22semidirect
26. C2×#107×C41C22semidirect
27. C2×#106×C41C22semidirect
28. C2×#103×C41C22semidirect
29. C2×#103×C41C22semidirect
30. C2×#103×C41C22semidirect
31. C2×#102×C41C22semidirect
32. C2×#102×C41C22semidirect
33. C2×#102×C41C22semidirect
53. C41×#340C22semidirect
54. C41×#340C22semidirect
55. C41×#340C22semidirect
56. C41×#340C22semidirect
57. C41×#340C22semidirect
58. C41×#340C22semidirect
355. #32709C41direct (N × H)
406. #2848C2×C41semidirect
408. #2077C2×C41semidirect
409. #2076C2×C41semidirect
410. #2075C2×C41semidirect
411. #2036C2×C41semidirect
412. #2036C2×C41semidirect
413. #2035C2×C41semidirect
414. #2034C2×C41semidirect
415. #2033C2×C41semidirect
416. #2033C2×C41semidirect
417. #2000C2×C41semidirect
418. #2000C2×C41semidirect
419. #2000C2×C41semidirect
420. #1779C2×C41semidirect
433. C22×SD16C22×C41semidirect
441. C2×#107C22×C41semidirect
442. C2×#107C22×C41semidirect
443. C2×#106C22×C41semidirect
444. C2×#103C22×C41semidirect
445. C2×#103C22×C41semidirect
446. C2×#103C22×C41semidirect
447. C2×#102C22×C41semidirect
448. C2×#102C22×C41semidirect
449. C2×#102C22×C41semidirect
469. #340C22×C41semidirect
470. #340C22×C41semidirect
471. #340C22×C41semidirect
472. #340C22×C41semidirect
473. #340C22×C41semidirect
474. #340C22×C41semidirect
475. C41#32709direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#28482
C41×#28472
C41×#20772
C41×#20762
C41×#20752
C41×#20362
C41×#20352
C41×#20342
C41×#20332
C41×#20002
C41×#17792
#3270941