Finite Group Databasebeta

← C41×#33090 #23809291

Subgroups — C41×#33090 #23809291

Order 10496.

770 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2645C211yesmaximal, characteristic, complemented
2C41×#2275C211yesmaximal, characteristic
3C41×#1928C211yesmaximal, characteristic, complemented
4C41×#1928C211yesmaximal, characteristic, complemented
5C41×#1927C211yesmaximal, characteristic, complemented
6C41×#1921C211yesmaximal, characteristic, complemented
7C41×#1920C211yesmaximal, characteristic, complemented
8C41×#1918C211yesmaximal, characteristic, complemented
9C41×#1877C211yesmaximal, characteristic
10C41×#1877C211yesmaximal, characteristic
11C41×#1877C211yesmaximal, characteristic
12C41×#1864C211yesmaximal, characteristic
13C41×#1862C211yesmaximal, characteristic
14C41×#1862C211yesmaximal, characteristic
15C41×#1840C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C2×C4×D4×C41C2211yescharacteristic
18C2×C4×D4×C41C2211yescharacteristic
19C2×C4×D4×C41C2211yescharacteristic
20C2×#107×C41C2211yescharacteristic
21C2×#107×C41C2211yescharacteristic
22C2×#106×C41C2211yescharacteristic
23C2×#103×C41C2211yescharacteristic
24C2×#103×C41C2211yescharacteristic
25C2×#103×C41C2211yescharacteristic
26C2×#102×C41C2211yescharacteristic
27C2×#102×C41C2211yescharacteristic
28C2×#102×C41C2211yescharacteristic
29C41×#401—21no—
30C41×#400—21no—
31C41×#400—21no—
32C41×#400—21no—
33C41×#391C2211yescharacteristic
34C41×#391C2211yescharacteristic
35C41×#391C2211yescharacteristic
36C41×#389C2211yescharacteristic
37C41×#389C2211yescharacteristic
38C41×#389C2211yescharacteristic
39C4×C4⋊C4×C41C2211yescharacteristic
40C4×C4⋊C4×C41C2211yescharacteristic
41C4×C4⋊C4×C41C2211yescharacteristic
42C4×C22⋊C4×C41—21no—
43C4×C22⋊C4×C41—21no—
44C4×C22⋊C4×C41—21no—
45C41×#376C2211yescharacteristic
46C2×#95×C41—21no—
47C41×#340C2211yescharacteristic
48C41×#340C2211yescharacteristic
49C41×#340C2211yescharacteristic
50C41×#340C2211yescharacteristic
51C41×#340C2211yescharacteristic
52C41×#340C2211yescharacteristic
53C41×#336C2211yescharacteristic
54C41×#336C2211yescharacteristic
55C41×#336C2211yescharacteristic
56C41×#336C2211yescharacteristic
57C41×#336C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C22×Q8×C41C2311yescharacteristic
60C22×D4×C41C2311yescharacteristic
61C23×C4×C41—21no—
62C23×C4×C41—21no—
63C23×C4×C41—21no—
64C2×SD16×C41—22no—
65C2×SD16×C41—22no—
66C2×SD16×C41—22no—
67C22×C8×C41C2311yescharacteristic
68C22×C8×C41C2311yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C22×C8×C41C2311yescharacteristic
71C4×D4×C41—22no—
72C4×D4×C41—22no—
73C4×D4×C41—22no—
74C4×D4×C41—22no—
75C4×D4×C41—22no—
76C4×D4×C41—22no—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41C2311yescharacteristic
81C2×C4⋊C4×C41C2311yescharacteristic
82C2×C4⋊C4×C41C2311yescharacteristic
83C2×C4⋊C4×C41C2311yescharacteristic
84C2×C4⋊C4×C41C2311yescharacteristic
85C2×C4⋊C4×C41C2311yescharacteristic
86C2×C22⋊C4×C41—21no—
87C2×C22⋊C4×C41—21no—
88C2×C22⋊C4×C41—21no—
89C2×C42×C41—21no—
90C2×C42×C41—21no—
91C2×C42×C41—21no—
92C2×C42×C41C2311yescharacteristic
93C2×C42×C41C2311yescharacteristic
94C2×C42×C41C2311yescharacteristic
95#107×C41—22no—
96#107×C41—22no—
97#106×C41—22no—
98#103×C41—22no—
99#103×C41—22no—
100#103×C41—22no—
101#102×C41—22no—
102#102×C41—22no—
103#102×C41—22no—
104#95×C41—21no—
105#95×C41—21no—
106#95×C41—21no—
107#95×C41—21no—
108#95×C41—21no—
109#95×C41—21no—
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×C41D411yescharacteristic
117#95×C41D411yescharacteristic
118#95×C41D411yescharacteristic
119#95×C41D411yescharacteristic
120C24×C41—21no—
121C2×Q8×C41—21no—
122C2×Q8×C41—21no—
123C2×Q8×C41—21no—
124C2×Q8×C41—21no—
125C2×Q8×C41—21no—
126C2×Q8×C41—21no—
127C2×D4×C41—21no—
128C2×D4×C41—21no—
129C2×D4×C41—21no—
130C2×D4×C41#4112yes—
131C2×D4×C41#4112yes—
132C2×D4×C41#4112yes—
133C22×C4×C41—21no—
134C22×C4×C41—21no—
135C22×C4×C41—21no—
136C22×C4×C41—24no—
137C22×C4×C41—24no—
138C22×C4×C41—24no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—21no—
142C22×C4×C41—21no—
143C22×C4×C41—81no—
144C22×C4×C41—81no—
145C22×C4×C41—81no—
146C22×C4×C41—81no—
147C22×C4×C41—81no—
148C22×C4×C41—81no—
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41C2×D411yescharacteristic
154C22×C4×C41C2×D411yescharacteristic
155C22×C4×C41C2411yescharacteristic
156SD16×C41—44no—
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—
165C2×C8×C41—21no—
166C2×C8×C41—21no—
167C2×C8×C41—21no—
168C2×C8×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—21no—
178C4⋊C4×C41—81no—
179C4⋊C4×C41—81no—
180C4⋊C4×C41—81no—
181C4⋊C4×C41#4112yes—
182C4⋊C4×C41#4112yes—
183C4⋊C4×C41#4112yes—
184C22⋊C4×C41—24no—
185C22⋊C4×C41—24no—
186C22⋊C4×C41—24no—
187C42×C41—21no—
188C42×C41—21no—
189C42×C41—21no—
190C42×C41—21no—
191C42×C41—21no—
192C42×C41—21no—
193C42×C41—81no—
194C42×C41—81no—
195C42×C41—81no—
196C23×C41—22no—
197C23×C41—22no—
198C23×C41—22no—
199C23×C41—41no—
200C23×C41—41no—
201C23×C41—41no—
202C23×C41—41no—
203C23×C41C22×D411yescharacteristic
204Q8×C41—41no—
205Q8×C41—41no—
206Q8×C41—41no—
207Q8×C41—41no—
208D4×C41—22no—
209D4×C41—22no—
210D4×C41—22no—
211D4×C41#12614yes—
212C2×C4×C41—21no—
213C2×C4×C41—21no—
214C2×C4×C41—21no—
215C2×C4×C41—21no—
216C2×C4×C41—21no—
217C2×C4×C41—21no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—21no—
222C2×C4×C41—21no—
223C2×C4×C41—21no—
224C2×C4×C41—21no—
225C2×C4×C41—21no—
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—41no—
234C2×C4×C41—41no—
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—84no—
252C2×C4×C41—84no—
253C2×C4×C41—84no—
254C2×C4×C41C2×#4111yescharacteristic
255C2×C4×C41C2×#4111yescharacteristic
256C2×C4×C41C2×#4111yescharacteristic
257C2×C4×C41C2×#4111yescharacteristic
258C2×C4×C41C2×#4111yescharacteristic
259C2×C4×C41C2×#4111yescharacteristic
260C8×C41—41no—
261C8×C41—41no—
262C8×C41—41no—
263C8×C41—41no—
264#33090C4111yesmaximal, characteristic, direct product factor, Sylow
265C22×C41—24no—
266C22×C41—42no—
267C22×C41—42no—
268C22×C41—42no—
269C22×C41—42no—
270C22×C41—42no—
271C22×C41—42no—
272C22×C41#52511yescharacteristic
273C22×C41#52511yescharacteristic
274C22×C41#52511yescharacteristic
275C22×C41#57611yescharacteristic
276C22×C41#57711yescharacteristic
277C22×C41#57711yescharacteristic
278C22×C41#57811yescharacteristic
279C4×C41—41no—
280C4×C41—41no—
281C4×C41—42no—
282C4×C41—42no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—42no—
287C4×C41—41no—
288C4×C41—81no—
289C4×C41—81no—
290C4×C41—81no—
291C4×C41—81no—
292C4×C41C2×#12611yescharacteristic
293C4×C41#52911yescharacteristic
294C4×C41#52911yescharacteristic
295C4×C41#52911yescharacteristic
296#2645C2×C4111yescharacteristic, complemented
297#2275C2×C4111yescharacteristic
298#1928C2×C4111yescharacteristic, complemented
299#1928C2×C4111yescharacteristic, complemented
300#1927C2×C4111yescharacteristic, complemented
301#1921C2×C4111yescharacteristic, complemented
302#1920C2×C4111yescharacteristic, complemented
303#1918C2×C4111yescharacteristic, complemented
304#1877C2×C4111yescharacteristic
305#1877C2×C4111yescharacteristic
306#1877C2×C4111yescharacteristic
307#1864C2×C4111yescharacteristic
308#1862C2×C4111yescharacteristic
309#1862C2×C4111yescharacteristic
310#1840C2×C4111yescharacteristic, complemented
311C2×C41—44no—
312C2×C41#285211yescharacteristic
313C2×C41#311811yescharacteristic
314C2×C41#311811yescharacteristic
315C2×C41#312011yescharacteristic
316C2×C41#312011yescharacteristic
317C2×C41#312311yescharacteristic
318C2×C41#312411yescharacteristic
319C22×SD16C22×C4111yescharacteristic
320C2×C4×D4C22×C4111yescharacteristic
321C2×C4×D4C22×C4111yescharacteristic
322C2×C4×D4C22×C4111yescharacteristic
323C2×#107C22×C4111yescharacteristic
324C2×#107C22×C4111yescharacteristic
325C2×#106C22×C4111yescharacteristic
326C2×#103C22×C4111yescharacteristic
327C2×#103C22×C4111yescharacteristic
328C2×#103C22×C4111yescharacteristic
329C2×#102C22×C4111yescharacteristic
330C2×#102C22×C4111yescharacteristic
331C2×#102C22×C4111yescharacteristic
332#401—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#391C22×C4111yescharacteristic
337#391C22×C4111yescharacteristic
338#391C22×C4111yescharacteristic
339#389C22×C4111yescharacteristic
340#389C22×C4111yescharacteristic
341#389C22×C4111yescharacteristic
342C4×C4⋊C4C22×C4111yescharacteristic
343C4×C4⋊C4C22×C4111yescharacteristic
344C4×C4⋊C4C22×C4111yescharacteristic
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347C4×C22⋊C4—21no—
348#376C22×C4111yescharacteristic
349C2×#95—21no—
350#340C22×C4111yescharacteristic
351#340C22×C4111yescharacteristic
352#340C22×C4111yescharacteristic
353#340C22×C4111yescharacteristic
354#340C22×C4111yescharacteristic
355#340C22×C4111yescharacteristic
356#336C22×C4111yescharacteristic
357#336C22×C4111yescharacteristic
358#336C22×C4111yescharacteristic
359#336C22×C4111yescharacteristic
360#336C22×C4111yescharacteristic
361#336C22×C4111yescharacteristic
362C41#3309011yescharacteristic, direct product factor, Sylow
363C22×Q8C23×C4111yescharacteristic
364C22×D4C23×C4111yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C22×C8C23×C4111yescharacteristic
372C22×C8C23×C4111yescharacteristic
373C22×C8C23×C4111yescharacteristic
374C22×C8C23×C4111yescharacteristic
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4C23×C4111yescharacteristic
385C2×C4⋊C4C23×C4111yescharacteristic
386C2×C4⋊C4C23×C4111yescharacteristic
387C2×C4⋊C4C23×C4111yescharacteristic
388C2×C4⋊C4C23×C4111yescharacteristic
389C2×C4⋊C4C23×C4111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42C23×C4111yescharacteristic
397C2×C42C23×C4111yescharacteristic
398C2×C42C23×C4111yescharacteristic
399#107—22no—
400#107—22no—
401#106—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#102—22no—
406#102—22no—
407#102—22no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C4111yescharacteristic
421#95D4×C4111yescharacteristic
422#95D4×C4111yescharacteristic
423#95D4×C4111yescharacteristic
424C24—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4#41×C4112yes—
435C2×D4#41×C4112yes—
436C2×D4#41×C4112yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4C2×D4×C4111yescharacteristic
454C22×C4C2×D4×C4111yescharacteristic
455C22×C4C2×D4×C4111yescharacteristic
456C22×C4C2×D4×C4111yescharacteristic
457C22×C4C2×D4×C4111yescharacteristic
458C22×C4C2×D4×C4111yescharacteristic
459C22×C4C24×C4111yescharacteristic
460SD16—44no—
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—
471C2×C8—21no—
472C2×C8—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—21no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4#41×C4112yes—
486C4⋊C4#41×C4112yes—
487C4⋊C4#41×C4112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—81no—
498C42—81no—
499C42—81no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×D4×C4111yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4#126×C4114yes—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
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—84no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4C2×#41×C4111yescharacteristic
559C2×C4C2×#41×C4111yescharacteristic
560C2×C4C2×#41×C4111yescharacteristic
561C2×C4C2×#41×C4111yescharacteristic
562C2×C4C2×#41×C4111yescharacteristic
563C2×C4C2×#41×C4111yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22C41×#52511yescharacteristic
576C22C41×#52511yescharacteristic
577C22C41×#52511yescharacteristic
578C22C41×#57611yescharacteristic
579C22C41×#57711yescharacteristic
580C22C41×#57711yescharacteristic
581C22C41×#57811yescharacteristic
582C4—41no—
583C4—41no—
584C4—42no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4C2×#126×C4111yescharacteristic
596C4C41×#52911yescharacteristic
597C4C41×#52911yescharacteristic
598C4C41×#52911yescharacteristic
599C2—44no—
600C2C41×#285211yescharacteristic
601C2C41×#311811yescharacteristic
602C2C41×#311811yescharacteristic
603C2C41×#312011yescharacteristic
604C2C41×#312011yescharacteristic
605C2C41×#312311yescharacteristic
606C2C41×#312411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×D4×C41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C41×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#2645C2semidirect
3. C41×#1928C2semidirect
4. C41×#1928C2semidirect
5. C41×#1927C2semidirect
6. C41×#1921C2semidirect
7. C41×#1920C2semidirect
8. C41×#1918C2semidirect
15. C41×#1840C2semidirect
264. #33090C41direct (N × H)
296. #2645C2×C41semidirect
298. #1928C2×C41semidirect
299. #1928C2×C41semidirect
300. #1927C2×C41semidirect
301. #1921C2×C41semidirect
302. #1920C2×C41semidirect
303. #1918C2×C41semidirect
310. #1840C2×C41semidirect
362. C41#33090direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#26452
C41×#22752
C41×#19282
C41×#19272
C41×#19212
C41×#19202
C41×#19182
C41×#18772
C41×#18642
C41×#18622
C41×#18402
#3309041