Finite Group Databasebeta

← C41×#29203 #23805404

Subgroups — C41×#29203 #23805404

Order 10496.

706 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2647C211yesmaximal, characteristic, complemented
2C41×#2326C211yesmaximal, characteristic
3C41×#2068C211yesmaximal, characteristic, complemented
4C41×#2067C211yesmaximal, characteristic
5C41×#2066C211yesmaximal, characteristic, complemented
6C41×#2065C211yesmaximal, characteristic
7C41×#1959C211yesmaximal, characteristic
8C41×#1958C211yesmaximal, characteristic
9C41×#1865C211yesmaximal, characteristic, complemented
10C41×#1864C211yesmaximal, characteristic
11C41×#1863C211yesmaximal, characteristic, complemented
12C41×#1862C211yesmaximal, characteristic
13C41×#1847C211yesmaximal, characteristic, complemented
14C41×#1834C211yesmaximal, characteristic, complemented
15C41×#1768C211yesmaximal, characteristic, complemented
16C2×#124×C41C2211yescharacteristic
17C2×C4×Q8×C41C2211yescharacteristic
18C2×C4×D4×C41C2211yescharacteristic
19C2×#107×C41C2211yescharacteristic
20C2×#107×C41C2211yescharacteristic
21C2×#106×C41C2211yescharacteristic
22C2×#106×C41C2211yescharacteristic
23C2×C4⋊C8×C41C2211yescharacteristic
24C2×C4⋊C8×C41C2211yescharacteristic
25C2×#103×C41C2211yescharacteristic
26C2×#103×C41C2211yescharacteristic
27C2×#103×C41C2211yescharacteristic
28C2×#103×C41C2211yescharacteristic
29C2×#102×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#97×C41C2211yescharacteristic
34C2×C4×C8×C41C2211yescharacteristic
35C41×#400—21no—
36C41×#400—21no—
37C41×#398—21no—
38C41×#398—21no—
39C41×#391C2211yescharacteristic
40C41×#390C2211yescharacteristic
41C41×#389C2211yescharacteristic
42C41×#389C2211yescharacteristic
43C41×#389C2211yescharacteristic
44C41×#389C2211yescharacteristic
45C41×#388—21no—
46C41×#388—21no—
47C41×#385—21no—
48C41×#385—21no—
49C41×#384C2211yescharacteristic
50C41×#384C2211yescharacteristic
51C41×#382C2211yescharacteristic
52C41×#376C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#336C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C22×Q8×C41C2311yescharacteristic
60C22×D4×C41C2311yescharacteristic
61C23×C4×C41—21no—
62C22×C8×C41C2311yescharacteristic
63C22×C8×C41C2311yescharacteristic
64C22×C8×C41C2311yescharacteristic
65C22×C8×C41C2311yescharacteristic
66#124×C41—22no—
67#124×C41Q814yes—
68C4×Q8×C41—41no—
69C4×Q8×C41—41no—
70C4×D4×C41—41no—
71C4×D4×C41—41no—
72C2×C4⋊C4×C41—21no—
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×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41—21no—
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×C42×C41—21no—
93C2×C42×C41C2311yescharacteristic
94C2×C42×C41C2311yescharacteristic
95C2×C42×C41C2311yescharacteristic
96#107×C41—41no—
97#107×C41—41no—
98#106×C41—41no—
99#106×C41—41no—
100C4⋊C8×C41—22no—
101C4⋊C8×C41—22no—
102#103×C41—22no—
103#103×C41—22no—
104#103×C41—41no—
105#103×C41—41no—
106#102×C41—22no—
107#102×C41—22no—
108#102×C41—41no—
109#102×C41—41no—
110#97×C41—22no—
111C4×C8×C41—22no—
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—
120#95×C41D411yescharacteristic
121#95×C41D411yescharacteristic
122#95×C41D411yescharacteristic
123#95×C41D411yescharacteristic
124C24×C41—21no—
125C2×Q8×C41—21no—
126C2×Q8×C41—21no—
127C2×Q8×C41—21no—
128C2×Q8×C41—21no—
129C2×Q8×C41—21no—
130C2×Q8×C41C2×Q812yes—
131C2×D4×C41—21no—
132C2×D4×C41—21no—
133C2×D4×C41—21no—
134C2×D4×C41—21no—
135C2×D4×C41—21no—
136C2×D4×C41C2×Q812yes—
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—81no—
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×C41C2×D411yescharacteristic
153C22×C4×C41C2411yescharacteristic
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—
165C2×C8×C41#4112yes—
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—21no—
178C4⋊C4×C41—42no—
179C4⋊C4×C41—81no—
180C4⋊C4×C41—81no—
181C4⋊C4×C41—81no—
182C4⋊C4×C41—81no—
183C4⋊C4×C41—81no—
184C4⋊C4×C41—81no—
185C4⋊C4×C41—81no—
186C4⋊C4×C41—81no—
187C22⋊C4×C41—24no—
188C22⋊C4×C41—24no—
189C22⋊C4×C41—42no—
190C22⋊C4×C41—81no—
191C22⋊C4×C41—81no—
192C42×C41—21no—
193C42×C41—21no—
194C42×C41—21no—
195C42×C41—21no—
196C42×C41—42no—
197C42×C41C2×Q812yes—
198C42×C41#4112yes—
199C23×C41—22no—
200C23×C41—41no—
201C23×C41—41no—
202C23×C41—41no—
203C23×C41—41no—
204C23×C41—41no—
205C23×C41—41no—
206C23×C41C22×D411yescharacteristic
207Q8×C41—22no—
208Q8×C41—22no—
209Q8×C41—41no—
210Q8×C41—41no—
211D4×C41—22no—
212D4×C41—22no—
213D4×C41—41no—
214D4×C41—41no—
215C2×C4×C41—21no—
216C2×C4×C41—21no—
217C2×C4×C41—21no—
218C2×C4×C41—21no—
219C2×C4×C41—22no—
220C2×C4×C41—21no—
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—41no—
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—41no—
252C2×C4×C41—84no—
253C2×C4×C41C22⋊Q812yes—
254C2×C4×C41C22⋊Q812yes—
255C2×C4×C41C22×Q811yescharacteristic
256C2×C4×C41C2×#4111yescharacteristic
257C2×C4×C41C2×#4111yescharacteristic
258C2×C4×C41C2×#4111yescharacteristic
259C2×C4×C41H(5,𝔽2)11yescharacteristic
260C2×C4×C41H(5,𝔽2)11yescharacteristic
261C8×C41—22no—
262C8×C41—22no—
263C8×C41—41no—
264C8×C41—41no—
265#29203C4111yesmaximal, characteristic, direct product factor, Sylow
266C22×C41—42no—
267C22×C41—42no—
268C22×C41—42no—
269C22×C41—81no—
270C22×C41—81no—
271C22×C41—81no—
272C22×C41—81no—
273C22×C41C2×C22⋊Q811yescharacteristic
274C22×C41#53211yescharacteristic
275C22×C41#53511yescharacteristic
276C22×C41#57611yescharacteristic
277C22×C41#57711yescharacteristic
278C22×C41#57711yescharacteristic
279C22×C41#57811yescharacteristic
280C4×C41—22no—
281C4×C41—22no—
282C4×C41—42no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—41no—
287C4×C41—81no—
288C4×C41—81no—
289C4×C41—81no—
290C4×C41—81no—
291C4×C41—81no—
292C4×C41—81no—
293C4×C41#55311yescharacteristic
294C4×C41#55311yescharacteristic
295C4×C41#55411yescharacteristic
296C4×C41#55411yescharacteristic
297#2647C2×C4111yescharacteristic, complemented
298#2326C2×C4111yescharacteristic
299#2068C2×C4111yescharacteristic, complemented
300#2067C2×C4111yescharacteristic
301#2066C2×C4111yescharacteristic, complemented
302#2065C2×C4111yescharacteristic
303#1959C2×C4111yescharacteristic
304#1958C2×C4111yescharacteristic
305#1865C2×C4111yescharacteristic, complemented
306#1864C2×C4111yescharacteristic
307#1863C2×C4111yescharacteristic, complemented
308#1862C2×C4111yescharacteristic
309#1847C2×C4111yescharacteristic, complemented
310#1834C2×C4111yescharacteristic, complemented
311#1768C2×C4111yescharacteristic, complemented
312C2×C41—82no—
313C2×C41#256611yescharacteristic
314C2×C41#308311yescharacteristic
315C2×C41#308411yescharacteristic
316C2×C41#317811yescharacteristic
317C2×C41#317911yescharacteristic
318C2×C41#322411yescharacteristic
319C2×C41#322511yescharacteristic
320C2×#124C22×C4111yescharacteristic
321C2×C4×Q8C22×C4111yescharacteristic
322C2×C4×D4C22×C4111yescharacteristic
323C2×#107C22×C4111yescharacteristic
324C2×#107C22×C4111yescharacteristic
325C2×#106C22×C4111yescharacteristic
326C2×#106C22×C4111yescharacteristic
327C2×C4⋊C8C22×C4111yescharacteristic
328C2×C4⋊C8C22×C4111yescharacteristic
329C2×#103C22×C4111yescharacteristic
330C2×#103C22×C4111yescharacteristic
331C2×#103C22×C4111yescharacteristic
332C2×#103C22×C4111yescharacteristic
333C2×#102C22×C4111yescharacteristic
334C2×#102C22×C4111yescharacteristic
335C2×#102C22×C4111yescharacteristic
336C2×#102C22×C4111yescharacteristic
337C2×#97C22×C4111yescharacteristic
338C2×C4×C8C22×C4111yescharacteristic
339#400—21no—
340#400—21no—
341#398—21no—
342#398—21no—
343#391C22×C4111yescharacteristic
344#390C22×C4111yescharacteristic
345#389C22×C4111yescharacteristic
346#389C22×C4111yescharacteristic
347#389C22×C4111yescharacteristic
348#389C22×C4111yescharacteristic
349#388—21no—
350#388—21no—
351#385—21no—
352#385—21no—
353#384C22×C4111yescharacteristic
354#384C22×C4111yescharacteristic
355#382C22×C4111yescharacteristic
356#376C22×C4111yescharacteristic
357#340C22×C4111yescharacteristic
358#340C22×C4111yescharacteristic
359#340C22×C4111yescharacteristic
360#340C22×C4111yescharacteristic
361#336C22×C4111yescharacteristic
362#336C22×C4111yescharacteristic
363C41#2920311yescharacteristic, direct product factor, Sylow
364C22×Q8C23×C4111yescharacteristic
365C22×D4C23×C4111yescharacteristic
366C23×C4—21no—
367C22×C8C23×C4111yescharacteristic
368C22×C8C23×C4111yescharacteristic
369C22×C8C23×C4111yescharacteristic
370C22×C8C23×C4111yescharacteristic
371#124—22no—
372#124Q8×C4114yes—
373C4×Q8—41no—
374C4×Q8—41no—
375C4×D4—41no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4C23×C4111yescharacteristic
387C2×C4⋊C4C23×C4111yescharacteristic
388C2×C4⋊C4C23×C4111yescharacteristic
389C2×C4⋊C4C23×C4111yescharacteristic
390C2×C4⋊C4C23×C4111yescharacteristic
391C2×C4⋊C4C23×C4111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42C23×C4111yescharacteristic
399C2×C42C23×C4111yescharacteristic
400C2×C42C23×C4111yescharacteristic
401#107—41no—
402#107—41no—
403#106—41no—
404#106—41no—
405C4⋊C8—22no—
406C4⋊C8—22no—
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—22no—
416C4×C8—22no—
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#95D4×C4111yescharacteristic
426#95D4×C4111yescharacteristic
427#95D4×C4111yescharacteristic
428#95D4×C4111yescharacteristic
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×Q8×C4112yes—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×Q8×C4112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—81no—
451C22×C4—81no—
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#41×C4112yes—
470C2×C8#41×C4112yes—
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—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—42no—
502C42C2×Q8×C4112yes—
503C42#41×C4112yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C22×D4×C4111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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—41no—
556C2×C4—41no—
557C2×C4—84no—
558C2×C4C22⋊Q8×C4112yes—
559C2×C4C22⋊Q8×C4112yes—
560C2×C4C22×Q8×C4111yescharacteristic
561C2×C4C2×#41×C4111yescharacteristic
562C2×C4C2×#41×C4111yescharacteristic
563C2×C4C2×#41×C4111yescharacteristic
564C2×C4H(5,𝔽2)×C4111yescharacteristic
565C2×C4H(5,𝔽2)×C4111yescharacteristic
566C8—22no—
567C8—22no—
568C8—41no—
569C8—41no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C22⋊Q8×C4111yescharacteristic
578C22C41×#53211yescharacteristic
579C22C41×#53511yescharacteristic
580C22C41×#57611yescharacteristic
581C22C41×#57711yescharacteristic
582C22C41×#57711yescharacteristic
583C22C41×#57811yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C41×#55311yescharacteristic
598C4C41×#55311yescharacteristic
599C4C41×#55411yescharacteristic
600C4C41×#55411yescharacteristic
601C2—82no—
602C2C41×#256611yescharacteristic
603C2C41×#308311yescharacteristic
604C2C41×#308411yescharacteristic
605C2C41×#317811yescharacteristic
606C2C41×#317911yescharacteristic
607C2C41×#322411yescharacteristic
608C2C41×#322511yescharacteristic
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×#2647C2semidirect
3. C41×#2068C2semidirect
5. C41×#2066C2semidirect
9. C41×#1865C2semidirect
11. C41×#1863C2semidirect
13. C41×#1847C2semidirect
14. C41×#1834C2semidirect
15. C41×#1768C2semidirect
265. #29203C41direct (N × H)
297. #2647C2×C41semidirect
299. #2068C2×C41semidirect
301. #2066C2×C41semidirect
305. #1865C2×C41semidirect
307. #1863C2×C41semidirect
309. #1847C2×C41semidirect
310. #1834C2×C41semidirect
311. #1768C2×C41semidirect
363. C41#29203direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#26472
C41×#23262
C41×#20682
C41×#20672
C41×#20662
C41×#20652
C41×#19592
C41×#19582
C41×#18652
C41×#18642
C41×#18632
C41×#18622
C41×#18472
C41×#18342
C41×#17682
#2920341