Finite Group Databasebeta

← C41×#21291 #23797492

Subgroups — C41×#21291 #23797492

Order 10496.

814 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
1C2×C41×#440C211yesmaximal, characteristic
2C41×#2320C211yesmaximal, characteristic, complemented
3C41×#2319C211yesmaximal, characteristic
4C41×#1973C211yesmaximal, characteristic
5C41×#1968C211yesmaximal, characteristic
6C41×#1943C211yesmaximal, characteristic, complemented
7C41×#1942C211yesmaximal, characteristic, complemented
8C41×#1936C211yesmaximal, characteristic
9C41×#1935C211yesmaximal, characteristic, complemented
10C41×#1934C211yesmaximal, characteristic
11C41×#1933C211yesmaximal, characteristic, complemented
12C41×#1776C211yesmaximal, characteristic, complemented
13C4×#103×C41C211yesmaximal, characteristic, complemented
14C4×#102×C41C211yesmaximal, characteristic
15C41×#1726C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C2×C4×Q8×C41C2211yescharacteristic
18C2×C4×D4×C41C2211yescharacteristic
19C41×#440C418yescomplemented
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
29C2×#97×C41C2211yescharacteristic
30C2×#97×C41C2211yescharacteristic
31C2×#97×C41C2211yescharacteristic
32C2×C4×C8×C41C2211yescharacteristic
33C2×C4×C8×C41C2211yescharacteristic
34C2×C4×C8×C41C2211yescharacteristic
35C41×#391C2211yescharacteristic
36C41×#391C2211yescharacteristic
37C41×#390C2211yescharacteristic
38C41×#390C2211yescharacteristic
39C41×#389C2211yescharacteristic
40C41×#389C2211yescharacteristic
41C41×#389C2211yescharacteristic
42C41×#389C2211yescharacteristic
43C41×#388—21no—
44C41×#388—21no—
45C41×#387—21no—
46C41×#387—21no—
47C41×#383—21no—
48C41×#382—21no—
49C41×#381—21no—
50C41×#380—21no—
51C4×C4⋊C4×C41C2211yescharacteristic
52C4×C4⋊C4×C41C2211yescharacteristic
53C41×#376C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C22×Q8×C41C2311yescharacteristic
61C22×D4×C41C2311yescharacteristic
62C23×C4×C41—21no—
63C2×SD16×C41—22no—
64C2×SD16×C41—22no—
65C2×SD16×C41C2×C414yes—
66C22×C8×C41C2311yescharacteristic
67C22×C8×C41C2311yescharacteristic
68C22×C8×C41C2311yescharacteristic
69C22×C8×C41C2311yescharacteristic
70C4×Q8×C41—22no—
71C4×Q8×C41C2×C414yes—
72C4×D4×C41—22no—
73C4×D4×C41C2×C414yes—
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×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×C42×C41—21no—
91C2×C42×C41—21no—
92C2×C42×C41—21no—
93C2×C42×C41C2311yescharacteristic
94C2×C42×C41C2311yescharacteristic
95C2×C42×C41C2311yescharacteristic
96#107×C41—22no—
97#107×C41C2×C414yes—
98#106×C41—22no—
99#103×C41—22no—
100#103×C41—22no—
101#103×C41C2×C414yes—
102#102×C41—22no—
103#102×C41—22no—
104#102×C41C2×C414yes—
105#97×C41—22no—
106#97×C41—22no—
107#97×C41C2×C414yes—
108C4×C8×C41—22no—
109C4×C8×C41—22no—
110C4×C8×C41—22no—
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—
120#95×C41—21no—
121#95×C41D411yescharacteristic
122#95×C41D411yescharacteristic
123#95×C41D411yescharacteristic
124#95×C41D411yescharacteristic
125C24×C41—21no—
126C2×Q8×C41—21no—
127C2×Q8×C41—21no—
128C2×Q8×C41—21no—
129C2×Q8×C41—21no—
130C2×Q8×C41—21no—
131C2×Q8×C41C22×C412yes—
132C2×D4×C41—21no—
133C2×D4×C41—21no—
134C2×D4×C41—21no—
135C2×D4×C41—21no—
136C2×D4×C41—21no—
137C2×D4×C41C22×C412yes—
138C22×C4×C41—21no—
139C22×C4×C41—21no—
140C22×C4×C41—21no—
141C22×C4×C41—24no—
142C22×C4×C41—21no—
143C22×C4×C41—21no—
144C22×C4×C41—21no—
145C22×C4×C41—21no—
146C22×C4×C41—81no—
147C22×C4×C41—81no—
148C22×C4×C41C2×D411yescharacteristic
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41C2×D411yescharacteristic
154C22×C4×C41C2411yescharacteristic
155SD16×C41—28no—
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×C41C22×C412yes—
163C2×C8×C41C22×C412yes—
164C2×C8×C41#4112yes—
165C2×C8×C41#4112yes—
166C2×C8×C41#4112yes—
167C2×C8×C41#4112yes—
168C4⋊C4×C41—24no—
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—21no—
179C4⋊C4×C41—81no—
180C4⋊C4×C41—81no—
181C4⋊C4×C41—81no—
182C4⋊C4×C41—81no—
183C4⋊C4×C41C22×C412yes—
184C4⋊C4×C41C22×C412yes—
185C22⋊C4×C41—24no—
186C22⋊C4×C41—81no—
187C22⋊C4×C41—81no—
188C22⋊C4×C41—81no—
189C22⋊C4×C41—81no—
190C42×C41—24no—
191C42×C41—21no—
192C42×C41—21no—
193C42×C41—21no—
194C42×C41—21no—
195C42×C41—81no—
196C42×C41—81no—
197C42×C41C22×C412yes—
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—22no—
221C2×C4×C41—22no—
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—21no—
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×C41C4×D412yes—
254C2×C4×C41C4×D412yes—
255C2×C4×C41C23×C411yescharacteristic
256C2×C4×C41C2×#4111yescharacteristic
257C2×C4×C41C2×#4111yescharacteristic
258C2×C4×C41C2×#4111yescharacteristic
259C2×C4×C41C2×#4111yescharacteristic
260C2×C4×C41C2×#4111yescharacteristic
261C8×C41—22no—
262C8×C41—22no—
263C8×C41—22no—
264C8×C41#11714yes—
265#21291C4111yesmaximal, 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×C4×D411yescharacteristic
274C22×C41#53211yescharacteristic
275C22×C41#53211yescharacteristic
276C22×C41#57611yescharacteristic
277C22×C41#57711yescharacteristic
278C22×C41#57711yescharacteristic
279C22×C41#57811yescharacteristic
280C4×C41—22no—
281C4×C41—22no—
282C4×C41—41no—
283C4×C41—41no—
284C4×C41—41no—
285C4×C41—41no—
286C4×C41—42no—
287C4×C41—42no—
288C4×C41—42no—
289C4×C41—81no—
290C4×C41—81no—
291C4×C41—81no—
292C4×C41—81no—
293C4×C41C2×#11711yescharacteristic
294C4×C41C4×#4111yescharacteristic
295C4×C41#52911yescharacteristic
296C4×C41#52911yescharacteristic
297C2×#440C2×C4111yescharacteristic
298#2320C2×C4111yescharacteristic, complemented
299#2319C2×C4111yescharacteristic
300#1973C2×C4111yescharacteristic
301#1968C2×C4111yescharacteristic
302#1943C2×C4111yescharacteristic, complemented
303#1942C2×C4111yescharacteristic, complemented
304#1936C2×C4111yescharacteristic
305#1935C2×C4111yescharacteristic, complemented
306#1934C2×C4111yescharacteristic
307#1933C2×C4111yescharacteristic, complemented
308#1776C2×C4111yescharacteristic, complemented
309C4×#103C2×C4111yescharacteristic, complemented
310C4×#102C2×C4111yescharacteristic
311#1726C2×C4111yescharacteristic, complemented
312C2×C41—82no—
313C2×C41#229311yescharacteristic
314C2×C41#294611yescharacteristic
315C2×C41#294711yescharacteristic
316C2×C41#317411yescharacteristic
317C2×C41#317511yescharacteristic
318C2×C41#317811yescharacteristic
319C2×C41#317911yescharacteristic
320C22×SD16C22×C4111yescharacteristic
321C2×C4×Q8C22×C4111yescharacteristic
322C2×C4×D4C22×C4111yescharacteristic
323#440C4×C4118yescomplemented
324C2×#107C22×C4111yescharacteristic
325C2×#107C22×C4111yescharacteristic
326C2×#106C22×C4111yescharacteristic
327C2×#103C22×C4111yescharacteristic
328C2×#103C22×C4111yescharacteristic
329C2×#103C22×C4111yescharacteristic
330C2×#102C22×C4111yescharacteristic
331C2×#102C22×C4111yescharacteristic
332C2×#102C22×C4111yescharacteristic
333C2×#97C22×C4111yescharacteristic
334C2×#97C22×C4111yescharacteristic
335C2×#97C22×C4111yescharacteristic
336C2×C4×C8C22×C4111yescharacteristic
337C2×C4×C8C22×C4111yescharacteristic
338C2×C4×C8C22×C4111yescharacteristic
339#391C22×C4111yescharacteristic
340#391C22×C4111yescharacteristic
341#390C22×C4111yescharacteristic
342#390C22×C4111yescharacteristic
343#389C22×C4111yescharacteristic
344#389C22×C4111yescharacteristic
345#389C22×C4111yescharacteristic
346#389C22×C4111yescharacteristic
347#388—21no—
348#388—21no—
349#387—21no—
350#387—21no—
351#383—21no—
352#382—21no—
353#381—21no—
354#380—21no—
355C4×C4⋊C4C22×C4111yescharacteristic
356C4×C4⋊C4C22×C4111yescharacteristic
357#376C22×C4111yescharacteristic
358#340C22×C4111yescharacteristic
359#340C22×C4111yescharacteristic
360#340C22×C4111yescharacteristic
361#340C22×C4111yescharacteristic
362#340C22×C4111yescharacteristic
363#340C22×C4111yescharacteristic
364C41#2129111yescharacteristic, direct product factor, Sylow
365C22×Q8C23×C4111yescharacteristic
366C22×D4C23×C4111yescharacteristic
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C2×C4×C4114yes—
371C22×C8C23×C4111yescharacteristic
372C22×C8C23×C4111yescharacteristic
373C22×C8C23×C4111yescharacteristic
374C22×C8C23×C4111yescharacteristic
375C4×Q8—22no—
376C4×Q8C2×C4×C4114yes—
377C4×D4—22no—
378C4×D4C2×C4×C4114yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
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×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C4111yescharacteristic
399C2×C42C23×C4111yescharacteristic
400C2×C42C23×C4111yescharacteristic
401#107—22no—
402#107C2×C4×C4114yes—
403#106—22no—
404#103—22no—
405#103—22no—
406#103C2×C4×C4114yes—
407#102—22no—
408#102—22no—
409#102C2×C4×C4114yes—
410#97—22no—
411#97—22no—
412#97C2×C4×C4114yes—
413C4×C8—22no—
414C4×C8—22no—
415C4×C8—22no—
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—
426#95D4×C4111yescharacteristic
427#95D4×C4111yescharacteristic
428#95D4×C4111yescharacteristic
429#95D4×C4111yescharacteristic
430C24—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C22×C4×C4112yes—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C22×C4×C4112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
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—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C22×C4×C4112yes—
468C2×C8C22×C4×C4112yes—
469C2×C8#41×C4112yes—
470C2×C8#41×C4112yes—
471C2×C8#41×C4112yes—
472C2×C8#41×C4112yes—
473C4⋊C4—24no—
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—21no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4C22×C4×C4112yes—
489C4⋊C4C22×C4×C4112yes—
490C22⋊C4—24no—
491C22⋊C4—81no—
492C22⋊C4—81no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—24no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—81no—
501C42—81no—
502C42C22×C4×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—22no—
526C2×C4—22no—
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—21no—
538C2×C4—21no—
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×C4C4×D4×C4112yes—
559C2×C4C4×D4×C4112yes—
560C2×C4C23×C4×C4111yescharacteristic
561C2×C4C2×#41×C4111yescharacteristic
562C2×C4C2×#41×C4111yescharacteristic
563C2×C4C2×#41×C4111yescharacteristic
564C2×C4C2×#41×C4111yescharacteristic
565C2×C4C2×#41×C4111yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8#117×C4114yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×C4×D4×C4111yescharacteristic
578C22C41×#53211yescharacteristic
579C22C41×#53211yescharacteristic
580C22C41×#57611yescharacteristic
581C22C41×#57711yescharacteristic
582C22C41×#57711yescharacteristic
583C22C41×#57811yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4—81no—
597C4C2×#117×C4111yescharacteristic
598C4C4×#41×C4111yescharacteristic
599C4C41×#52911yescharacteristic
600C4C41×#52911yescharacteristic
601C2—82no—
602C2C41×#229311yescharacteristic
603C2C41×#294611yescharacteristic
604C2C41×#294711yescharacteristic
605C2C41×#317411yescharacteristic
606C2C41×#317511yescharacteristic
607C2C41×#317811yescharacteristic
608C2C41×#317911yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC22×D4×C41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C41×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2320C2semidirect
6. C41×#1943C2semidirect
7. C41×#1942C2semidirect
9. C41×#1935C2semidirect
11. C41×#1933C2semidirect
12. C41×#1776C2semidirect
13. C4×#103×C41C2semidirect
15. C41×#1726C2semidirect
19. C41×#440C4semidirect
265. #21291C41direct (N × H)
298. #2320C2×C41semidirect
302. #1943C2×C41semidirect
303. #1942C2×C41semidirect
305. #1935C2×C41semidirect
307. #1933C2×C41semidirect
308. #1776C2×C41semidirect
309. C4×#103C2×C41semidirect
311. #1726C2×C41semidirect
323. #440C4×C41semidirect
364. C41#21291direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4402
C41×#23202
C41×#23192
C41×#19732
C41×#19682
C41×#19432
C41×#19422
C41×#19362
C41×#19352
C41×#19342
C41×#19332
C41×#17762
C4×#103×C412
C4×#102×C412
C41×#17262
#2129141