Finite Group Databasebeta

← C41×#9241 #23785442

Subgroups — C41×#9241 #23785442

Order 10496.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#449C211yesmaximal, characteristic
2C41×#2880C211yesmaximal, characteristic, complemented
3C41×#1789C211yesmaximal, characteristic, complemented
4C41×#1507C211yesmaximal, characteristic, complemented
5C41×#1471C211yesmaximal, characteristic, complemented
6C41×#1293C211yesmaximal, characteristic, complemented
7C41×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C41C2211yescharacteristic
9C22×SD16×C41C411yescharacteristic, complemented
10C22×D8×C41C411yescharacteristic, complemented
11C2×#131×C41—21no—
12C2×#121×C41C2211yescharacteristic
13C41×#449—21no—
14C41×#449—21no—
15C41×#449—21no—
16C41×#449—21no—
17C2×#104×C41—21no—
18C2×#104×C41—21no—
19C2×#103×C41C411yescharacteristic, complemented
20C2×#102×C41C411yescharacteristic, complemented
21C41×#408—21no—
22C41×#408—22no—
23C41×#407—21no—
24C41×#407C2211yescharacteristic
25C41×#407C2211yescharacteristic
26C2×C22⋊C8×C41—21no—
27C2×C22⋊C8×C41C2211yescharacteristic
28C2×C22⋊C8×C41C2211yescharacteristic
29C4×C22⋊C4×C41C2211yescharacteristic
30C41×#327—22no—
31C41×#323—21no—
32C41×#323—21no—
33C2×#41×C41—21no—
34C2×#41×C41—21no—
35C2×#41×C41—42no—
36C2×#41×C41—42no—
37C2×#41×C41D411yescharacteristic
38C2×#41×C41D411yescharacteristic
39C2×#41×C41D411yescharacteristic
40C2×#41×C41D411yescharacteristic
41C22×Q8×C41C2×C411yescharacteristic
42C22×D4×C41—21no—
43C22×D4×C41—21no—
44C22×D4×C41C2×C411yescharacteristic
45C22×D4×C41C2×C411yescharacteristic
46C23×C4×C41—21no—
47C23×C4×C41C2311yescharacteristic
48C2×SD16×C41—21no—
49C2×SD16×C41—21no—
50C2×SD16×C41—42no—
51C2×D8×C41—21no—
52C2×D8×C41—21no—
53C2×D8×C41—42no—
54#131×C41—42no—
55#131×C41—42no—
56C2×M16×C41—22no—
57C2×M16×C41—21no—
58C2×M16×C41—21no—
59C22×C8×C41—22no—
60C22×C8×C41—21no—
61C22×C8×C41C2×C411yescharacteristic
62C22×C8×C41C2×C411yescharacteristic
63#121×C41—21no—
64#121×C41—21no—
65#121×C41—21no—
66#121×C41—21no—
67C2×C4⋊C4×C41C2×C411yescharacteristic
68C2×C22⋊C4×C41—21no—
69C2×C22⋊C4×C41—21no—
70C2×C42×C41—21no—
71#104×C41—42no—
72#104×C41—42no—
73#103×C41—21no—
74#103×C41—21no—
75#102×C41—21no—
76#102×C41—21no—
77C22⋊C8×C41—22no—
78C22⋊C8×C41—22no—
79C22⋊C8×C41—21no—
80C22⋊C8×C41—21no—
81C22⋊C8×C41—21no—
82C22⋊C8×C41—21no—
83C22⋊C8×C41—21no—
84C22⋊C8×C41—21no—
85C22⋊C8×C41D411yescharacteristic
86C22⋊C8×C41D411yescharacteristic
87C22⋊C8×C41D412yes—
88#95×C41—21no—
89C24×C41—21no—
90C24×C41—21no—
91C24×C41#4111yescharacteristic
92#41×C41—22no—
93#41×C41—22no—
94#41×C41—22no—
95#41×C41—22no—
96#41×C41—41no—
97#41×C41—41no—
98#41×C41—41no—
99#41×C41—41no—
100#41×C41—44no—
101#41×C41—44no—
102C2×Q8×C41—21no—
103C2×Q8×C41—22no—
104C2×Q8×C41—41no—
105C2×Q8×C41C22⋊C411yescharacteristic
106C2×Q8×C41C22⋊C411yescharacteristic
107C2×D4×C41—21no—
108C2×D4×C41—22no—
109C2×D4×C41—21no—
110C2×D4×C41—21no—
111C2×D4×C41—21no—
112C2×D4×C41—21no—
113C2×D4×C41—21no—
114C2×D4×C41—21no—
115C2×D4×C41—41no—
116C2×D4×C41—41no—
117C2×D4×C41—41no—
118C2×D4×C41—44no—
119C2×D4×C41—41no—
120C2×D4×C41—41no—
121C2×D4×C41—82no—
122C2×D4×C41C22⋊C411yescharacteristic
123C2×D4×C41C22⋊C411yescharacteristic
124C22×C4×C41—21no—
125C22×C4×C41—21no—
126C22×C4×C41—21no—
127C22×C4×C41—21no—
128C22×C4×C41—21no—
129C22×C4×C41—21no—
130C22×C4×C41—41no—
131C22×C4×C41—41no—
132C22×C4×C41—44no—
133C22×C4×C41—41no—
134C22×C4×C41C22×C411yescharacteristic
135C22×C4×C41C2×D411yescharacteristic
136C22×C4×C41C2×D411yescharacteristic
137C22×C4×C41C2×D411yescharacteristic
138C22×C4×C41C2×D411yescharacteristic
139C22×C4×C41#4111yescharacteristic
140SD16×C41—42no—
141SD16×C41—42no—
142D8×C41—42no—
143D8×C41—42no—
144M16×C41—44no—
145M16×C41—41no—
146M16×C41—41no—
147M16×C41—41no—
148M16×C41—41no—
149C2×C8×C41—21no—
150C2×C8×C41—21no—
151C2×C8×C41—21no—
152C2×C8×C41—22no—
153C2×C8×C41—21no—
154C2×C8×C41—44no—
155C2×C8×C41—41no—
156C2×C8×C41—41no—
157C2×C8×C41—41no—
158C2×C8×C41—41no—
159C2×C8×C41—41no—
160C4⋊C4×C41—21no—
161C4⋊C4×C41—21no—
162C22⋊C4×C41—22no—
163C22⋊C4×C41—41no—
164C22⋊C4×C41—41no—
165C22⋊C4×C41—41no—
166C42×C41—41no—
167C42×C41—41no—
168C23×C41—21no—
169C23×C41—21no—
170C23×C41—21no—
171C23×C41—21no—
172C23×C41—41no—
173C23×C41—41no—
174C23×C41—42no—
175C23×C41—41no—
176C23×C41—41no—
177C23×C41—41no—
178C23×C41—41no—
179C23×C41—41no—
180C23×C41—81no—
181C23×C41—81no—
182C23×C41—81no—
183C23×C41C4×D411yescharacteristic
184C23×C41#12111yescharacteristic
185C23×C41#12311yescharacteristic
186Q8×C41—21no—
187Q8×C41—21no—
188Q8×C41—21no—
189Q8×C41—42no—
190Q8×C41#9912yes—
191D4×C41—24no—
192D4×C41—21no—
193D4×C41—21no—
194D4×C41—21no—
195D4×C41—42no—
196D4×C41—42no—
197D4×C41—42no—
198D4×C41—42no—
199D4×C41—41no—
200D4×C41—41no—
201D4×C41—81no—
202D4×C41—82no—
203D4×C41—82no—
204D4×C41#9912yes—
205C2×C4×C41—24no—
206C2×C4×C41—21no—
207C2×C4×C41—21no—
208C2×C4×C41—21no—
209C2×C4×C41—21no—
210C2×C4×C41—21no—
211C2×C4×C41—21no—
212C2×C4×C41—21no—
213C2×C4×C41—21no—
214C2×C4×C41—41no—
215C2×C4×C41—41no—
216C2×C4×C41—41no—
217C2×C4×C41—42no—
218C2×C4×C41—42no—
219C2×C4×C41—42no—
220C2×C4×C41—42no—
221C2×C4×C41—42no—
222C2×C4×C41—41no—
223C2×C4×C41—81no—
224C2×C4×C41—81no—
225C2×C4×C41—81no—
226C2×C4×C41C2×C22⋊C411yescharacteristic
227C2×C4×C41C4×D411yescharacteristic
228C2×C4×C41#12011yescharacteristic
229C2×C4×C41#12111yescharacteristic
230C8×C41—41no—
231C8×C41—42no—
232C8×C41—41no—
233C8×C41—41no—
234C8×C41—41no—
235C8×C41—81no—
236#9241C4111yesmaximal, characteristic, direct product factor, Sylow
237C22×C41—21no—
238C22×C41—21no—
239C22×C41—21no—
240C22×C41—21no—
241C22×C41—21no—
242C22×C41—21no—
243C22×C41—22no—
244C22×C41—21no—
245C22×C41—21no—
246C22×C41—41no—
247C22×C41—41no—
248C22×C41—41no—
249C22×C41—41no—
250C22×C41—41no—
251C22×C41—81no—
252C22×C41—81no—
253C22×C41—82no—
254C22×C41—82no—
255C22×C41—81no—
256C22×C41—81no—
257C22×C41—81no—
258C22×C41—161no—
259C22×C41—161no—
260C22×C41#38611yescharacteristic
261C22×C41#44311yescharacteristic
262C22×C41#44411yescharacteristic
263C4×C41—21no—
264C4×C41—21no—
265C4×C41—22no—
266C4×C41—21no—
267C4×C41—41no—
268C4×C41—82no—
269C4×C41—81no—
270C4×C41C2×#9911yescharacteristic
271C4×C41C2×#9911yescharacteristic
272C2×#449C2×C4111yescharacteristic
273#2880C2×C4111yescharacteristic, complemented
274#1789C2×C4111yescharacteristic, complemented
275#1507C2×C4111yescharacteristic, complemented
276#1471C2×C4111yescharacteristic, complemented
277#1293C2×C4111yescharacteristic, complemented
278#1282C2×C4111yescharacteristic, complemented
279C2×C41—21no—
280C2×C41—21no—
281C2×C41—41no—
282C2×C41—41no—
283C2×C41—42no—
284C2×C41—81no—
285C2×C41—161no—
286C2×C41#187611yescharacteristic
287C2×C41#189811yescharacteristic
288C2×C41#190311yescharacteristic
289C22×#41C22×C4111yescharacteristic
290C22×SD16C4×C4111yescharacteristic, complemented
291C22×D8C4×C4111yescharacteristic, complemented
292C2×#131—21no—
293C2×#121C22×C4111yescharacteristic
294#449—21no—
295#449—21no—
296#449—21no—
297#449—21no—
298C2×#104—21no—
299C2×#104—21no—
300C2×#103C4×C4111yescharacteristic, complemented
301C2×#102C4×C4111yescharacteristic, complemented
302#408—21no—
303#408—22no—
304#407—21no—
305#407C22×C4111yescharacteristic
306#407C22×C4111yescharacteristic
307C2×C22⋊C8—21no—
308C2×C22⋊C8C22×C4111yescharacteristic
309C2×C22⋊C8C22×C4111yescharacteristic
310C4×C22⋊C4C22×C4111yescharacteristic
311#327—22no—
312#323—21no—
313#323—21no—
314C41#924111yescharacteristic, direct product factor, Sylow
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C4111yescharacteristic
320C2×#41D4×C4111yescharacteristic
321C2×#41D4×C4111yescharacteristic
322C2×#41D4×C4111yescharacteristic
323C22×Q8C2×C4×C4111yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C4111yescharacteristic
327C22×D4C2×C4×C4111yescharacteristic
328C23×C4—21no—
329C23×C4C23×C4111yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C4111yescharacteristic
344C22×C8C2×C4×C4111yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C4111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C4111yescharacteristic
368C22⋊C8D4×C4111yescharacteristic
369C22⋊C8D4×C4112yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C4111yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C4111yescharacteristic
388C2×Q8C22⋊C4×C4111yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C4111yescharacteristic
405C2×D4C22⋊C4×C4111yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C4111yescharacteristic
417C22×C4C2×D4×C4111yescharacteristic
418C22×C4C2×D4×C4111yescharacteristic
419C22×C4C2×D4×C4111yescharacteristic
420C22×C4C2×D4×C4111yescharacteristic
421C22×C4#41×C4111yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C4111yescharacteristic
466C23#121×C4111yescharacteristic
467C23#123×C4111yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C4112yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C4112yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C4111yescharacteristic
509C2×C4C4×D4×C4111yescharacteristic
510C2×C4#120×C4111yescharacteristic
511C2×C4#121×C4111yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—22no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22C41×#38611yescharacteristic
542C22C41×#44311yescharacteristic
543C22C41×#44411yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C4111yescharacteristic
552C4C2×#99×C4111yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C41×#187611yescharacteristic
561C2C41×#189811yescharacteristic
562C2C41×#190311yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC2×C41×#449C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2880C2semidirect
3. C41×#1789C2semidirect
4. C41×#1507C2semidirect
5. C41×#1471C2semidirect
6. C41×#1293C2semidirect
7. C41×#1282C2semidirect
9. C22×SD16×C41C4semidirect
10. C22×D8×C41C4semidirect
19. C2×#103×C41C4semidirect
20. C2×#102×C41C4semidirect
236. #9241C41direct (N × H)
273. #2880C2×C41semidirect
274. #1789C2×C41semidirect
275. #1507C2×C41semidirect
276. #1471C2×C41semidirect
277. #1293C2×C41semidirect
278. #1282C2×C41semidirect
290. C22×SD16C4×C41semidirect
291. C22×D8C4×C41semidirect
300. C2×#103C4×C41semidirect
301. C2×#102C4×C41semidirect
314. C41#9241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4492
C41×#28802
C41×#17892
C41×#15072
C41×#14712
C41×#12932
C41×#12822
#924141