Finite Group Databasebeta

← C41×#32997 #23809198

Subgroups — C41×#32997 #23809198

Order 10496.

1326 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#520C211yesmaximal, characteristic, complemented
2C41×#3094C211yesmaximal, characteristic, complemented
3C41×#3006C211yesmaximal, characteristic
4C41×#2504C211yesmaximal, characteristic, complemented
5C41×#1883C214yesmaximal, complemented
6C41×#1860C214yesmaximal, complemented
7C41×#1826C211yesmaximal, characteristic, complemented
8C41×#1821C211yesmaximal, characteristic, complemented
9C41×#1789C211yesmaximal, characteristic, complemented
10C22×#41×C41C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C41C2212yes—
12C2×#121×C41C2211yescharacteristic
13C41×#520—22no—
14C41×#520—22no—
15C41×#520—22no—
16C41×#520C2214yes—
17C2×C4×Q8×C41—21no—
18C2×C4×D4×C41—21no—
19C2×C4×D4×C41—22no—
20C2×#117×C41—21no—
21C2×#117×C41C2211yescharacteristic
22C22×C4⋊C4×C41—21no—
23C22×C4⋊C4×C41C2211yescharacteristic
24C41×#482—22no—
25C41×#481—21no—
26C41×#480—21no—
27C41×#449—22no—
28C41×#448—21no—
29C41×#447—21no—
30C41×#428C2212yescomplemented
31C2×#104×C41C2214yes—
32C41×#418C2212yescomplemented
33C41×#417C2212yes—
34C41×#407C2211yescharacteristic
35C41×#407C2211yescharacteristic
36C41×#397—22no—
37C41×#390C2212yescomplemented
38C41×#386—22no—
39C41×#382C2212yescomplemented
40C4×C22⋊C4×C41C2211yescharacteristic
41C41×#343C2214yescomplemented
42C41×#339C2214yescomplemented
43C2×#41×C41—28no—
44C2×#41×C41—21no—
45C2×#41×C41—21no—
46C2×#41×C41D412yes—
47C2×#41×C41C2312yes—
48C22×Q8×C41D411yescharacteristic
49C22×D4×C41—21no—
50C22×D4×C41—21no—
51C22×D4×C41D411yescharacteristic
52C22×D4×C41C2311yescharacteristic
53C23×C4×C41—21no—
54C23×C4×C41—22no—
55C23×C4×C41D412yes—
56C23×C4×C41C2311yescharacteristic
57AGL(1,ℤ/8)×C41—28no—
58C2×SD16×C41—22no—
59C2×D8×C41—22no—
60C2×M16×C41C2312yes—
61C2×M16×C41C2312yes—
62#121×C41—21no—
63#121×C41—21no—
64#121×C41—21no—
65#121×C41—21no—
66C4×Q8×C41—24no—
67C4×Q8×C41—24no—
68C4×D4×C41—28no—
69C4×D4×C41—24no—
70C4×D4×C41—24no—
71C4×D4×C41—28no—
72#117×C41—24no—
73#117×C41—21no—
74#117×C41—21no—
75#117×C41—24no—
76#117×C41D412yes—
77#117×C41C2312yes—
78C2×C4⋊C4×C41—22no—
79C2×C4⋊C4×C41—24no—
80C2×C4⋊C4×C41—21no—
81C2×C4⋊C4×C41—21no—
82C2×C4⋊C4×C41—21no—
83C2×C4⋊C4×C41—21no—
84C2×C4⋊C4×C41—24no—
85C2×C4⋊C4×C41D412yes—
86C2×C4⋊C4×C41D411yescharacteristic
87C2×C4⋊C4×C41D411yescharacteristic
88C2×C4⋊C4×C41C2311yescharacteristic
89C2×C4⋊C4×C41C2312yes—
90C2×C22⋊C4×C41—22no—
91C2×C22⋊C4×C41—21no—
92C2×C22⋊C4×C41—21no—
93C2×C22⋊C4×C41—21no—
94C2×C22⋊C4×C41—24no—
95C2×C42×C41—22no—
96C2×C42×C41—21no—
97C2×C42×C41C2312yes—
98#107×C41—22no—
99#106×C41—22no—
100#104×C41—28no—
101#103×C41—22no—
102#102×C41—22no—
103#102×C41—22no—
104#102×C41—22no—
105C22⋊C8×C41—21no—
106C22⋊C8×C41—21no—
107C22⋊C8×C41—21no—
108C22⋊C8×C41—21no—
109#95×C41—21no—
110#95×C41—24no—
111C24×C41—21no—
112C24×C41—21no—
113C24×C41C2×D411yescharacteristic
114#41×C41—28no—
115#41×C41—28no—
116#41×C41—24no—
117#41×C41—24no—
118#41×C41—24no—
119#41×C41#4118yes—
120C2×Q8×C41—24no—
121C2×Q8×C41—21no—
122C2×Q8×C41C2×D412yes—
123C2×D4×C41—28no—
124C2×D4×C41—22no—
125C2×D4×C41—22no—
126C2×D4×C41—24no—
127C2×D4×C41—21no—
128C2×D4×C41—21no—
129C2×D4×C41—21no—
130C2×D4×C41—24no—
131C2×D4×C41—44no—
132C2×D4×C41—41no—
133C2×D4×C41—41no—
134C2×D4×C41C2×D412yes—
135C22×C4×C41—28no—
136C22×C4×C41—21no—
137C22×C4×C41—22no—
138C22×C4×C41—22no—
139C22×C4×C41—24no—
140C22×C4×C41—21no—
141C22×C4×C41—22no—
142C22×C4×C41—21no—
143C22×C4×C41—28no—
144C22×C4×C41—22no—
145C22×C4×C41—21no—
146C22×C4×C41—22no—
147C22×C4×C41—82no—
148C22×C4×C41—84no—
149C22×C4×C41C2×D411yescharacteristic
150C22×C4×C41C2×D411yescharacteristic
151C22×C4×C41C2×D411yescharacteristic
152C22×C4×C41C2×D411yescharacteristic
153C22×C4×C41C2×D411yescharacteristic
154C22×C4×C41C2×D414yes—
155C22×C4×C41C2411yescharacteristic
156SD16×C41—44no—
157D8×C41—44no—
158M16×C41—24no—
159M16×C41—24no—
160C2×C8×C41—22no—
161C2×C8×C41—22no—
162C4⋊C4×C41—28no—
163C4⋊C4×C41—22no—
164C4⋊C4×C41—21no—
165C4⋊C4×C41—22no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—22no—
168C4⋊C4×C41—22no—
169C4⋊C4×C41—21no—
170C4⋊C4×C41—21no—
171C4⋊C4×C41C2×D412yes—
172C4⋊C4×C41C2×D412yes—
173C22⋊C4×C41—28no—
174C22⋊C4×C41—22no—
175C22⋊C4×C41—22no—
176C22⋊C4×C41—42no—
177C22⋊C4×C41—41no—
178C22⋊C4×C41—41no—
179C22⋊C4×C41—84no—
180C42×C41—28no—
181C42×C41—22no—
182C42×C41—22no—
183C42×C41—24no—
184C23×C41—24no—
185C23×C41—22no—
186C23×C41—22no—
187C23×C41—22no—
188C23×C41—41no—
189C23×C41—42no—
190C23×C41—42no—
191C23×C41—42no—
192C23×C41—42no—
193C23×C41—41no—
194C23×C41—42no—
195C23×C41#12011yescharacteristic
196C23×C41#12011yescharacteristic
197C23×C41C22×D411yescharacteristic
198Q8×C41—24no—
199Q8×C41—22no—
200Q8×C41#12314yes—
201D4×C41—28no—
202D4×C41—24no—
203D4×C41—28no—
204D4×C41—22no—
205D4×C41—42no—
206D4×C41—42no—
207D4×C41—82no—
208D4×C41—82no—
209D4×C41#12314yes—
210C2×C4×C41—24no—
211C2×C4×C41—28no—
212C2×C4×C41—22no—
213C2×C4×C41—22no—
214C2×C4×C41—22no—
215C2×C4×C41—22no—
216C2×C4×C41—22no—
217C2×C4×C41—28no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—24no—
221C2×C4×C41—22no—
222C2×C4×C41—44no—
223C2×C4×C41—42no—
224C2×C4×C41—42no—
225C2×C4×C41—44no—
226C2×C4×C41—42no—
227C2×C4×C41—42no—
228C2×C4×C41—42no—
229C2×C4×C41—41no—
230C2×C4×C41—42no—
231C2×C4×C41—82no—
232C2×C4×C41—88no—
233C2×C4×C41#12011yescharacteristic
234C2×C4×C41#12011yescharacteristic
235C2×C4×C41C22×D411yescharacteristic
236C2×C4×C41C22×D411yescharacteristic
237C2×C4×C41C2×#4114yes—
238C8×C41—42no—
239C8×C41—42no—
240#32997C4111yesmaximal, characteristic, direct product factor, Sylow
241C22×C41—21no—
242C22×C41—21no—
243C22×C41—21no—
244C22×C41—21no—
245C22×C41—21no—
246C22×C41—24no—
247C22×C41—21no—
248C22×C41—21no—
249C22×C41—44no—
250C22×C41—48no—
251C22×C41—42no—
252C22×C41—42no—
253C22×C41—84no—
254C22×C41—81no—
255C22×C41—81no—
256C22×C41—81no—
257C22×C41#45412yes—
258C22×C41C2×#12011yescharacteristic
259C22×C41#52512yes—
260C4×C41—21no—
261C4×C41—24no—
262C4×C41—21no—
263C4×C41—42no—
264C4×C41—44no—
265C4×C41—42no—
266C4×C41—82no—
267C4×C41—81no—
268C4×C41C2×#12312yes—
269C4×C41#52512yes—
270C2×#520C2×C4111yescharacteristic, complemented
271#3094C2×C4111yescharacteristic, complemented
272#3006C2×C4111yescharacteristic
273#2504C2×C4111yescharacteristic, complemented
274#1883C2×C4114yescomplemented
275#1860C2×C4114yescomplemented
276#1826C2×C4111yescharacteristic, complemented
277#1821C2×C4111yescharacteristic, complemented
278#1789C2×C4111yescharacteristic, complemented
279C2×C41—22no—
280C2×C41—22no—
281C2×C41—41no—
282C2×C41—44no—
283C2×C41—161no—
284C2×C41#284911yescharacteristic
285C2×C41C2×#45411yescharacteristic
286C2×C41#301911yescharacteristic
287C22×#41C22×C4111yescharacteristic
288C2×AGL(1,ℤ/8)C22×C4112yes—
289C2×#121C22×C4111yescharacteristic
290#520—22no—
291#520—22no—
292#520—22no—
293#520C22×C4114yes—
294C2×C4×Q8—21no—
295C2×C4×D4—21no—
296C2×C4×D4—22no—
297C2×#117—21no—
298C2×#117C22×C4111yescharacteristic
299C22×C4⋊C4—21no—
300C22×C4⋊C4C22×C4111yescharacteristic
301#482—22no—
302#481—21no—
303#480—21no—
304#449—22no—
305#448—21no—
306#447—21no—
307#428C22×C4112yescomplemented
308C2×#104C22×C4114yes—
309#418C22×C4112yescomplemented
310#417C22×C4112yes—
311#407C22×C4111yescharacteristic
312#407C22×C4111yescharacteristic
313#397—22no—
314#390C22×C4112yescomplemented
315#386—22no—
316#382C22×C4112yescomplemented
317C4×C22⋊C4C22×C4111yescharacteristic
318#343C22×C4114yescomplemented
319#339C22×C4114yescomplemented
320C41#3299711yescharacteristic, direct product factor, Sylow
321C2×#41—28no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41D4×C4112yes—
325C2×#41C23×C4112yes—
326C22×Q8D4×C4111yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4D4×C4111yescharacteristic
330C22×D4C23×C4111yescharacteristic
331C23×C4—21no—
332C23×C4—22no—
333C23×C4D4×C4112yes—
334C23×C4C23×C4111yescharacteristic
335AGL(1,ℤ/8)—28no—
336C2×SD16—22no—
337C2×D8—22no—
338C2×M16C23×C4112yes—
339C2×M16C23×C4112yes—
340#121—21no—
341#121—21no—
342#121—21no—
343#121—21no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×D4—28no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—28no—
350#117—24no—
351#117—21no—
352#117—21no—
353#117—24no—
354#117D4×C4112yes—
355#117C23×C4112yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4D4×C4112yes—
364C2×C4⋊C4D4×C4111yescharacteristic
365C2×C4⋊C4D4×C4111yescharacteristic
366C2×C4⋊C4C23×C4111yescharacteristic
367C2×C4⋊C4C23×C4112yes—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C42—22no—
374C2×C42—21no—
375C2×C42C23×C4112yes—
376#107—22no—
377#106—22no—
378#104—28no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—21no—
387#95—21no—
388#95—24no—
389C24—21no—
390C24—21no—
391C24C2×D4×C4111yescharacteristic
392#41—28no—
393#41—28no—
394#41—24no—
395#41—24no—
396#41—24no—
397#41#41×C4118yes—
398C2×Q8—24no—
399C2×Q8—21no—
400C2×Q8C2×D4×C4112yes—
401C2×D4—28no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—24no—
409C2×D4—44no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4C2×D4×C4112yes—
413C22×C4—28no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—28no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—82no—
426C22×C4—84no—
427C22×C4C2×D4×C4111yescharacteristic
428C22×C4C2×D4×C4111yescharacteristic
429C22×C4C2×D4×C4111yescharacteristic
430C22×C4C2×D4×C4111yescharacteristic
431C22×C4C2×D4×C4111yescharacteristic
432C22×C4C2×D4×C4114yes—
433C22×C4C24×C4111yescharacteristic
434SD16—44no—
435D8—44no—
436M16—24no—
437M16—24no—
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—28no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4C2×D4×C4112yes—
450C4⋊C4C2×D4×C4112yes—
451C22⋊C4—28no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—84no—
458C42—28no—
459C42—22no—
460C42—22no—
461C42—24no—
462C23—24no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23#120×C4111yescharacteristic
474C23#120×C4111yescharacteristic
475C23C22×D4×C4111yescharacteristic
476Q8—24no—
477Q8—22no—
478Q8#123×C4114yes—
479D4—28no—
480D4—24no—
481D4—28no—
482D4—22no—
483D4—42no—
484D4—42no—
485D4—82no—
486D4—82no—
487D4#123×C4114yes—
488C2×C4—24no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—28no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—88no—
511C2×C4#120×C4111yescharacteristic
512C2×C4#120×C4111yescharacteristic
513C2×C4C22×D4×C4111yescharacteristic
514C2×C4C22×D4×C4111yescharacteristic
515C2×C4C2×#41×C4114yes—
516C8—42no—
517C8—42no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—24no—
524C22—21no—
525C22—21no—
526C22—44no—
527C22—48no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22C41×#45412yes—
535C22C2×#120×C4111yescharacteristic
536C22C41×#52512yes—
537C4—21no—
538C4—24no—
539C4—21no—
540C4—42no—
541C4—44no—
542C4—42no—
543C4—82no—
544C4—81no—
545C4C2×#123×C4112yes—
546C4C41×#52512yes—
547C2—22no—
548C2—22no—
549C2—41no—
550C2—44no—
551C2—161no—
552C2C41×#284911yescharacteristic
553C2C2×C41×#45411yescharacteristic
554C2C41×#301911yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#520C2semidirect
2. C41×#3094C2semidirect
4. C41×#2504C2semidirect
5. C41×#1883C2semidirect
6. C41×#1860C2semidirect
7. C41×#1826C2semidirect
8. C41×#1821C2semidirect
9. C41×#1789C2semidirect
30. C41×#428C22semidirect
32. C41×#418C22semidirect
37. C41×#390C22semidirect
39. C41×#382C22semidirect
41. C41×#343C22semidirect
42. C41×#339C22semidirect
240. #32997C41direct (N × H)
270. C2×#520C2×C41semidirect
271. #3094C2×C41semidirect
273. #2504C2×C41semidirect
274. #1883C2×C41semidirect
275. #1860C2×C41semidirect
276. #1826C2×C41semidirect
277. #1821C2×C41semidirect
278. #1789C2×C41semidirect
307. #428C22×C41semidirect
309. #418C22×C41semidirect
314. #390C22×C41semidirect
316. #382C22×C41semidirect
318. #343C22×C41semidirect
319. #339C22×C41semidirect
320. C41#32997direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#5202
C41×#30942
C41×#30062
C41×#25042
C41×#18832
C41×#18602
C41×#18262
C41×#18212
C41×#17892
#3299741