Finite Group Databasebeta

← C41×#61891 #23838092

Subgroups — C41×#61891 #23838092

Order 10496.

2034 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3497C211yesmaximal, characteristic, complemented
2C2×C41×#559C211yesmaximal, characteristic, complemented
3C41×#3399C218yesmaximal, complemented
4C41×#3373C218yesmaximal, complemented
5C41×#3213C214yesmaximal, complemented
6C41×#3205C212yesmaximal, complemented
7C41×#3109C214yesmaximal, complemented
8C41×#3103C212yesmaximal, complemented
9C41×#2983C211yesmaximal, characteristic, complemented
10C2×2−1+4×C41—21no—
11C41×#559—24no—
12C41×#559C2218yes—
13C41×#550C2214yescomplemented
14D4×Q8×C41C2214yescomplemented
15C41×#548—24no—
16C41×#537—21no—
17C41×#537—22no—
18C41×#532C2212yes—
19C41×#532C2214yes—
20C2×#127×C41C2211yescharacteristic
21C2×#124×C41—21no—
22C2×#124×C41C2212yes—
23C2×#123×C41—22no—
24C2×C4×Q8×C41C2211yescharacteristic
25C2×C4×Q8×C41C2211yescharacteristic
26C2×C4×D4×C41—21no—
27C2×C4×D4×C41C2212yes—
28C41×#496C2218yescomplemented
29C41×#493C2214yes—
30C41×#489C2218yescomplemented
31C41×#486C2214yes—
32C41×#481C2214yes—
33C41×#476C2218yescomplemented
34C41×#475C2214yescomplemented
35C41×#463C22116yescomplemented
36C41×#460C2214yescomplemented
37C41×#459C2218yes—
38C41×#459C2218yescomplemented
39C41×#448C2214yes—
40C41×#447C2218yes—
41C41×#446C2218yescomplemented
42C41×#442C22116yescomplemented
43C4×SD16×C41C2218yescomplemented
44C41×#432C2214yes—
45C41×#431C2212yes—
462−1+4×C41—48no—
47C2×#41×C41—24no—
48C2×#41×C41—24no—
49C2×#41×C41—22no—
50C22×Q8×C41—24no—
51C22×Q8×C41D411yescharacteristic
52C22×Q8×C41C2311yescharacteristic
53C22×D4×C41—21no—
54C22×D4×C41—21no—
55C22×D4×C41C2312yes—
56C23×C4×C41—22no—
57C2×SD16×C41C2318yes—
58C2×D8×C41C23116yes—
59C4⋊Q8×C41C2312yes—
60C4⋊Q8×C41C2314yes—
61#127×C41—22no—
62#127×C41C2314yes—
63#127×C41C2314yes—
64#127×C41C2312yes—
65#124×C41—28no—
66#124×C41—24no—
67#124×C41—24no—
68#124×C41—22no—
69#124×C41C2318yes—
70#123×C41—216no—
71C22⋊Q8×C41—24no—
72C22⋊Q8×C41—28no—
73#121×C41—24no—
74#121×C41—22no—
75#121×C41—24no—
76#121×C41—28no—
77#121×C41C2314yes—
78C4×Q8×C41—22no—
79C4×Q8×C41D414yes—
80C4×Q8×C41C2314yes—
81C4×Q8×C41C2314yes—
82C4×D4×C41—28no—
83C4×D4×C41—24no—
84C4×D4×C41—24no—
85C4×D4×C41—22no—
86C4×D4×C41C2318yes—
87C4×D4×C41C2314yes—
88C4×D4×C41C2318yes—
89C2×C4⋊C4×C41—21no—
90C2×C4⋊C4×C41D411yescharacteristic
91C2×C4⋊C4×C41D412yes—
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C22⋊C4×C41—22no—
94C2×C22⋊C4×C41—22no—
95C2×C22⋊C4×C41—22no—
96C2×C42×C41—21no—
97C2×C42×C41C2312yes—
98C2×C42×C41C2311yescharacteristic
99#106×C41C2318yes—
100C4⋊C8×C41C2314yes—
101C4⋊C8×C41C2318yes—
102#103×C41C2318yes—
103#102×C41C2318yes—
104#102×C41C23116yes—
105C22⋊C8×C41C2314yes—
106#97×C41C2318yes—
107C4×C8×C41C2314yes—
108C24×C41—22no—
109#41×C41—416no—
110#41×C41—416no—
111#41×C41—48no—
112C2×Q8×C41—24no—
113C2×Q8×C41—21no—
114C2×Q8×C41—24no—
115C2×Q8×C41—22no—
116C2×Q8×C41—42no—
117C2×Q8×C41—416no—
118C2×Q8×C41C2×D414yes—
119C2×Q8×C41C2412yes—
120C2×D4×C41—24no—
121C2×D4×C41—22no—
122C2×D4×C41—24no—
123C2×D4×C41—24no—
124C2×D4×C41—22no—
125C2×D4×C41—24no—
126C2×D4×C41—22no—
127C2×D4×C41—24no—
128C2×D4×C41—44no—
129C2×D4×C41—44no—
130C2×D4×C41—82no—
131C2×D4×C41C2414yes—
132C2×D4×C41C2414yes—
133C22×C4×C41—21no—
134C22×C4×C41—21no—
135C22×C4×C41—28no—
136C22×C4×C41—24no—
137C22×C4×C41—28no—
138C22×C4×C41—84no—
139C22×C4×C41C2×D412yes—
140C22×C4×C41C2×D412yes—
141C22×C4×C41C2×D411yescharacteristic
142C22×C4×C41C2×D411yescharacteristic
143C22×C4×C41C2411yescharacteristic
144SD16×C41—48no—
145D8×C41—416no—
146C2×C8×C41C2418yes—
147C4⋊C4×C41—24no—
148C4⋊C4×C41—21no—
149C4⋊C4×C41—24no—
150C4⋊C4×C41—22no—
151C4⋊C4×C41C2×D414yes—
152C4⋊C4×C41C2×D418yes—
153C4⋊C4×C41C2414yes—
154C4⋊C4×C41C2412yes—
155C22⋊C4×C41—28no—
156C22⋊C4×C41—28no—
157C22⋊C4×C41—28no—
158C22⋊C4×C41—24no—
159C22⋊C4×C41—28no—
160C22⋊C4×C41—24no—
161C42×C41—24no—
162C42×C41C2×D414yes—
163C42×C41C2×D412yes—
164C42×C41C2412yes—
165C42×C41C2414yes—
166C23×C41—24no—
167C23×C41—24no—
168C23×C41—44no—
169C23×C41—44no—
170C23×C41—44no—
171C23×C41C22×D411yescharacteristic
172Q8×C41—28no—
173Q8×C41—24no—
174Q8×C41—42no—
175Q8×C41—48no—
176Q8×C41—44no—
177D4×C41—28no—
178D4×C41—28no—
179D4×C41—44no—
180D4×C41—48no—
181D4×C41—48no—
182D4×C41—48no—
183D4×C41—44no—
184D4×C41—84no—
185D4×C41—82no—
186D4×C41—84no—
187C2×C4×C41—24no—
188C2×C4×C41—22no—
189C2×C4×C41—22no—
190C2×C4×C41—22no—
191C2×C4×C41—24no—
192C2×C4×C41—42no—
193C2×C4×C41—41no—
194C2×C4×C41—416no—
195C2×C4×C41—42no—
196C2×C4×C41—42no—
197C2×C4×C41—48no—
198C2×C4×C41—88no—
199C2×C4×C41AGL(1,ℤ/8)14yes—
200C2×C4×C41C22×D411yescharacteristic
201C2×C4×C41C22×D414yes—
202C2×C4×C41C22×D414yes—
203C2×C4×C41C22×D412yes—
204C2×C4×C41C22×D412yes—
205C2×C4×C41C2511yescharacteristic
206C8×C41—28no—
207#61891C4111yesmaximal, characteristic, direct product factor, Sylow
208C22×C41—21no—
209C22×C41—21no—
210C22×C41—44no—
211C22×C41—44no—
212C22×C41—44no—
213C22×C41—44no—
214C22×C41—44no—
215C22×C41—44no—
216C22×C41—88no—
217C22×C41C2×AGL(1,ℤ/8)12yes—
218C22×C41C23×D411yescharacteristic
219C4×C41—24no—
220C4×C41—22no—
221C4×C41—21no—
222C4×C41—24no—
223C4×C41—42no—
224C4×C41—42no—
225C4×C41—44no—
226C4×C41C2×AGL(1,ℤ/8)14yes—
227C4×C41#58512yes—
228#3497C2×C4111yescharacteristic, complemented
229C2×#559C2×C4111yescharacteristic, complemented
230#3399C2×C4118yescomplemented
231#3373C2×C4118yescomplemented
232#3213C2×C4114yescomplemented
233#3205C2×C4112yescomplemented
234#3109C2×C4114yescomplemented
235#3103C2×C4112yescomplemented
236#2983C2×C4111yescharacteristic, complemented
237C2×C41—22no—
238C2×C41—84no—
239C2×C41—84no—
240C2×C41#348711yescharacteristic
241C2×C41C22×AGL(1,ℤ/8)11yescharacteristic
242C2×C41#358511yescharacteristic
243C2×2−1+4—21no—
244#559—24no—
245#559C22×C4118yes—
246#550C22×C4114yescomplemented
247D4×Q8C22×C4114yescomplemented
248#548—24no—
249#537—21no—
250#537—22no—
251#532C22×C4112yes—
252#532C22×C4114yes—
253C2×#127C22×C4111yescharacteristic
254C2×#124—21no—
255C2×#124C22×C4112yes—
256C2×#123—22no—
257C2×C4×Q8C22×C4111yescharacteristic
258C2×C4×Q8C22×C4111yescharacteristic
259C2×C4×D4—21no—
260C2×C4×D4C22×C4112yes—
261#496C22×C4118yescomplemented
262#493C22×C4114yes—
263#489C22×C4118yescomplemented
264#486C22×C4114yes—
265#481C22×C4114yes—
266#476C22×C4118yescomplemented
267#475C22×C4114yescomplemented
268#463C22×C41116yescomplemented
269#460C22×C4114yescomplemented
270#459C22×C4118yes—
271#459C22×C4118yescomplemented
272#448C22×C4114yes—
273#447C22×C4118yes—
274#446C22×C4118yescomplemented
275#442C22×C41116yescomplemented
276C4×SD16C22×C4118yescomplemented
277#432C22×C4114yes—
278#431C22×C4112yes—
279C41#6189111yescharacteristic, direct product factor, Sylow
2802−1+4—48no—
281C2×#41—24no—
282C2×#41—24no—
283C2×#41—22no—
284C22×Q8—24no—
285C22×Q8D4×C4111yescharacteristic
286C22×Q8C23×C4111yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C23×C4112yes—
290C23×C4—22no—
291C2×SD16C23×C4118yes—
292C2×D8C23×C41116yes—
293C4⋊Q8C23×C4112yes—
294C4⋊Q8C23×C4114yes—
295#127—22no—
296#127C23×C4114yes—
297#127C23×C4114yes—
298#127C23×C4112yes—
299#124—28no—
300#124—24no—
301#124—24no—
302#124—22no—
303#124C23×C4118yes—
304#123—216no—
305C22⋊Q8—24no—
306C22⋊Q8—28no—
307#121—24no—
308#121—22no—
309#121—24no—
310#121—28no—
311#121C23×C4114yes—
312C4×Q8—22no—
313C4×Q8D4×C4114yes—
314C4×Q8C23×C4114yes—
315C4×Q8C23×C4114yes—
316C4×D4—28no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4C23×C4118yes—
321C4×D4C23×C4114yes—
322C4×D4C23×C4118yes—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C4111yescharacteristic
325C2×C4⋊C4D4×C4112yes—
326C2×C4⋊C4C23×C4111yescharacteristic
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C42—21no—
331C2×C42C23×C4112yes—
332C2×C42C23×C4111yescharacteristic
333#106C23×C4118yes—
334C4⋊C8C23×C4114yes—
335C4⋊C8C23×C4118yes—
336#103C23×C4118yes—
337#102C23×C4118yes—
338#102C23×C41116yes—
339C22⋊C8C23×C4114yes—
340#97C23×C4118yes—
341C4×C8C23×C4114yes—
342C24—22no—
343#41—416no—
344#41—416no—
345#41—48no—
346C2×Q8—24no—
347C2×Q8—21no—
348C2×Q8—24no—
349C2×Q8—22no—
350C2×Q8—42no—
351C2×Q8—416no—
352C2×Q8C2×D4×C4114yes—
353C2×Q8C24×C4112yes—
354C2×D4—24no—
355C2×D4—22no—
356C2×D4—24no—
357C2×D4—24no—
358C2×D4—22no—
359C2×D4—24no—
360C2×D4—22no—
361C2×D4—24no—
362C2×D4—44no—
363C2×D4—44no—
364C2×D4—82no—
365C2×D4C24×C4114yes—
366C2×D4C24×C4114yes—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—28no—
370C22×C4—24no—
371C22×C4—28no—
372C22×C4—84no—
373C22×C4C2×D4×C4112yes—
374C22×C4C2×D4×C4112yes—
375C22×C4C2×D4×C4111yescharacteristic
376C22×C4C2×D4×C4111yescharacteristic
377C22×C4C24×C4111yescharacteristic
378SD16—48no—
379D8—416no—
380C2×C8C24×C4118yes—
381C4⋊C4—24no—
382C4⋊C4—21no—
383C4⋊C4—24no—
384C4⋊C4—22no—
385C4⋊C4C2×D4×C4114yes—
386C4⋊C4C2×D4×C4118yes—
387C4⋊C4C24×C4114yes—
388C4⋊C4C24×C4112yes—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—24no—
393C22⋊C4—28no—
394C22⋊C4—24no—
395C42—24no—
396C42C2×D4×C4114yes—
397C42C2×D4×C4112yes—
398C42C24×C4112yes—
399C42C24×C4114yes—
400C23—24no—
401C23—24no—
402C23—44no—
403C23—44no—
404C23—44no—
405C23C22×D4×C4111yescharacteristic
406Q8—28no—
407Q8—24no—
408Q8—48no—
409Q8—42no—
410Q8—44no—
411D4—28no—
412D4—28no—
413D4—44no—
414D4—48no—
415D4—48no—
416D4—48no—
417D4—44no—
418D4—84no—
419D4—84no—
420D4—82no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—416no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—48no—
432C2×C4—88no—
433C2×C4AGL(1,ℤ/8)×C4114yes—
434C2×C4C22×D4×C4111yescharacteristic
435C2×C4C22×D4×C4114yes—
436C2×C4C22×D4×C4114yes—
437C2×C4C22×D4×C4112yes—
438C2×C4C22×D4×C4112yes—
439C2×C4C25×C4111yescharacteristic
440C8—28no—
441C22—21no—
442C22—21no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—44no—
447C22—44no—
448C22—44no—
449C22—88no—
450C22C2×AGL(1,ℤ/8)×C4112yes—
451C22C23×D4×C4111yescharacteristic
452C4—24no—
453C4—24no—
454C4—22no—
455C4—21no—
456C4—44no—
457C4—42no—
458C4—42no—
459C4C2×AGL(1,ℤ/8)×C4114yes—
460C4C41×#58512yes—
461C2—22no—
462C2—84no—
463C2—84no—
464C2C41×#348711yescharacteristic
465C2C22×AGL(1,ℤ/8)×C4111yescharacteristic
466C2C41×#358511yescharacteristic
subgroupG/H
center, socleC22×C41C23×D4
commutator, Frattini, cosocleC2×C4C25×C41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C4×Q8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3497C2semidirect
2. C2×C41×#559C2semidirect
3. C41×#3399C2semidirect
4. C41×#3373C2semidirect
5. C41×#3213C2semidirect
6. C41×#3205C2semidirect
7. C41×#3109C2semidirect
8. C41×#3103C2semidirect
9. C41×#2983C2semidirect
13. C41×#550C22semidirect
14. D4×Q8×C41C22semidirect
28. C41×#496C22semidirect
30. C41×#489C22semidirect
33. C41×#476C22semidirect
34. C41×#475C22semidirect
35. C41×#463C22semidirect
36. C41×#460C22semidirect
38. C41×#459C22semidirect
41. C41×#446C22semidirect
42. C41×#442C22semidirect
43. C4×SD16×C41C22semidirect
207. #61891C41direct (N × H)
228. #3497C2×C41semidirect
229. C2×#559C2×C41semidirect
230. #3399C2×C41semidirect
231. #3373C2×C41semidirect
232. #3213C2×C41semidirect
233. #3205C2×C41semidirect
234. #3109C2×C41semidirect
235. #3103C2×C41semidirect
236. #2983C2×C41semidirect
246. #550C22×C41semidirect
247. D4×Q8C22×C41semidirect
261. #496C22×C41semidirect
263. #489C22×C41semidirect
266. #476C22×C41semidirect
267. #475C22×C41semidirect
268. #463C22×C41semidirect
269. #460C22×C41semidirect
271. #459C22×C41semidirect
274. #446C22×C41semidirect
275. #442C22×C41semidirect
276. C4×SD16C22×C41semidirect
279. C41#61891direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#34972
C2×C41×#5592
C41×#33992
C41×#33732
C41×#32132
C41×#32052
C41×#31092
C41×#31032
C41×#29832
#6189141