Finite Group Databasebeta

← C41×#3268 #19107048

Subgroups — C41×#3268 #19107048

Order 5248.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×AGL(1,ℤ/8)×C41C211yesmaximal, characteristic, complemented
2C2×#135×C41C211yesmaximal, characteristic, complemented
3C41×#550C211yesmaximal, characteristic, complemented
4C41×#546C211yesmaximal, characteristic, complemented
5C41×#496C211yesmaximal, characteristic, complemented
6C41×#468C211yesmaximal, characteristic, complemented
7C41×#466C211yesmaximal, characteristic, complemented
8C41×#464C211yesmaximal, characteristic, complemented
9C41×#459C211yesmaximal, characteristic, complemented
10C41×#452C211yesmaximal, characteristic, complemented
11C41×#449C211yesmaximal, characteristic, complemented
12C41×#449C211yesmaximal, characteristic, complemented
13C41×#447C211yesmaximal, characteristic, complemented
14C41×#440C211yesmaximal, characteristic, complemented
15C41×#435C211yesmaximal, characteristic, complemented
16C2×#41×C41C2211yescharacteristic
17C2×#41×C41C2211yescharacteristic
18C2×#41×C41C2211yescharacteristic, complemented
19C22×D4×C41C2211yescharacteristic
20AGL(1,ℤ/8)×C41—24no—
21#135×C41—24no—
22C2×Q16×C41C2211yescharacteristic, complemented
23C2×SD16×C41C2211yescharacteristic
24C2×SD16×C41C2211yescharacteristic
25C2×SD16×C41C2211yescharacteristic, complemented
26C2×SD16×C41C2211yescharacteristic, complemented
27C2×D8×C41C2211yescharacteristic
28C2×D8×C41C2211yescharacteristic
29C2×D8×C41C2211yescharacteristic
30C2×D8×C41C2211yescharacteristic
31C2×M16×C41C2211yescharacteristic
32C22×C8×C41C2211yescharacteristic, complemented
33#127×C41—21no—
34#127×C41C2211yescharacteristic, complemented
35#124×C41C2211yescharacteristic
36#123×C41—21no—
37C22⋊Q8×C41C2211yescharacteristic
38#121×C41—21no—
39#121×C41—21no—
40#121×C41—21no—
41#121×C41C2211yescharacteristic
42#121×C41C2211yescharacteristic
43#121×C41C2211yescharacteristic, complemented
44#120×C41—21no—
45C4×Q8×C41C2211yescharacteristic, complemented
46C4×D4×C41—21no—
47C4×D4×C41C2211yescharacteristic
48C4×D4×C41C2211yescharacteristic
49C2×C22⋊C4×C41—21no—
50#107×C41C2211yescharacteristic, complemented
51C4⋊C8×C41C2211yescharacteristic, complemented
52#103×C41C2211yescharacteristic, complemented
53#103×C41C2211yescharacteristic, complemented
54#102×C41C2211yescharacteristic
55#102×C41C2211yescharacteristic
56#102×C41C2211yescharacteristic, complemented
57#102×C41C2211yescharacteristic, complemented
58C22⋊C8×C41C2211yescharacteristic
59C22⋊C8×C41C2211yescharacteristic, complemented
60#97×C41C2211yescharacteristic, complemented
61C24×C41—21no—
62#41×C41—22no—
63#41×C41—22no—
64#41×C41—22no—
65#41×C41—41no—
66#41×C41—41no—
67#41×C41—41no—
68C2×Q8×C41C2311yescharacteristic
69C2×Q8×C41C2311yescharacteristic
70C2×D4×C41—22no—
71C2×D4×C41—21no—
72C2×D4×C41—21no—
73C2×D4×C41—21no—
74C2×D4×C41—21no—
75C2×D4×C41—21no—
76C2×D4×C41—21no—
77C2×D4×C41—21no—
78C2×D4×C41—21no—
79C2×D4×C41—21no—
80C2×D4×C41—41no—
81C2×D4×C41D411yescharacteristic
82C2×D4×C41C2311yescharacteristic
83C2×D4×C41C2311yescharacteristic
84C2×D4×C41C2311yescharacteristic
85C2×D4×C41C2311yescharacteristic
86C22×C4×C41—21no—
87C22×C4×C41—21no—
88C22×C4×C41—21no—
89C22×C4×C41—21no—
90C22×C4×C41C2311yescharacteristic
91C22×C4×C41C2311yescharacteristic
92Q16×C41—22no—
93SD16×C41—22no—
94SD16×C41—22no—
95SD16×C41—41no—
96SD16×C41D414yescomplemented
97D8×C41—22no—
98D8×C41—22no—
99D8×C41—22no—
100D8×C41—41no—
101M16×C41—22no—
102C2×C8×C41—22no—
103C2×C8×C41C2311yescharacteristic
104C2×C8×C41C2311yescharacteristic
105C2×C8×C41C2311yescharacteristic
106C2×C8×C41C2311yescharacteristic
107C4⋊C4×C41—21no—
108C4⋊C4×C41—21no—
109C4⋊C4×C41D411yescharacteristic
110C4⋊C4×C41C2311yescharacteristic
111C4⋊C4×C41C2311yescharacteristic
112C22⋊C4×C41—21no—
113C22⋊C4×C41—21no—
114C22⋊C4×C41—21no—
115C22⋊C4×C41—21no—
116C22⋊C4×C41—21no—
117C22⋊C4×C41—21no—
118C22⋊C4×C41—21no—
119C22⋊C4×C41D411yescharacteristic
120C22⋊C4×C41D411yescharacteristic
121C42×C41—21no—
122C42×C41C2311yescharacteristic
123C23×C41—21no—
124C23×C41—21no—
125C23×C41—21no—
126C23×C41—21no—
127C23×C41—42no—
128C23×C41—42no—
129C23×C41—81no—
130C23×C41C2×D411yescharacteristic
131C23×C41C2×D411yescharacteristic
132Q8×C41—21no—
133Q8×C41—21no—
134Q8×C41—21no—
135Q8×C41C2×D412yes—
136D4×C41—21no—
137D4×C41—21no—
138D4×C41—21no—
139D4×C41—21no—
140D4×C41—21no—
141D4×C41—21no—
142D4×C41—21no—
143D4×C41—41no—
144D4×C41—42no—
145D4×C41—42no—
146D4×C41—42no—
147D4×C41—42no—
148D4×C41—42no—
149D4×C41—81no—
150D4×C41—81no—
151D4×C41—81no—
152D4×C41—81no—
153D4×C41C2×D412yes—
154C2×C4×C41—21no—
155C2×C4×C41—21no—
156C2×C4×C41—21no—
157C2×C4×C41—21no—
158C2×C4×C41—21no—
159C2×C4×C41—21no—
160C2×C4×C41—21no—
161C2×C4×C41—21no—
162C2×C4×C41—42no—
163C2×C4×C41—42no—
164C2×C4×C41—42no—
165C2×C4×C41—81no—
166C2×C4×C41C2×D411yescharacteristic
167C2×C4×C41C2×D411yescharacteristic
168C2×C4×C41C2×D411yescharacteristic
169C2×C4×C41C2×D411yescharacteristic
170C2×C4×C41C2411yescharacteristic
171C8×C41—21no—
172C8×C41—21no—
173C8×C41—21no—
174C8×C41C2×D412yes—
175C22×C41—21no—
176C22×C41—21no—
177C22×C41—22no—
178C22×C41—21no—
179C22×C41—21no—
180C22×C41—21no—
181C22×C41—21no—
182C22×C41—41no—
183C22×C41—41no—
184C22×C41—41no—
185C22×C41—41no—
186C22×C41—41no—
187C22×C41—41no—
188C22×C41—41no—
189C22×C41—41no—
190C22×C41—41no—
191C22×C41—41no—
192C22×C41—41no—
193C22×C41—84no—
194C22×C41C22×D411yescharacteristic
195C4×C41—21no—
196C4×C41—21no—
197C4×C41—22no—
198C4×C41—21no—
199C4×C41—21no—
200C4×C41—41no—
201C4×C41—41no—
202C4×C41—41no—
203C4×C41C22×D411yescharacteristic
204C4×C41H(5,𝔽2)11yescharacteristic
205#3268C4111yesmaximal, characteristic, direct product factor, Sylow
206C2×C41—41no—
207C2×C41—41no—
208C2×C41—42no—
209C2×C41—81no—
210C2×C41—81no—
211C2×C41—81no—
212C2×C41D4211yescharacteristic
213C2×C41#57511yescharacteristic
214C2×C41#57611yescharacteristic
215C2×AGL(1,ℤ/8)C2×C4111yescharacteristic, complemented
216C2×#135C2×C4111yescharacteristic, complemented
217#550C2×C4111yescharacteristic, complemented
218#546C2×C4111yescharacteristic, complemented
219#496C2×C4111yescharacteristic, complemented
220#468C2×C4111yescharacteristic, complemented
221#466C2×C4111yescharacteristic, complemented
222#464C2×C4111yescharacteristic, complemented
223#459C2×C4111yescharacteristic, complemented
224#452C2×C4111yescharacteristic, complemented
225#449C2×C4111yescharacteristic, complemented
226#449C2×C4111yescharacteristic, complemented
227#447C2×C4111yescharacteristic, complemented
228#440C2×C4111yescharacteristic, complemented
229#435C2×C4111yescharacteristic, complemented
230C41#326811yescharacteristic, direct product factor, Sylow
231C2×#41C22×C4111yescharacteristic
232C2×#41C22×C4111yescharacteristic
233C2×#41C22×C4111yescharacteristic, complemented
234C22×D4C22×C4111yescharacteristic
235AGL(1,ℤ/8)—24no—
236#135—24no—
237C2×Q16C22×C4111yescharacteristic, complemented
238C2×SD16C22×C4111yescharacteristic
239C2×SD16C22×C4111yescharacteristic
240C2×SD16C22×C4111yescharacteristic, complemented
241C2×SD16C22×C4111yescharacteristic, complemented
242C2×D8C22×C4111yescharacteristic
243C2×D8C22×C4111yescharacteristic
244C2×D8C22×C4111yescharacteristic
245C2×D8C22×C4111yescharacteristic
246C2×M16C22×C4111yescharacteristic
247C22×C8C22×C4111yescharacteristic, complemented
248#127—21no—
249#127C22×C4111yescharacteristic, complemented
250#124C22×C4111yescharacteristic
251#123—21no—
252C22⋊Q8C22×C4111yescharacteristic
253#121—21no—
254#121—21no—
255#121—21no—
256#121C22×C4111yescharacteristic
257#121C22×C4111yescharacteristic
258#121C22×C4111yescharacteristic, complemented
259#120—21no—
260C4×Q8C22×C4111yescharacteristic, complemented
261C4×D4—21no—
262C4×D4C22×C4111yescharacteristic
263C4×D4C22×C4111yescharacteristic
264C2×C22⋊C4—21no—
265#107C22×C4111yescharacteristic, complemented
266C4⋊C8C22×C4111yescharacteristic, complemented
267#103C22×C4111yescharacteristic, complemented
268#103C22×C4111yescharacteristic, complemented
269#102C22×C4111yescharacteristic
270#102C22×C4111yescharacteristic
271#102C22×C4111yescharacteristic, complemented
272#102C22×C4111yescharacteristic, complemented
273C22⋊C8C22×C4111yescharacteristic
274C22⋊C8C22×C4111yescharacteristic, complemented
275#97C22×C4111yescharacteristic, complemented
276C24—21no—
277#41—22no—
278#41—22no—
279#41—22no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8C23×C4111yescharacteristic
284C2×Q8C23×C4111yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4D4×C4111yescharacteristic
297C2×D4C23×C4111yescharacteristic
298C2×D4C23×C4111yescharacteristic
299C2×D4C23×C4111yescharacteristic
300C2×D4C23×C4111yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4C23×C4111yescharacteristic
306C22×C4C23×C4111yescharacteristic
307Q16—22no—
308SD16—22no—
309SD16—22no—
310SD16—41no—
311SD16D4×C4114yescomplemented
312D8—22no—
313D8—22no—
314D8—22no—
315D8—41no—
316M16—22no—
317C2×C8—22no—
318C2×C8C23×C4111yescharacteristic
319C2×C8C23×C4111yescharacteristic
320C2×C8C23×C4111yescharacteristic
321C2×C8C23×C4111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4D4×C4111yescharacteristic
325C4⋊C4C23×C4111yescharacteristic
326C4⋊C4C23×C4111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4D4×C4111yescharacteristic
335C22⋊C4D4×C4111yescharacteristic
336C42—21no—
337C42C23×C4111yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23C2×D4×C4111yescharacteristic
346C23C2×D4×C4111yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×D4×C4112yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—42no—
362D4—42no—
363D4—42no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4C2×D4×C4112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4C2×D4×C4111yescharacteristic
382C2×C4C2×D4×C4111yescharacteristic
383C2×C4C2×D4×C4111yescharacteristic
384C2×C4C2×D4×C4111yescharacteristic
385C2×C4C24×C4111yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8C2×D4×C4112yes—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—84no—
409C22C22×D4×C4111yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4C22×D4×C4111yescharacteristic
419C4H(5,𝔽2)×C4111yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—81no—
425C2—81no—
426C2D42×C4111yescharacteristic
427C2C41×#57511yescharacteristic
428C2C41×#57611yescharacteristic
subgroupG/H
center, socleC22×C41C22×D4
commutator, Frattini, cosocleC2×C4C24×C41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×AGL(1,ℤ/8)×C41C2semidirect
2. C2×#135×C41C2semidirect
3. C41×#550C2semidirect
4. C41×#546C2semidirect
5. C41×#496C2semidirect
6. C41×#468C2semidirect
7. C41×#466C2semidirect
8. C41×#464C2semidirect
9. C41×#459C2semidirect
10. C41×#452C2semidirect
11. C41×#449C2semidirect
12. C41×#449C2semidirect
13. C41×#447C2semidirect
14. C41×#440C2semidirect
15. C41×#435C2semidirect
18. C2×#41×C41C22semidirect
22. C2×Q16×C41C22semidirect
25. C2×SD16×C41C22semidirect
26. C2×SD16×C41C22semidirect
32. C22×C8×C41C22semidirect
34. #127×C41C22semidirect
43. #121×C41C22semidirect
45. C4×Q8×C41C22semidirect
50. #107×C41C22semidirect
51. C4⋊C8×C41C22semidirect
52. #103×C41C22semidirect
53. #103×C41C22semidirect
56. #102×C41C22semidirect
57. #102×C41C22semidirect
59. C22⋊C8×C41C22semidirect
60. #97×C41C22semidirect
96. SD16×C41D4semidirect
205. #3268C41direct (N × H)
215. C2×AGL(1,ℤ/8)C2×C41semidirect
216. C2×#135C2×C41semidirect
217. #550C2×C41semidirect
218. #546C2×C41semidirect
219. #496C2×C41semidirect
220. #468C2×C41semidirect
221. #466C2×C41semidirect
222. #464C2×C41semidirect
223. #459C2×C41semidirect
224. #452C2×C41semidirect
225. #449C2×C41semidirect
226. #449C2×C41semidirect
227. #447C2×C41semidirect
228. #440C2×C41semidirect
229. #435C2×C41semidirect
230. C41#3268direct (N × H)
233. C2×#41C22×C41semidirect
237. C2×Q16C22×C41semidirect
240. C2×SD16C22×C41semidirect
241. C2×SD16C22×C41semidirect
247. C22×C8C22×C41semidirect
249. #127C22×C41semidirect
258. #121C22×C41semidirect
260. C4×Q8C22×C41semidirect
265. #107C22×C41semidirect
266. C4⋊C8C22×C41semidirect
267. #103C22×C41semidirect
268. #103C22×C41semidirect
271. #102C22×C41semidirect
272. #102C22×C41semidirect
274. C22⋊C8C22×C41semidirect
275. #97C22×C41semidirect
311. SD16D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×AGL(1,ℤ/8)×C412
C2×#135×C412
C41×#5502
C41×#5462
C41×#4962
C41×#4682
C41×#4662
C41×#4642
C41×#4592
C41×#4522
C41×#4492
C41×#4472
C41×#4402
C41×#4352
#326841