Finite Group Databasebeta

← C41×#33468 #23809669

Subgroups — C41×#33468 #23809669

Order 10496.

652 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3414C211yesmaximal, characteristic
2C2×C41×#444C211yesmaximal, characteristic, complemented
3C41×#2943C211yesmaximal, characteristic, complemented
4C41×AGL(1,ℤ/16)C214yesmaximal, complemented
5C41×#2180C214yesmaximal, complemented
6C41×#2155C211yesmaximal, characteristic, complemented
7C41×#2148C211yesmaximal, characteristic, complemented
8C41×#2145C211yesmaximal, characteristic, complemented
9C2×C41×#347C211yesmaximal, characteristic, complemented
10C2×#135×C41C2211yescharacteristic
11C2×#135×C41C2211yescharacteristic
12C2×#131×C41—21no—
13C4×#41×C41—21no—
14C41×#510C412yescomplemented
15C41×#510C2212yes—
16C41×#509C412yescomplemented
17C41×#509C2212yes—
18C41×#508C414yescomplemented
19C2×M32×C41C2211yescharacteristic
20C2×M32×C41C2211yescharacteristic
21C41×#444—22no—
22C41×#444C2214yes—
23C41×#442C2212yescomplemented
24C41×#441C2212yescomplemented
25C41×#440—22no—
26C2×#108×C41C2211yescharacteristic
27C41×#427C2211yescharacteristic
28C2×#104×C41—21no—
29C41×#416—21no—
30C2×#97×C41C2211yescharacteristic
31C41×#365C2214yescomplemented
32C41×#362C2212yescomplemented
33C41×#361C2212yescomplemented
34C41×#360C2214yes—
35C41×#347C2214yescomplemented
36C2×#41×C41—21no—
37C2×#41×C41—21no—
38#135×C41—21no—
39#135×C41—21no—
40#135×C41—21no—
41#135×C41—21no—
42#135×C41C2×C412yes—
43#135×C41C2×C412yes—
44#135×C41C2×C412yescomplemented
45#135×C41C2312yes—
46C2×Q16×C41C2×C411yescharacteristic, complemented
47C2×Q16×C41C2311yescharacteristic
48C2×SD16×C41—21no—
49C2×SD16×C41—21no—
50C2×D8×C41C2×C411yescharacteristic, complemented
51C2×D8×C41C2311yescharacteristic
52#131×C41—24no—
53#131×C41—42no—
54C2×M16×C41—21no—
55C2×M16×C41—41no—
56C22×C8×C41—41no—
57C22×C8×C41D411yescharacteristic
58C22×C8×C41C2311yescharacteristic
59C4×Q8×C41—22no—
60C4×D4×C41—22no—
61C4×D4×C41—42no—
62#117×C41—21no—
63#117×C41—41no—
64C2×C42×C41—41no—
65C2×C42×C41D411yescharacteristic
66Q32×C41C2×C414yescomplemented
67SD32×C41C2×C414yescomplemented
68SD32×C41C2×C414yescomplemented
69D16×C41C2×C414yescomplemented
70M32×C41—21no—
71M32×C41C2×C412yescomplemented
72M32×C41C2312yes—
73M32×C41C2312yes—
74C2×C16×C41—21no—
75C2×C16×C41C2×C412yescomplemented
76#108×C41—21no—
77#108×C41C2312yes—
78#107×C41—21no—
79#106×C41C2312yes—
80#104×C41—24no—
81#103×C41—22no—
82#102×C41—22no—
83#97×C41D412yes—
84#97×C41C2312yes—
85#41×C41—22no—
86#41×C41—22no—
87#41×C41—22no—
88#41×C41—22no—
89#41×C41—41no—
90#41×C41—41no—
91#41×C41—41no—
92#41×C41—41no—
93C2×Q8×C41—21no—
94C2×Q8×C41—21no—
95C2×D4×C41—21no—
96C2×D4×C41—21no—
97C2×D4×C41—41no—
98C2×D4×C41—41no—
99C22×C4×C41—21no—
100C22×C4×C41—42no—
101C22×C4×C41—41no—
102C22×C4×C41—41no—
103C22×C4×C41C2×D411yescharacteristic
104Q16×C41—21no—
105Q16×C41—21no—
106Q16×C41C22×C412yes—
107Q16×C41C22×C412yes—
108SD16×C41—22no—
109SD16×C41—22no—
110SD16×C41—22no—
111SD16×C41—22no—
112D8×C41—21no—
113D8×C41—21no—
114D8×C41C22×C412yes—
115D8×C41C22×C412yes—
116M16×C41—22no—
117M16×C41—44no—
118M16×C41—41no—
119C2×C8×C41—21no—
120C2×C8×C41—21no—
121C2×C8×C41—44no—
122C2×C8×C41—41no—
123C2×C8×C41C22×C411yescharacteristic
124C2×C8×C41C22×C411yescharacteristic
125C2×C8×C41C2×D412yes—
126C2×C8×C41C2×D411yescharacteristic
127C2×C8×C41#4111yescharacteristic
128C2×C8×C41#4111yescharacteristic
129C2×C8×C41C2411yescharacteristic
130C4⋊C4×C41—22no—
131C4⋊C4×C41—42no—
132C22⋊C4×C41—42no—
133C22⋊C4×C41—41no—
134C42×C41—21no—
135C42×C41—42no—
136C42×C41—41no—
137C42×C41C2×D412yes—
138C16×C41—22no—
139C16×C41C22×C414yes—
140C23×C41—41no—
141C23×C41—41no—
142C23×C41AGL(1,ℤ/8)11yescharacteristic
143Q8×C41—22no—
144Q8×C41—22no—
145Q8×C41—41no—
146Q8×C41—41no—
147D4×C41—22no—
148D4×C41—22no—
149D4×C41—42no—
150D4×C41—42no—
151D4×C41—42no—
152D4×C41—42no—
153D4×C41—41no—
154D4×C41—41no—
155C2×C4×C41—22no—
156C2×C4×C41—41no—
157C2×C4×C41—41no—
158C2×C4×C41—42no—
159C2×C4×C41—42no—
160C2×C4×C41—42no—
161C2×C4×C41—42no—
162C2×C4×C41—42no—
163C2×C4×C41—81no—
164C2×C4×C41—84no—
165C2×C4×C41C4×D411yescharacteristic
166C2×C4×C41C4×D411yescharacteristic
167C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C41AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C41C22×D411yescharacteristic
171C8×C41—22no—
172C8×C41—42no—
173C8×C41C4×D411yescharacteristic
174C8×C41C4×D411yescharacteristic
175C8×C41C23×C411yescharacteristic
176C8×C41C2×#4111yescharacteristic
177#33468C4111yesmaximal, characteristic, direct product factor, Sylow
178C22×C41—41no—
179C22×C41—42no—
180C22×C41—42no—
181C22×C41—82no—
182C22×C41—82no—
183C22×C41#44211yescharacteristic
184C22×C41#44211yescharacteristic
185C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
186C4×C41—42no—
187C4×C41—42no—
188C4×C41—42no—
189C4×C41—82no—
190C4×C41#44211yescharacteristic
191C4×C41#44211yescharacteristic
192C4×C41C2×C4×D411yescharacteristic
193C4×C41C2×AGL(1,ℤ/8)11yescharacteristic
194#3414C2×C4111yescharacteristic
195C2×#444C2×C4111yescharacteristic, complemented
196#2943C2×C4111yescharacteristic, complemented
197AGL(1,ℤ/16)C2×C4114yescomplemented
198#2180C2×C4114yescomplemented
199#2155C2×C4111yescharacteristic, complemented
200#2148C2×C4111yescharacteristic, complemented
201#2145C2×C4111yescharacteristic, complemented
202C2×#347C2×C4111yescharacteristic, complemented
203C2×C41—21no—
204C2×C41—21no—
205C2×C41—21no—
206C2×C41—82no—
207C2×C41—82no—
208C2×C41C2×#44211yescharacteristic
209C2×#135C22×C4111yescharacteristic
210C2×#135C22×C4111yescharacteristic
211C2×#131—21no—
212C4×#41—21no—
213#510C4×C4112yescomplemented
214#510C22×C4112yes—
215#509C4×C4112yescomplemented
216#509C22×C4112yes—
217#508C4×C4114yescomplemented
218C2×M32C22×C4111yescharacteristic
219C2×M32C22×C4111yescharacteristic
220#444—22no—
221#444C22×C4114yes—
222#442C22×C4112yescomplemented
223#441C22×C4112yescomplemented
224#440—22no—
225C2×#108C22×C4111yescharacteristic
226#427C22×C4111yescharacteristic
227C2×#104—21no—
228#416—21no—
229C2×#97C22×C4111yescharacteristic
230#365C22×C4114yescomplemented
231#362C22×C4112yescomplemented
232#361C22×C4112yescomplemented
233#360C22×C4114yes—
234#347C22×C4114yescomplemented
235C41#3346811yescharacteristic, direct product factor, Sylow
236C2×#41—21no—
237C2×#41—21no—
238#135—21no—
239#135—21no—
240#135—21no—
241#135—21no—
242#135C2×C4×C4112yes—
243#135C2×C4×C4112yes—
244#135C2×C4×C4112yescomplemented
245#135C23×C4112yes—
246C2×Q16C2×C4×C4111yescharacteristic, complemented
247C2×Q16C23×C4111yescharacteristic
248C2×SD16—21no—
249C2×SD16—21no—
250C2×D8C2×C4×C4111yescharacteristic, complemented
251C2×D8C23×C4111yescharacteristic
252#131—24no—
253#131—42no—
254C2×M16—21no—
255C2×M16—41no—
256C22×C8—41no—
257C22×C8D4×C4111yescharacteristic
258C22×C8C23×C4111yescharacteristic
259C4×Q8—22no—
260C4×D4—22no—
261C4×D4—42no—
262#117—21no—
263#117—41no—
264C2×C42—41no—
265C2×C42D4×C4111yescharacteristic
266Q32C2×C4×C4114yescomplemented
267SD32C2×C4×C4114yescomplemented
268SD32C2×C4×C4114yescomplemented
269D16C2×C4×C4114yescomplemented
270M32—21no—
271M32C2×C4×C4112yescomplemented
272M32C23×C4112yes—
273M32C23×C4112yes—
274C2×C16—21no—
275C2×C16C2×C4×C4112yescomplemented
276#108—21no—
277#108C23×C4112yes—
278#107—21no—
279#106C23×C4112yes—
280#104—24no—
281#103—22no—
282#102—22no—
283#97D4×C4112yes—
284#97C23×C4112yes—
285#41—22no—
286#41—22no—
287#41—22no—
288#41—22no—
289#41—41no—
290#41—41no—
291#41—41no—
292#41—41no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C4111yescharacteristic
304Q16—21no—
305Q16—21no—
306Q16C22×C4×C4112yes—
307Q16C22×C4×C4112yes—
308SD16—22no—
309SD16—22no—
310SD16—22no—
311SD16—22no—
312D8—21no—
313D8—21no—
314D8C22×C4×C4112yes—
315D8C22×C4×C4112yes—
316M16—22no—
317M16—44no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—44no—
322C2×C8—41no—
323C2×C8C22×C4×C4111yescharacteristic
324C2×C8C22×C4×C4111yescharacteristic
325C2×C8C2×D4×C4112yes—
326C2×C8C2×D4×C4111yescharacteristic
327C2×C8#41×C4111yescharacteristic
328C2×C8#41×C4111yescharacteristic
329C2×C8C24×C4111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—41no—
334C42—21no—
335C42—42no—
336C42—41no—
337C42C2×D4×C4112yes—
338C16—22no—
339C16C22×C4×C4114yes—
340C23—41no—
341C23—41no—
342C23AGL(1,ℤ/8)×C4111yescharacteristic
343Q8—22no—
344Q8—22no—
345Q8—41no—
346Q8—41no—
347D4—22no—
348D4—22no—
349D4—42no—
350D4—42no—
351D4—42no—
352D4—42no—
353D4—41no—
354D4—41no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—81no—
364C2×C4—84no—
365C2×C4C4×D4×C4111yescharacteristic
366C2×C4C4×D4×C4111yescharacteristic
367C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
368C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
369C2×C4AGL(1,ℤ/8)×C4111yescharacteristic
370C2×C4C22×D4×C4111yescharacteristic
371C8—22no—
372C8—42no—
373C8C4×D4×C4111yescharacteristic
374C8C4×D4×C4111yescharacteristic
375C8C23×C4×C4111yescharacteristic
376C8C2×#41×C4111yescharacteristic
377C22—41no—
378C22—42no—
379C22—42no—
380C22—82no—
381C22—82no—
382C22C41×#44211yescharacteristic
383C22C41×#44211yescharacteristic
384C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
385C4—42no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4C41×#44211yescharacteristic
390C4C41×#44211yescharacteristic
391C4C2×C4×D4×C4111yescharacteristic
392C4C2×AGL(1,ℤ/8)×C4111yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—82no—
398C2C2×C41×#44211yescharacteristic
subgroupG/H
centerC4×C41#442
commutatorC8C23×C4×C41
Frattini, cosocleC2×C8C24×C41
socleC2×C41C2×#442
prime radicalC41×#3414C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C41 ◁ C22×C4×C41 ◁ C2×#97×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×#444C2semidirect
3. C41×#2943C2semidirect
4. C41×AGL(1,ℤ/16)C2semidirect
5. C41×#2180C2semidirect
6. C41×#2155C2semidirect
7. C41×#2148C2semidirect
8. C41×#2145C2semidirect
9. C2×C41×#347C2semidirect
14. C41×#510C4semidirect
16. C41×#509C4semidirect
18. C41×#508C4semidirect
23. C41×#442C22semidirect
24. C41×#441C22semidirect
31. C41×#365C22semidirect
32. C41×#362C22semidirect
33. C41×#361C22semidirect
35. C41×#347C22semidirect
44. #135×C41C2×C4semidirect
46. C2×Q16×C41C2×C4semidirect
50. C2×D8×C41C2×C4semidirect
66. Q32×C41C2×C4semidirect
67. SD32×C41C2×C4semidirect
68. SD32×C41C2×C4semidirect
69. D16×C41C2×C4semidirect
71. M32×C41C2×C4semidirect
75. C2×C16×C41C2×C4semidirect
177. #33468C41direct (N × H)
195. C2×#444C2×C41semidirect
196. #2943C2×C41semidirect
197. AGL(1,ℤ/16)C2×C41semidirect
198. #2180C2×C41semidirect
199. #2155C2×C41semidirect
200. #2148C2×C41semidirect
201. #2145C2×C41semidirect
202. C2×#347C2×C41semidirect
213. #510C4×C41semidirect
215. #509C4×C41semidirect
217. #508C4×C41semidirect
222. #442C22×C41semidirect
223. #441C22×C41semidirect
230. #365C22×C41semidirect
231. #362C22×C41semidirect
232. #361C22×C41semidirect
234. #347C22×C41semidirect
235. C41#33468direct (N × H)
244. #135C2×C4×C41semidirect
246. C2×Q16C2×C4×C41semidirect
250. C2×D8C2×C4×C41semidirect
266. Q32C2×C4×C41semidirect
267. SD32C2×C4×C41semidirect
268. SD32C2×C4×C41semidirect
269. D16C2×C4×C41semidirect
271. M32C2×C4×C41semidirect
275. C2×C16C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#34142
C2×C41×#4442
C41×#29432
C41×AGL(1,ℤ/16)2
C41×#21802
C41×#21552
C41×#21482
C41×#21452
C2×C41×#3472
#3346841