Finite Group Databasebeta

← C41×#9717 #23785918

Subgroups — C41×#9717 #23785918

Order 10496.

468 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3167C211yesmaximal, characteristic
2C41×#1986C211yesmaximal, characteristic, complemented
3C41×#1980C211yesmaximal, characteristic
4C4×#106×C41C211yesmaximal, characteristic, complemented
5C41×#1503C211yesmaximal, characteristic, complemented
6C41×#1502C211yesmaximal, characteristic
7C8×M16×C41C211yesmaximal, characteristic, complemented
8C41×#533C2211yescharacteristic
9C41×#532C2211yescharacteristic
10C41×#498C411yescharacteristic, complemented
11C41×#492C411yescharacteristic, complemented
12C41×#487C411yescharacteristic, complemented
13C41×#486C411yescharacteristic, complemented
14C41×#465—21no—
15C41×#465—21no—
16C4×SD16×C41—21no—
17C4×SD16×C41—21no—
18C41×#431C2211yescharacteristic
19C2×#106×C41—21no—
20C2×#104×C41—22no—
21C4×M16×C41C2211yescharacteristic
22C2×C4×C8×C41C2211yescharacteristic
23C4×C4⋊C4×C41C2211yescharacteristic
24C4×C4⋊C4×C41C2211yescharacteristic
25C41×#340—21no—
26C41×#339—22no—
27C41×#328—22no—
28C41×#327—22no—
29C41×#322—21no—
30C82×C41—21no—
31C2×#41×C41—21no—
32C2×SD16×C41—21no—
33C2×SD16×C41—21no—
34C2×M16×C41D412yes—
35C22×C8×C41D411yescharacteristic
36C22×C8×C41D411yescharacteristic
37C4⋊Q8×C41C2×C411yescharacteristic
38C4⋊Q8×C41C2×C411yescharacteristic
39C4⋊Q8×C41C2×C411yescharacteristic
40#127×C41C2×C411yescharacteristic
41#125×C41—21no—
42#124×C41—21no—
43C22⋊Q8×C41—21no—
44C22⋊Q8×C41—21no—
45#121×C41—21no—
46#121×C41—21no—
47C4×Q8×C41—21no—
48C4×Q8×C41—21no—
49C4×D4×C41—21no—
50C4×D4×C41—21no—
51#117×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C42×C41—21no—
55C2×C42×C41—21no—
56C2×C42×C41C2311yescharacteristic
57#106×C41—24no—
58#106×C41—21no—
59#106×C41—21no—
60C4⋊C8×C41—21no—
61#104×C41—44no—
62#103×C41—21no—
63#103×C41—21no—
64#102×C41—21no—
65#102×C41—21no—
66C22⋊C8×C41D412yes—
67#97×C41—21no—
68C4×C8×C41—21no—
69C4×C8×C41—21no—
70C4×C8×C41C2×C411yescharacteristic
71C4×C8×C41C2×C411yescharacteristic
72C4×C8×C41D411yescharacteristic
73C4×C8×C41D411yescharacteristic
74#95×C41—21no—
75#95×C41—21no—
76#41×C41—42no—
77#41×C41—42no—
78C2×Q8×C41—21no—
79C2×Q8×C41—21no—
80C2×Q8×C41—21no—
81C2×D4×C41—21no—
82C2×D4×C41—21no—
83C2×D4×C41—21no—
84C2×D4×C41—41no—
85C22×C4×C41—41no—
86C22×C4×C41—41no—
87C22×C4×C41—41no—
88C22×C4×C41C2×D411yescharacteristic
89C22×C4×C41C2×D411yescharacteristic
90C22×C4×C41C2×D411yescharacteristic
91SD16×C41—42no—
92SD16×C41—42no—
93M16×C41—22no—
94M16×C41SD1614yescomplemented
95C2×C8×C41—22no—
96C2×C8×C41—22no—
97C2×C8×C41—22no—
98C2×C8×C41—41no—
99C2×C8×C41C22⋊C411yescharacteristic
100C2×C8×C41C22⋊C411yescharacteristic
101C2×C8×C41C22⋊C411yescharacteristic
102C2×C8×C41C22⋊C411yescharacteristic
103C4⋊C4×C41—22no—
104C4⋊C4×C41—22no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—21no—
107C4⋊C4×C41—21no—
108C4⋊C4×C41—21no—
109C4⋊C4×C41—21no—
110C4⋊C4×C41—21no—
111C4⋊C4×C41—41no—
112C4⋊C4×C41—41no—
113C4⋊C4×C41—41no—
114C4⋊C4×C41—41no—
115C22⋊C4×C41—41no—
116C22⋊C4×C41—41no—
117C22⋊C4×C41—41no—
118C42×C41—41no—
119C42×C41—42no—
120C42×C41—42no—
121C42×C41C22×C411yescharacteristic
122C42×C41C2×D411yescharacteristic
123C42×C41#4111yescharacteristic
124C42×C41#4111yescharacteristic
125C23×C41—41no—
126C23×C41#12711yescharacteristic
127Q8×C41—41no—
128Q8×C41—41no—
129Q8×C41—42no—
130Q8×C41—81no—
131D4×C41—41no—
132D4×C41—41no—
133D4×C41—42no—
134D4×C41—81no—
135D4×C41—81no—
136D4×C41—81no—
137C2×C4×C41—21no—
138C2×C4×C41—21no—
139C2×C4×C41—41no—
140C2×C4×C41—42no—
141C2×C4×C41—42no—
142C2×C4×C41—41no—
143C2×C4×C41—41no—
144C2×C4×C41—41no—
145C2×C4×C41—81no—
146C2×C4×C41—81no—
147C2×C4×C41—81no—
148C2×C4×C41—81no—
149C2×C4×C41—82no—
150C2×C4×C41C2×C22⋊C411yescharacteristic
151C2×C4×C41C4×D411yescharacteristic
152C2×C4×C41C4×D411yescharacteristic
153C2×C4×C41#12111yescharacteristic
154C2×C4×C41#12111yescharacteristic
155C2×C4×C41#12411yescharacteristic
156C2×C4×C41C2×SD1612yes—
157C2×C4×C41#13512yes—
158C8×C41—21no—
159C8×C41—21no—
160C8×C41—21no—
161C8×C41—24no—
162C8×C41—42no—
163C8×C41#10412yescomplemented
164#9717C4111yesmaximal, characteristic, direct product factor, Sylow
165C22×C41—21no—
166C22×C41—21no—
167C22×C41—81no—
168C22×C41—81no—
169C22×C41—81no—
170C22×C41#39011yescharacteristic
171C22×C41#49211yescharacteristic
172C22×C41#49511yescharacteristic
173C4×C41—21no—
174C4×C41—21no—
175C4×C41—21no—
176C4×C41—82no—
177C4×C41—82no—
178C4×C41—81no—
179C4×C41—81no—
180C4×C41—81no—
181C4×C41C2×#10411yescharacteristic
182C4×C41#42111yescharacteristic
183C4×C41C4×SD1612yes—
184C4×C41#46512yes—
185#3167C2×C4111yescharacteristic
186#1986C2×C4111yescharacteristic, complemented
187#1980C2×C4111yescharacteristic
188C4×#106C2×C4111yescharacteristic, complemented
189#1503C2×C4111yescharacteristic, complemented
190#1502C2×C4111yescharacteristic
191C8×M16C2×C4111yescharacteristic, complemented
192C2×C41—21no—
193C2×C41—21no—
194C2×C41—161no—
195C2×C41#196811yescharacteristic
196C2×C41#197611yescharacteristic
197C2×C41#198011yescharacteristic
198#533C22×C4111yescharacteristic
199#532C22×C4111yescharacteristic
200#498C4×C4111yescharacteristic, complemented
201#492C4×C4111yescharacteristic, complemented
202#487C4×C4111yescharacteristic, complemented
203#486C4×C4111yescharacteristic, complemented
204#465—21no—
205#465—21no—
206C4×SD16—21no—
207C4×SD16—21no—
208#431C22×C4111yescharacteristic
209C2×#106—21no—
210C2×#104—22no—
211C4×M16C22×C4111yescharacteristic
212C2×C4×C8C22×C4111yescharacteristic
213C4×C4⋊C4C22×C4111yescharacteristic
214C4×C4⋊C4C22×C4111yescharacteristic
215#340—21no—
216#339—22no—
217#328—22no—
218#327—22no—
219#322—21no—
220C82—21no—
221C41#971711yescharacteristic, direct product factor, Sylow
222C2×#41—21no—
223C2×SD16—21no—
224C2×SD16—21no—
225C2×M16D4×C4112yes—
226C22×C8D4×C4111yescharacteristic
227C22×C8D4×C4111yescharacteristic
228C4⋊Q8C2×C4×C4111yescharacteristic
229C4⋊Q8C2×C4×C4111yescharacteristic
230C4⋊Q8C2×C4×C4111yescharacteristic
231#127C2×C4×C4111yescharacteristic
232#125—21no—
233#124—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236#121—21no—
237#121—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×D4—21no—
241C4×D4—21no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42C23×C4111yescharacteristic
248#106—24no—
249#106—21no—
250#106—21no—
251C4⋊C8—21no—
252#104—44no—
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257C22⋊C8D4×C4112yes—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8C2×C4×C4111yescharacteristic
262C4×C8C2×C4×C4111yescharacteristic
263C4×C8D4×C4111yescharacteristic
264C4×C8D4×C4111yescharacteristic
265#95—21no—
266#95—21no—
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C2×D4×C4111yescharacteristic
280C22×C4C2×D4×C4111yescharacteristic
281C22×C4C2×D4×C4111yescharacteristic
282SD16—42no—
283SD16—42no—
284M16—22no—
285M16SD16×C4114yescomplemented
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8C22⋊C4×C4111yescharacteristic
291C2×C8C22⋊C4×C4111yescharacteristic
292C2×C8C22⋊C4×C4111yescharacteristic
293C2×C8C22⋊C4×C4111yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42—42no—
311C42—42no—
312C42C22×C4×C4111yescharacteristic
313C42C2×D4×C4111yescharacteristic
314C42#41×C4111yescharacteristic
315C42#41×C4111yescharacteristic
316C23—41no—
317C23#127×C4111yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—42no—
321Q8—81no—
322D4—41no—
323D4—41no—
324D4—42no—
325D4—81no—
326D4—81no—
327D4—81no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4C2×C22⋊C4×C4111yescharacteristic
342C2×C4C4×D4×C4111yescharacteristic
343C2×C4C4×D4×C4111yescharacteristic
344C2×C4#121×C4111yescharacteristic
345C2×C4#121×C4111yescharacteristic
346C2×C4#124×C4111yescharacteristic
347C2×C4C2×SD16×C4112yes—
348C2×C4#135×C4112yes—
349C8—21no—
350C8—21no—
351C8—21no—
352C8—24no—
353C8—42no—
354C8#104×C4112yescomplemented
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C41×#39011yescharacteristic
361C22C41×#49211yescharacteristic
362C22C41×#49511yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4C2×#104×C4111yescharacteristic
372C4C41×#42111yescharacteristic
373C4C4×SD16×C4112yes—
374C4C41×#46512yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2C41×#196811yescharacteristic
379C2C41×#197611yescharacteristic
380C2C41×#198011yescharacteristic
subgroupG/H
centerC2×C4×C41#121
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#390
prime radicalC41×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1986C2semidirect
4. C4×#106×C41C2semidirect
5. C41×#1503C2semidirect
7. C8×M16×C41C2semidirect
10. C41×#498C4semidirect
11. C41×#492C4semidirect
12. C41×#487C4semidirect
13. C41×#486C4semidirect
94. M16×C41SD16semidirect
163. C8×C41#104semidirect
164. #9717C41direct (N × H)
186. #1986C2×C41semidirect
188. C4×#106C2×C41semidirect
189. #1503C2×C41semidirect
191. C8×M16C2×C41semidirect
200. #498C4×C41semidirect
201. #492C4×C41semidirect
202. #487C4×C41semidirect
203. #486C4×C41semidirect
221. C41#9717direct (N × H)
285. M16SD16×C41semidirect
354. C8#104×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31672
C41×#19862
C41×#19802
C4×#106×C412
C41×#15032
C41×#15022
C8×M16×C412
#971741