Finite Group Databasebeta

← C41×#10281 #23786482

Subgroups — C41×#10281 #23786482

Order 10496.

690 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3206C211yesmaximal, characteristic, complemented
2C41×#3205C211yesmaximal, characteristic
3C41×#2858C211yesmaximal, characteristic, complemented
4C41×#1962C211yesmaximal, characteristic, complemented
5C41×#1548C211yesmaximal, characteristic, complemented
6C41×#1545C211yesmaximal, characteristic, complemented
7C41×#1276C211yesmaximal, characteristic, complemented
8C41×#532C2211yescharacteristic
9C2×C4⋊Q8×C41C2211yescharacteristic
10C2×#127×C41C2211yescharacteristic
11C2×#124×C41—22no—
12C41×#493—21no—
13C41×#492—21no—
14C41×#487—21no—
15C41×#486—21no—
16C41×#461—22no—
17C41×#459—22no—
18C41×#448—22no—
19C41×#447—22no—
20C41×#431C2211yescharacteristic
21C41×#431C2211yescharacteristic
22C41×#423C2211yescharacteristic
23C2×#104×C41—22no—
24C41×#390—22no—
25C41×#390—22no—
26C43×C41C2211yescharacteristic
27C41×#333—22no—
28C41×#331—22no—
29C2×#41×C41—21no—
30C22×Q8×C41D412yes—
31C22×D4×C41—21no—
32C22×D4×C41—21no—
33C22×D4×C41D412yes—
34C2×SD16×C41—24no—
35C2×D8×C41—24no—
36C2×M16×C41—21no—
37C4⋊Q8×C41—21no—
38C4⋊Q8×C41—21no—
39C4⋊Q8×C41—21no—
40C4⋊Q8×C41—21no—
41C4⋊Q8×C41D411yescharacteristic
42#127×C41—21no—
43#127×C41—21no—
44#127×C41—21no—
45#127×C41—21no—
46#127×C41D411yescharacteristic
47#124×C41—21no—
48#124×C41—48no—
49#121×C41—21no—
50#121×C41—21no—
51C4×D4×C41—21no—
52C4×D4×C41—21no—
53C2×C4⋊C4×C41—21no—
54C2×C4⋊C4×C41—21no—
55C2×C22⋊C4×C41—28no—
56C2×C42×C41—21no—
57C2×C42×C41—21no—
58C2×C42×C41D412yes—
59C2×C42×C41C2311yescharacteristic
60C4⋊C8×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41D412yes—
63C4⋊C8×C41D412yes—
64#104×C41—44no—
65#103×C41—24no—
66#102×C41—24no—
67C22⋊C8×C41—21no—
68C22⋊C8×C41—21no—
69C4×C8×C41—21no—
70C4×C8×C41—21no—
71C24×C41—22no—
72#41×C41—42no—
73#41×C41—42no—
74C2×Q8×C41—22no—
75C2×Q8×C41—21no—
76C2×Q8×C41—22no—
77C2×Q8×C41—44no—
78C2×D4×C41—22no—
79C2×D4×C41—21no—
80C2×D4×C41—21no—
81C2×D4×C41—21no—
82C2×D4×C41—22no—
83C2×D4×C41—44no—
84C2×D4×C41—44no—
85C2×D4×C41—41no—
86C2×D4×C41—41no—
87C2×D4×C41—41no—
88C2×D4×C41—41no—
89C2×D4×C41—41no—
90C2×D4×C41—42no—
91C2×D4×C41—42no—
92C22×C4×C41—22no—
93C22×C4×C41—22no—
94C22×C4×C41—41no—
95C22×C4×C41C2×D411yescharacteristic
96C22×C4×C41C2×D411yescharacteristic
97C22×C4×C41C2×D411yescharacteristic
98SD16×C41—84no—
99D8×C41—84no—
100M16×C41—42no—
101C2×C8×C41—22no—
102C2×C8×C41—22no—
103C2×C8×C41—41no—
104C4⋊C4×C41—21no—
105C4⋊C4×C41—21no—
106C4⋊C4×C41—41no—
107C4⋊C4×C41—41no—
108C4⋊C4×C41—41no—
109C4⋊C4×C41—41no—
110C22⋊C4×C41—416no—
111C22⋊C4×C41—41no—
112C22⋊C4×C41—41no—
113C42×C41—24no—
114C42×C41—22no—
115C42×C41—22no—
116C42×C41—42no—
117C42×C41C2×D411yescharacteristic
118C42×C41C2×D411yescharacteristic
119C42×C41C2×D411yescharacteristic
120C42×C41#4111yescharacteristic
121C23×C41—44no—
122C23×C41—44no—
123C23×C41—41no—
124C23×C41—42no—
125C23×C41—44no—
126C23×C41#12011yescharacteristic
127Q8×C41—44no—
128Q8×C41—42no—
129Q8×C41—82no—
130D4×C41—42no—
131D4×C41—42no—
132D4×C41—44no—
133D4×C41—42no—
134D4×C41—82no—
135D4×C41—82no—
136D4×C41—82no—
137D4×C41—82no—
138D4×C41—82no—
139D4×C41—81no—
140D4×C41—81no—
141C2×C4×C41—22no—
142C2×C4×C41—22no—
143C2×C4×C41—24no—
144C2×C4×C41—42no—
145C2×C4×C41—42no—
146C2×C4×C41—44no—
147C2×C4×C41—41no—
148C2×C4×C41—42no—
149C2×C4×C41—81no—
150C2×C4×C41—81no—
151C2×C4×C41#12011yescharacteristic
152C2×C4×C41#12011yescharacteristic
153C2×C4×C41#12111yescharacteristic
154C2×C4×C41#12111yescharacteristic
155C2×C4×C41#12111yescharacteristic
156C2×C4×C41#12711yescharacteristic
157C2×C4×C41#13512yes—
158C2×C4×C41AGL(1,ℤ/8)12yes—
159C8×C41—42no—
160C8×C41—42no—
161C8×C41—81no—
162#10281C4111yesmaximal, characteristic, direct product factor, Sylow
163C22×C41—21no—
164C22×C41—21no—
165C22×C41—88no—
166C22×C41—81no—
167C22×C41—82no—
168C22×C41—82no—
169C22×C41—81no—
170C22×C41—81no—
171C22×C41—82no—
172C22×C41#39211yescharacteristic
173C22×C41#44912yes—
174C4×C41—21no—
175C4×C41—21no—
176C4×C41—44no—
177C4×C41—82no—
178C4×C41—81no—
179C4×C41#45312yes—
180C4×C41#45512yes—
181C4×C41#46312yes—
182C4×C41#49511yescharacteristic
183C4×C41#49611yescharacteristic
184#3206C2×C4111yescharacteristic, complemented
185#3205C2×C4111yescharacteristic
186#2858C2×C4111yescharacteristic, complemented
187#1962C2×C4111yescharacteristic, complemented
188#1548C2×C4111yescharacteristic, complemented
189#1545C2×C4111yescharacteristic, complemented
190#1276C2×C4111yescharacteristic, complemented
191C2×C41—22no—
192C2×C41—161no—
193C2×C41—162no—
194C2×C41#200211yescharacteristic
195C2×C41#200411yescharacteristic
196C2×C41#201211yescharacteristic
197#532C22×C4111yescharacteristic
198C2×C4⋊Q8C22×C4111yescharacteristic
199C2×#127C22×C4111yescharacteristic
200C2×#124—22no—
201#493—21no—
202#492—21no—
203#487—21no—
204#486—21no—
205#461—22no—
206#459—22no—
207#448—22no—
208#447—22no—
209#431C22×C4111yescharacteristic
210#431C22×C4111yescharacteristic
211#423C22×C4111yescharacteristic
212C2×#104—22no—
213#390—22no—
214#390—22no—
215C43C22×C4111yescharacteristic
216#333—22no—
217#331—22no—
218C41#1028111yescharacteristic, direct product factor, Sylow
219C2×#41—21no—
220C22×Q8D4×C4112yes—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4D4×C4112yes—
224C2×SD16—24no—
225C2×D8—24no—
226C2×M16—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8D4×C4111yescharacteristic
232#127—21no—
233#127—21no—
234#127—21no—
235#127—21no—
236#127D4×C4111yescharacteristic
237#124—21no—
238#124—48no—
239#121—21no—
240#121—21no—
241C4×D4—21no—
242C4×D4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C22⋊C4—28no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42D4×C4112yes—
249C2×C42C23×C4111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C4112yes—
253C4⋊C8D4×C4112yes—
254#104—44no—
255#103—24no—
256#102—24no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C4×C8—21no—
260C4×C8—21no—
261C24—22no—
262#41—42no—
263#41—42no—
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4C2×D4×C4111yescharacteristic
286C22×C4C2×D4×C4111yescharacteristic
287C22×C4C2×D4×C4111yescharacteristic
288SD16—84no—
289D8—84no—
290M16—42no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—416no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42C2×D4×C4111yescharacteristic
308C42C2×D4×C4111yescharacteristic
309C42C2×D4×C4111yescharacteristic
310C42#41×C4111yescharacteristic
311C23—44no—
312C23—44no—
313C23—41no—
314C23—42no—
315C23—44no—
316C23#120×C4111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—82no—
320D4—42no—
321D4—42no—
322D4—44no—
323D4—42no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—82no—
328D4—82no—
329D4—81no—
330D4—81no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#120×C4111yescharacteristic
342C2×C4#120×C4111yescharacteristic
343C2×C4#121×C4111yescharacteristic
344C2×C4#121×C4111yescharacteristic
345C2×C4#121×C4111yescharacteristic
346C2×C4#127×C4111yescharacteristic
347C2×C4#135×C4112yes—
348C2×C4AGL(1,ℤ/8)×C4112yes—
349C8—42no—
350C8—42no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—82no—
360C22—81no—
361C22C41×#39211yescharacteristic
362C22C41×#44912yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—81no—
367C4—82no—
368C4C41×#45312yes—
369C4C41×#45512yes—
370C4C41×#46312yes—
371C4C41×#49511yescharacteristic
372C4C41×#49611yescharacteristic
373C2—22no—
374C2—162no—
375C2—161no—
376C2C41×#200211yescharacteristic
377C2C41×#200411yescharacteristic
378C2C41×#201211yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC41×#3205C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3206C2semidirect
3. C41×#2858C2semidirect
4. C41×#1962C2semidirect
5. C41×#1548C2semidirect
6. C41×#1545C2semidirect
7. C41×#1276C2semidirect
162. #10281C41direct (N × H)
184. #3206C2×C41semidirect
186. #2858C2×C41semidirect
187. #1962C2×C41semidirect
188. #1548C2×C41semidirect
189. #1545C2×C41semidirect
190. #1276C2×C41semidirect
218. C41#10281direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32062
C41×#32052
C41×#28582
C41×#19622
C41×#15482
C41×#15452
C41×#12762
#1028141