Finite Group Databasebeta

← C41×#10292 #23786493

Subgroups — C41×#10292 #23786493

Order 10496.

640 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3230C211yesmaximal, characteristic, complemented
2C41×#3208C211yesmaximal, characteristic
3C41×#2858C211yesmaximal, characteristic
4C41×#1994C211yesmaximal, characteristic, complemented
5C41×#1549C211yesmaximal, characteristic, complemented
6C41×#1545C211yesmaximal, characteristic
7C41×#1276C211yesmaximal, characteristic, complemented
8C41×#533C2211yescharacteristic
9C2×C4⋊Q8×C41C2211yescharacteristic
10C2×#127×C41C2211yescharacteristic
11C2×#124×C41—22no—
12C41×#500—21no—
13C41×#492—21no—
14C41×#487—21no—
15C41×#486—21no—
16C41×#484—22no—
17C41×#477—22no—
18C41×#460—22no—
19C41×#450—22no—
20C41×#431C2211yescharacteristic
21C41×#431C2211yescharacteristic
22C41×#423C2211yescharacteristic
23C41×#390—22no—
24C41×#390—22no—
25C43×C41C2211yescharacteristic
26C41×#339—22no—
27C41×#332—22no—
28C41×#331—22no—
29C22×Q8×C41—21no—
30C22×D4×C41—21no—
31C22×D4×C41—21no—
32C22×D4×C41D412yes—
33C2×SD16×C41—24no—
34C2×M16×C41—21no—
35C4⋊Q8×C41—21no—
36C4⋊Q8×C41—21no—
37C4⋊Q8×C41—21no—
38C4⋊Q8×C41—21no—
39C4⋊Q8×C41D411yescharacteristic
40C4⋊Q8×C41D411yescharacteristic
41#127×C41—21no—
42#127×C41—21no—
43#127×C41—21no—
44#127×C41—21no—
45#125×C41—21no—
46#124×C41—48no—
47C22⋊Q8×C41—21no—
48C22⋊Q8×C41—21no—
49C4×Q8×C41—21no—
50C4×Q8×C41—21no—
51#117×C41—21no—
52C2×C4⋊C4×C41—21no—
53C2×C4⋊C4×C41D412yes—
54C2×C22⋊C4×C41—28no—
55C2×C42×C41—21no—
56C2×C42×C41—21no—
57C2×C42×C41D412yes—
58C2×C42×C41C2311yescharacteristic
59#107×C41—24no—
60C4⋊C8×C41—21no—
61C4⋊C8×C41—21no—
62C4⋊C8×C41D412yes—
63C4⋊C8×C41D412yes—
64#103×C41—24no—
65#102×C41—24no—
66C22⋊C8×C41—21no—
67C22⋊C8×C41—21no—
68C4×C8×C41—21no—
69C4×C8×C41—21no—
70C24×C41—22no—
71C2×Q8×C41—21no—
72C2×Q8×C41—21no—
73C2×Q8×C41—44no—
74C2×Q8×C41—41no—
75C2×Q8×C41—41no—
76C2×D4×C41—22no—
77C2×D4×C41—22no—
78C2×D4×C41—44no—
79C2×D4×C41—44no—
80C2×D4×C41—41no—
81C2×D4×C41—41no—
82C2×D4×C41—41no—
83C2×D4×C41—41no—
84C2×D4×C41—42no—
85C2×D4×C41—42no—
86C22×C4×C41—22no—
87C22×C4×C41—22no—
88C22×C4×C41C2×D411yescharacteristic
89C22×C4×C41C2×D411yescharacteristic
90C22×C4×C41C2×D411yescharacteristic
91SD16×C41—84no—
92M16×C41—42no—
93C2×C8×C41—22no—
94C2×C8×C41—22no—
95C2×C8×C41—41no—
96C4⋊C4×C41—21no—
97C4⋊C4×C41—22no—
98C4⋊C4×C41—21no—
99C4⋊C4×C41—22no—
100C4⋊C4×C41—21no—
101C4⋊C4×C41—21no—
102C4⋊C4×C41—41no—
103C4⋊C4×C41—41no—
104C4⋊C4×C41—41no—
105C4⋊C4×C41—41no—
106C22⋊C4×C41—416no—
107C22⋊C4×C41—41no—
108C42×C41—24no—
109C42×C41—22no—
110C42×C41—22no—
111C42×C41—42no—
112C42×C41—41no—
113C42×C41C2×D411yescharacteristic
114C42×C41C2×D411yescharacteristic
115C42×C41C2×D411yescharacteristic
116C42×C41#4111yescharacteristic
117C23×C41—44no—
118C23×C41—44no—
119C23×C41—42no—
120C23×C41—44no—
121C23×C41#12011yescharacteristic
122Q8×C41—42no—
123Q8×C41—42no—
124Q8×C41—82no—
125Q8×C41—82no—
126D4×C41—44no—
127D4×C41—82no—
128D4×C41—82no—
129D4×C41—82no—
130D4×C41—82no—
131D4×C41—81no—
132D4×C41—81no—
133C2×C4×C41—22no—
134C2×C4×C41—22no—
135C2×C4×C41—24no—
136C2×C4×C41—42no—
137C2×C4×C41—42no—
138C2×C4×C41—44no—
139C2×C4×C41—41no—
140C2×C4×C41—41no—
141C2×C4×C41—42no—
142C2×C4×C41#12011yescharacteristic
143C2×C4×C41#12011yescharacteristic
144C2×C4×C41#12111yescharacteristic
145C2×C4×C41#12111yescharacteristic
146C2×C4×C41#12111yescharacteristic
147C2×C4×C41#12711yescharacteristic
148C2×C4×C41#13512yes—
149C2×C4×C41#13712yes—
150C8×C41—42no—
151C8×C41—42no—
152C8×C41—81no—
153#10292C4111yesmaximal, characteristic, direct product factor, Sylow
154C22×C41—21no—
155C22×C41—21no—
156C22×C41—88no—
157C22×C41—82no—
158C22×C41—82no—
159C22×C41—82no—
160C22×C41#39211yescharacteristic
161C22×C41#45212yes—
162C4×C41—21no—
163C4×C41—21no—
164C4×C41—44no—
165C4×C41—82no—
166C4×C41—81no—
167C4×C41—81no—
168C4×C41#45312yes—
169C4×C41#45412yes—
170C4×C41#46412yes—
171C4×C41#49511yescharacteristic
172C4×C41#49711yescharacteristic
173#3230C2×C4111yescharacteristic, complemented
174#3208C2×C4111yescharacteristic
175#2858C2×C4111yescharacteristic
176#1994C2×C4111yescharacteristic, complemented
177#1549C2×C4111yescharacteristic, complemented
178#1545C2×C4111yescharacteristic
179#1276C2×C4111yescharacteristic, complemented
180C2×C41—22no—
181C2×C41—162no—
182C2×C41#200211yescharacteristic
183C2×C41#200311yescharacteristic
184C2×C41#201511yescharacteristic
185#533C22×C4111yescharacteristic
186C2×C4⋊Q8C22×C4111yescharacteristic
187C2×#127C22×C4111yescharacteristic
188C2×#124—22no—
189#500—21no—
190#492—21no—
191#487—21no—
192#486—21no—
193#484—22no—
194#477—22no—
195#460—22no—
196#450—22no—
197#431C22×C4111yescharacteristic
198#431C22×C4111yescharacteristic
199#423C22×C4111yescharacteristic
200#390—22no—
201#390—22no—
202C43C22×C4111yescharacteristic
203#339—22no—
204#332—22no—
205#331—22no—
206C41#1029211yescharacteristic, direct product factor, Sylow
207C22×Q8—21no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4D4×C4112yes—
211C2×SD16—24no—
212C2×M16—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C4111yescharacteristic
218C4⋊Q8D4×C4111yescharacteristic
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#125—21no—
224#124—48no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229#117—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4D4×C4112yes—
232C2×C22⋊C4—28no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42D4×C4112yes—
236C2×C42C23×C4111yescharacteristic
237#107—24no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C4112yes—
241C4⋊C8D4×C4112yes—
242#103—24no—
243#102—24no—
244C22⋊C8—21no—
245C22⋊C8—21no—
246C4×C8—21no—
247C4×C8—21no—
248C24—22no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—44no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—44no—
257C2×D4—44no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—42no—
263C2×D4—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4C2×D4×C4111yescharacteristic
267C22×C4C2×D4×C4111yescharacteristic
268C22×C4C2×D4×C4111yescharacteristic
269SD16—84no—
270M16—42no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—41no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—416no—
285C22⋊C4—41no—
286C42—24no—
287C42—22no—
288C42—22no—
289C42—42no—
290C42—41no—
291C42C2×D4×C4111yescharacteristic
292C42C2×D4×C4111yescharacteristic
293C42C2×D4×C4111yescharacteristic
294C42#41×C4111yescharacteristic
295C23—44no—
296C23—44no—
297C23—42no—
298C23—44no—
299C23#120×C4111yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—82no—
304D4—44no—
305D4—82no—
306D4—82no—
307D4—82no—
308D4—82no—
309D4—81no—
310D4—81no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4#120×C4111yescharacteristic
321C2×C4#120×C4111yescharacteristic
322C2×C4#121×C4111yescharacteristic
323C2×C4#121×C4111yescharacteristic
324C2×C4#121×C4111yescharacteristic
325C2×C4#127×C4111yescharacteristic
326C2×C4#135×C4112yes—
327C2×C4#137×C4112yes—
328C8—42no—
329C8—42no—
330C8—81no—
331C22—21no—
332C22—21no—
333C22—88no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22C41×#39211yescharacteristic
338C22C41×#45212yes—
339C4—21no—
340C4—21no—
341C4—44no—
342C4—82no—
343C4—81no—
344C4—81no—
345C4C41×#45312yes—
346C4C41×#45412yes—
347C4C41×#46412yes—
348C4C41×#49511yescharacteristic
349C4C41×#49711yescharacteristic
350C2—22no—
351C2—162no—
352C2C41×#200211yescharacteristic
353C2C41×#200311yescharacteristic
354C2C41×#201511yescharacteristic
subgroupG/H
center, socleC22×C41#392
commutator, Frattini, cosocleC2×C42C23×C41
prime radicalC2×#127×C41C22
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×#3230C2semidirect
4. C41×#1994C2semidirect
5. C41×#1549C2semidirect
7. C41×#1276C2semidirect
153. #10292C41direct (N × H)
173. #3230C2×C41semidirect
176. #1994C2×C41semidirect
177. #1549C2×C41semidirect
179. #1276C2×C41semidirect
206. C41#10292direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32302
C41×#32082
C41×#28582
C41×#19942
C41×#15492
C41×#15452
C41×#12762
#1029241