Finite Group Databasebeta

← C41×#13675 #23789876

Subgroups — C41×#13675 #23789876

Order 10496.

408 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3292C211yesmaximal, characteristic
2C41×#2198C212yesmaximal, complemented
3C41×#1620C211yesmaximal, characteristic, complemented
4C41×#1408C211yesmaximal, characteristic, complemented
5C41×#1402C212yesmaximal, complemented
6C41×#576—22no—
7C41×#559C2211yescharacteristic, complemented
8C41×#493C2211yescharacteristic
9C41×#472—22no—
10C41×#460—21no—
11C41×#458—22no—
12C41×#453—21no—
13C41×#453C2212yes—
14C41×#443—21no—
15C41×#353C2212yescomplemented
16C41×#352—22no—
17C41×#331C2211yescharacteristic, complemented
18C41×Q8⋊C8—21no—
19H(5,𝔽2)×C41—21no—
20H(5,𝔽2)×C41D412yes—
21AGL(1,ℤ/8)×C41—22no—
22AGL(1,ℤ/8)×C41—22no—
23AGL(1,ℤ/8)×C41—42no—
24AGL(1,ℤ/8)×C41—42no—
25#135×C41—21no—
26#135×C41—42no—
27C2×SD16×C41—41no—
28C2×D8×C41—22no—
29C2×D8×C41—42no—
30#131×C41—22no—
31#127×C41D411yescharacteristic
32#127×C41C2311yescharacteristic
33#124×C41—41no—
34#123×C41—22no—
35#123×C41—42no—
36C4×Q8×C41—21no—
37C4×D4×C41—41no—
38#108×C41—21no—
39C4⋊C8×C41—21no—
40#104×C41—22no—
41#102×C41—41no—
42#100×C41—21no—
43#100×C41D412yes—
44#99×C41—22no—
45#99×C41—42no—
46C4×C8×C41D411yescharacteristic
47#41×C41—22no—
48#41×C41—42no—
49#41×C41—42no—
50C2×Q8×C41—21no—
51C2×D4×C41—21no—
52C2×D4×C41—41no—
53C2×D4×C41—41no—
54C2×D4×C41—42no—
55C2×D4×C41—42no—
56C2×D4×C41—42no—
57C2×D4×C41—81no—
58C2×D4×C41C2×D412yes—
59C22×C4×C41—22no—
60Q16×C41—21no—
61SD16×C41—22no—
62SD16×C41—42no—
63SD16×C41—42no—
64SD16×C41—82no—
65D8×C41—21no—
66D8×C41—42no—
67D8×C41—42no—
68D8×C41—42no—
69D8×C41—42no—
70M16×C41—22no—
71M16×C41—42no—
72C2×C8×C41—21no—
73C2×C8×C41—42no—
74C2×C8×C41—41no—
75C4⋊C4×C41—21no—
76C4⋊C4×C41—41no—
77C4⋊C4×C41—82no—
78C22⋊C4×C41—22no—
79C22⋊C4×C41—42no—
80C22⋊C4×C41—42no—
81C22⋊C4×C41—82no—
82C42×C41—41no—
83C42×C41C2×D411yescharacteristic
84C23×C41—22no—
85C23×C41—42no—
86C23×C41—41no—
87C23×C41—81no—
88Q8×C41—22no—
89Q8×C41—41no—
90Q8×C41—41no—
91D4×C41—22no—
92D4×C41—42no—
93D4×C41—42no—
94D4×C41—42no—
95D4×C41—81no—
96D4×C41—81no—
97D4×C41—81no—
98D4×C41—81no—
99D4×C41—82no—
100D4×C41—82no—
101C2×C4×C41—21no—
102C2×C4×C41—42no—
103C2×C4×C41—42no—
104C2×C4×C41—41no—
105C2×C4×C41—41no—
106C2×C4×C41—81no—
107C2×C4×C41—82no—
108C2×C4×C41—82no—
109C2×C4×C41#12011yescharacteristic
110C8×C41—21no—
111C8×C41—21no—
112C8×C41—42no—
113C8×C41—81no—
114#13675C4111yesmaximal, characteristic, direct product factor, Sylow
115C22×C41—42no—
116C22×C41—42no—
117C22×C41—82no—
118C22×C41—81no—
119C22×C41—161no—
120C22×C41—162no—
121C22×C41—321no—
122C22×C41B(4,𝔽2)11yescharacteristic
123C4×C41—21no—
124C4×C41—21no—
125C4×C41—21no—
126C4×C41—42no—
127C4×C41—81no—
128C4×C41—81no—
129C4×C41—162no—
130#3292C2×C4111yescharacteristic
131#2198C2×C4112yescomplemented
132#1620C2×C4111yescharacteristic, complemented
133#1408C2×C4111yescharacteristic, complemented
134#1402C2×C4112yescomplemented
135C2×C41—21no—
136C2×C41—82no—
137C2×C41—82no—
138C2×C41—161no—
139C2×C41#219611yescharacteristic
140#576—22no—
141#559C22×C4111yescharacteristic, complemented
142#493C22×C4111yescharacteristic
143#472—22no—
144#460—21no—
145#458—22no—
146#453—21no—
147#453C22×C4112yes—
148#443—21no—
149#353C22×C4112yescomplemented
150#352—22no—
151#331C22×C4111yescharacteristic, complemented
152Q8⋊C8—21no—
153C41#1367511yescharacteristic, direct product factor, Sylow
154H(5,𝔽2)—21no—
155H(5,𝔽2)D4×C4112yes—
156AGL(1,ℤ/8)—22no—
157AGL(1,ℤ/8)—22no—
158AGL(1,ℤ/8)—42no—
159AGL(1,ℤ/8)—42no—
160#135—21no—
161#135—42no—
162C2×SD16—41no—
163C2×D8—22no—
164C2×D8—42no—
165#131—22no—
166#127D4×C4111yescharacteristic
167#127C23×C4111yescharacteristic
168#124—41no—
169#123—22no—
170#123—42no—
171C4×Q8—21no—
172C4×D4—41no—
173#108—21no—
174C4⋊C8—21no—
175#104—22no—
176#102—41no—
177#100—21no—
178#100D4×C4112yes—
179#99—22no—
180#99—42no—
181C4×C8D4×C4111yescharacteristic
182#41—22no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×D4—21no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—81no—
193C2×D4C2×D4×C4112yes—
194C22×C4—22no—
195Q16—21no—
196SD16—22no—
197SD16—42no—
198SD16—42no—
199SD16—82no—
200D8—21no—
201D8—42no—
202D8—42no—
203D8—42no—
204D8—42no—
205M16—22no—
206M16—42no—
207C2×C8—21no—
208C2×C8—42no—
209C2×C8—41no—
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—22no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—41no—
218C42C2×D4×C4111yescharacteristic
219C23—22no—
220C23—42no—
221C23—41no—
222C23—81no—
223Q8—22no—
224Q8—41no—
225Q8—41no—
226D4—22no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—81no—
234D4—82no—
235D4—82no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4#120×C4111yescharacteristic
245C8—21no—
246C8—21no—
247C8—42no—
248C8—81no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22—81no—
253C22—161no—
254C22—162no—
255C22—321no—
256C22C41×B(4,𝔽2)11yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—81no—
262C4—81no—
263C4—162no—
264C2—21no—
265C2—82no—
266C2—82no—
267C2—161no—
268C2C41×#219611yescharacteristic
subgroupG/H
center, socleC2×C41#2196
commutator, Frattini, cosocle#127C23×C41
prime radicalC41×#3292C2
LCSG ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C41 ◁ C22×C41 ◁ C2×C4×C41 ◁ #127×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2198C2semidirect
3. C41×#1620C2semidirect
4. C41×#1408C2semidirect
5. C41×#1402C2semidirect
7. C41×#559C22semidirect
15. C41×#353C22semidirect
17. C41×#331C22semidirect
114. #13675C41direct (N × H)
131. #2198C2×C41semidirect
132. #1620C2×C41semidirect
133. #1408C2×C41semidirect
134. #1402C2×C41semidirect
141. #559C22×C41semidirect
149. #353C22×C41semidirect
151. #331C22×C41semidirect
153. C41#13675direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32922
C41×#21982
C41×#16202
C41×#14082
C41×#14022
#1367541