Finite Group Databasebeta

← C41×#20302 #23796503

Subgroups — C41×#20302 #23796503

Order 10496.

690 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 198 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×#3325C214yesmaximal, complemented
2C41×#1709C211yesmaximal, characteristic, complemented
3C41×#1697C214yesmaximal, complemented
4C41×#1634C212yesmaximal, complemented
5C41×#1619C212yesmaximal, complemented
6C41×#1589C212yesmaximal, complemented
7C41×#555C2212yes—
8D42×C41C2212yescomplemented
9C41×#494C2211yescharacteristic, complemented
10C41×#493C2211yescharacteristic
11C41×#486C2214yescomplemented
12C41×#482—24no—
13C41×#476C2214yescomplemented
14C41×#469—24no—
15C41×#459C2214yes—
16C41×#447—24no—
17C4×D8×C41C2212yes—
18C41×#436C2214yescomplemented
19C41×#418—24no—
20C41×#335C2212yescomplemented
21C41×#333C2212yescomplemented
22C41×#331C2212yescomplemented
23C41×D4⋊C8C2214yescomplemented
24C82×C41C2211yescharacteristic, complemented
25C22×D4×C41—24no—
26C2×Q16×C41—41no—
27C2×D8×C41—24no—
28C2×D8×C41—41no—
29C2×D8×C41D412yes—
30C2×M16×C41—24no—
31C4⋊Q8×C41C2312yes—
32#127×C41C2312yes—
33#124×C41—42no—
34#121×C41—24no—
35#121×C41—24no—
36#120×C41—42no—
37C4×D4×C41C2314yes—
38#117×C41—24no—
39#107×C41D412yes—
40#106×C41—24no—
41C4⋊C8×C41C2314yes—
42#102×C41—24no—
43#102×C41—24no—
44#102×C41—24no—
45#102×C41—24no—
46#102×C41D414yes—
47C22⋊C8×C41—24no—
48C4×C8×C41C2311yescharacteristic
49C4×C8×C41C2312yes—
50C24×C41—42no—
51C2×Q8×C41—22no—
52C2×D4×C41—24no—
53C2×D4×C41—22no—
54C2×D4×C41—44no—
55C2×D4×C41—48no—
56C2×D4×C41—42no—
57C2×D4×C41—84no—
58C2×D4×C41C2×D414yes—
59C22×C4×C41—24no—
60Q16×C41—82no—
61D8×C41—42no—
62D8×C41—82no—
63D8×C41—84no—
64M16×C41—84no—
65C2×C8×C41—21no—
66C2×C8×C41—24no—
67C2×C8×C41C2×D412yes—
68C2×C8×C41C2×D412yes—
69C4⋊C4×C41—24no—
70C4⋊C4×C41C2×D414yes—
71C22⋊C4×C41—24no—
72C22⋊C4×C41—42no—
73C22⋊C4×C41—44no—
74C42×C41—42no—
75C42×C41C2411yescharacteristic
76C23×C41—24no—
77C23×C41—42no—
78C23×C41—88no—
79C23×C41—162no—
80Q8×C41—82no—
81D4×C41—24no—
82D4×C41—24no—
83D4×C41—44no—
84D4×C41—44no—
85D4×C41—82no—
86D4×C41—88no—
87D4×C41—162no—
88C2×C4×C41—24no—
89C2×C4×C41—44no—
90C2×C4×C41—44no—
91C2×C4×C41—42no—
92C2×C4×C41C22×D412yes—
93C2×C4×C41H(5,𝔽2)11yescharacteristic
94C8×C41—22no—
95C8×C41—22no—
96C8×C41—22no—
97C8×C41—44no—
98#20302C4111yesmaximal, characteristic, direct product factor, Sylow
99C22×C41—44no—
100C22×C41—44no—
101C22×C41—44no—
102C22×C41—84no—
103C22×C41—82no—
104C22×C41—168no—
105C22×C41D4211yescharacteristic
106C4×C41—21no—
107C4×C41—44no—
108C4×C41—82no—
109C4×C41#57512yes—
110C4×C41#57612yes—
111#3325C2×C4114yescomplemented
112#1709C2×C4111yescharacteristic, complemented
113#1697C2×C4114yescomplemented
114#1634C2×C4112yescomplemented
115#1619C2×C4112yescomplemented
116#1589C2×C4112yescomplemented
117C2×C41—84no—
118C2×C41—162no—
119C2×C41#327312yes—
120C2×C41#329211yescharacteristic
121#555C22×C4112yes—
122D42C22×C4112yescomplemented
123#494C22×C4111yescharacteristic, complemented
124#493C22×C4111yescharacteristic
125#486C22×C4114yescomplemented
126#482—24no—
127#476C22×C4114yescomplemented
128#469—24no—
129#459C22×C4114yes—
130#447—24no—
131C4×D8C22×C4112yes—
132#436C22×C4114yescomplemented
133#418—24no—
134#335C22×C4112yescomplemented
135#333C22×C4112yescomplemented
136#331C22×C4112yescomplemented
137D4⋊C8C22×C4114yescomplemented
138C82C22×C4111yescharacteristic, complemented
139C41#2030211yescharacteristic, direct product factor, Sylow
140C22×D4—24no—
141C2×Q16—41no—
142C2×D8—24no—
143C2×D8—41no—
144C2×D8D4×C4112yes—
145C2×M16—24no—
146C4⋊Q8C23×C4112yes—
147#127C23×C4112yes—
148#124—42no—
149#121—24no—
150#121—24no—
151#120—42no—
152C4×D4C23×C4114yes—
153#117—24no—
154#107D4×C4112yes—
155#106—24no—
156C4⋊C8C23×C4114yes—
157#102—24no—
158#102—24no—
159#102—24no—
160#102—24no—
161#102D4×C4114yes—
162C22⋊C8—24no—
163C4×C8C23×C4111yescharacteristic
164C4×C8C23×C4112yes—
165C24—42no—
166C2×Q8—22no—
167C2×D4—24no—
168C2×D4—22no—
169C2×D4—44no—
170C2×D4—48no—
171C2×D4—42no—
172C2×D4—84no—
173C2×D4C2×D4×C4114yes—
174C22×C4—24no—
175Q16—82no—
176D8—42no—
177D8—82no—
178D8—84no—
179M16—84no—
180C2×C8—21no—
181C2×C8—24no—
182C2×C8C2×D4×C4112yes—
183C2×C8C2×D4×C4112yes—
184C4⋊C4—24no—
185C4⋊C4C2×D4×C4114yes—
186C22⋊C4—24no—
187C22⋊C4—42no—
188C22⋊C4—44no—
189C42—42no—
190C42C24×C4111yescharacteristic
191C23—24no—
192C23—42no—
193C23—88no—
194C23—162no—
195Q8—82no—
196D4—24no—
197D4—24no—
198D4—44no—
199D4—44no—
200D4—82no—
201D4—88no—
202D4—162no—
203C2×C4—24no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4C22×D4×C4112yes—
208C2×C4H(5,𝔽2)×C4111yescharacteristic
209C8—22no—
210C8—22no—
211C8—22no—
212C8—44no—
213C22—44no—
214C22—44no—
215C22—44no—
216C22—82no—
217C22—84no—
218C22—168no—
219C22D42×C4111yescharacteristic
220C4—21no—
221C4—44no—
222C4—82no—
223C4C41×#57512yes—
224C4C41×#57612yes—
225C2—84no—
226C2—162no—
227C2C41×#327312yes—
228C2C41×#329211yescharacteristic
subgroupG/H
center, socleC22×C41D42
commutator, Frattini, cosocleC42C24×C41
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3325C2semidirect
2. C41×#1709C2semidirect
3. C41×#1697C2semidirect
4. C41×#1634C2semidirect
5. C41×#1619C2semidirect
6. C41×#1589C2semidirect
8. D42×C41C22semidirect
9. C41×#494C22semidirect
11. C41×#486C22semidirect
13. C41×#476C22semidirect
18. C41×#436C22semidirect
20. C41×#335C22semidirect
21. C41×#333C22semidirect
22. C41×#331C22semidirect
23. C41×D4⋊C8C22semidirect
24. C82×C41C22semidirect
98. #20302C41direct (N × H)
111. #3325C2×C41semidirect
112. #1709C2×C41semidirect
113. #1697C2×C41semidirect
114. #1634C2×C41semidirect
115. #1619C2×C41semidirect
116. #1589C2×C41semidirect
122. D42C22×C41semidirect
123. #494C22×C41semidirect
125. #486C22×C41semidirect
127. #476C22×C41semidirect
132. #436C22×C41semidirect
134. #335C22×C41semidirect
135. #333C22×C41semidirect
136. #331C22×C41semidirect
137. D4⋊C8C22×C41semidirect
138. C82C22×C41semidirect
139. C41#20302direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#33252
C41×#17092
C41×#16972
C41×#16342
C41×#16192
C41×#15892
#2030241