Finite Group Databasebeta

← C2×#20299340 #28404694

Subgroups — C2×#20299340 #28404694

Order 14464.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#20299340C2116yesmaximal, direct product factor
2C2×#16813611C212yesmaximal, complemented
3C2×#16813610C212yesmaximal, complemented
4C2×#16813608C214yesmaximal, complemented
5C2×#16813592C214yesmaximal, complemented
6C2×#16813590C212yesmaximal, complemented
7C2×#124×C113C211yesmaximal, characteristic, complemented
8C24×D113C2212yescomplemented
9C22×Dic226C2212yescomplemented
10C22×D452C2212yes—
11C22×D452C2212yes—
12C22×C22⋊D113C2214yes—
13#16813611C22116yescomplemented
14#16813610C22116yescomplemented
15#16813608C22132yescomplemented
16#16813592C22132yescomplemented
17#16813590C22116yescomplemented
18C2×C22⋊Dic113C2212yescomplemented
19C2×#14268624C2214yescomplemented
20C2×#14268624C2214yescomplemented
21C2×#14268624C2214yescomplemented
22C2×C4×Dic113C2212yescomplemented
23C22×Q8×C113C2211yescharacteristic, complemented
24C22×D4×C113C2211yescharacteristic
25#124×C113C2218yescomplemented
26C2×C22⋊C4×C113C2214yescomplemented
27C2×C42×C113C2211yescharacteristic, complemented
28C23×D113—48no—
29C23×D113—44no—
30C23×D113C2314yes—
31C23×D113C2318yescomplemented
32C2×Dic226—44no—
33C2×Dic226C2318yescomplemented
34C2×D452—44no—
35C2×D452—44no—
36C2×D452C2318yes—
37C2×D452C2318yes—
38C2×C22⋊D113—48no—
39C2×C22⋊D113C23116yes—
40C22×Dic113C2314yes—
41C22⋊Dic113C2318yescomplemented
42#14268624C23116yescomplemented
43#14268624C23116yescomplemented
44#14268624C23116yescomplemented
45C4×Dic113C2318yescomplemented
46C24×C113C2312yes—
47C2×Q8×C113—42no—
48C2×Q8×C113C2314yescomplemented
49C2×D4×C113—42no—
50C2×D4×C113C2314yes—
51C22×C4×C113C2312yes—
52C22×C4×C113C2311yescharacteristic
53C22×C4×C113C2312yes—
54C22⋊C4×C113C23116yescomplemented
55C42×C113C2314yescomplemented
56C23×C113—24no—
57C23×C113—28no—
58C23×C113C2414yes—
59C23×C113C2411yescharacteristic
60C22×D113—28no—
61C22×D113—28no—
62C22×D113—28no—
63C22×D113—48no—
64C22×D113—416no—
65C22×D113—432no—
66C22×D113C2418yes—
67Q8×C113—44no—
68D4×C113—44no—
69C2×C4×C113—22no—
70C2×C4×C113—24no—
71C2×C4×C113—24no—
72C2×C4×C113C2414yes—
73C2×C4×C113C2412yes—
74C2×C4×C113C2414yes—
75C22⋊D113—416no—
76C2×Dic113—28no—
77C2×Dic113C2418yes—
78D452—48no—
79D452—48no—
80Dic226—48no—
81C22×C113—28no—
82C22×C113—24no—
83C22×C113—48no—
84C22×C113H(5,𝔽2)12yes—
85C22×C113H(5,𝔽2)14yes—
86C22×C113C2511yescharacteristic
87C2×D113—28no—
88C2×D113—28no—
89C2×D113—28no—
90C2×D113—432no—
91C2×D113—416no—
92C4×C113—24no—
93C4×C113—24no—
94C4×C113—22no—
95Dic113—28no—
96C2×C113—44no—
97C2×C113H(3,𝔽4)14yescomplemented
98C2×C113C2×H(5,𝔽2)11yescharacteristic
99C2×C113C2×H(5,𝔽2)12yes—
100D113—48no—
101C2×H(3,𝔽4)—1131nomaximal, Sylow
102C113C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
103H(3,𝔽4)—11316no—
104C2×#124—1132no—
105C2×#124—1134no—
106C2×#124—1132no—
107C2×#124D11311yescharacteristic, complemented
108C2×#120—1132no—
109C2×#120—1134no—
110C25—1132no—
111C22×Q8—1132no—
112C22×Q8C2×D11311yescharacteristic, complemented
113C22×D4—1134no—
114C22×D4—1132no—
115C22×D4—1132no—
116C22×D4C2×D11311yescharacteristic
117#124—11316no—
118#124—11332no—
119#124—11316no—
120#124C2×D11318yescomplemented
121#120—11316no—
122#120—11332no—
123C2×C22⋊C4—1132no—
124C2×C22⋊C4—1134no—
125C2×C22⋊C4—1134no—
126C2×C22⋊C4—1134no—
127C2×C22⋊C4C2×D11314yescomplemented
128C2×C42—1132no—
129C2×C42C2×D11311yescharacteristic, complemented
130C24—1138no—
131C24—1134no—
132C24—4524no—
133C24—4528no—
134C24C22×D11312yes—
135C2×Q8—42no—
136C2×Q8—1138no—
137C2×Q8—4524no—
138C2×Q8C22×D11314yescomplemented
139C2×D4—42no—
140C2×D4—11316no—
141C2×D4—1138no—
142C2×D4—1138no—
143C2×D4—4524no—
144C2×D4—4524no—
145C2×D4—4528no—
146C2×D4C22×D11314yes—
147C22×C4—1134no—
148C22×C4C22×D11312yes—
149C22×C4C22×D11311yescharacteristic
150C22×C4C22×D11312yes—
151C22⋊C4—1138no—
152C22⋊C4—11316no—
153C22⋊C4—11316no—
154C22⋊C4—11316no—
155C22⋊C4C22×D113116yescomplemented
156C42—1138no—
157C42C22×D11314yescomplemented
158C23—24no—
159C23—28no—
160C23—1138no—
161C23—4528no—
162C23—45216no—
163C23—45232no—
164C23—2268no—
165C23—2268no—
166C23—2268no—
167C23C23×D11314yes—
168C23C23×D11311yescharacteristic
169Q8—44no—
170Q8—4528no—
171D4—44no—
172D4—4528no—
173D4—4528no—
174D4—45216no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—1138no—
179C2×C4—2268no—
180C2×C4C23×D11314yes—
181C2×C4C23×D11312yes—
182C2×C4C23×D11314yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—45232no—
187C22—45216no—
188C22—2268no—
189C22—2268no—
190C22—2268no—
191C22#1681366712yes—
192C22#1681366814yes—
193C22C24×D11311yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—2268no—
198C2—44no—
199C2—4528no—
200C2#2029934014yesdirect product factor
201C2C2×#1681366711yescharacteristic
202C2C2×#1681366812yes—
subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#124×C113C2
socleC23×C113C24
hypercenterC2×#124D113
hypocenterC113C2×H(3,𝔽4)
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #20299340C2direct (N × H)
2. C2×#16813611C2semidirect
3. C2×#16813610C2semidirect
4. C2×#16813608C2semidirect
5. C2×#16813592C2semidirect
6. C2×#16813590C2semidirect
7. C2×#124×C113C2semidirect
8. C24×D113C22semidirect
9. C22×Dic226C22semidirect
13. #16813611C22semidirect
14. #16813610C22semidirect
15. #16813608C22semidirect
16. #16813592C22semidirect
17. #16813590C22semidirect
18. C2×C22⋊Dic113C22semidirect
19. C2×#14268624C22semidirect
20. C2×#14268624C22semidirect
21. C2×#14268624C22semidirect
22. C2×C4×Dic113C22semidirect
23. C22×Q8×C113C22semidirect
25. #124×C113C22semidirect
26. C2×C22⋊C4×C113C22semidirect
27. C2×C42×C113C22semidirect
31. C23×D113C23semidirect
33. C2×Dic226C23semidirect
41. C22⋊Dic113C23semidirect
42. #14268624C23semidirect
43. #14268624C23semidirect
44. #14268624C23semidirect
45. C4×Dic113C23semidirect
48. C2×Q8×C113C23semidirect
54. C22⋊C4×C113C23semidirect
55. C42×C113C23semidirect
97. C2×C113H(3,𝔽4)semidirect
102. C113C2×H(3,𝔽4)semidirect
107. C2×#124D113semidirect
112. C22×Q8C2×D113semidirect
120. #124C2×D113semidirect
127. C2×C22⋊C4C2×D113semidirect
129. C2×C42C2×D113semidirect
138. C2×Q8C22×D113semidirect
155. C22⋊C4C22×D113semidirect
157. C42C22×D113semidirect
200. C2#20299340direct (N × H)

Maximal subgroups

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

subgroupindex
#202993402
C2×#168136112
C2×#168136102
C2×#168136082
C2×#168135922
C2×#168135902
C2×#124×C1132
C2×H(3,𝔽4)113