Finite Group Databasebeta

← C2×#20299233 #28404013

Subgroups — C2×#20299233 #28404013

Order 14464.

2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 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
1C22×D4×D113C214yesmaximal, complemented
2#20299233C2116yesmaximal, direct product factor
3C2×#16813593C214yesmaximal, complemented
4C2×#16813590C214yesmaximal, complemented
5C2×C4×D452C212yesmaximal, complemented
6C2×#127×C113C211yesmaximal, characteristic, complemented
7C24×D113C2214yescomplemented
8C22×D452C2212yes—
9C22×C22⋊D113C2218yescomplemented
10C2×D4×D113—232no—
11C2×D4×D113C22132yescomplemented
12C22×C4×D113C2214yescomplemented
13#16813593C22132yescomplemented
14#16813590C22132yescomplemented
15C4×D452C22116yescomplemented
16C2×C4⋊Dic113C2212yescomplemented
17C2×C22⋊Dic113C2214yescomplemented
18C2×#14268624C2214yescomplemented
19C22×D4×C113C2214yescomplemented
20C22×D4×C113C2212yescomplemented
21#127×C113C2218yescomplemented
22C2×C42×C113C2211yescharacteristic, complemented
23C23×D113—232no—
24C23×D113—48no—
25C23×D113C2314yes—
26C23×D113C23116yescomplemented
27C2×D452D4116yescomplemented
28C2×D452C2318yes—
29C2×C22⋊D113—232no—
30C2×C22⋊D113C23132yescomplemented
31D4×D113—2128no—
32C22×Dic113C2314yes—
33C2×C4×D113—216no—
34C2×C4×D113C23116yescomplemented
35C4⋊Dic113C2318yescomplemented
36C22⋊Dic113C23116yescomplemented
37#14268624C23116yescomplemented
38C24×C113C2314yes—
39C2×D4×C113—216no—
40C2×D4×C113—44no—
41C2×D4×C113C23116yescomplemented
42C2×D4×C113C2318yescomplemented
43C22×C4×C113C2311yescharacteristic
44C22×C4×C113C2312yes—
45C42×C113C2314yescomplemented
46C23×C113—216no—
47C23×C113—28no—
48C23×C113C2418yes—
49C23×C113C2411yescharacteristic
50C22×D113—28no—
51C22×D113—28no—
52C22×D113—264no—
53C22×D113—416no—
54C22×D113—464no—
55C22×D113C2×D4116yescomplemented
56C22×D113C2418yes—
57D4×C113—232no—
58D4×C113—48no—
59C2×C4×C113—22no—
60C2×C4×C113C2×D418yescomplemented
61C2×C4×C113C2412yes—
62C2×C4×C113C2414yes—
63C22⋊D113—264no—
64C2×Dic113—28no—
65C2×Dic113C2418yes—
66D452C2×D4132yescomplemented
67C4×D113—232no—
68C22×C113—216no—
69C22×C113—28no—
70C22×C113—416no—
71C22×C113C22×D414yes—
72C22×C113H(5,𝔽2)12yes—
73C22×C113C2511yescharacteristic
74C2×D113—232no—
75C2×D113—28no—
76C2×D113—28no—
77C2×D113—464no—
78C2×D113C22×D4116yescomplemented
79C4×C113—22no—
80C4×C113C22×D418yescomplemented
81Dic113—28no—
82C2×C113—48no—
83C2×C113D4214yescomplemented
84C2×C113C23×D412yes—
85C2×C113C2×H(5,𝔽2)11yescharacteristic
86D113—216no—
87C2×D42—1131nomaximal, Sylow
88C113C2×D4211yescharacteristic, complemented, Sylow
89C23×D4—1134no—
90D42—11316no—
91C2×#127D11311yescharacteristic, complemented
92C2×#121—1134no—
93C2×#120—1134no—
94C2×C4×D4—1132no—
95C25—1134no—
96C22×D4—1138no—
97C22×D4—11332no—
98C22×D4—1132no—
99C22×D4—22632no—
100C22×D4C2×D11314yescomplemented
101C22×D4C2×D11312yescomplemented
102C23×C4—1134no—
103#127C2×D11318yescomplemented
104#121—11332no—
105#120—11332no—
106C4×D4—11316no—
107C2×C4⋊C4—1132no—
108C2×C22⋊C4—1134no—
109C2×C22⋊C4—1134no—
110C2×C42C2×D11311yescharacteristic, complemented
111C24—1134no—
112C24—11316no—
113C24—4528no—
114C24—22632no—
115C24C22×D11314yes—
116C2×D4—216no—
117C2×D4—44no—
118C2×D4—11332no—
119C2×D4—11316no—
120C2×D4—1138no—
121C2×D4—226128no—
122C2×D4—22632no—
123C2×D4C22×D113116yescomplemented
124C2×D4C22×D11318yescomplemented
125C22×C4—1134no—
126C22×C4—11316no—
127C22×C4—22616no—
128C22×C4C22×D11311yescharacteristic
129C22×C4C22×D11312yes—
130C4⋊C4—1138no—
131C22⋊C4—11316no—
132C22⋊C4—11316no—
133C42C22×D11314yescomplemented
134C23—216no—
135C23—28no—
136C23—11316no—
137C23—1138no—
138C23—45216no—
139C23—45264no—
140C23—22664no—
141C23—2268no—
142C23—2268no—
143C23C23×D11318yes—
144C23C23×D11311yescharacteristic
145D4—232no—
146D4—48no—
147D4—11332no—
148D4—22664no—
149C2×C4—22no—
150C2×C4—1138no—
151C2×C4—2268no—
152C2×C4—22632no—
153C2×C4D4×D11318yescomplemented
154C2×C4C23×D11312yes—
155C2×C4C23×D11314yes—
156C22—216no—
157C22—28no—
158C22—416no—
159C22—11316no—
160C22—45264no—
161C22—2268no—
162C22—2268no—
163C22—22632no—
164C22C2×D4×D11314yes—
165C22#1681366712yes—
166C22C24×D11311yescharacteristic
167C4—22no—
168C4—2268no—
169C4C2×D4×D11318yescomplemented
170C2—48no—
171C2—22616no—
172C2#2029923314yesdirect product factor
173C2C22×D4×D11312yes—
174C2C2×#1681366711yescharacteristic
subgroupG/H
centerC23C23×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC2×#127×C113C2
socleC23×C113C24
hypercenterC2×#127D113
hypocenterC113C2×D42
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. #20299233C2direct (N × H)
3. C2×#16813593C2semidirect
4. C2×#16813590C2semidirect
5. C2×C4×D452C2semidirect
6. C2×#127×C113C2semidirect
7. C24×D113C22semidirect
9. C22×C22⋊D113C22semidirect
11. C2×D4×D113C22semidirect
12. C22×C4×D113C22semidirect
13. #16813593C22semidirect
14. #16813590C22semidirect
15. C4×D452C22semidirect
16. C2×C4⋊Dic113C22semidirect
17. C2×C22⋊Dic113C22semidirect
18. C2×#14268624C22semidirect
19. C22×D4×C113C22semidirect
20. C22×D4×C113C22semidirect
21. #127×C113C22semidirect
22. C2×C42×C113C22semidirect
26. C23×D113C23semidirect
27. C2×D452D4semidirect
30. C2×C22⋊D113C23semidirect
34. C2×C4×D113C23semidirect
35. C4⋊Dic113C23semidirect
36. C22⋊Dic113C23semidirect
37. #14268624C23semidirect
41. C2×D4×C113C23semidirect
42. C2×D4×C113C23semidirect
45. C42×C113C23semidirect
55. C22×D113C2×D4semidirect
60. C2×C4×C113C2×D4semidirect
66. D452C2×D4semidirect
78. C2×D113C22×D4semidirect
80. C4×C113C22×D4semidirect
83. C2×C113D42semidirect
88. C113C2×D42semidirect
91. C2×#127D113semidirect
100. C22×D4C2×D113semidirect
101. C22×D4C2×D113semidirect
103. #127C2×D113semidirect
110. C2×C42C2×D113semidirect
123. C2×D4C22×D113semidirect
124. C2×D4C22×D113semidirect
133. C42C22×D113semidirect
153. C2×C4D4×D113semidirect
169. C4C2×D4×D113semidirect
172. C2#20299233direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1132
#202992332
C2×#168135932
C2×#168135902
C2×C4×D4522
C2×#127×C1132
C2×D42113