Finite Group Databasebeta

← C22×#16813618 #28403845

Subgroups — C22×#16813618 #28403845

Order 14464.

3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 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
1C23×D452C211yesmaximal, characteristic, complemented
2C23×C22⋊D113C214yesmaximal, complemented
3C2×#16813618C2124yesmaximal, direct product factor
4C22×C4×Dic113C211yesmaximal, characteristic, complemented
5C23×D4×C113C211yesmaximal, characteristic, complemented
6C24×D113C2212yes—
7C22×D452—28no—
8C22×D452C22112yescomplemented
9C22×C22⋊D113—232no—
10C22×C22⋊D113C22148yescomplemented
11C23×Dic113C2212yes—
12#16813618C22164yesdirect product factor
13C2×C4×Dic113C22112yescomplemented
14C25×C113C2212yes—
15C22×D4×C113—28no—
16C22×D4×C113C22112yescomplemented
17C23×C4×C113C2211yescharacteristic
18C23×D113—216no—
19C23×D113—28no—
20C23×D113C23112yes—
21C2×D452—248no—
22C2×D452C23116yescomplemented
23C2×C22⋊D113—2192no—
24C2×C22⋊D113C23164yescomplemented
25C22×Dic113D4116yescomplemented
26C22×Dic113C23112yes—
27C4×Dic113C23116yescomplemented
28C24×C113—216no—
29C24×C113—28no—
30C24×C113C23112yes—
31C24×C113C2311yescharacteristic
32C2×D4×C113—248no—
33C2×D4×C113C23116yescomplemented
34C22×C4×C113D418yescomplemented
35C22×C4×C113C2316yes—
36C23×C113—224no—
37C23×C113—248no—
38C23×C113—432no—
39C23×C113C2×D418yes—
40C23×C113C2×D414yes—
41C23×C113C2418yes—
42C23×C113C2413yes—
43C22×D113—248no—
44C22×D113—224no—
45C22×D113—432no—
46C22×D113C2418yes—
47D4×C113—232no—
48C2×C4×C113C2×D4124yescomplemented
49C2×C4×C113C2414yes—
50C22⋊D113—2128no—
51C2×Dic113C2×D4148yescomplemented
52C2×Dic113C2418yes—
53D452—232no—
54C22×C113—216no—
55C22×C113—28no—
56C22×C113—448no—
57C22×C113#127116yescomplemented
58C22×C113C22×D4112yes—
59C22×C113C22×D416yes—
60C22×C113C2511yescharacteristic
61C2×D113—28no—
62C2×D113—216no—
63C2×D113—448no—
64C4×C113C22×D418yescomplemented
65Dic113C22×D4116yescomplemented
66C2×C113—48no—
67C2×C113C2×#127112yescomplemented
68C2×C113C23×D412yes—
69C2×C113C23×D411yescharacteristic
70D113—48no—
71C22×#127—1131nomaximal, Sylow
72C113C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—1134no—
74C23×D4—1131no—
75C23×D4D11311yescharacteristic, complemented
76C2×#127—11324no—
77C22×C42—1131no—
78C25—1132no—
79C25C2×D11312yes—
80C22×D4—28no—
81C22×D4—11348no—
82C22×D4—11312no—
83C22×D4—22632no—
84C22×D4—2268no—
85C22×D4C2×D113112yescomplemented
86C23×C4—1132no—
87C23×C4C2×D11311yescharacteristic
88#127—11364no—
89C2×C42—11312no—
90C24—216no—
91C24—28no—
92C24—11312no—
93C24—22616no—
94C24—2268no—
95C24C22×D113112yes—
96C24C22×D11311yescharacteristic
97C2×D4—248no—
98C2×D4—11364no—
99C2×D4—11316no—
100C2×D4—226192no—
101C2×D4—22648no—
102C2×D4C22×D113116yescomplemented
103C22×C4—11316no—
104C22×C4—11312no—
105C22×C4C22⋊D11318yescomplemented
106C22×C4C22×D11316yes—
107C42—11316no—
108C23—248no—
109C23—224no—
110C23—432no—
111C23—1138no—
112C23—45232no—
113C23—22648no—
114C23—22624no—
115C23D4×D11318yes—
116C23C2×C22⋊D11314yes—
117C23C23×D11318yes—
118C23C23×D11313yes—
119D4—232no—
120D4—226128no—
121D4—22632no—
122C2×C4—11348no—
123C2×C4—1138no—
124C2×C4C2×C22⋊D113124yescomplemented
125C2×C4C23×D11314yes—
126C22—216no—
127C22—28no—
128C22—448no—
129C22—45248no—
130C22—22616no—
131C22—2268no—
132C22#16813618116yesdirect product factor
133C22C2×D4×D113112yes—
134C22C22×C22⋊D11316yes—
135C22C24×D11311yescharacteristic
136C4—11316no—
137C4C22×C22⋊D11318yescomplemented
138C2—48no—
139C2—4528no—
140C2C2×#16813618112yesdirect product factor
141C2C22×D4×D11312yes—
142C2C23×C22⋊D11311yescharacteristic
subgroupG/H
centerC24C22×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC23×D4×C113C2
socleC24×C113C23
hypercenterC23×D4D113
hypocenterC113C22×#127
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D452C2semidirect
2. C23×C22⋊D113C2semidirect
3. C2×#16813618C2direct (N × H)
4. C22×C4×Dic113C2semidirect
5. C23×D4×C113C2semidirect
8. C22×D452C22semidirect
10. C22×C22⋊D113C22semidirect
12. #16813618C22direct (N × H)
13. C2×C4×Dic113C22semidirect
16. C22×D4×C113C22semidirect
22. C2×D452C23semidirect
24. C2×C22⋊D113C23semidirect
25. C22×Dic113D4semidirect
27. C4×Dic113C23semidirect
33. C2×D4×C113C23semidirect
34. C22×C4×C113D4semidirect
48. C2×C4×C113C2×D4semidirect
51. C2×Dic113C2×D4semidirect
57. C22×C113#127semidirect
64. C4×C113C22×D4semidirect
65. Dic113C22×D4semidirect
67. C2×C113C2×#127semidirect
72. C113C22×#127semidirect
75. C23×D4D113semidirect
85. C22×D4C2×D113semidirect
102. C2×D4C22×D113semidirect
105. C22×C4C22⋊D113semidirect
124. C2×C4C2×C22⋊D113semidirect
132. C22#16813618direct (N × H)
137. C4C22×C22⋊D113semidirect
140. C2C2×#16813618direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4522
C23×C22⋊D1132
C2×#168136182
C22×C4×Dic1132
C23×D4×C1132
C22×#127113