Finite Group Databasebeta

← #28389895

Subgroups — #28389895

Order 14464.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#20299346C211yesmaximal, characteristic
2#20298960C212yesmaximal, complemented
3#20298340C211yesmaximal, characteristic, complemented
4#20298337C212yesmaximal, complemented
5#491×C113C211yesmaximal, characteristic, complemented
6#16813610C2212yes—
7#16813607—22no—
8#16813600—22no—
9#16813597—22no—
10#16813545—22no—
11#16813542—22no—
12#16813533C2212yes—
13C4⋊Q8×C113C2211yescharacteristic
14#125×C113C2211yescharacteristic
15#103×C113—22no—
16#97×C113C2211yescharacteristic
17C2×Dic226D412yes—
18C2×D452—22no—
19C2×D452D412yes—
20C2×C4×D113—22no—
21C2×#11744751—22no—
22#14268626—22no—
23#14268624—22no—
24#14268624—22no—
25#14268624—22no—
26C2×Q8×C113—21no—
27C2×C8×C113—21no—
28C4⋊C4×C113—22no—
29C4⋊C4×C113—22no—
30C4⋊C4×C113D412yes—
31C42×C113C2311yescharacteristic
32C22×D113—22no—
33Q8×C113—42no—
34C2×C4×C113—22no—
35C2×C4×C113—41no—
36C2×C4×C113C2×D412yes—
37C2×C4×C113C2×D411yescharacteristic
38C2×Dic113—22no—
39D452—42no—
40D452—82no—
41C4×D113—82no—
42Dic226—42no—
43C8×C113—41no—
44#11744751—42no—
45C22×C113#12011yescharacteristic
46C2×D113—42no—
47C2×D113—42no—
48C2×D113—42no—
49C4×C113—21no—
50C4×C113—22no—
51C4×C113—42no—
52C4×C113—81no—
53Dic113—42no—
54C2×C113#45411yescharacteristic
55C2×C113#45512yes—
56D113—82no—
57#1662—1131nomaximal, Sylow
58C113#166211yescharacteristic, complemented, Sylow
59#562—1131no—
60#491D11311yescharacteristic, complemented
61#489—1132no—
62#330—1131no—
63#329—1132no—
64C4⋊Q8C2×D11311yescharacteristic
65#125C2×D11311yescharacteristic
66#124—1132no—
67#123—2262no—
68C22⋊Q8—2262no—
69#121—2262no—
70#103—22no—
71#103—2262no—
72#102—2262no—
73#97—1132no—
74#97C2×D11311yescharacteristic
75C2×Q8—21no—
76C2×Q8—1132no—
77C2×D4—1132no—
78C2×D4—2262no—
79C22×C4—2262no—
80C2×C8—21no—
81C2×C8—2262no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—2262no—
85C4⋊C4C22⋊D11312yes—
86C22⋊C4—2262no—
87C22⋊C4—2262no—
88C22⋊C4—2262no—
89C42C22×D11311yescharacteristic
90C23—2262no—
91Q8—42no—
92Q8—4522no—
93D4—9042no—
94D4—4522no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—9042no—
98C2×C4—2262no—
99C2×C4D4×D11312yes—
100C2×C4C2×C22⋊D11311yescharacteristic
101C8—41no—
102C8—4522no—
103C22—4522no—
104C22—4522no—
105C22—4522no—
106C22#1681359011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—4522no—
112C2—9042no—
113C2#2029877011yescharacteristic
114C2#2029877412yes—
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#491×C113C2
socleC22×C113#120
prime radical#20299346C2
hypercenter#491D113
hypocenterC113#1662
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #20298960C2semidirect
3. #20298340C2semidirect
4. #20298337C2semidirect
5. #491×C113C2semidirect
58. C113#1662semidirect
60. #491D113semidirect

Maximal subgroups

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

subgroupindex
#202993462
#202989602
#202983402
#202983372
#491×C1132
#1662113