Finite Group Databasebeta

← C83⋊#1308 #24905375

Subgroups — C83⋊#1308 #24905375

Order 10624.

122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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#19127758C211yesmaximal, characteristic
2#19127758C211yesmaximal, characteristic
3#432×C83C211yesmaximal, characteristic
4C4⋊(C83⋊C8)—21no—
5C4⋊(C83⋊C8)—21no—
6C22⋊(C83⋊C8)C412yes—
7C22⋊(C83⋊C8)C412yes—
8#14581703—21no—
9#14581703—21no—
10C2×C42×C83C2211yescharacteristic
11C4⋊C8×C83—21no—
12C22⋊C8×C83C412yes—
13#97×C83—21no—
14C2×C83⋊C8—22no—
15C2×C83⋊C8—22no—
16C22×C4×C83C2×C411yescharacteristic
17C22×C4×C83C2×C411yescharacteristic
18C22×C4×C83C2×C411yescharacteristic
19C2×C8×C83—22no—
20C42×C83D411yescharacteristic
21C42×C83D411yescharacteristic
22C42×C83D411yescharacteristic
23C42×C83Q811yescharacteristic
24C23×C83C4211yescharacteristic
25C2×C4×C83—41no—
26C2×C4×C83—41no—
27C2×C4×C83—41no—
28C2×C4×C83C22⋊C411yescharacteristic
29C2×C4×C83C22⋊C411yescharacteristic
30C2×C4×C83C22⋊C411yescharacteristic
31C2×C4×C83C4⋊C411yescharacteristic
32C2×C4×C83C4⋊C411yescharacteristic
33C2×C4×C83C4⋊C411yescharacteristic
34C8×C83—42no—
35C83⋊C8—42no—
36C83⋊C8—42no—
37C22×C83—21no—
38C22×C83—21no—
39C22×C83—21no—
40C22×C83#9511yescharacteristic
41C4×C83—21no—
42C4×C83—21no—
43C4×C83—21no—
44C4×C83—21no—
45C4×C83—21no—
46C4×C83—21no—
47C2×C83—41no—
48C2×C83#34411yescharacteristic
49C2×C83#34411yescharacteristic
50C2×C83#34411yescharacteristic
51#1308—831nomaximal, Sylow
52C83#130811yescharacteristic, complemented, Sylow
53#432—831no—
54#432—831no—
55#432D8311yescharacteristic
56C2×C42C2×D8311yescharacteristic
57C4⋊C8—21no—
58C4⋊C8—1661no—
59C4⋊C8—1661no—
60C22⋊C8—832no—
61C22⋊C8—832no—
62C22⋊C8Dic8312yes—
63#97—21no—
64#97—1661no—
65#97—1661no—
66C22×C4C4×D8311yescharacteristic
67C22×C4C4×D8311yescharacteristic
68C22×C4C2×Dic8311yescharacteristic
69C2×C8—22no—
70C2×C8—1662no—
71C2×C8—1662no—
72C42Dic16611yescharacteristic
73C42D33211yescharacteristic
74C42C22⋊D8311yescharacteristic
75C42C22⋊D8311yescharacteristic
76C23C4×Dic8311yescharacteristic
77C2×C4—41no—
78C2×C4—41no—
79C2×C4—41no—
80C2×C4(C2×D83)⋊C411yescharacteristic
81C2×C4(C2×D83)⋊C411yescharacteristic
82C2×C4C22⋊Dic8311yescharacteristic
83C2×C4Dic83⋊C411yescharacteristic
84C2×C4Dic83⋊C411yescharacteristic
85C2×C4C4⋊Dic8311yescharacteristic
86C8—42no—
87C8—3322no—
88C8—3322no—
89C22—21no—
90C22—21no—
91C22—21no—
92C22C83⋊#9511yescharacteristic
93C4—21no—
94C4—21no—
95C4—21no—
96C4—21no—
97C4—21no—
98C4—21no—
99C2—41no—
100C2#1912747111yescharacteristic
101C2#1912747211yescharacteristic
102C2#1912747311yescharacteristic
subgroupG/H
centerC22C83⋊#95
commutator, prime radicalC23×C83C42
FrattiniC2×C42C2×D83
Fitting#432×C83C2
socleC22×C83#95
cosocleC2×C42×C83C22
hypercenter#432D83
hypocenterC83#1308
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
52. C83#1308semidirect