Finite Group Databasebeta

← C79⋊#1308 #23761312

Subgroups — C79⋊#1308 #23761312

Order 10112.

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#19098620C211yesmaximal, characteristic
2#19098620C211yesmaximal, characteristic
3#432×C79C211yesmaximal, characteristic
4C4⋊(C79⋊C8)—21no—
5C4⋊(C79⋊C8)—21no—
6C22⋊(C79⋊C8)C412yes—
7C22⋊(C79⋊C8)C412yes—
8#14579072—21no—
9#14579072—21no—
10C2×C42×C79C2211yescharacteristic
11C4⋊C8×C79—21no—
12C22⋊C8×C79C412yes—
13#97×C79—21no—
14C2×C79⋊C8—22no—
15C2×C79⋊C8—22no—
16C22×C4×C79C2×C411yescharacteristic
17C22×C4×C79C2×C411yescharacteristic
18C22×C4×C79C2×C411yescharacteristic
19C2×C8×C79—22no—
20C42×C79D411yescharacteristic
21C42×C79D411yescharacteristic
22C42×C79D411yescharacteristic
23C42×C79Q811yescharacteristic
24C23×C79C4211yescharacteristic
25C2×C4×C79—41no—
26C2×C4×C79—41no—
27C2×C4×C79—41no—
28C2×C4×C79C22⋊C411yescharacteristic
29C2×C4×C79C22⋊C411yescharacteristic
30C2×C4×C79C22⋊C411yescharacteristic
31C2×C4×C79C4⋊C411yescharacteristic
32C2×C4×C79C4⋊C411yescharacteristic
33C2×C4×C79C4⋊C411yescharacteristic
34C8×C79—42no—
35C79⋊C8—42no—
36C79⋊C8—42no—
37C22×C79—21no—
38C22×C79—21no—
39C22×C79—21no—
40C22×C79#9511yescharacteristic
41C4×C79—21no—
42C4×C79—21no—
43C4×C79—21no—
44C4×C79—21no—
45C4×C79—21no—
46C4×C79—21no—
47C2×C79—41no—
48C2×C79#34411yescharacteristic
49C2×C79#34411yescharacteristic
50C2×C79#34411yescharacteristic
51#1308—791nomaximal, Sylow
52C79#130811yescharacteristic, complemented, Sylow
53#432—791no—
54#432—791no—
55#432D7911yescharacteristic
56C2×C42C2×D7911yescharacteristic
57C4⋊C8—21no—
58C4⋊C8—1581no—
59C4⋊C8—1581no—
60C22⋊C8—792no—
61C22⋊C8—792no—
62C22⋊C8Dic7912yes—
63#97—21no—
64#97—1581no—
65#97—1581no—
66C22×C4C4×D7911yescharacteristic
67C22×C4C4×D7911yescharacteristic
68C22×C4C2×Dic7911yescharacteristic
69C2×C8—22no—
70C2×C8—1582no—
71C2×C8—1582no—
72C42Dic15811yescharacteristic
73C42D31611yescharacteristic
74C42C22⋊D7911yescharacteristic
75C42C22⋊D7911yescharacteristic
76C23C4×Dic7911yescharacteristic
77C2×C4—41no—
78C2×C4—41no—
79C2×C4—41no—
80C2×C4(C2×D79)⋊C411yescharacteristic
81C2×C4(C2×D79)⋊C411yescharacteristic
82C2×C4C22⋊Dic7911yescharacteristic
83C2×C4Dic79⋊C411yescharacteristic
84C2×C4Dic79⋊C411yescharacteristic
85C2×C4C4⋊Dic7911yescharacteristic
86C8—42no—
87C8—3162no—
88C8—3162no—
89C22—21no—
90C22—21no—
91C22—21no—
92C22C79⋊#9511yescharacteristic
93C4—21no—
94C4—21no—
95C4—21no—
96C4—21no—
97C4—21no—
98C4—21no—
99C2—41no—
100C2#1909833311yescharacteristic
101C2#1909833411yescharacteristic
102C2#1909833511yescharacteristic
subgroupG/H
centerC22C79⋊#95
commutator, prime radicalC23×C79C42
FrattiniC2×C42C2×D79
Fitting#432×C79C2
socleC22×C79#95
cosocleC2×C42×C79C22
hypercenter#432D79
hypocenterC79#1308
LCSG ▷ C23×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
52. C79#1308semidirect