Finite Group Databasebeta

← #23761507

Subgroups — #23761507

Order 10112.

140 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14579101C211yesmaximal, characteristic
2#19098601C211yesmaximal, characteristic
3C2×#106×C79C211yesmaximal, characteristic
4#14579120—21no—
5#14579101—21no—
6#14579101C412yescomplemented
7C2×C79⋊C16—21no—
8#14579095C412yescomplemented
9#14579093—21no—
10C22×C8×C79C2211yescharacteristic
11C2×C4⋊C4×C79—21no—
12#106×C79—21no—
13#106×C79C412yescomplemented
14C4⋊Dic79—22no—
15C22⋊Dic79—41no—
16C4×Dic79—41no—
17C79⋊C16—22no—
18C22×C4×C79—41no—
19C22×C4×C79D411yescharacteristic
20C2×C8×C79C2×C411yescharacteristic
21C2×C8×C79C2×C411yescharacteristic
22C2×C8×C79C2×C411yescharacteristic
23C2×C8×C79D411yescharacteristic
24C2×C8×C79D411yescharacteristic
25C2×C8×C79Q811yescharacteristic
26C4⋊C4×C79—22no—
27C4⋊C4×C79—41no—
28C23×C79D811yescharacteristic
29C2×C4×C79—42no—
30C2×C4×C79—82no—
31C2×C4×C79C22⋊C411yescharacteristic
32C2×C4×C79C22⋊C411yescharacteristic
33C2×C4×C79C4⋊C411yescharacteristic
34C2×C4×C79SD1611yescharacteristic
35C2×C4×C79SD1611yescharacteristic
36C2×C4×C79Q1611yescharacteristic
37C2×Dic79—42no—
38C8×C79C4211yescharacteristic
39C8×C79C22⋊C411yescharacteristic
40C8×C79C4⋊C411yescharacteristic
41C8×C79C4⋊C411yescharacteristic
42C22×C79—22no—
43C22×C79#10211yescharacteristic
44C22×C79#10211yescharacteristic
45C22×C79#10711yescharacteristic
46C4×C79—82no—
47C4×C79#9511yescharacteristic
48C4×C79#10311yescharacteristic
49C4×C79#10311yescharacteristic
50C4×C79#10611yescharacteristic
51Dic79—82no—
52C2×C79—21no—
53C2×C79—21no—
54C2×C79#34011yescharacteristic
55C2×C79#36012yes—
56#1386—791nomaximal, Sylow
57C79#138611yescharacteristic, complemented, Sylow
58C2×M32—791no—
59#427—791no—
60C2×#106D7911yescharacteristic
61C22×C8C2×D7911yescharacteristic
62#117—1581no—
63C2×C4⋊C4—21no—
64M32—792no—
65M32—1581no—
66C2×C16—1581no—
67#107—792no—
68#106—21no—
69#106—1581no—
70#106Dic7912yescomplemented
71C22×C4—41no—
72C22×C4C22⋊D7911yescharacteristic
73C2×C8Dic15811yescharacteristic
74C2×C8C4×D7911yescharacteristic
75C2×C8C4×D7911yescharacteristic
76C2×C8D31611yescharacteristic
77C2×C8C2×Dic7911yescharacteristic
78C2×C8C22⋊D7911yescharacteristic
79C4⋊C4—22no—
80C4⋊C4—41no—
81C4⋊C4—1582no—
82C22⋊C4—3161no—
83C42—3161no—
84C16—1582no—
85C23#1192960911yescharacteristic
86C2×C4—42no—
87C2×C4—82no—
88C2×C4—3162no—
89C2×C4(C2×D79)⋊C411yescharacteristic
90C2×C4C22⋊Dic7911yescharacteristic
91C2×C4Dic79⋊C411yescharacteristic
92C2×C4#1192961111yescharacteristic
93C2×C4#1192961211yescharacteristic
94C2×C4#1192961411yescharacteristic
95C8C4×Dic7911yescharacteristic
96C8(C2×D79)⋊C411yescharacteristic
97C8Dic79⋊C411yescharacteristic
98C8C4⋊Dic7911yescharacteristic
99C22—22no—
100C22#1457908111yescharacteristic
101C22#1457908211yescharacteristic
102C22#1457909411yescharacteristic
103C4—82no—
104C4—6322no—
105C4C79⋊#9511yescharacteristic
106C4#1457908411yescharacteristic
107C4#1457908511yescharacteristic
108C4#1457909211yescharacteristic
109C2—21no—
110C2—21no—
111C2#1909832511yescharacteristic
112C2#1909837212yes—
subgroupG/H
centerC22#14579081
commutatorC8×C79C42
FrattiniC22×C8C2×D79
FittingC2×#106×C79C2
socleC22×C79#102
prime radicalC23×C79D8
cosocleC22×C8×C79C22
hypercenterC2×#106D79
hypocenterC79#1386
LCSG ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
6. #14579101C4semidirect
8. #14579095C4semidirect
13. #106×C79C4semidirect
57. C79#1386semidirect
70. #106Dic79semidirect