Finite Group Databasebeta

← #23765525

Subgroups — #23765525

Order 10112.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic632C211yesmaximal, characteristic, complemented
2#19098838C212yesmaximal
3#19098393C211yesmaximal, characteristic, complemented
4#19098380C212yesmaximal, complemented
5#504×C79C211yesmaximal, characteristic
6#14579191—22no—
7C2×Dic316C2212yes—
8Dic632—21no—
9Dic632—21no—
10#14579097C2212yes—
11#14579079—22no—
12#131×C79C2211yescharacteristic
13M32×C79—21no—
14M32×C79C2211yescharacteristic
15C2×C16×C79—21no—
16C2×C16×C79C2211yescharacteristic
17C2×Dic158—22no—
18Dic316—22no—
19Dic316—22no—
20#11929614—42no—
21#11929612—42no—
22#11929608—22no—
23#41×C79D411yescharacteristic
24M16×C79—21no—
25M16×C79D411yescharacteristic
26C2×C8×C79—21no—
27C2×C8×C79C2311yescharacteristic
28C16×C79—21no—
29C16×C79D411yescharacteristic
30C16×C79D411yescharacteristic
31Q8×C79D811yescharacteristic
32D4×C79—21no—
33D4×C79D811yescharacteristic
34C2×C4×C79—21no—
35C2×C4×C79C2×D411yescharacteristic
36C2×Dic79—42no—
37Dic158—42no—
38Dic158—42no—
39C8×C79—21no—
40C8×C79C2×D411yescharacteristic
41C8×C79#4111yescharacteristic
42C79⋊C8—42no—
43C22×C79—21no—
44C22×C79#13511yescharacteristic
45C4×C79—21no—
46C4×C79#12111yescharacteristic
47C4×C79C2×D811yescharacteristic
48Dic79—82no—
49C2×C79—21no—
50C2×C79—41no—
51C2×C79#46611yescharacteristic
52#2222—791nomaximal, Sylow
53C79#222211yescharacteristic, complemented, Sylow
54C2×Q32—791no—
55#504D7911yescharacteristic
56#473—792no—
57#368—791no—
58#362—792no—
59#137—1582no—
60C2×Q16—792no—
61#131C2×D7911yescharacteristic
62Q32—1581no—
63Q32—1581no—
64M32—21no—
65M32C2×D7911yescharacteristic
66C2×C16—21no—
67C2×C16C2×D7911yescharacteristic
68#108—792no—
69#101—1582no—
70#41D31611yescharacteristic
71C2×Q8—1582no—
72Q16—3162no—
73Q16—1582no—
74Q16—1582no—
75SD16—3162no—
76M16—21no—
77M16—1582no—
78M16D31611yescharacteristic
79C2×C8—21no—
80C2×C8C22×D7911yescharacteristic
81C16—21no—
82C16C22⋊D7911yescharacteristic
83C16C22⋊D7911yescharacteristic
84Q8—3162no—
85Q8—3162no—
86Q8D63211yescharacteristic
87D4—21no—
88D4D63211yescharacteristic
89C2×C4—21no—
90C2×C4—3162no—
91C2×C4C2×D31611yescharacteristic
92C8—21no—
93C8—3162no—
94C8C2×C22⋊D7911yescharacteristic
95C8#1192962411yescharacteristic
96C22—21no—
97C22#1457918311yescharacteristic
98C4—21no—
99C4—6322no—
100C4#1457913511yescharacteristic
101C4C2×D63211yescharacteristic
102C2—21no—
103C2—41no—
104C2#1909879911yescharacteristic
subgroupG/H
centerC2#19098799
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#504×C79C2
socleC2×C79#466
prime radical#41×C79D4
hypercenter#504D79
hypocenterC79#2222
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic632C2semidirect
3. #19098393C2semidirect
4. #19098380C2semidirect
53. C79#2222semidirect