Finite Group Databasebeta

← #23761413

Subgroups — #23761413

Order 10112.

116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 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#19098804C211yesmaximal, characteristic
2#19098326C211yesmaximal, characteristic
3C22⋊C16×C79C211yesmaximal, characteristic
4C2×Dic316C411yescharacteristic, complemented
5#14579140—21no—
6C2×C4⋊Dic79—21no—
7#14579095C411yescharacteristic, complemented
8#14579086—21no—
9C22×C8×C79C2211yescharacteristic
10C2×C16×C79—21no—
11C2×Dic158—21no—
12C22×Dic79—41no—
13Dic316—41no—
14C4⋊Dic79—22no—
15C4⋊Dic79—21no—
16C4⋊Dic79—41no—
17Dic79⋊C4—41no—
18C22⋊Dic79—41no—
19C22×C4×C79D411yescharacteristic
20C2×C8×C79—41no—
21C2×C8×C79C2×C411yescharacteristic
22C2×C8×C79D411yescharacteristic
23C16×C79—41no—
24C23×C79D811yescharacteristic
25C2×C4×C79—21no—
26C2×C4×C79—21no—
27C2×C4×C79C22⋊C411yescharacteristic
28C2×C4×C79SD1611yescharacteristic
29C2×Dic79—42no—
30C2×Dic79—41no—
31C2×Dic79—41no—
32C2×Dic79—81no—
33C2×Dic79—81no—
34Dic158—41no—
35Dic158—41no—
36C8×C79—21no—
37C8×C79—21no—
38C22×C79—21no—
39C22×C79—21no—
40C22×C79#10211yescharacteristic
41C22×C79SD3211yescharacteristic
42C22×C79Q3211yescharacteristic
43C4×C79—21no—
44C4×C79#9911yescharacteristic
45C4×C79#10411yescharacteristic
46Dic79—82no—
47Dic79—81no—
48Dic79—81no—
49C2×C79—21no—
50C2×C79—21no—
51C2×C79#32711yescharacteristic
52C2×C79#35811yescharacteristic
53C2×C79#36011yescharacteristic
54#1348—791nomaximal, Sylow
55C79#134811yescharacteristic, complemented, Sylow
56#467—791no—
57C22⋊C16D7911yescharacteristic
58#340—791no—
59C2×Q16—791no—
60C22×C8C2×D7911yescharacteristic
61C22⋊Q8—1581no—
62C2×C4⋊C4—1581no—
63C2×C16—21no—
64#107—791no—
65#103—1581no—
66C2×Q8—1581no—
67C22×C4—3161no—
68C22×C4D31611yescharacteristic
69Q16—3161no—
70C2×C8—41no—
71C2×C8C4×D7911yescharacteristic
72C2×C8C22⋊D7911yescharacteristic
73C4⋊C4—3161no—
74C4⋊C4—3161no—
75C4⋊C4—1582no—
76C4⋊C4—1581no—
77C22⋊C4—3161no—
78C16—41no—
79C23D63211yescharacteristic
80Q8—3161no—
81Q8—3161no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—3162no—
85C2×C4—3161no—
86C2×C4—3161no—
87C2×C4—6321no—
88C2×C4—6321no—
89C2×C4(C2×D79)⋊C411yescharacteristic
90C2×C4#1192961311yescharacteristic
91C8—21no—
92C8—21no—
93C22—21no—
94C22—21no—
95C22#1457908311yescharacteristic
96C22#1457910611yescharacteristic
97C22Dic63211yescharacteristic
98C4—21no—
99C4—6322no—
100C4—6321no—
101C4—6321no—
102C4#1457907511yescharacteristic
103C4#1457908711yescharacteristic
104C2—21no—
105C2—21no—
106C2#1909829811yescharacteristic
107C2#1909836811yescharacteristic
108C2#1909837411yescharacteristic
subgroupG/H
centerC22#14579083
commutatorC2×C8×C79C2×C4
FrattiniC22×C8C2×D79
FittingC22⋊C16×C79C2
socleC22×C79#102
prime radicalC23×C79D8
cosocleC22×C8×C79C22
hypercenterC22⋊C16D79
hypocenterC79#1348
LCSG ▷ C2×C8×C79 ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
4. C2×Dic316C4semidirect
7. #14579095C4semidirect
55. C79#1348semidirect