Finite Group Databasebeta

← #23761362

Subgroups — #23761362

Order 10112.

110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C4×D632C211yesmaximal, characteristic
2#19098316C211yesmaximal, characteristic, complemented
3C4×C16×C79C211yesmaximal, characteristic, complemented
4C2×D632C411yescharacteristic
5C4×D316—21no—
6#14579095C411yescharacteristic
7C4⋊(C79⋊C8)—21no—
8#14579083—21no—
9C2×C16×C79—21no—
10C4×C8×C79C2211yescharacteristic
11C2×D316—21no—
12C2×C4×D79—41no—
13D632—21no—
14D632C812yescomplemented
15C2×C79⋊C8—41no—
16C4⋊Dic79—21no—
17(C2×D79)⋊C4—41no—
18C2×C8×C79C2×C411yescharacteristic
19C2×C8×C79D411yescharacteristic
20C42×C79D411yescharacteristic
21C16×C79—22no—
22C22×D79—41no—
23C2×C4×C79C22⋊C411yescharacteristic
24C2×C4×C79D811yescharacteristic
25C2×C4×C79SD1611yescharacteristic
26C2×Dic79—41no—
27D316—22no—
28D316—41no—
29C4×D79—81no—
30C4×D79—81no—
31C8×C79—21no—
32C8×C79C2×C811yescharacteristic
33C8×C79M1611yescharacteristic
34C79⋊C8—81no—
35C22×C79#10211yescharacteristic
36C2×D79—42no—
37C2×D79—81no—
38C2×D79—81no—
39C4×C79—21no—
40C4×C79C22⋊C811yescharacteristic
41C4×C79#10411yescharacteristic
42C4×C79D1611yescharacteristic
43C4×C79SD3211yescharacteristic
44Dic79—81no—
45C2×C79D4⋊C811yescharacteristic
46C2×C79#35711yescharacteristic
47C2×C79#35911yescharacteristic
48D79—82no—
49#1331—791nomaximal, Sylow
50C79#133111yescharacteristic, complemented, Sylow
51C4×D8—791no—
52C4×C16D7911yescharacteristic, complemented
53#335—791no—
54C2×D8—791no—
55C4×D4—1581no—
56C2×C16—21no—
57#107—791no—
58C4⋊C8—1581no—
59#102—1581no—
60C4×C8C2×D7911yescharacteristic
61C2×D4—1581no—
62C22×C4—3161no—
63D8—792no—
64D8—1581no—
65C2×C8—3161no—
66C2×C8C4×D7911yescharacteristic
67C2×C8C22⋊D7911yescharacteristic
68C4⋊C4—1581no—
69C22⋊C4—3161no—
70C42D31611yescharacteristic
71C16—22no—
72C23—3161no—
73D4—3161no—
74D4—1582no—
75C2×C4—3161no—
76C2×C4—6321no—
77C2×C4—6321no—
78C2×C4(C2×D79)⋊C411yescharacteristic
79C2×C4D63211yescharacteristic
80C2×C4#1192961311yescharacteristic
81C8—21no—
82C8—6321no—
83C8C8×D7911yescharacteristic
84C8#1192960711yescharacteristic
85C22—3162no—
86C22—6321no—
87C22—6321no—
88C22#1457908311yescharacteristic
89C4—21no—
90C4—6321no—
91C4(C2×D79)⋊C811yescharacteristic
92C4#1457908911yescharacteristic
93C4D126411yescharacteristic
94C4#1457910611yescharacteristic
95C2—6322no—
96C2#1909829211yescharacteristic
97C2#1909836511yescharacteristic
98C2#1909837111yescharacteristic
subgroupG/H
centerC2×C4D632
commutatorC8×C79C2×C8
FrattiniC4×C8C2×D79
FittingC4×C16×C79C2
socleC22×C79#102
prime radicalC2×D632C4
cosocleC4×C8×C79C22
hypercenterC4×C16D79
hypocenterC79#1331
LCSG ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×C16

Complements

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

NH ≅ G/Ntype
2. #19098316C2semidirect
3. C4×C16×C79C2semidirect
14. D632C8semidirect
50. C79#1331semidirect
52. C4×C16D79semidirect