Finite Group Databasebeta

← #23765603

Subgroups — #23765603

Order 10112.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 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#19098804C211yesmaximal, characteristic
2C2×#14579095C211yesmaximal, characteristic
3#19098389C212yesmaximal, complemented
4#19098368C212yesmaximal, complemented
5C22⋊C16×C79C211yesmaximal, characteristic
6C2×Dic316C2211yescharacteristic
7#14579140—21no—
8C2×C4⋊Dic79—21no—
9#14579095—21no—
10#14579095C2212yes—
11#14579095C2211yescharacteristic
12#14579086—21no—
13C22×C8×C79C2211yescharacteristic
14C2×C16×C79C2212yes—
15C2×Dic158—21no—
16C22×Dic79—41no—
17Dic316—22no—
18C4⋊Dic79—21no—
19C4⋊Dic79—22no—
20C4⋊Dic79—41no—
21Dic79⋊C4—41no—
22C22⋊Dic79—41no—
23C22×C4×C79D411yescharacteristic
24C2×C8×C79—22no—
25C2×C8×C79D411yescharacteristic
26C2×C8×C79C2311yescharacteristic
27C16×C79—22no—
28C23×C79D811yescharacteristic
29C2×C4×C79—21no—
30C2×C4×C79—21no—
31C2×C4×C79D811yescharacteristic
32C2×C4×C79C2×D411yescharacteristic
33C2×Dic79—41no—
34C2×Dic79—41no—
35C2×Dic79—42no—
36C2×Dic79—82no—
37Dic158—41no—
38Dic158—41no—
39C8×C79—21no—
40C8×C79#4112yes—
41C22×C79—21no—
42C22×C79—21no—
43C22×C79Q3212yes—
44C22×C79C2×D811yescharacteristic
45C4×C79—21no—
46C4×C79#12311yescharacteristic
47C4×C79#13711yescharacteristic
48Dic79—81no—
49Dic79—81no—
50Dic79—82no—
51C2×C79—22no—
52C2×C79#48011yescharacteristic
53C2×C79C2×Q3211yescharacteristic
54C2×C79#50911yescharacteristic
55#2236—791nomaximal, Sylow
56C79#223611yescharacteristic, complemented, Sylow
57#467—791no—
58C2×#107—791no—
59#366—792no—
60#358—792no—
61C22⋊C16D7911yescharacteristic
62C2×Q16—791no—
63C22×C8C2×D7911yescharacteristic
64C22⋊Q8—1581no—
65C2×C4⋊C4—1581no—
66C2×C16C2×D7912yes—
67#107—792no—
68#107—791no—
69#107—1581no—
70#103—1581no—
71C2×Q8—1581no—
72C22×C4—3161no—
73C22×C4D31611yescharacteristic
74Q16—1582no—
75C2×C8—22no—
76C2×C8D31611yescharacteristic
77C2×C8C22×D7911yescharacteristic
78C4⋊C4—3161no—
79C4⋊C4—3161no—
80C4⋊C4—1581no—
81C4⋊C4—1582no—
82C22⋊C4—3161no—
83C16—22no—
84C23D63211yescharacteristic
85Q8—3161no—
86Q8—3161no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—3161no—
90C2×C4—3161no—
91C2×C4—3162no—
92C2×C4—6322no—
93C2×C4D63211yescharacteristic
94C2×C4C2×D31611yescharacteristic
95C8—21no—
96C8#1192962312yes—
97C22—21no—
98C22—21no—
99C22Dic63212yes—
100C22C2×D63211yescharacteristic
101C4—21no—
102C4—6322no—
103C4—6321no—
104C4—6321no—
105C4#1457914511yescharacteristic
106C4#1457919411yescharacteristic
107C2—22no—
108C2#1909887711yescharacteristic
109C2C2×Dic63211yescharacteristic
110C2#1909900111yescharacteristic
subgroupG/H
centerC22C2×D632
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
FittingC22⋊C16×C79C2
socleC22×C79C2×D8
prime radicalC23×C79D8
hypercenterC22⋊C16D79
hypocenterC79#2236
LCSG ▷ C2×C8×C79 ▷ 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
3. #19098389C2semidirect
4. #19098368C2semidirect
56. C79#2236semidirect