Finite Group Databasebeta

← #23765600

Subgroups — #23765600

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
1C2×#14579095C211yesmaximal, characteristic
2#19098388C212yesmaximal, complemented
3#19098367C212yesmaximal, complemented
4C22⋊(C79⋊C16)C211yesmaximal, characteristic
5#467×C79C211yesmaximal, characteristic
6C2×C4⋊Dic79—21no—
7C2×C79⋊C16C2212yes—
8#14579095—21no—
9#14579095C2212yes—
10C2×Q16×C79C2211yescharacteristic
11C22×C8×C79C2211yescharacteristic
12C22⋊Q8×C79—21no—
13#107×C79C2211yescharacteristic
14#103×C79—21no—
15C22×Dic79—41no—
16C4⋊Dic79—22no—
17C4⋊Dic79—41no—
18C79⋊C16—22no—
19C2×Q8×C79—21no—
20C22×C4×C79D411yescharacteristic
21Q16×C79—22no—
22C2×C8×C79—22no—
23C2×C8×C79D411yescharacteristic
24C2×C8×C79C2311yescharacteristic
25C4⋊C4×C79—21no—
26C4⋊C4×C79—41no—
27C22⋊C4×C79—41no—
28C23×C79D811yescharacteristic
29Q8×C79—41no—
30Q8×C79—41no—
31C2×C4×C79—21no—
32C2×C4×C79—21no—
33C2×C4×C79—41no—
34C2×C4×C79—41no—
35C2×C4×C79D811yescharacteristic
36C2×C4×C79C2×D411yescharacteristic
37C2×Dic79—42no—
38C2×Dic79—82no—
39C8×C79—21no—
40C8×C79#4112yes—
41C22×C79—21no—
42C22×C79—21no—
43C22×C79Q3212yes—
44C22×C79C2×D811yescharacteristic
45C4×C79—21no—
46C4×C79—81no—
47C4×C79—81no—
48C4×C79#12311yescharacteristic
49C4×C79#13711yescharacteristic
50Dic79—82no—
51C2×C79—22no—
52C2×C79#48011yescharacteristic
53C2×C79C2×Q3211yescharacteristic
54C2×C79#50911yescharacteristic
55#2236—791nomaximal, Sylow
56C79#223611yescharacteristic, complemented, Sylow
57#467D7911yescharacteristic
58C2×#107—791no—
59#366—792no—
60#358—792no—
61C22⋊C16—791no—
62C2×Q16C2×D7911yescharacteristic
63C22×C8C2×D7911yescharacteristic
64C22⋊Q8—21no—
65C2×C4⋊C4—1581no—
66C2×C16—792no—
67#107—792no—
68#107—1581no—
69#107C2×D7911yescharacteristic
70#103—21no—
71C2×Q8—21no—
72C22×C4—3161no—
73C22×C4C22⋊D7911yescharacteristic
74Q16—22no—
75C2×C8—22no—
76C2×C8C22⋊D7911yescharacteristic
77C2×C8C22×D7911yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—41no—
80C4⋊C4—3161no—
81C4⋊C4—1582no—
82C22⋊C4—41no—
83C16—1582no—
84C23#1192960911yescharacteristic
85Q8—41no—
86Q8—41no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—3162no—
92C2×C4—6322no—
93C2×C4#1192960911yescharacteristic
94C2×C4C2×C22⋊D7911yescharacteristic
95C8—21no—
96C8#1192962312yes—
97C22—21no—
98C22—21no—
99C22#1457910712yes—
100C22C2×#1192960911yescharacteristic
101C4—21no—
102C4—81no—
103C4—81no—
104C4—6322no—
105C4#1457914211yescharacteristic
106C4#1457919111yescharacteristic
107C2—22no—
108C2#1909887411yescharacteristic
109C2C2×#1457910711yescharacteristic
110C2#1909899811yescharacteristic
subgroupG/H
centerC22C2×#11929609
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#467×C79C2
socleC22×C79C2×D8
prime radicalC23×C79D8
hypercenter#467D79
hypocenterC79#2236
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #19098388C2semidirect
3. #19098367C2semidirect
56. C79#2236semidirect