Finite Group Databasebeta

← #23765636

Subgroups — #23765636

Order 10112.

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

normal subgroups only

This group has 142 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#19098968C211yesmaximal, characteristic, complemented
2#19098367C212yesmaximal, complemented
3#19098364C212yesmaximal
4#19098339C211yesmaximal, characteristic, complemented
5#495×C79C211yesmaximal, characteristic
6#14579161—21no—
7C2×C79⋊C16C2212yes—
8#14579095—21no—
9#14579095C2212yes—
10C2×Q16×C79C2211yescharacteristic
11C2×SD16×C79—21no—
12C2×D8×C79C2211yescharacteristic
13#124×C79—21no—
14C4×C8×C79C2211yescharacteristic
15C2×Dic158—41no—
16C4⋊Dic79—22no—
17C4⋊Dic79—41no—
18C79⋊C16—22no—
19C2×Q8×C79—21no—
20C2×D4×C79—21no—
21Q16×C79—22no—
22SD16×C79—42no—
23D8×C79—22no—
24C2×C8×C79D411yescharacteristic
25C2×C8×C79C2311yescharacteristic
26C22⋊C4×C79—41no—
27C22⋊C4×C79—41no—
28C42×C79D411yescharacteristic
29C23×C79—41no—
30Q8×C79—41no—
31Q8×C79—41no—
32D4×C79—41no—
33D4×C79—41no—
34C2×C4×C79—41no—
35C2×C4×C79D811yescharacteristic
36C2×C4×C79D811yescharacteristic
37C2×C4×C79C2×D411yescharacteristic
38C2×Dic79—42no—
39Dic158—82no—
40C8×C79SD1612yes—
41C8×C79#4112yes—
42C22×C79—81no—
43C22×C79—81no—
44C22×C79—81no—
45C22×C79C2×D811yescharacteristic
46C4×C79—21no—
47C4×C79—21no—
48C4×C79—81no—
49C4×C79#12411yescharacteristic
50C4×C79C2×SD1611yescharacteristic
51Dic79—82no—
52C2×C79—161no—
53C2×C79#48611yescharacteristic
54C2×C79#50911yescharacteristic
55C2×C79#51011yescharacteristic
56#2243—791nomaximal, Sylow
57C79#224311yescharacteristic, complemented, Sylow
58#500—791no—
59#495D7911yescharacteristic
60#358—792no—
61#357—792no—
62#346—791no—
63C2×Q16C2×D7911yescharacteristic
64C2×SD16—21no—
65C2×D8C2×D7911yescharacteristic
66C4⋊Q8—1581no—
67#124—21no—
68C2×C16—792no—
69#107—792no—
70#107—1581no—
71C4×C8C2×D7911yescharacteristic
72C2×Q8—21no—
73C2×Q8—3161no—
74C2×D4—21no—
75Q16—22no—
76SD16—42no—
77D8—22no—
78C2×C8C22⋊D7911yescharacteristic
79C2×C8C22×D7911yescharacteristic
80C4⋊C4—3161no—
81C4⋊C4—1582no—
82C22⋊C4—41no—
83C22⋊C4—41no—
84C42C22⋊D7911yescharacteristic
85C16—1582no—
86C23—41no—
87Q8—41no—
88Q8—41no—
89Q8—6322no—
90D4—41no—
91D4—41no—
92C2×C4—41no—
93C2×C4—3162no—
94C2×C4#1192960911yescharacteristic
95C2×C4#1192960911yescharacteristic
96C2×C4C2×C22⋊D7911yescharacteristic
97C8#1192961212yes—
98C8#1192962312yes—
99C22—81no—
100C22—81no—
101C22—81no—
102C22C2×#1192960911yescharacteristic
103C4—21no—
104C4—21no—
105C4—81no—
106C4—6322no—
107C4#1457914811yescharacteristic
108C4C2×#1192961211yescharacteristic
109C2—161no—
110C2#1909890911yescharacteristic
111C2#1909899811yescharacteristic
112C2#1909900311yescharacteristic
subgroupG/H
centerC22C2×#11929609
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#495×C79C2
socleC22×C79C2×D8
prime radicalC2×D8×C79C22
hypercenter#495D79
hypocenterC79#2243
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #19098968C2semidirect
2. #19098367C2semidirect
4. #19098339C2semidirect
57. C79#2243semidirect