Finite Group Databasebeta

← #23765561

Subgroups — #23765561

Order 10112.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic316C211yesmaximal, characteristic
2#19098390C211yesmaximal, characteristic
3#19098388C211yesmaximal, characteristic
4C4⋊(C79⋊C16)C211yesmaximal, characteristic
5#19098366C211yesmaximal, characteristic
6#19098366C211yesmaximal, characteristic
7#499×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9C4×Dic158—21no—
10C2×C79⋊C16C2211yescharacteristic
11C2×C79⋊C16C2211yescharacteristic
12#14579095C2211yescharacteristic
13#14579086—21no—
14#125×C79—21no—
15#107×C79C2211yescharacteristic
16#107×C79C2211yescharacteristic
17#106×C79—21no—
18C4×C8×C79C2211yescharacteristic
19C2×Dic158—21no—
20Dic316—21no—
21Dic316Q812yes—
22C4⋊Dic79—21no—
23Dic79⋊C4—41no—
24C4×Dic79—41no—
25C79⋊C16—21no—
26C79⋊C16—21no—
27C2×C8×C79D411yescharacteristic
28C2×C8×C79C2311yescharacteristic
29C4⋊C4×C79—21no—
30C4⋊C4×C79—21no—
31C4⋊C4×C79—41no—
32C4⋊C4×C79—41no—
33C42×C79D411yescharacteristic
34C2×C4×C79—41no—
35C2×C4×C79—41no—
36C2×C4×C79D811yescharacteristic
37C2×C4×C79D811yescharacteristic
38C2×C4×C79C2×D411yescharacteristic
39C2×Dic79—41no—
40C2×Dic79—41no—
41Dic158—22no—
42Dic158—41no—
43C8×C79—21no—
44C8×C79C2×Q811yescharacteristic
45C8×C79#4111yescharacteristic
46C22×C79C2×D811yescharacteristic
47C4×C79—21no—
48C4×C79—21no—
49C4×C79—81no—
50C4×C79—81no—
51C4×C79C22⋊Q811yescharacteristic
52C4×C79#13711yescharacteristic
53Dic79—42no—
54Dic79—81no—
55C2×C79#47411yescharacteristic
56C2×C79#50811yescharacteristic
57C2×C79#51011yescharacteristic
58#2229—791nomaximal, Sylow
59C79#222911yescharacteristic, complemented, Sylow
60#499D7911yescharacteristic
61C4×Q16—791no—
62#367—791no—
63#366—791no—
64C4⋊C16—791no—
65#358—791no—
66#358—791no—
67C2×Q16—791no—
68#125—21no—
69C4×Q8—1581no—
70C2×C16—791no—
71C2×C16—791no—
72#107—791no—
73#107C2×D7911yescharacteristic
74#107C2×D7911yescharacteristic
75#106—21no—
76#103—1581no—
77C4×C8C2×D7911yescharacteristic
78C2×Q8—1581no—
79Q16—792no—
80Q16—1581no—
81C2×C8C22⋊D7911yescharacteristic
82C2×C8C22×D7911yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—3161no—
88C4⋊C4—1581no—
89C42—3161no—
90C42C22⋊D7911yescharacteristic
91C16—1581no—
92C16—1581no—
93Q8—3161no—
94Q8—1582no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—3161no—
98C2×C4—3161no—
99C2×C4#1192960911yescharacteristic
100C2×C4#1192960911yescharacteristic
101C2×C4C2×C22⋊D7911yescharacteristic
102C8—21no—
103C8Q8×D7911yescharacteristic
104C8#1192962511yescharacteristic
105C22C2×#1192960911yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—3162no—
111C4—6321no—
112C4#1457913711yescharacteristic
113C4#1457919211yescharacteristic
114C2#1909884011yescharacteristic
115C2#1909899311yescharacteristic
116C2#1909900311yescharacteristic
subgroupG/H
centerC22C2×#11929609
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#499×C79C2
socle, prime radicalC22×C79C2×D8
hypercenter#499D79
hypocenterC79#2229
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
59. C79#2229semidirect