Finite Group Databasebeta

← #23765563

Subgroups — #23765563

Order 10112.

124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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#19098964C211yesmaximal, characteristic
2#19098657C211yesmaximal, characteristic
3#19098390C211yesmaximal, characteristic
4Dic79⋊C16C211yesmaximal, characteristic
5#19098368C211yesmaximal, characteristic
6#19098366C211yesmaximal, characteristic
7#366×C79C211yesmaximal, characteristic
8C2×Dic316C2211yescharacteristic
9#14579152—21no—
10#14579126—21no—
11C2×C79⋊C16C2211yescharacteristic
12#14579095C2211yescharacteristic
13#14579092—21no—
14#14579084—21no—
15C8×Dic79C2211yescharacteristic
16C2×C16×C79C2211yescharacteristic
17#107×C79C2211yescharacteristic
18#107×C79C2211yescharacteristic
19C2×Dic158—21no—
20Dic316—21no—
21Dic316Q812yes—
22C2×C79⋊C8D411yescharacteristic
23C4⋊Dic79—21no—
24C4⋊Dic79—41no—
25Dic79⋊C4—41no—
26Dic79⋊C4—41no—
27C4×Dic79—41no—
28C4×Dic79D411yescharacteristic
29C79⋊C16—21no—
30C2×C8×C79C2311yescharacteristic
31C4⋊C4×C79—21no—
32C4⋊C4×C79—21no—
33C16×C79—21no—
34C2×C4×C79—41no—
35C2×C4×C79—41no—
36C2×C4×C79C2×D411yescharacteristic
37C2×Dic79—41no—
38C2×Dic79—41no—
39C2×Dic79D811yescharacteristic
40C2×Dic79D811yescharacteristic
41Dic158—22no—
42Dic158—41no—
43C8×C79C2×Q811yescharacteristic
44C8×C79#4111yescharacteristic
45C79⋊C8—21no—
46C22×C79C2×D811yescharacteristic
47C4×C79—81no—
48C4×C79—81no—
49C4×C79C22⋊Q811yescharacteristic
50C4×C79#13711yescharacteristic
51Dic79—21no—
52Dic79—21no—
53Dic79—42no—
54Dic79—81no—
55C2×C79#47411yescharacteristic
56C2×C79#50811yescharacteristic
57C2×C79#51011yescharacteristic
58#2229—791nomaximal, Sylow
59C79#222911yescharacteristic, complemented, Sylow
60#499—791no—
61C4×Q16—791no—
62#367—791no—
63#366D7911yescharacteristic
64C4⋊C16—791no—
65#358—791no—
66#358—791no—
67C2×Q16—791no—
68#125—1581no—
69C4×Q8—1581no—
70C2×C16—791no—
71C2×C16C2×D7911yescharacteristic
72#107—791no—
73#107C2×D7911yescharacteristic
74#107C2×D7911yescharacteristic
75#106—1581no—
76#103—1581no—
77C4×C8—791no—
78C2×Q8—1581no—
79Q16—792no—
80Q16—1581no—
81C2×C8—791no—
82C2×C8C22×D7911yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—3161no—
86C4⋊C4—3161no—
87C4⋊C4—3161no—
88C4⋊C4—1581no—
89C42—3161no—
90C42—791no—
91C16—21no—
92C16—1581no—
93Q8—3161no—
94Q8—1582no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—3161no—
98C2×C4—3161no—
99C2×C4—791no—
100C2×C4—791no—
101C2×C4D4×D7911yescharacteristic
102C8—1581no—
103C8Q8×D7911yescharacteristic
104C8#1192962411yescharacteristic
105C22D8×D7911yescharacteristic
106C4—81no—
107C4—81no—
108C4—3162no—
109C4—6321no—
110C4—1581no—
111C4—1581no—
112C4#1457913911yescharacteristic
113C4#1457919311yescharacteristic
114C2#1909884211yescharacteristic
115C2#1909899211yescharacteristic
116C2#1909900511yescharacteristic
subgroupG/H
centerC22D8×D79
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#366×C79C2
socle, prime radicalC22×C79C2×D8
hypercenter#366D79
hypocenterC79#2229
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
59. C79#2229semidirect