Finite Group Databasebeta

← #19212048

Subgroups — #19212048

Order 5888.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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#15672698C211yesmaximal, characteristic
2#15671430C211yesmaximal, characteristic
3C23×#1412C211yesmaximal, characteristic
4C23⋊#564C411yescharacteristic, complemented
5#13092781—21no—
6#13092195—21no—
7#13092159C411yescharacteristic, complemented
8#13092158—21no—
9C23×#490C2211yescharacteristic
10C23×#353—21no—
11C23×#127D411yescharacteristic
12C23×#125C2×C411yescharacteristic
13#10625061—41no—
14#10625060—41no—
15#10625060—41no—
16#10625041—21no—
17C23×#102—41no—
18C23×#99—41no—
19C23×#97D411yescharacteristic
20#10625014—41no—
21#10625014—41no—
22#10624994—41no—
23#10624985—21no—
24C2×D4×C23—21no—
25C2×D4×C23—41no—
26C2×C8×C23—21no—
27C4⋊C4×C23—21no—
28C4⋊C4×C23—41no—
29C22⋊C4×C23—81no—
30C42×C23C22⋊C411yescharacteristic
31C4⋊Dic23—21no—
32C4⋊Dic23—21no—
33C4⋊Dic23—41no—
34Dic23⋊C4—41no—
35Dic23⋊C4—41no—
36Dic23⋊C4—41no—
37Dic23⋊C4—41no—
38C4×Dic23—41no—
39C2×C23⋊C8—41no—
40C23⋊C16—42no—
41#7524—231nomaximal, Sylow
42C23×C23—41no—
43D4×C23—81no—
44D4×C23—82no—
45C2×C4×C23—21no—
46C2×C4×C23—41no—
47C2×C4×C23—161no—
48C2×C4×C23#9911yescharacteristic
49C2×Dic23—41no—
50C2×Dic23—41no—
51C8×C23—41no—
52C23⋊C8—81no—
53#1658—231no—
54#1412D2311yescharacteristic
55#1355—231no—
56C22×C23—81no—
57C22×C23—161no—
58C22×C23AΣL(1,𝔽16)11yescharacteristic
59C4×C23—21no—
60C4×C23—41no—
61C4×C23—81no—
62C4×C23—321no—
63Dic23—81no—
64Dic23—81no—
65#564—231no—
66#490—461no—
67#490C2×D2311yescharacteristic
68#353—21no—
69#347—461no—
70#330—231no—
71#330—461no—
72C2×C23—21no—
73C2×C23—161no—
74C2×C23#140411yescharacteristic
75#127C22⋊D2311yescharacteristic
76#125—461no—
77#125—921no—
78#125—921no—
79#125—921no—
80#125C4×D2311yescharacteristic
81M32—921no—
82#102—41no—
83#102—921no—
84#102—921no—
85#99—41no—
86#97—461no—
87#97D9211yescharacteristic
88C23#752411yescharacteristic, complemented, Sylow
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—921no—
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—461no—
96C4⋊C4—461no—
97C4⋊C4—921no—
98C4⋊C4—921no—
99C4⋊C4—921no—
100C4⋊C4—921no—
101C4⋊C4—921no—
102C22⋊C4—81no—
103C42—921no—
104C42(C2×D23)⋊C411yescharacteristic
105C16—922no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—161no—
112C2×C4—921no—
113C2×C4—921no—
114C2×C4#1062498811yescharacteristic
115C8—41no—
116C8—1841no—
117C22—81no—
118C22—161no—
119C22#1309220311yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—321no—
124C4—1841no—
125C4—1841no—
126C2—21no—
127C2—161no—
128C2#1567154711yescharacteristic
subgroupG/H
centerC2#15671547
commutatorC23×#125C2×C4
Frattini#490C2×D23
FittingC23×#1412C2
socleC2×C23#1404
hypercenter#1412D23
hypocenterC23#7524
LCSG ▷ C23×#125 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1412

Complements

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

NH ≅ G/Ntype
4. C23⋊#564C4semidirect
7. #13092159C4semidirect
88. C23#7524semidirect