Finite Group Databasebeta

← #19212032

Subgroups — #19212032

Order 5888.

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

normal subgroups only

This group has 148 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#15672516C211yesmaximal, characteristic
2#15671564C211yesmaximal, characteristic
3C23×#1359C211yesmaximal, characteristic
4#13093153C411yescharacteristic
5#13092709—21no—
6#13092216—21no—
7#13092161C411yescharacteristic
8#13092149—21no—
9C23×#492C2211yescharacteristic
10C23×#364—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×#127C2×C411yescharacteristic
14#10625107—41no—
15#10625106—41no—
16D4×Dic23—41no—
17C4×Dic46—21no—
18C23×M32—41no—
19C4×C8×C23D411yescharacteristic
20#10625018—41no—
21#10624992—41no—
22#10624989—41no—
23C4⋊(C23⋊C8)—21no—
24C2×Q8×C23—21no—
25C2×D4×C23—21no—
26C2×D4×C23—41no—
27C22×Dic23—41no—
28C2×Dic46—21no—
29SD16×C23—81no—
30SD16×C23—81no—
31C2×C8×C23—21no—
32C4⋊C4×C23—41no—
33C42×C23C22⋊C411yescharacteristic
34C22⋊Dic23—42no—
35C22⋊Dic23—41no—
36C4⋊Dic23—21no—
37Dic23⋊C4—41no—
38C4×Dic23—41no—
39#67267—81no—
40C2×C23⋊C8—41no—
41C16×C23—81no—
42#7518—231nomaximal, Sylow
43C23×C23—41no—
44Q8×C23—81no—
45D4×C23—81no—
46D4×C23—81no—
47D4×C23—81no—
48C2×C4×C23—21no—
49C2×C4×C23—41no—
50C2×C4×C23#9911yescharacteristic
51C2×Dic23—41no—
52C2×Dic23—41no—
53C2×Dic23—161no—
54Dic46—41no—
55Dic46—41no—
56C8×C23—21no—
57C8×C23—21no—
58C23⋊C8—81no—
59C23⋊C8—161no—
60#1630—231no—
61#1410—231no—
62#1359D2311yescharacteristic
63C22×C23—82no—
64C22×C23—81no—
65C22×C23AΣL(1,𝔽16)11yescharacteristic
66C4×C23—21no—
67C4×C23—21no—
68C4×C23—21no—
69C4×C23—81no—
70Dic23—81no—
71Dic23—81no—
72#559—231no—
73#492C2×D2311yescharacteristic
74#477—461no—
75#364—21no—
76#356—461no—
77#331—231no—
78Q8⋊C8—461no—
79C2×C23—21no—
80C2×C23—161no—
81C2×C23#140211yescharacteristic
82C2×SD16—41no—
83C4⋊Q8D9211yescharacteristic
84#127C4×D2311yescharacteristic
85#124—921no—
86#123—921no—
87C4×Q8—461no—
88C4×D4—921no—
89M32—41no—
90#107—921no—
91C4⋊C8—461no—
92#103—921no—
93#101—921no—
94C4×C8C22⋊D2311yescharacteristic
95C23#751811yescharacteristic, complemented, Sylow
96C2×Q8—21no—
97C2×Q8—461no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—921no—
101SD16—81no—
102SD16—81no—
103M16—1841no—
104C2×C8—21no—
105C2×C8—921no—
106C4⋊C4—41no—
107C4⋊C4—461no—
108C4⋊C4—921no—
109C22⋊C4—922no—
110C22⋊C4—921no—
111C42—921no—
112C42(C2×D23)⋊C411yescharacteristic
113C16—81no—
114C23—41no—
115Q8—81no—
116Q8—921no—
117Q8—921no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—921no—
124C2×C4—921no—
125C2×C4—3681no—
126C2×C4#1062498811yescharacteristic
127C8—21no—
128C8—21no—
129C8—3681no—
130C8—1841no—
131C22—82no—
132C22—81no—
133C22#1309220511yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—1841no—
139C4—1841no—
140C2—21no—
141C2—161no—
142C2#1567154311yescharacteristic
subgroupG/H
centerC2#15671543
commutatorC23×#127C2×C4
Frattini#492C2×D23
FittingC23×#1359C2
socleC2×C23#1402
hypercenter#1359D23
hypocenterC23#7518
LCSG ▷ C23×#127 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

Complements

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

NH ≅ G/Ntype
95. C23#7518semidirect