Finite Group Databasebeta

← #19212052

Subgroups — #19212052

Order 5888.

138 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 27 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#15671570C211yesmaximal, characteristic, complemented
2#15671432C211yesmaximal, characteristic, complemented
3C23×#1662C211yesmaximal, characteristic
4#13092216—21no—
5#13092195—21no—
6C23×#562C411yescharacteristic
7C23×#491C2211yescharacteristic
8C23×#489—21no—
9C23×#330C411yescharacteristic
10C23×#329—21no—
11C23×C4⋊Q8D411yescharacteristic
12C23×#125C2×C411yescharacteristic
13C23×#124—21no—
14C23×#123—41no—
15C23×C22⋊Q8—41no—
16C23×#121—41no—
17C23×#103—41no—
18C23×#103—41no—
19C23×#102—41no—
20C23×#97—21no—
21C23×#97D411yescharacteristic
22#10625018—41no—
23#10624994—41no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—41no—
28C22×C4×C23—41no—
29C2×C8×C23—21no—
30C2×C8×C23—41no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—41no—
33C4⋊C4×C23—41no—
34C4⋊C4×C23—41no—
35C22⋊C4×C23—41no—
36C22⋊C4×C23—41no—
37C22⋊C4×C23—41no—
38C42×C23C22⋊C411yescharacteristic
39#67267—81no—
40C23⋊C16—42no—
41#7525—231nomaximal, Sylow
42C23×C23—41no—
43Q8×C23—81no—
44Q8×C23—81no—
45D4×C23—81no—
46D4×C23—161no—
47C2×C4×C23—21no—
48C2×C4×C23—41no—
49C2×C4×C23—41no—
50C2×C4×C23—41no—
51C2×C4×C23—161no—
52C2×C4×C23#9911yescharacteristic
53C8×C23—41no—
54C8×C23—81no—
55C23⋊C8—161no—
56#1662D2311yescharacteristic
57#1413—231no—
58#1356—231no—
59C22×C23—81no—
60C22×C23—81no—
61C22×C23—81no—
62C22×C23AΣL(1,𝔽16)11yescharacteristic
63C4×C23—21no—
64C4×C23—41no—
65C4×C23—81no—
66C4×C23—81no—
67C4×C23—81no—
68#562Dic2311yescharacteristic
69#491C2×D2311yescharacteristic
70#489—21no—
71#356—461no—
72#347—461no—
73#330Dic2311yescharacteristic
74#329—21no—
75C2×C23—21no—
76C2×C23—161no—
77C2×C23#140411yescharacteristic
78C4⋊Q8C22⋊D2311yescharacteristic
79#125C2×Dic2311yescharacteristic
80#124—21no—
81#123—41no—
82C22⋊Q8—41no—
83#121—41no—
84M32—921no—
85#103—41no—
86#103—41no—
87#102—41no—
88#101—921no—
89#97—21no—
90#97C22⋊D2311yescharacteristic
91C23#752511yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—21no—
94C2×D4—21no—
95C2×D4—41no—
96C22×C4—41no—
97M16—1841no—
98C2×C8—21no—
99C2×C8—41no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—41no—
106C22⋊C4—41no—
107C42C22⋊Dic2311yescharacteristic
108C16—922no—
109C23—41no—
110Q8—81no—
111Q8—81no—
112D4—81no—
113D4—161no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—161no—
119C2×C4#1062501611yescharacteristic
120C8—41no—
121C8—81no—
122C8—3681no—
123C22—81no—
124C22—81no—
125C22—81no—
126C22#1309220411yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—81no—
132C2—21no—
133C2—161no—
134C2#1567154811yescharacteristic
subgroupG/H
centerC2#15671548
commutatorC23×#125C2×C4
Frattini#491C2×D23
FittingC23×#1662C2
socleC2×C23#1404
hypercenter#1662D23
hypocenterC23#7525
LCSG ▷ C23×#125 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1662

Complements

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

NH ≅ G/Ntype
1. #15671570C2semidirect
2. #15671432C2semidirect
91. C23#7525semidirect