Finite Group Databasebeta

← #19212054

Subgroups — #19212054

Order 5888.

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

normal subgroups only

This group has 126 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#15672723C211yesmaximal, characteristic
2#15671432C211yesmaximal, characteristic
3C23×#1413C211yesmaximal, characteristic
4C23⋊#564C411yescharacteristic
5#13092823—21no—
6#13092195—21no—
7#13092159C411yescharacteristic
8#13092158—21no—
9C23×#491C2211yescharacteristic
10C23×#356—21no—
11C23×C4⋊Q8D411yescharacteristic
12C23×#125C2×C411yescharacteristic
13#10625061—41no—
14#10625060—41no—
15#10625060—41no—
16#10625041—21no—
17C23×#103—41no—
18C23×#101—41no—
19C23×#97D411yescharacteristic
20#10624994—41no—
21#10624990—41no—
22#10624989—41no—
23#10624985—21no—
24C2×Q8×C23—21no—
25M16×C23—81no—
26C2×C8×C23—21no—
27C4⋊C4×C23—21no—
28C4⋊C4×C23—41no—
29C4⋊C4×C23—41no—
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#7526—231nomaximal, Sylow
42Q8×C23—81no—
43C2×C4×C23—21no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23#9911yescharacteristic
47C2×Dic23—41no—
48C2×Dic23—41no—
49C8×C23—41no—
50C8×C23—161no—
51C23⋊C8—42no—
52#1663—231no—
53#1413D2311yescharacteristic
54#1356—231no—
55C22×C23AΣL(1,𝔽16)11yescharacteristic
56C4×C23—21no—
57C4×C23—41no—
58C4×C23—81no—
59C4×C23—81no—
60Dic23—81no—
61Dic23—81no—
62#564—231no—
63#501—461no—
64#491C2×D2311yescharacteristic
65#356—21no—
66#347—461no—
67#330—231no—
68#330—461no—
69C2×C23—21no—
70C2×C23#140411yescharacteristic
71C4⋊Q8C22⋊D2311yescharacteristic
72#125—461no—
73#125—921no—
74#125—921no—
75#125—921no—
76#125C4×D2311yescharacteristic
77M32—921no—
78#107—921no—
79#106—921no—
80#103—41no—
81#101—41no—
82#97—461no—
83#97D9211yescharacteristic
84C23#752611yescharacteristic, complemented, Sylow
85C2×Q8—21no—
86M16—81no—
87C2×C8—21no—
88C2×C8—921no—
89C4⋊C4—21no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—461no—
93C4⋊C4—461no—
94C4⋊C4—921no—
95C4⋊C4—921no—
96C4⋊C4—921no—
97C4⋊C4—921no—
98C4⋊C4—921no—
99C42—921no—
100C42(C2×D23)⋊C411yescharacteristic
101C16—922no—
102Q8—81no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—921no—
107C2×C4—921no—
108C2×C4#1062498811yescharacteristic
109C8—41no—
110C8—161no—
111C8—922no—
112C22#1309220311yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—1841no—
118C4—1841no—
119C2—21no—
120C2#1567154711yescharacteristic
subgroupG/H
centerC2#15671547
commutatorC23×#125C2×C4
Frattini#491C2×D23
FittingC23×#1413C2
socleC2×C23#1404
hypercenter#1413D23
hypocenterC23#7526
LCSG ▷ C23×#125 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #491 ◁ #1413

Complements

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

NH ≅ G/Ntype
84. C23#7526semidirect