Finite Group Databasebeta

← #19212051

Subgroups — #19212051

Order 5888.

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

normal subgroups only

This group has 138 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#15672718C211yesmaximal, characteristic
2#15671432C211yesmaximal, characteristic, complemented
3C23×#1413C211yesmaximal, characteristic, complemented
4#13093165C411yescharacteristic
5#13092779—21no—
6#13092195—21no—
7#13092159C411yescharacteristic
8#13092156—21no—
9C23×#491C2211yescharacteristic
10C23×#356—21no—
11C23×C4⋊Q8D411yescharacteristic
12C23×#125C2×C411yescharacteristic
13#10625067—41no—
14#10625066—41no—
15#10625065—41no—
16#10625046—21no—
17C23×#103—41no—
18C23×#101—41no—
19C23×#97D411yescharacteristic
20#10624994—41no—
21#10624992—41no—
22#10624991—41no—
23#10624985—21no—
24C2×Q8×C23—21no—
25C2×D92—21no—
26C2×D92—41no—
27C2×C4×D23—41no—
28C2×Dic46—21no—
29M16×C23—81no—
30C2×C8×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—41no—
33C4⋊C4×C23—41no—
34C42×C23C22⋊C411yescharacteristic
35(C2×D23)⋊C4—41no—
36(C2×D23)⋊C4—41no—
37(C2×D23)⋊C4—41no—
38Dic23⋊C4—41no—
39C2×C23⋊C8—41no—
40C23⋊C16—42no—
41#7525—231nomaximal, Sylow
42C22×D23—41no—
43Q8×C23—81no—
44C2×C4×C23—21no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23#9911yescharacteristic
48C2×Dic23—41no—
49D92—81no—
50D92—161no—
51C4×D23—161no—
52Dic46—81no—
53C8×C23—41no—
54C8×C23—161no—
55C23⋊C8—81no—
56#1662—231no—
57#1413D2311yescharacteristic, complemented
58#1356—231no—
59C22×C23AΣL(1,𝔽16)11yescharacteristic
60C2×D23—81no—
61C2×D23—81no—
62C2×D23—81no—
63C4×C23—21no—
64C4×C23—41no—
65C4×C23—81no—
66C4×C23—81no—
67Dic23—81no—
68#562—231no—
69#491C2×D2311yescharacteristic
70#489—461no—
71#356—21no—
72#347—461no—
73#330—231no—
74#329—461no—
75C2×C23—21no—
76C2×C23#140411yescharacteristic
77D23—161no—
78C4⋊Q8C22⋊D2311yescharacteristic
79#125C4×D2311yescharacteristic
80#124—461no—
81#123—921no—
82C22⋊Q8—921no—
83#121—921no—
84M32—921no—
85#103—41no—
86#103—921no—
87#102—921no—
88#101—41no—
89#97—461no—
90#97D9211yescharacteristic
91C23#752511yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—461no—
94C2×D4—461no—
95C2×D4—921no—
96C22×C4—921no—
97M16—81no—
98C2×C8—21no—
99C2×C8—921no—
100C4⋊C4—21no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—921no—
104C22⋊C4—921no—
105C22⋊C4—921no—
106C22⋊C4—921no—
107C42(C2×D23)⋊C411yescharacteristic
108C16—922no—
109C23—921no—
110Q8—81no—
111Q8—1841no—
112D4—3681no—
113D4—1841no—
114C2×C4—21no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—921no—
118C2×C4—3681no—
119C2×C4#1062498811yescharacteristic
120C8—41no—
121C8—161no—
122C8—1841no—
123C22—1841no—
124C22—1841no—
125C22—1841no—
126C22#1309220311yescharacteristic
127C4—21no—
128C4—41no—
129C4—81no—
130C4—81no—
131C4—1841no—
132C2—21no—
133C2—3681no—
134C2#1567154711yescharacteristic
subgroupG/H
centerC2#15671547
commutatorC23×#125C2×C4
Frattini#491C2×D23
FittingC23×#1413C2
socleC2×C23#1404
hypercenter#1413D23
hypocenterC23#7525
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
2. #15671432C2semidirect
3. C23×#1413C2semidirect
57. #1413D23semidirect
91. C23#7525semidirect