Finite Group Databasebeta

← #19212076

Subgroups — #19212076

Order 5888.

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

normal subgroups only

This group has 128 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#15673028C211yesmaximal, characteristic
2#15671566C211yesmaximal, characteristic
3C23×#1411C211yesmaximal, characteristic
4#13092815C411yescharacteristic
5#13092813—21no—
6#13092769—21no—
7#13092216—21no—
8#13092138C411yescharacteristic
9C23×#494C2211yescharacteristic
10C23×#356—21no—
11C2×Q16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×C4⋊Q8D411yescharacteristic
14#10625040—21no—
15C23×#101—41no—
16C4×C8×C23C2×C411yescharacteristic
17#10625018—41no—
18#10624999—41no—
19#10624992—42no—
20#10624990—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×Q8×C23—21no—
24C2×Dic46—41no—
25Q16×C23—82no—
26M16×C23—81no—
27C2×C8×C23—21no—
28C4⋊C4×C23—41no—
29C4⋊C4×C23—41no—
30C42×C23C22⋊C411yescharacteristic
31C4⋊Dic23—41no—
32C4⋊Dic23—41no—
33#67267—81no—
34C2×C23⋊C8—22no—
35#7534—231nomaximal, Sylow
36Q8×C23—81no—
37Q8×C23—81no—
38C2×C4×C23—21no—
39C2×C4×C23—41no—
40C2×C4×C23—41no—
41C2×C4×C23#9911yescharacteristic
42C2×Dic23—81no—
43Dic46—82no—
44C8×C23—22no—
45C8×C23—161no—
46C23⋊C8—42no—
47C23⋊C8—161no—
48#1716—231no—
49#1411—231no—
50#1411D2311yescharacteristic
51C22×C23#35311yescharacteristic
52C4×C23—22no—
53C4×C23—21no—
54C4×C23—81no—
55C4×C23—81no—
56Dic23—161no—
57#498—231no—
58#498—461no—
59#494C2×D2311yescharacteristic
60#487—461no—
61#356—21no—
62#356—461no—
63#322—231no—
64C2×C23—21no—
65C2×C23#140911yescharacteristic
66C2×Q16—41no—
67C4⋊Q8—461no—
68C4⋊Q8D9211yescharacteristic
69C4⋊Q8C22⋊D2311yescharacteristic
70#106—922no—
71#106—921no—
72#103—922no—
73#101—41no—
74#101—921no—
75C4×C8—461no—
76C4×C8C4×D2311yescharacteristic
77C23#753411yescharacteristic, complemented, Sylow
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—921no—
81Q16—82no—
82M16—81no—
83M16—1841no—
84C2×C8—21no—
85C2×C8—462no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—921no—
89C4⋊C4—921no—
90C42(C2×D23)⋊C411yescharacteristic
91Q8—81no—
92Q8—81no—
93Q8—1842no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—1841no—
98C2×C4#1062498811yescharacteristic
99C8—22no—
100C8—161no—
101C8—922no—
102C8—3681no—
103C22#1309220911yescharacteristic
104C4—22no—
105C4—21no—
106C4—81no—
107C4—81no—
108C4—3681no—
109C2—21no—
110C2#1567156111yescharacteristic
subgroupG/H
centerC2#15671561
commutatorC4×C8×C23C2×C4
Frattini#494C2×D23
FittingC23×#1411C2
socleC2×C23#1409
hypercenter#1411D23
hypocenterC23#7534
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
77. C23#7534semidirect