Finite Group Databasebeta

← #19212073

Subgroups — #19212073

Order 5888.

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

normal subgroups only

This group has 156 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#15673023C211yesmaximal, characteristic
2#15671560C211yesmaximal, characteristic
3C23×#1408C211yesmaximal, characteristic
4#13092815C411yescharacteristic, complemented
5#13092789—21no—
6#13092763—21no—
7#13092210—21no—
8#13092138C411yescharacteristic, complemented
9C23×#493C2211yescharacteristic
10C23×#353—21no—
11C2×D8×C23—41no—
12C23×#127D411yescharacteristic
13C23×#127D411yescharacteristic
14C2×#67273—42no—
15#10625040—21no—
16C23×#99—41no—
17C4×C8×C23C2×C411yescharacteristic
18#10625016—41no—
19#10625014—42no—
20#10624999—41no—
21C4×C23⋊C8—21no—
22C2×D4×C23—21no—
23C2×D4×C23—21no—
24C2×D4×C23—41no—
25C2×D4×C23—41no—
26C2×Dic46—41no—
27D8×C23—82no—
28C2×C8×C23—21no—
29C22⋊C4×C23—81no—
30C42×C23C22⋊C411yescharacteristic
31C22⋊Dic23—81no—
32#67273—84no—
33C4⋊Dic23—41no—
34C4⋊Dic23—41no—
35C2×C23⋊C8—22no—
36#7533—231nomaximal, Sylow
37C23×C23—41no—
38C23×C23—41no—
39D4×C23—81no—
40D4×C23—81no—
41D4×C23—82no—
42D4×C23—82no—
43C2×C4×C23—21no—
44C2×C4×C23—161no—
45C2×C4×C23#9911yescharacteristic
46C2×Dic23—81no—
47C2×Dic23—161no—
48Dic46—82no—
49C8×C23—22no—
50C23⋊C8—42no—
51#1715—231no—
52#1408—231no—
53#1408D2311yescharacteristic
54C22×C23—81no—
55C22×C23—81no—
56C22×C23—161no—
57C22×C23—161no—
58C22×C23#35311yescharacteristic
59C4×C23—22no—
60C4×C23—21no—
61C4×C23—321no—
62Dic23—161no—
63Dic23—321no—
64#498—231no—
65#493C2×D2311yescharacteristic
66#492—461no—
67#486—461no—
68#353—21no—
69#353—461no—
70#322—231no—
71C2×C23—21no—
72C2×C23—161no—
73C2×C23—161no—
74C2×C23#140911yescharacteristic
75C2×SD16—922no—
76C2×D8—41no—
77C4⋊Q8—461no—
78#127D9211yescharacteristic
79#127C22⋊D2311yescharacteristic
80#106—921no—
81#102—922no—
82#99—41no—
83#99—921no—
84C4×C8—461no—
85C4×C8C4×D2311yescharacteristic
86C23#753311yescharacteristic, complemented, Sylow
87C2×Q8—921no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—1844no—
93D8—82no—
94C2×C8—21no—
95C2×C8—462no—
96C4⋊C4—921no—
97C4⋊C4—921no—
98C22⋊C4—81no—
99C22⋊C4—1841no—
100C42(C2×D23)⋊C411yescharacteristic
101C23—41no—
102C23—41no—
103Q8—1842no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—3681no—
111C2×C4—1841no—
112C2×C4#1062498811yescharacteristic
113C8—22no—
114C8—922no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1309220911yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—3681no—
124C4—7361no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#1567156111yescharacteristic
subgroupG/H
centerC2#15671561
commutatorC4×C8×C23C2×C4
Frattini#493C2×D23
FittingC23×#1408C2
socleC2×C23#1409
hypercenter#1408D23
hypocenterC23#7533
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #13092815C4semidirect
8. #13092138C4semidirect
86. C23#7533semidirect