Finite Group Databasebeta

← #19212077

Subgroups — #19212077

Order 5888.

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

normal subgroups only

This group has 150 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#15672983C211yesmaximal, characteristic
2#15671564C211yesmaximal, characteristic
3C23×#1409C211yesmaximal, characteristic
4#13092815C411yescharacteristic, complemented
5#13092813—21no—
6#13092789—21no—
7#13092216—21no—
8C8×C23⋊C8C411yescharacteristic, complemented
9C23×#492C2211yescharacteristic
10C23×#353—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×#127D411yescharacteristic
14C2×#67273—42no—
15#10625040—21no—
16C23×#99—41no—
17C4×C8×C23C2×C411yescharacteristic
18#10625018—41no—
19#10624999—41no—
20#10624990—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×D4×C23—21no—
24C2×D4×C23—41no—
25C2×Dic46—41no—
26SD16×C23—82no—
27C2×C8×C23—21no—
28C4⋊C4×C23—41no—
29C22⋊C4×C23—81no—
30C42×C23C22⋊C411yescharacteristic
31#67273—84no—
32C4⋊Dic23—41no—
33C4⋊Dic23—41no—
34#67267—81no—
35C2×C23⋊C8—22no—
36#7535—231nomaximal, Sylow
37C23×C23—41no—
38Q8×C23—81no—
39D4×C23—81no—
40D4×C23—82no—
41C2×C4×C23—21no—
42C2×C4×C23—41no—
43C2×C4×C23—161no—
44C2×C4×C23#9911yescharacteristic
45C2×Dic23—81no—
46Dic46—82no—
47C8×C23—22no—
48C23⋊C8—24no—
49C23⋊C8—161no—
50#1705—231no—
51#1410—231no—
52#1409D2311yescharacteristic
53C22×C23—81no—
54C22×C23—161no—
55C22×C23#35311yescharacteristic
56C4×C23—22no—
57C4×C23—21no—
58C4×C23—81no—
59C4×C23—321no—
60Dic23—161no—
61#498—231no—
62#498—461no—
63#492—461no—
64#492C2×D2311yescharacteristic
65#356—461no—
66#353—21no—
67C82—231no—
68C2×C23—21no—
69C2×C23—161no—
70C2×C23#140911yescharacteristic
71C2×SD16—41no—
72C2×SD16—922no—
73C4⋊Q8—461no—
74C4⋊Q8D9211yescharacteristic
75#127C22⋊D2311yescharacteristic
76#106—922no—
77#106—921no—
78#101—921no—
79#99—41no—
80C4×C8—461no—
81C4×C8C4×D2311yescharacteristic
82C23#753511yescharacteristic, complemented, Sylow
83C2×Q8—21no—
84C2×Q8—921no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—1844no—
89M16—1841no—
90C2×C8—21no—
91C2×C8—462no—
92C4⋊C4—41no—
93C4⋊C4—921no—
94C4⋊C4—921no—
95C22⋊C4—81no—
96C42(C2×D23)⋊C411yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—1842no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—161no—
105C2×C4—1841no—
106C2×C4#1062498811yescharacteristic
107C8—22no—
108C8—464no—
109C8—3681no—
110C22—81no—
111C22—161no—
112C22#1309220911yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—321no—
117C4—3681no—
118C2—21no—
119C2—161no—
120C2#1567156111yescharacteristic
subgroupG/H
centerC2#15671561
commutatorC4×C8×C23C2×C4
Frattini#492C2×D23
FittingC23×#1409C2
socleC2×C23#1409
hypercenter#1409D23
hypocenterC23#7535
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
4. #13092815C4semidirect
8. C8×C23⋊C8C4semidirect
82. C23#7535semidirect