Finite Group Databasebeta

← #19212036

Subgroups — #19212036

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#15672473C211yesmaximal, characteristic
2#15671438C211yesmaximal, characteristic
3C23×#1409C211yesmaximal, characteristic
4#13093147C411yescharacteristic, complemented
5#13092614—21no—
6#13092238—21no—
7#13092166C411yescharacteristic, complemented
8#13092149—21no—
9C23×#492C2211yescharacteristic
10C23×#353—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8C2×C411yescharacteristic
13C23×#127D411yescharacteristic
14#10625115—41no—
15C2×#67273—41no—
16#10625059—41no—
17#10625058—41no—
18C4×Dic46—21no—
19C23×#99—41no—
20C4×C8×C23D411yescharacteristic
21#10625014—41no—
22#10624994—41no—
23C4⋊(C23⋊C8)—21no—
24C2×Q8×C23—21no—
25C2×D4×C23—21no—
26C2×D4×C23—41no—
27C2×Dic46—21no—
28C2×Dic46—41no—
29SD16×C23—81no—
30SD16×C23—81no—
31C2×C8×C23—21no—
32C4⋊C4×C23—41no—
33C22⋊C4×C23—81no—
34C42×C23C22⋊C411yescharacteristic
35#67273—82no—
36C4⋊Dic23—21no—
37Dic23⋊C4—42no—
38Dic23⋊C4—41no—
39C4×Dic23—41no—
40C4×Dic23—41no—
41C2×C23⋊C8—41no—
42C23⋊C16—81no—
43#7520—231nomaximal, Sylow
44C23×C23—41no—
45Q8×C23—81no—
46D4×C23—81no—
47D4×C23—81no—
48D4×C23—81no—
49C2×C4×C23—21no—
50C2×C4×C23—41no—
51C2×C4×C23—161no—
52C2×C4×C23#9911yescharacteristic
53C2×Dic23—41no—
54C2×Dic23—41no—
55Dic46—22no—
56Dic46—41no—
57Dic46—161no—
58C8×C23—21no—
59C8×C23—21no—
60C23⋊C8—81no—
61#1623—231no—
62#1409D2311yescharacteristic
63#1359—231no—
64C22×C23—81no—
65C22×C23—161no—
66C22×C23AΣL(1,𝔽16)11yescharacteristic
67C4×C23—21no—
68C4×C23—21no—
69C4×C23—21no—
70C4×C23—81no—
71C4×C23—321no—
72Dic23—42no—
73Dic23—81no—
74Q82—231no—
75#492C2×D2311yescharacteristic
76#460—461no—
77#364—461no—
78#353—21no—
79#333—231no—
80Q8⋊C8—461no—
81C2×C23—21no—
82C2×C23—161no—
83C2×C23#140211yescharacteristic
84C2×SD16—41no—
85C2×SD16—921no—
86C4⋊Q8—921no—
87C4⋊Q8—921no—
88C4⋊Q8C4×D2311yescharacteristic
89#127C22⋊D2311yescharacteristic
90C4×Q8—461no—
91C4×Q8—921no—
92M32—921no—
93C4⋊C8—461no—
94#102—921no—
95#99—41no—
96C4×C8D9211yescharacteristic
97C23#752011yescharacteristic, complemented, Sylow
98C2×Q8—21no—
99C2×Q8—461no—
100C2×Q8—921no—
101C2×D4—21no—
102C2×D4—41no—
103SD16—81no—
104SD16—81no—
105SD16—1842no—
106C2×C8—21no—
107C2×C8—921no—
108C4⋊C4—41no—
109C4⋊C4—461no—
110C4⋊C4—922no—
111C4⋊C4—921no—
112C22⋊C4—81no—
113C42—921no—
114C42—921no—
115C42(C2×D23)⋊C411yescharacteristic
116C16—1841no—
117C23—41no—
118Q8—81no—
119Q8—462no—
120Q8—921no—
121Q8—3681no—
122D4—81no—
123D4—81no—
124D4—81no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—161no—
128C2×C4—921no—
129C2×C4—921no—
130C2×C4#1062498811yescharacteristic
131C8—21no—
132C8—21no—
133C8—1841no—
134C22—81no—
135C22—161no—
136C22#1309220311yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—81no—
141C4—321no—
142C4—922no—
143C4—1841no—
144C2—21no—
145C2—161no—
146C2#1567154111yescharacteristic
subgroupG/H
centerC2#15671541
commutatorC23×C4⋊Q8C2×C4
Frattini#492C2×D23
FittingC23×#1409C2
socleC2×C23#1402
hypercenter#1409D23
hypocenterC23#7520
LCSG ▷ C23×C4⋊Q8 ▷ 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. #13093147C4semidirect
7. #13092166C4semidirect
97. C23#7520semidirect