Finite Group Databasebeta

← #19212028

Subgroups — #19212028

Order 5888.

196 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 27 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#15671564C211yesmaximal, characteristic, complemented
2#15671438C211yesmaximal, characteristic, complemented
3C23×#1629C211yesmaximal, characteristic
4#13092238—21no—
5#13092216—21no—
6D42×C23C411yescharacteristic
7C23×#492C2211yescharacteristic
8C23×#476—21no—
9C23×#331C411yescharacteristic
10C23×D4⋊C8—21no—
11C22×D4×C23—41no—
12C2×SD16×C23—41no—
13C23×C4⋊Q8D411yescharacteristic
14C23×#127C2×C411yescharacteristic
15C23×#121—41no—
16C23×#120—41no—
17C4×D4×C23—21no—
18C23×#106—41no—
19C23×C4⋊C8—21no—
20C23×#102—41no—
21C4×C8×C23D411yescharacteristic
22#10625018—41no—
23#10624994—41no—
24C24×C23—41no—
25C2×Q8×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23—41no—
29C2×D4×C23—42no—
30C2×D4×C23—82no—
31C2×D4×C23—82no—
32C22×C4×C23—41no—
33SD16×C23—81no—
34SD16×C23—81no—
35C2×C8×C23—21no—
36C2×C8×C23—41no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—41no—
39C22⋊C4×C23—41no—
40C22⋊C4×C23—41no—
41C42×C23C22⋊C411yescharacteristic
42#67267—81no—
43C23⋊C16—81no—
44#7517—231nomaximal, Sylow
45C23×C23—41no—
46C23×C23—41no—
47C23×C23—84no—
48C23×C23—161no—
49Q8×C23—81no—
50D4×C23—22no—
51D4×C23—41no—
52D4×C23—81no—
53D4×C23—81no—
54D4×C23—81no—
55D4×C23—84no—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—81no—
60C2×C4×C23—81no—
61C2×C4×C23#9911yescharacteristic
62C8×C23—21no—
63C8×C23—21no—
64C8×C23—81no—
65C23⋊C8—161no—
66#1629D2311yescharacteristic
67#1410—231no—
68#1359—231no—
69C22×C23—42no—
70C22×C23—81no—
71C22×C23—82no—
72C22×C23—81no—
73C22×C23—81no—
74C22×C23—162no—
75C22×C23—162no—
76C22×C23AΣL(1,𝔽16)11yescharacteristic
77C4×C23—21no—
78C4×C23—21no—
79C4×C23—21no—
80C4×C23—81no—
81C4×C23—81no—
82D42Dic2311yescharacteristic
83#492C2×D2311yescharacteristic
84#476—21no—
85#364—461no—
86#356—461no—
87#331Dic2311yescharacteristic
88D4⋊C8—21no—
89C2×C23—21no—
90C2×C23—82no—
91C2×C23—161no—
92C2×C23#140211yescharacteristic
93C22×D4—41no—
94C2×SD16—41no—
95C4⋊Q8C22⋊D2311yescharacteristic
96#127C2×Dic2311yescharacteristic
97#121—41no—
98#120—41no—
99C4×D4—21no—
100M32—921no—
101#106—41no—
102C4⋊C8—21no—
103#102—41no—
104#101—921no—
105C4×C8C22⋊D2311yescharacteristic
106C23#751711yescharacteristic, complemented, Sylow
107C24—41no—
108C2×Q8—21no—
109C2×D4—21no—
110C2×D4—21no—
111C2×D4—41no—
112C2×D4—42no—
113C2×D4—82no—
114C2×D4—82no—
115C22×C4—41no—
116SD16—81no—
117SD16—81no—
118M16—1841no—
119C2×C8—21no—
120C2×C8—41no—
121C4⋊C4—21no—
122C4⋊C4—41no—
123C22⋊C4—41no—
124C22⋊C4—41no—
125C42C22⋊Dic2311yescharacteristic
126C16—1841no—
127C23—41no—
128C23—41no—
129C23—84no—
130C23—161no—
131Q8—81no—
132D4—22no—
133D4—41no—
134D4—81no—
135D4—81no—
136D4—81no—
137D4—84no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—81no—
142C2×C4—81no—
143C2×C4#1062501611yescharacteristic
144C8—21no—
145C8—21no—
146C8—81no—
147C8—3681no—
148C22—42no—
149C22—81no—
150C22—82no—
151C22—81no—
152C22—81no—
153C22—162no—
154C22—162no—
155C22#1309220411yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—81no—
160C4—81no—
161C2—21no—
162C2—82no—
163C2—161no—
164C2#1567154211yescharacteristic
subgroupG/H
centerC2#15671542
commutatorC23×#127C2×C4
Frattini#492C2×D23
FittingC23×#1629C2
socleC2×C23#1402
hypercenter#1629D23
hypocenterC23#7517
LCSG ▷ C23×#127 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1629

Complements

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

NH ≅ G/Ntype
1. #15671564C2semidirect
2. #15671438C2semidirect
106. C23#7517semidirect