Finite Group Databasebeta

← #19212034

Subgroups — #19212034

Order 5888.

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

normal subgroups only

This group has 162 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#15671562C211yesmaximal, characteristic, complemented
2#15671438C211yesmaximal, characteristic, complemented
3C23×#1624C211yesmaximal, characteristic
4#13092238—21no—
5#13092210—21no—
6C23×#555C411yescharacteristic, complemented
7C23×#492C2211yescharacteristic
8C23×#459—21no—
9C23×#333C411yescharacteristic, complemented
10C23×D4⋊C8—21no—
11C2×SD16×C23—41no—
12C2×D8×C23—41no—
13C23×C4⋊Q8C2×C411yescharacteristic
14C23×#127D411yescharacteristic
15C23×#124—41no—
16C23×#121—41no—
17C4×D4×C23—21no—
18C23×#117—41no—
19C23×C4⋊C8—21no—
20C23×#102—41no—
21C4×C8×C23D411yescharacteristic
22#10625016—41no—
23#10624994—41no—
24C2×Q8×C23—21no—
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—41no—
28C2×D4×C23—41no—
29C22×C4×C23—41no—
30SD16×C23—81no—
31SD16×C23—81no—
32D8×C23—82no—
33C2×C8×C23—21no—
34C2×C8×C23—41no—
35C4⋊C4×C23—21no—
36C4⋊C4×C23—41no—
37C22⋊C4×C23—42no—
38C22⋊C4×C23—41no—
39C42×C23—41no—
40C42×C23C22⋊C411yescharacteristic
41C22⋊Dic23—81no—
42C23⋊C16—81no—
43#7519—231nomaximal, Sylow
44C23×C23—41no—
45C23×C23—41no—
46Q8×C23—81no—
47D4×C23—41no—
48D4×C23—41no—
49D4×C23—81no—
50D4×C23—81no—
51D4×C23—81no—
52D4×C23—161no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23—81no—
57C2×C4×C23—81no—
58C2×C4×C23#9911yescharacteristic
59C2×Dic23—161no—
60C8×C23—21no—
61C8×C23—21no—
62C8×C23—81no—
63#1624D2311yescharacteristic
64#1409—231no—
65#1359—231no—
66C22×C23—81no—
67C22×C23—81no—
68C22×C23—81no—
69C22×C23—81no—
70C22×C23—161no—
71C22×C23AΣL(1,𝔽16)11yescharacteristic
72C4×C23—21no—
73C4×C23—21no—
74C4×C23—21no—
75C4×C23—81no—
76C4×C23—81no—
77Dic23—321no—
78#555Dic2311yescharacteristic, complemented
79#492C2×D2311yescharacteristic
80#459—21no—
81#364—461no—
82#353—461no—
83#333Dic2311yescharacteristic, complemented
84D4⋊C8—21no—
85C2×C23—21no—
86C2×C23—161no—
87C2×C23—161no—
88C2×C23#140211yescharacteristic
89C2×SD16—41no—
90C2×D8—41no—
91C4⋊Q8C2×Dic2311yescharacteristic
92#127C22⋊D2311yescharacteristic
93#124—41no—
94#121—41no—
95C4×D4—21no—
96#117—41no—
97M32—921no—
98C4⋊C8—21no—
99#102—41no—
100#99—921no—
101C4×C8C22⋊D2311yescharacteristic
102C23#751911yescharacteristic, complemented, Sylow
103C2×Q8—21no—
104C2×D4—21no—
105C2×D4—21no—
106C2×D4—41no—
107C2×D4—41no—
108C22×C4—41no—
109SD16—81no—
110SD16—81no—
111D8—82no—
112C2×C8—21no—
113C2×C8—41no—
114C4⋊C4—21no—
115C4⋊C4—41no—
116C22⋊C4—42no—
117C22⋊C4—41no—
118C22⋊C4—1841no—
119C42—41no—
120C42C22⋊Dic2311yescharacteristic
121C16—1841no—
122C23—41no—
123C23—41no—
124Q8—81no—
125D4—41no—
126D4—41no—
127D4—81no—
128D4—81no—
129D4—81no—
130D4—161no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—81no—
135C2×C4—81no—
136C2×C4—3681no—
137C2×C4#1062501611yescharacteristic
138C8—21no—
139C8—21no—
140C8—81no—
141C22—81no—
142C22—81no—
143C22—81no—
144C22—81no—
145C22—161no—
146C22#1309220411yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—81no—
151C4—81no—
152C4—7361no—
153C2—21no—
154C2—161no—
155C2—161no—
156C2#1567154211yescharacteristic
subgroupG/H
centerC2#15671542
commutatorC23×C4⋊Q8C2×C4
Frattini#492C2×D23
FittingC23×#1624C2
socleC2×C23#1402
hypercenter#1624D23
hypocenterC23#7519
LCSG ▷ C23×C4⋊Q8 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1624

Complements

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

NH ≅ G/Ntype
1. #15671562C2semidirect
2. #15671438C2semidirect
6. C23×#555C4semidirect
9. C23×#333C4semidirect
78. #555Dic23semidirect
83. #333Dic23semidirect
102. C23#7519semidirect