Finite Group Databasebeta

← #19212037

Subgroups — #19212037

Order 5888.

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

normal subgroups only

This group has 156 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
2#15671438C211yesmaximal, characteristic
3C23×#1623C211yesmaximal, characteristic
4#13092238—21no—
5#13092210—21no—
6Q82×C23C411yescharacteristic, complemented
7C23×#492C2211yescharacteristic
8C23×#460—21no—
9C23×#333C411yescharacteristic, complemented
10C23×Q8⋊C8—21no—
11C2×SD16×C23—41no—
12C2×SD16×C23—41no—
13C23×C4⋊Q8—41no—
14C23×C4⋊Q8—41no—
15C23×C4⋊Q8C2×C411yescharacteristic
16C23×#127D411yescharacteristic
17C4×Q8×C23—21no—
18C4×Q8×C23—41no—
19C23×C4⋊C8—21no—
20C23×#102—41no—
21C4×C8×C23D411yescharacteristic
22#10625016—41no—
23#10624994—41no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×Q8×C23—41no—
27C2×D4×C23—21no—
28C2×D4×C23—41no—
29SD16×C23—81no—
30SD16×C23—81no—
31SD16×C23—82no—
32C2×C8×C23—21no—
33C2×C8×C23—41no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23—41no—
36C4⋊C4×C23—42no—
37C4⋊C4×C23—41no—
38C42×C23—41no—
39C42×C23—41no—
40C42×C23C22⋊C411yescharacteristic
41C22⋊Dic23—81no—
42C23⋊C16—81no—
43#7520—231nomaximal, Sylow
44C23×C23—41no—
45Q8×C23—22no—
46Q8×C23—41no—
47Q8×C23—81no—
48Q8×C23—161no—
49D4×C23—81no—
50D4×C23—81no—
51D4×C23—81no—
52C2×C4×C23—21no—
53C2×C4×C23—41no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23#9911yescharacteristic
57C2×Dic23—161no—
58C8×C23—21no—
59C8×C23—21no—
60C8×C23—81no—
61#1623D2311yescharacteristic
62#1409—231no—
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—42no—
71C4×C23—81no—
72C4×C23—81no—
73Dic23—321no—
74Q82Dic2311yescharacteristic, complemented
75#492C2×D2311yescharacteristic
76#460—21no—
77#364—461no—
78#353—461no—
79#333Dic2311yescharacteristic, complemented
80Q8⋊C8—21no—
81C2×C23—21no—
82C2×C23—161no—
83C2×C23#140211yescharacteristic
84C2×SD16—41no—
85C2×SD16—41no—
86C4⋊Q8—41no—
87C4⋊Q8—41no—
88C4⋊Q8C2×Dic2311yescharacteristic
89#127C22⋊D2311yescharacteristic
90C4×Q8—21no—
91C4×Q8—41no—
92M32—921no—
93C4⋊C8—21no—
94#102—41no—
95#99—921no—
96C4×C8C22⋊D2311yescharacteristic
97C23#752011yescharacteristic, complemented, Sylow
98C2×Q8—21no—
99C2×Q8—21no—
100C2×Q8—41no—
101C2×D4—21no—
102C2×D4—41no—
103SD16—81no—
104SD16—81no—
105SD16—82no—
106C2×C8—21no—
107C2×C8—41no—
108C4⋊C4—21no—
109C4⋊C4—41no—
110C4⋊C4—42no—
111C4⋊C4—41no—
112C22⋊C4—1841no—
113C42—41no—
114C42—41no—
115C42C22⋊Dic2311yescharacteristic
116C16—1841no—
117C23—41no—
118Q8—22no—
119Q8—41no—
120Q8—81no—
121Q8—161no—
122D4—81no—
123D4—81no—
124D4—81no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—3681no—
130C2×C4#1062501611yescharacteristic
131C8—21no—
132C8—21no—
133C8—81no—
134C22—81no—
135C22—161no—
136C22#1309220411yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—81no—
142C4—81no—
143C4—7361no—
144C2—21no—
145C2—161no—
146C2#1567154211yescharacteristic
subgroupG/H
centerC2#15671542
commutatorC23×C4⋊Q8C2×C4
Frattini#492C2×D23
FittingC23×#1623C2
socleC2×C23#1402
hypercenter#1623D23
hypocenterC23#7520
LCSG ▷ C23×C4⋊Q8 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1623

Complements

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

NH ≅ G/Ntype
6. Q82×C23C4semidirect
9. C23×#333C4semidirect
74. Q82Dic23semidirect
79. #333Dic23semidirect
97. C23#7520semidirect