Finite Group Databasebeta

← #19212041

Subgroups — #19212041

Order 5888.

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

normal subgroups only

This group has 148 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#15672540C211yesmaximal, characteristic
2#15671566C211yesmaximal, characteristic, complemented
3C23×#1358C211yesmaximal, characteristic, complemented
4#13093133C411yescharacteristic
5#13092704—21no—
6#13092216—21no—
7#13092166C411yescharacteristic
8#13092146—21no—
9C23×#494C2211yescharacteristic
10C23×#364—21no—
11C2×Q16×C23—41no—
12C23×C4⋊Q8C2×C411yescharacteristic
13C23×C4⋊Q8D411yescharacteristic
14#10625118—41no—
15#10625066—41no—
16#10625063—41no—
17C4×D92—21no—
18C23×M32—41no—
19C4×C8×C23D411yescharacteristic
20#10625018—41no—
21#10624991—41no—
22#10624990—41no—
23C4⋊(C23⋊C8)—21no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×D92—21no—
27C2×D92—41no—
28C2×C4×D23—41no—
29Q16×C23—81no—
30Q16×C23—81no—
31C2×C8×C23—21no—
32C4⋊C4×C23—41no—
33C4⋊C4×C23—41no—
34C42×C23C22⋊C411yescharacteristic
35(C2×D23)⋊C4—42no—
36(C2×D23)⋊C4—41no—
37C4⋊Dic23—21no—
38C4×Dic23—41no—
39#67267—81no—
40C2×C23⋊C8—41no—
41C16×C23—81no—
42#7521—231nomaximal, Sylow
43C22×D23—41no—
44Q8×C23—81no—
45Q8×C23—81no—
46C2×C4×C23—21no—
47C2×C4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23#9911yescharacteristic
50C2×Dic23—41no—
51D92—41no—
52D92—41no—
53D92—161no—
54C4×D23—81no—
55C4×D23—81no—
56C8×C23—21no—
57C8×C23—21no—
58C23⋊C8—81no—
59C23⋊C8—161no—
60#1634—231no—
61#1411—231no—
62#1358D2311yescharacteristic, complemented
63C22×C23AΣL(1,𝔽16)11yescharacteristic
64C2×D23—81no—
65C2×D23—81no—
66C2×D23—81no—
67C4×C23—21no—
68C4×C23—21no—
69C4×C23—21no—
70C4×C23—81no—
71C4×C23—81no—
72Dic23—81no—
73#555—231no—
74#494C2×D2311yescharacteristic
75#476—461no—
76#364—21no—
77#356—461no—
78#333—231no—
79D4⋊C8—461no—
80C2×C23—21no—
81C2×C23#140211yescharacteristic
82D23—161no—
83C2×Q16—41no—
84C4⋊Q8C4×D2311yescharacteristic
85C4⋊Q8D9211yescharacteristic
86#124—921no—
87#121—921no—
88C4×D4—461no—
89#117—921no—
90M32—41no—
91#106—921no—
92C4⋊C8—461no—
93#102—921no—
94#101—921no—
95C4×C8C22⋊D2311yescharacteristic
96C23#752111yescharacteristic, complemented, Sylow
97C2×Q8—21no—
98C2×Q8—21no—
99C2×D4—461no—
100C2×D4—921no—
101C22×C4—921no—
102Q16—81no—
103Q16—81no—
104M16—1841no—
105C2×C8—21no—
106C2×C8—921no—
107C4⋊C4—41no—
108C4⋊C4—41no—
109C4⋊C4—461no—
110C22⋊C4—922no—
111C22⋊C4—921no—
112C42—921no—
113C42(C2×D23)⋊C411yescharacteristic
114C16—81no—
115C23—921no—
116Q8—81no—
117Q8—81no—
118D4—921no—
119D4—921no—
120D4—3681no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—921no—
125C2×C4—1841no—
126C2×C4—1841no—
127C2×C4#1062498811yescharacteristic
128C8—21no—
129C8—21no—
130C8—3681no—
131C8—1841no—
132C22—1841no—
133C22—1841no—
134C22—1841no—
135C22#1309220511yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—81no—
140C4—81no—
141C4—1841no—
142C2—21no—
143C2—3681no—
144C2#1567154311yescharacteristic
subgroupG/H
centerC2#15671543
commutatorC23×C4⋊Q8C2×C4
Frattini#494C2×D23
FittingC23×#1358C2
socleC2×C23#1402
hypercenter#1358D23
hypocenterC23#7521
LCSG ▷ C23×C4⋊Q8 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1358

Complements

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

NH ≅ G/Ntype
2. #15671566C2semidirect
3. C23×#1358C2semidirect
62. #1358D23semidirect
96. C23#7521semidirect