Finite Group Databasebeta

← #19212042

Subgroups — #19212042

Order 5888.

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

normal subgroups only

This group has 142 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#15672535C211yesmaximal, characteristic
2#15671436C211yesmaximal, characteristic
3C23×#1411C211yesmaximal, characteristic
4#13093147C411yescharacteristic
5#13092709—21no—
6#13092238—21no—
7#13092166C411yescharacteristic
8#13092149—21no—
9C23×#494C2211yescharacteristic
10C23×#356—21no—
11C2×Q16×C23—41no—
12C23×C4⋊Q8C2×C411yescharacteristic
13C23×C4⋊Q8D411yescharacteristic
14#10625115—41no—
15#10625059—41no—
16#10625058—41no—
17C4×Dic46—21no—
18C23×#101—41no—
19C4×C8×C23D411yescharacteristic
20#10624994—41no—
21#10624992—41no—
22#10624989—41no—
23C4⋊(C23⋊C8)—21no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×Dic46—21no—
27C2×Dic46—41no—
28Q16×C23—81no—
29Q16×C23—81no—
30M16×C23—81no—
31C2×C8×C23—21no—
32C4⋊C4×C23—41no—
33C4⋊C4×C23—41no—
34C42×C23C22⋊C411yescharacteristic
35C4⋊Dic23—21no—
36Dic23⋊C4—42no—
37Dic23⋊C4—41no—
38C4×Dic23—41no—
39C4×Dic23—41no—
40C2×C23⋊C8—41no—
41C23⋊C16—81no—
42#7522—231nomaximal, Sylow
43Q8×C23—81no—
44Q8×C23—81no—
45C2×C4×C23—21no—
46C2×C4×C23—41no—
47C2×C4×C23—41no—
48C2×C4×C23#9911yescharacteristic
49C2×Dic23—41no—
50C2×Dic23—41no—
51Dic46—22no—
52Dic46—41no—
53Dic46—161no—
54C8×C23—21no—
55C8×C23—21no—
56C8×C23—161no—
57C23⋊C8—81no—
58#1633—231no—
59#1411D2311yescharacteristic
60#1358—231no—
61C22×C23AΣL(1,𝔽16)11yescharacteristic
62C4×C23—21no—
63C4×C23—21no—
64C4×C23—21no—
65C4×C23—81no—
66C4×C23—81no—
67Dic23—42no—
68Dic23—81no—
69Q82—231no—
70#494C2×D2311yescharacteristic
71#477—461no—
72#364—461no—
73#356—21no—
74#333—231no—
75Q8⋊C8—461no—
76C2×C23—21no—
77C2×C23#140211yescharacteristic
78C2×Q16—41no—
79C4⋊Q8—921no—
80C4⋊Q8—921no—
81C4⋊Q8C4×D2311yescharacteristic
82C4⋊Q8C22⋊D2311yescharacteristic
83C4×Q8—461no—
84C4×Q8—921no—
85M32—921no—
86#107—921no—
87C4⋊C8—461no—
88#103—921no—
89#101—41no—
90C4×C8D9211yescharacteristic
91C23#752211yescharacteristic, complemented, Sylow
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—461no—
95C2×Q8—921no—
96Q16—81no—
97Q16—81no—
98M16—81no—
99C2×C8—21no—
100C2×C8—921no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—461no—
104C4⋊C4—922no—
105C4⋊C4—921no—
106C42—921no—
107C42—921no—
108C42(C2×D23)⋊C411yescharacteristic
109C16—1841no—
110Q8—81no—
111Q8—81no—
112Q8—462no—
113Q8—921no—
114Q8—3681no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—921no—
119C2×C4—921no—
120C2×C4#1062498811yescharacteristic
121C8—21no—
122C8—21no—
123C8—161no—
124C8—1841no—
125C22#1309220311yescharacteristic
126C4—21no—
127C4—21no—
128C4—21no—
129C4—81no—
130C4—81no—
131C4—922no—
132C4—1841no—
133C2—21no—
134C2#1567154111yescharacteristic
subgroupG/H
centerC2#15671541
commutatorC23×C4⋊Q8C2×C4
Frattini#494C2×D23
FittingC23×#1411C2
socleC2×C23#1402
hypercenter#1411D23
hypocenterC23#7522
LCSG ▷ C23×C4⋊Q8 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
91. C23#7522semidirect