Finite Group Databasebeta

← #19212082

Subgroups — #19212082

Order 5888.

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

normal subgroups only

This group has 138 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#15672996C211yesmaximal, characteristic
2#15671562C211yesmaximal, characteristic
3C23×#1410C211yesmaximal, characteristic
4#13092815C411yescharacteristic, complemented
5#13092769—21no—
6#13092763—21no—
7#13092210—21no—
8C8×C23⋊C8C411yescharacteristic, complemented
9C23×#492C2211yescharacteristic
10C23×#356—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×#127D411yescharacteristic
14#10625040—21no—
15C23×#101—41no—
16C4×C8×C23C2×C411yescharacteristic
17#10625016—41no—
18#10625014—42no—
19#10624999—41no—
20#10624992—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×D4×C23—21no—
24C2×D4×C23—41no—
25C2×Dic46—41no—
26SD16×C23—82no—
27M16×C23—81no—
28C2×C8×C23—21no—
29C4⋊C4×C23—41no—
30C42×C23C22⋊C411yescharacteristic
31C22⋊Dic23—81no—
32C4⋊Dic23—41no—
33C4⋊Dic23—41no—
34C2×C23⋊C8—22no—
35#7536—231nomaximal, Sylow
36C23×C23—41no—
37Q8×C23—81no—
38D4×C23—81no—
39D4×C23—82no—
40C2×C4×C23—21no—
41C2×C4×C23—41no—
42C2×C4×C23#9911yescharacteristic
43C2×Dic23—81no—
44C2×Dic23—161no—
45Dic46—82no—
46C8×C23—22no—
47C8×C23—161no—
48C23⋊C8—42no—
49#1708—231no—
50#1410D2311yescharacteristic
51#1409—231no—
52C22×C23—81no—
53C22×C23—161no—
54C22×C23#35311yescharacteristic
55C4×C23—22no—
56C4×C23—21no—
57C4×C23—81no—
58Dic23—161no—
59Dic23—321no—
60#498—231no—
61#492C2×D2311yescharacteristic
62#487—461no—
63#486—461no—
64#356—21no—
65#353—461no—
66C82—231no—
67C2×C23—21no—
68C2×C23—161no—
69C2×C23#140911yescharacteristic
70C2×SD16—41no—
71C4⋊Q8—461no—
72C4⋊Q8C22⋊D2311yescharacteristic
73#127D9211yescharacteristic
74#106—921no—
75#103—922no—
76#102—922no—
77#101—41no—
78#99—921no—
79C4×C8—461no—
80C4×C8C4×D2311yescharacteristic
81C23#753611yescharacteristic, complemented, Sylow
82C2×Q8—21no—
83C2×Q8—921no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—81no—
88C2×C8—21no—
89C2×C8—462no—
90C4⋊C4—41no—
91C4⋊C4—921no—
92C4⋊C4—921no—
93C22⋊C4—1841no—
94C42(C2×D23)⋊C411yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—1842no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—3681no—
103C2×C4—1841no—
104C2×C4#1062498811yescharacteristic
105C8—22no—
106C8—161no—
107C8—922no—
108C22—81no—
109C22—161no—
110C22#1309220911yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—3681no—
115C4—7361no—
116C2—21no—
117C2—161no—
118C2#1567156111yescharacteristic
subgroupG/H
centerC2#15671561
commutatorC4×C8×C23C2×C4
Frattini#492C2×D23
FittingC23×#1410C2
socleC2×C23#1409
hypercenter#1410D23
hypocenterC23#7536
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1410

Complements

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

NH ≅ G/Ntype
4. #13092815C4semidirect
8. C8×C23⋊C8C4semidirect
81. C23#7536semidirect