Finite Group Databasebeta

← #19212057

Subgroups — #19212057

Order 5888.

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

normal subgroups only

This group has 164 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#15673061C211yesmaximal, characteristic
2#15671564C211yesmaximal, characteristic, complemented
3C23×#1409C211yesmaximal, characteristic, complemented
4#13092794C411yescharacteristic, complemented
5#13092793—21no—
6#13092765—21no—
7#13092216—21no—
8#13092138C411yescharacteristic, complemented
9C23×#492C2211yescharacteristic
10C23×#353—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×#127D411yescharacteristic
14C2×#67272—42no—
15C2×D184—41no—
16#10625045—21no—
17C23×#99—41no—
18C4×C8×C23C2×C411yescharacteristic
19#10625018—41no—
20#10624991—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×D4×C23—21no—
24C2×D4×C23—41no—
25C2×D92—41no—
26C2×D92—41no—
27C2×D92—41no—
28SD16×C23—82no—
29C2×C8×C23—21no—
30C4⋊C4×C23—41no—
31C22⋊C4×C23—81no—
32C42×C23C22⋊C411yescharacteristic
33#67272—84no—
34#67267—81no—
35C2×C23⋊C8—22no—
36D184—82no—
37#7527—231nomaximal, Sylow
38C23×C23—41no—
39C22×D23—81no—
40Q8×C23—81no—
41D4×C23—81no—
42D4×C23—82no—
43C2×C4×C23—21no—
44C2×C4×C23—41no—
45C2×C4×C23—161no—
46C2×C4×C23#9911yescharacteristic
47D92—82no—
48D92—82no—
49D92—82no—
50C8×C23—22no—
51C23⋊C8—42no—
52C23⋊C8—161no—
53#1721—231no—
54#1410—231no—
55#1409D2311yescharacteristic, complemented
56C22×C23—81no—
57C22×C23—161no—
58C22×C23#35311yescharacteristic
59C2×D23—161no—
60C2×D23—161no—
61C2×D23—161no—
62C4×C23—22no—
63C4×C23—21no—
64C4×C23—81no—
65C4×C23—321no—
66#493—231no—
67#493—461no—
68#492C2×D2311yescharacteristic
69#486—461no—
70#356—461no—
71#353—21no—
72#322—231no—
73C2×C23—21no—
74C2×C23—161no—
75C2×C23#140811yescharacteristic
76D23—321no—
77C2×SD16—41no—
78C2×D8—921no—
79C2×D8—922no—
80C4⋊Q8D9211yescharacteristic
81#127—461no—
82#127C22⋊D2311yescharacteristic
83#102—922no—
84#101—921no—
85#99—41no—
86C4×C8—461no—
87C4×C8C4×D2311yescharacteristic
88C23#752711yescharacteristic, complemented, Sylow
89C2×Q8—21no—
90C2×D4—21no—
91C2×D4—41no—
92C2×D4—921no—
93C2×D4—921no—
94C2×D4—921no—
95SD16—82no—
96D8—1842no—
97D8—1844no—
98M16—1841no—
99C2×C8—21no—
100C2×C8—462no—
101C4⋊C4—41no—
102C22⋊C4—81no—
103C42(C2×D23)⋊C411yescharacteristic
104C23—41no—
105C23—1841no—
106Q8—81no—
107D4—81no—
108D4—82no—
109D4—1842no—
110D4—1842no—
111D4—1842no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—161no—
115C2×C4#1062498811yescharacteristic
116C8—22no—
117C8—922no—
118C8—3681no—
119C22—81no—
120C22—161no—
121C22—3681no—
122C22—3681no—
123C22—3681no—
124C22#1309220911yescharacteristic
125C4—22no—
126C4—21no—
127C4—81no—
128C4—321no—
129C2—21no—
130C2—161no—
131C2—7361no—
132C2#1567155911yescharacteristic
subgroupG/H
centerC2#15671559
commutatorC4×C8×C23C2×C4
Frattini#492C2×D23
FittingC23×#1409C2
socleC2×C23#1408
hypercenter#1409D23
hypocenterC23#7527
LCSG ▷ C4×C8×C23 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
2. #15671564C2semidirect
3. C23×#1409C2semidirect
4. #13092794C4semidirect
8. #13092138C4semidirect
55. #1409D23semidirect
88. C23#7527semidirect