Finite Group Databasebeta

← #19212069

Subgroups — #19212069

Order 5888.

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

normal subgroups only

This group has 136 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#15673013C211yesmaximal, characteristic
2#15671566C211yesmaximal, characteristic
3C23×#1411C211yesmaximal, characteristic
4#13092820—21no—
5#13092820—21no—
6#13092797C411yescharacteristic
7#13092216—21no—
8C8×C23⋊C8C411yescharacteristic
9C23×#494C2211yescharacteristic
10C23×#356—21no—
11C2×Q16×C23—41no—
12C23×C4⋊Q8D411yescharacteristic
13C23×C4⋊Q8D411yescharacteristic
14C2×Dic92—41no—
15#10625040—21no—
16C23×#101—41no—
17C4×C8×C23C2×C411yescharacteristic
18#10625018—41no—
19#10624989—42no—
20#10624989—42no—
21C4×C23⋊C8—21no—
22C2×Q8×C23—21no—
23C2×Q8×C23—21no—
24C2×Dic46—41no—
25Q16×C23—82no—
26M16×C23—81no—
27C2×C8×C23—21no—
28C4⋊C4×C23—41no—
29C4⋊C4×C23—41no—
30C42×C23C22⋊C411yescharacteristic
31C4⋊Dic23—41no—
32C4⋊Dic23—41no—
33#67267—81no—
34C2×C23⋊C8—22no—
35Dic92—82no—
36#7532—231nomaximal, Sylow
37Q8×C23—81no—
38Q8×C23—81no—
39C2×C4×C23—21no—
40C2×C4×C23—41no—
41C2×C4×C23—41no—
42C2×C4×C23#9911yescharacteristic
43C2×Dic23—81no—
44Dic46—82no—
45C8×C23—22no—
46C8×C23—161no—
47C23⋊C8—24no—
48C23⋊C8—161no—
49#1713—231no—
50#1411—231no—
51#1411D2311yescharacteristic
52C22×C23#35311yescharacteristic
53C4×C23—22no—
54C4×C23—21no—
55C4×C23—81no—
56C4×C23—81no—
57Dic23—161no—
58#500—461no—
59#500—461no—
60#494—231no—
61#494C2×D2311yescharacteristic
62#356—21no—
63#356—461no—
64C82—231no—
65C2×C23—21no—
66C2×C23#140811yescharacteristic
67C2×Q16—41no—
68C2×Q16—921no—
69C4⋊Q8—461no—
70C4⋊Q8D9211yescharacteristic
71C4⋊Q8C22⋊D2311yescharacteristic
72#107—922no—
73#107—922no—
74#101—41no—
75#101—921no—
76C4×C8—461no—
77C4×C8C4×D2311yescharacteristic
78C23#753211yescharacteristic, complemented, Sylow
79C2×Q8—21no—
80C2×Q8—21no—
81C2×Q8—921no—
82Q16—82no—
83Q16—1842no—
84M16—81no—
85M16—1841no—
86C2×C8—21no—
87C2×C8—462no—
88C4⋊C4—41no—
89C4⋊C4—41no—
90C4⋊C4—921no—
91C4⋊C4—921no—
92C42(C2×D23)⋊C411yescharacteristic
93Q8—81no—
94Q8—81no—
95Q8—1842no—
96C2×C4—21no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4—1841no—
100C2×C4#1062498811yescharacteristic
101C8—22no—
102C8—161no—
103C8—464no—
104C8—3681no—
105C22#1309220911yescharacteristic
106C4—22no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—3681no—
111C2—21no—
112C2#1567155911yescharacteristic
subgroupG/H
centerC2#15671559
commutatorC4×C8×C23C2×C4
Frattini#494C2×D23
FittingC23×#1411C2
socleC2×C23#1408
hypercenter#1411D23
hypocenterC23#7532
LCSG ▷ C4×C8×C23 ▷ 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
78. C23#7532semidirect