Finite Group Databasebeta

← #19212047

Subgroups — #19212047

Order 5888.

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

normal subgroups only

This group has 158 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#15672689C211yesmaximal, characteristic
2#15671568C211yesmaximal, characteristic, complemented
3C23×#1355C211yesmaximal, characteristic, complemented
4#13093165C411yescharacteristic, complemented
5#13092804—21no—
6#13092210—21no—
7#13092159C411yescharacteristic, complemented
8#13092156—21no—
9C23×#490C2211yescharacteristic
10C23×#347—21no—
11C23×#127D411yescharacteristic
12C23×#125C2×C411yescharacteristic
13C2×#67273—41no—
14C2×#67272—41no—
15#10625067—41no—
16#10625066—41no—
17#10625065—41no—
18#10625046—21no—
19C23×M32—41no—
20C23×#102—41no—
21C23×#97D411yescharacteristic
22#10625016—41no—
23#10624985—21no—
24C2×D4×C23—21no—
25C2×D4×C23—41no—
26C2×D92—21no—
27C2×D92—41no—
28C2×C4×D23—41no—
29C2×Dic46—21no—
30C2×C8×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—41no—
33C42×C23C22⋊C411yescharacteristic
34C22⋊Dic23—81no—
35#67273—82no—
36#67272—82no—
37(C2×D23)⋊C4—41no—
38(C2×D23)⋊C4—41no—
39(C2×D23)⋊C4—41no—
40Dic23⋊C4—41no—
41C2×C23⋊C8—41no—
42C16×C23—42no—
43#7523—231nomaximal, Sylow
44C23×C23—41no—
45C22×D23—41no—
46D4×C23—81no—
47D4×C23—81no—
48D4×C23—81no—
49C2×C4×C23—21no—
50C2×C4×C23—41no—
51C2×C4×C23#9911yescharacteristic
52C2×Dic23—41no—
53C2×Dic23—161no—
54D92—81no—
55D92—161no—
56C4×D23—161no—
57Dic46—81no—
58C8×C23—41no—
59C23⋊C8—42no—
60#1656—231no—
61#1412—231no—
62#1355D2311yescharacteristic, complemented
63C22×C23—81no—
64C22×C23—161no—
65C22×C23AΣL(1,𝔽16)11yescharacteristic
66C2×D23—81no—
67C2×D23—81no—
68C2×D23—81no—
69C4×C23—21no—
70C4×C23—41no—
71C4×C23—81no—
72Dic23—81no—
73Dic23—321no—
74#562—231no—
75#496—461no—
76#490C2×D2311yescharacteristic
77#353—461no—
78#347—21no—
79#330—231no—
80#329—461no—
81C2×C23—21no—
82C2×C23—161no—
83C2×C23#140411yescharacteristic
84D23—161no—
85C2×SD16—921no—
86C2×D8—921no—
87#127D9211yescharacteristic
88#125C4×D2311yescharacteristic
89#124—461no—
90#123—921no—
91C22⋊Q8—921no—
92#121—921no—
93M32—41no—
94#102—41no—
95#99—921no—
96#97—461no—
97#97C22⋊D2311yescharacteristic
98C23#752311yescharacteristic, complemented, Sylow
99C2×Q8—461no—
100C2×D4—21no—
101C2×D4—41no—
102C2×D4—461no—
103C2×D4—921no—
104C22×C4—921no—
105SD16—1842no—
106D8—1842no—
107C2×C8—21no—
108C2×C8—921no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—921no—
112C22⋊C4—921no—
113C22⋊C4—921no—
114C22⋊C4—921no—
115C22⋊C4—1841no—
116C42(C2×D23)⋊C411yescharacteristic
117C16—42no—
118C23—41no—
119C23—921no—
120Q8—1841no—
121D4—81no—
122D4—81no—
123D4—81no—
124D4—3681no—
125D4—1841no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—921no—
129C2×C4—3681no—
130C2×C4—3681no—
131C2×C4#1062498811yescharacteristic
132C8—41no—
133C8—922no—
134C22—81no—
135C22—161no—
136C22—1841no—
137C22—1841no—
138C22—1841no—
139C22#1309220511yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—1841no—
144C4—7361no—
145C2—21no—
146C2—161no—
147C2—3681no—
148C2#1567154911yescharacteristic
subgroupG/H
centerC2#15671549
commutatorC23×#125C2×C4
Frattini#490C2×D23
FittingC23×#1355C2
socleC2×C23#1404
hypercenter#1355D23
hypocenterC23#7523
LCSG ▷ C23×#125 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1355

Complements

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

NH ≅ G/Ntype
2. #15671568C2semidirect
3. C23×#1355C2semidirect
4. #13093165C4semidirect
7. #13092159C4semidirect
62. #1355D23semidirect
98. C23#7523semidirect