Finite Group Databasebeta

← #19212035

Subgroups — #19212035

Order 5888.

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

normal subgroups only

This group has 162 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#15672478C211yesmaximal, characteristic
2#15671562C211yesmaximal, characteristic, complemented
3C23×#1359C211yesmaximal, characteristic, complemented
4#13093133C411yescharacteristic, complemented
5#13092609—21no—
6#13092210—21no—
7#13092166C411yescharacteristic, complemented
8#13092146—21no—
9C23×#492C2211yescharacteristic
10C23×#364—21no—
11C2×SD16×C23—41no—
12C23×C4⋊Q8C2×C411yescharacteristic
13C23×#127D411yescharacteristic
14#10625118—41no—
15C2×#67272—41no—
16#10625066—41no—
17#10625063—41no—
18C4×D92—21no—
19C23×M32—41no—
20C4×C8×C23D411yescharacteristic
21#10625016—41no—
22#10625014—41no—
23C4⋊(C23⋊C8)—21no—
24C2×Q8×C23—21no—
25C2×D4×C23—21no—
26C2×D4×C23—41no—
27C2×D92—21no—
28C2×D92—41no—
29C2×C4×D23—41no—
30SD16×C23—81no—
31SD16×C23—81no—
32C2×C8×C23—21no—
33C4⋊C4×C23—41no—
34C42×C23C22⋊C411yescharacteristic
35C22⋊Dic23—81no—
36#67272—82no—
37(C2×D23)⋊C4—42no—
38(C2×D23)⋊C4—41no—
39C4⋊Dic23—21no—
40C4×Dic23—41no—
41C2×C23⋊C8—41no—
42C16×C23—81no—
43#7519—231nomaximal, Sylow
44C23×C23—41no—
45C22×D23—41no—
46Q8×C23—81no—
47D4×C23—81no—
48D4×C23—81no—
49D4×C23—81no—
50C2×C4×C23—21no—
51C2×C4×C23—41no—
52C2×C4×C23#9911yescharacteristic
53C2×Dic23—41no—
54C2×Dic23—161no—
55D92—41no—
56D92—41no—
57D92—161no—
58C4×D23—81no—
59C4×D23—81no—
60C8×C23—21no—
61C8×C23—21no—
62C23⋊C8—81no—
63#1624—231no—
64#1409—231no—
65#1359D2311yescharacteristic, complemented
66C22×C23—81no—
67C22×C23—161no—
68C22×C23AΣL(1,𝔽16)11yescharacteristic
69C2×D23—81no—
70C2×D23—81no—
71C2×D23—81no—
72C4×C23—21no—
73C4×C23—21no—
74C4×C23—21no—
75C4×C23—81no—
76Dic23—81no—
77Dic23—321no—
78#555—231no—
79#492C2×D2311yescharacteristic
80#459—461no—
81#364—21no—
82#353—461no—
83#333—231no—
84D4⋊C8—461no—
85C2×C23—21no—
86C2×C23—161no—
87C2×C23#140211yescharacteristic
88D23—161no—
89C2×SD16—41no—
90C2×D8—921no—
91C4⋊Q8C4×D2311yescharacteristic
92#127D9211yescharacteristic
93#124—921no—
94#121—921no—
95C4×D4—461no—
96#117—921no—
97M32—41no—
98C4⋊C8—461no—
99#102—921no—
100#99—921no—
101C4×C8C22⋊D2311yescharacteristic
102C23#751911yescharacteristic, complemented, Sylow
103C2×Q8—21no—
104C2×D4—21no—
105C2×D4—41no—
106C2×D4—461no—
107C2×D4—921no—
108C22×C4—921no—
109SD16—81no—
110SD16—81no—
111D8—1842no—
112C2×C8—21no—
113C2×C8—921no—
114C4⋊C4—41no—
115C4⋊C4—461no—
116C22⋊C4—922no—
117C22⋊C4—921no—
118C22⋊C4—1841no—
119C42—921no—
120C42(C2×D23)⋊C411yescharacteristic
121C16—81no—
122C23—41no—
123C23—921no—
124Q8—81no—
125D4—81no—
126D4—81no—
127D4—81no—
128D4—921no—
129D4—921no—
130D4—3681no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—921no—
134C2×C4—3681no—
135C2×C4—1841no—
136C2×C4—1841no—
137C2×C4#1062498811yescharacteristic
138C8—21no—
139C8—21no—
140C8—1841no—
141C22—81no—
142C22—161no—
143C22—1841no—
144C22—1841no—
145C22—1841no—
146C22#1309220511yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—81no—
151C4—1841no—
152C4—7361no—
153C2—21no—
154C2—161no—
155C2—3681no—
156C2#1567154311yescharacteristic
subgroupG/H
centerC2#15671543
commutatorC23×C4⋊Q8C2×C4
Frattini#492C2×D23
FittingC23×#1359C2
socleC2×C23#1402
hypercenter#1359D23
hypocenterC23#7519
LCSG ▷ C23×C4⋊Q8 ▷ C42×C23 ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

Complements

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

NH ≅ G/Ntype
2. #15671562C2semidirect
3. C23×#1359C2semidirect
4. #13093133C4semidirect
7. #13092166C4semidirect
65. #1359D23semidirect
102. C23#7519semidirect