Finite Group Databasebeta

← #19142662

Subgroups — #19142662

Order 5504.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#13063317C211yesmaximal, characteristic
2#14582838C212yesmaximal
3#14582837C212yesmaximal
4#14582832C214yesmaximal
5#14582830C212yesmaximal
6#14582829C212yesmaximal
7#14582765C211yesmaximal, characteristic
8C2×#125×C43C211yesmaximal, characteristic
9#13063317—24no—
10C2×C4⋊Dic43C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×C4⋊Dic43C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2214yes—
16C43⋊#95C2214yes—
17C43⋊#95C2212yes—
18C43⋊#95C2214yes—
19C43⋊#95C2212yes—
20C43⋊#95C2214yes—
21#125×C43—24no—
22C2×C4⋊C4×C43C2212yes—
23C2×C4⋊C4×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2212yes—
25C2×C4⋊C4×C43C2211yescharacteristic
26C2×C42×C43C2211yescharacteristic
27C22×C4×C43C2312yes—
28C22×C4×C43C2312yes—
29C22×C4×C43C2311yescharacteristic
30C22×C4×C43C2311yescharacteristic
31C22×C4×C43C2311yescharacteristic
32C22×Dic43C2314yes—
33C22×Dic43C2312yes—
34C22×Dic43C2312yes—
35C4⋊C4×C43—22no—
36C4⋊C4×C43—24no—
37C4⋊C4×C43—22no—
38C4⋊C4×C43—24no—
39C42×C43D414yes—
40C4⋊Dic43—22no—
41C4⋊Dic43—22no—
42C4⋊Dic43—42no—
43Dic43⋊C4—24no—
44Dic43⋊C4—24no—
45Dic43⋊C4—44no—
46C23×C43C2411yescharacteristic
47C2×C4×C43—21no—
48C2×C4×C43—22no—
49C2×C4×C43—21no—
50C2×C4×C43—22no—
51C2×C4×C43—22no—
52C2×C4×C43—22no—
53C2×C4×C43—22no—
54C2×C4×C43—24no—
55C2×C4×C43—22no—
56C2×C4×C43C2×D412yes—
57C2×C4×C43C2×D412yes—
58C2×C4×C43C2×D412yes—
59C2×Dic43—22no—
60C2×Dic43—22no—
61C2×Dic43—22no—
62C2×Dic43—24no—
63C2×Dic43—22no—
64C2×Dic43—24no—
65C2×Dic43—24no—
66C2×Dic43—24no—
67C22×C43C22×D411yescharacteristic
68C22×C43H(5,𝔽2)11yescharacteristic
69C22×C432−1+412yes—
70C22×C432−1+411yescharacteristic
71C22×C432−1+412yes—
72C4×C43—22no—
73C4×C43—22no—
74C4×C43—22no—
75C4×C43—42no—
76C4×C43—42no—
77Dic43—42no—
78Dic43—42no—
79Dic43—44no—
80#2822—431nomaximal, Sylow
81C2×C43#53611yescharacteristic
82C2×C43#53611yescharacteristic
83C2×C43#53711yescharacteristic
84C2×C43#56312yes—
85C2×C43#56412yes—
86C2×#125—431no—
87C2×#125D4311yescharacteristic
88#400—432no—
89#400—432no—
90#398—432no—
91#398—432no—
92#398—434no—
93#382—431no—
94C43#282211yescharacteristic, complemented, Sylow
95#125—24no—
96#125—864no—
97C2×C4⋊C4—432no—
98C2×C4⋊C4—432no—
99C2×C4⋊C4—431no—
100C2×C4⋊C4—431no—
101C2×C4⋊C4—434no—
102C2×C4⋊C4—432no—
103C2×C4⋊C4C2×D4312yes—
104C2×C4⋊C4C2×D4311yescharacteristic
105C2×C4⋊C4C2×D4312yes—
106C2×C4⋊C4C2×D4311yescharacteristic
107C2×C42C2×D4311yescharacteristic
108#95—432no—
109#95—432no—
110#95—434no—
111#95—434no—
112#95—434no—
113C22×C4—434no—
114C22×C4—432no—
115C22×C4—432no—
116C22×C4C22×D4312yes—
117C22×C4C22×D4312yes—
118C22×C4C22×D4311yescharacteristic
119C22×C4C22×D4311yescharacteristic
120C22×C4C22×D4311yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—864no—
126C4⋊C4—864no—
127C4⋊C4—862no—
128C4⋊C4—862no—
129C4⋊C4—1724no—
130C4⋊C4—1722no—
131C42C22⋊D4314yes—
132C23C23×D4311yescharacteristic
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—24no—
141C2×C4—22no—
142C2×C4—862no—
143C2×C4—862no—
144C2×C4—864no—
145C2×C4—862no—
146C2×C4—864no—
147C2×C4—862no—
148C2×C4—864no—
149C2×C4—864no—
150C2×C4C2×C22⋊D4312yes—
151C2×C4C2×C22⋊D4312yes—
152C2×C4C2×C22⋊D4312yes—
153C22C22×C22⋊D4311yescharacteristic
154C22#1306337111yescharacteristic
155C22#1306337212yes—
156C22#1306337211yescharacteristic
157C22#1306337312yes—
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—1724no—
164C4—1722no—
165C4—1722no—
166C2#1458347011yescharacteristic
167C2#1458347311yescharacteristic
168C2#1458347711yescharacteristic
169C2#1458365312yes—
170C2C43⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#125×C43C2
hypercenterC2×#125D43
hypocenterC43#2822
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
94. C43#2822semidirect