Finite Group Databasebeta

← #37549621

Subgroups — #37549621

Order 23168.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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#26042251C212yesmaximal
2#26042159C214yesmaximal, complemented
3C2×C4⋊C4×D181C211yesmaximal, characteristic
4C2×#15668458C2214yes—
5#19153873—22no—
6#19153873—22no—
7C22×C4×D181C412yes—
8C22×C4×D181C2211yescharacteristic
9C2×C4⋊Dic181C411yescharacteristic
10C2×#15668428C2212yes—
11C4⋊C4×D181—22no—
12C4⋊C4×D181—22no—
13C2×C4⋊C4×C181C411yescharacteristic
14#15668458—28no—
15C2×#13089685—24no—
16C23×D181C2×C411yescharacteristic
17C22×Dic181C2×C412yes—
18C22×Dic181C2311yescharacteristic
19C2×C4×D181—24no—
20C2×C4×D181—22no—
21C2×C4×D181—22no—
22C2×C4×D181—44no—
23C2×C4×D181D412yes—
24C2×C4×D181D412yes—
25C4⋊Dic181—22no—
26#15668428—24no—
27C22×C4×C181C2×C412yes—
28C22×C4×C181C2×C411yescharacteristic
29C4⋊C4×C181—22no—
30#13089685—44no—
31C22×D181—22no—
32C22×D181—22no—
33C22×D181—22no—
34C22×D181C22⋊C411yescharacteristic
35C22×D181C22⋊C411yescharacteristic
36C2×Dic181—22no—
37C2×Dic181—42no—
38C2×Dic181C2×D412yes—
39C2×Dic181#4114yes—
40C4×D181—24no—
41C4×D181—24no—
42C4×D181—44no—
43C4×D181—44no—
44C23×C181C22×C411yescharacteristic
45C2×C4×C181—22no—
46C2×C4×C181—22no—
47C2×C4×C181—42no—
48C2×C4×C181C22⋊C412yes—
49C22×C181—21no—
50C22×C181—21no—
51C22×C181C2×C22⋊C411yescharacteristic
52C22×C181#11712yes—
53C2×D181—28no—
54C2×D181—21no—
55C2×D181—21no—
56C2×D181—21no—
57C2×D181—21no—
58C2×D181#10012yes—
59C2×D181#10112yes—
60C4×C181—22no—
61C4×C181—42no—
62Dic181—42no—
63Dic181#12314yes—
64C2×C181—22no—
65C2×C181#38111yescharacteristic
66C2×C181C2×#10011yescharacteristic
67C2×C181C2×#10111yescharacteristic
68D181—22no—
69D181—22no—
70C181#182111yescharacteristic, complemented, Sylow
71#1821—1811nomaximal, Sylow
72C22×C4⋊C4—1811no—
73#407—1812no—
74#343—1814no—
75C23×C4—1811no—
76C23×C4—1812no—
77C2×M16—1814no—
78C2×C4⋊C4—3622no—
79C2×C4⋊C4—3622no—
80C2×C4⋊C4—1812no—
81C2×C4⋊C4—1811no—
82C2×C4⋊C4#1062438211yescharacteristic
83C22⋊C8—3622no—
84C22⋊C8—3622no—
85C24—1811no—
86C22×C4—3624no—
87C22×C4—3622no—
88C22×C4—3622no—
89C22×C4—1812no—
90C22×C4—1812no—
91C22×C4—1812no—
92C22×C4—1811no—
93C22×C4—7244no—
94C22×C4C2×#1062438212yes—
95C22×C4C2×#1062438211yescharacteristic
96M16—3628no—
97C2×C8—3624no—
98C4⋊C4—22no—
99C4⋊C4—3624no—
100C4⋊C4—3622no—
101C23—3622no—
102C23—3622no—
103C23—3622no—
104C23—1811no—
105C23—1811no—
106C23C22×#1062438211yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—3624no—
111C2×C4—3624no—
112C2×C4—3622no—
113C2×C4—1812no—
114C2×C4—1814no—
115C2×C4—7244no—
116C2×C4—7244no—
117C2×C4—7242no—
118C2×C4C22⋊#1062438212yes—
119C8—7244no—
120C22—21no—
121C22—21no—
122C22—3628no—
123C22—3621no—
124C22—3621no—
125C22—3621no—
126C22—3621no—
127C22—1812no—
128C22—1812no—
129C22C2×C22⋊#1062438211yescharacteristic
130C22#1915389512yes—
131C4—22no—
132C4—42no—
133C4—1814no—
134C4—7242no—
135C2—22no—
136C2—3622no—
137C2—3622no—
138C2#2604222211yescharacteristic
139C2D181⋊#10011yescharacteristic
140C2D181⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181C2×C4
cosocleC22×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1821
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #26042159C2semidirect
70. C181#1821semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260422512
#260421592
C2×C4⋊C4×D1812
#1821181