Finite Group Databasebeta

← #37548994

Subgroups — #37548994

Order 23168.

204 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 62 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#26042300C211yesmaximal, characteristic
2#26042296C211yesmaximal, characteristic
3#26042124C214yesmaximal
4C2×#19153807C211yesmaximal, characteristic
5#19153883—21no—
6C4⋊#13089685—21no—
7C22⋊#13089685C2212yes—
8C22⋊#13089685C2212yes—
9#19153871—21no—
10C4×#13089685—21no—
11#19153807—21no—
12#19153807—21no—
13#19153807—21no—
14#19153807—21no—
15C2×C4⋊Dic181C411yescharacteristic
16C2×C4⋊Dic181C2212yes—
17C2×#15668428C412yes—
18C2×C4×Dic181C2211yescharacteristic
19C2×C4⋊C4×C181C411yescharacteristic
20C2×#13089685—22no—
21C2×#13089685—22no—
22C22×Dic181C2×C411yescharacteristic
23C22×Dic181C2×C412yes—
24C22×Dic181C2311yescharacteristic
25C4⋊Dic181—22no—
26C4⋊Dic181—22no—
27C4⋊Dic181—21no—
28C4⋊Dic181—21no—
29#15668428—22no—
30#15668428—22no—
31C4×Dic181D411yescharacteristic
32C4×Dic181D411yescharacteristic
33C4×Dic181D411yescharacteristic
34C4×Dic181D411yescharacteristic
35C22×C4×C181C2×C412yes—
36C22×C4×C181C2×C411yescharacteristic
37C4⋊C4×C181—21no—
38C4⋊C4×C181—21no—
39#13089685—42no—
40#13089685—42no—
41C2×Dic181—22no—
42C2×Dic181—22no—
43C2×Dic181—41no—
44C2×Dic181—42no—
45C2×Dic181C22⋊C411yescharacteristic
46C2×Dic181C22⋊C411yescharacteristic
47C2×Dic181C2×D411yescharacteristic
48C2×Dic181C2×D411yescharacteristic
49C23×C181C22×C411yescharacteristic
50C2×C4×C181—22no—
51C2×C4×C181—22no—
52C2×C4×C181—24no—
53C2×C4×C181C22⋊C411yescharacteristic
54C2×C4×C181C22⋊C411yescharacteristic
55C22×C181—21no—
56C22×C181—21no—
57C22×C181C2×C22⋊C411yescharacteristic
58C22×C181#13112yes—
59C4×C181—21no—
60C4×C181—42no—
61C4×C181#10112yes—
62Dic181—21no—
63Dic181—21no—
64Dic181—21no—
65Dic181—21no—
66Dic181—42no—
67C2×C181—22no—
68C2×C181#40811yescharacteristic
69C2×C181#41011yescharacteristic
70C2×C181C2×#10111yescharacteristic
71C181#147011yescharacteristic, complemented, Sylow
72#1470—1811nomaximal, Sylow
73C2×#125—1811no—
74#432—1811no—
75#431—1811no—
76#324—1814no—
77#125—3621no—
78#125—3621no—
79#125—3621no—
80#125—3621no—
81C2×C4⋊C4—1812no—
82C2×C4⋊C4—1812no—
83C2×C4⋊C4—1811no—
84C2×C4⋊C4#1062438211yescharacteristic
85C2×C42—1811no—
86C4⋊C8—3621no—
87C4⋊C8—3621no—
88C22⋊C8—1812no—
89C22⋊C8—1812no—
90#97—3621no—
91C4×C8—3621no—
92C22×C4—1811no—
93C22×C4—1812no—
94C22×C4—1811no—
95C22×C4C2×#1062438212yes—
96C22×C4C2×#1062438211yescharacteristic
97C2×C8—3622no—
98C2×C8—3622no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—3622no—
102C4⋊C4—3622no—
103C4⋊C4—3622no—
104C4⋊C4—3622no—
105C4⋊C4—3621no—
106C4⋊C4—3621no—
107C42—1811no—
108C42—1811no—
109C42—1811no—
110C42—1811no—
111C23C22×#1062438211yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—24no—
115C2×C4—3622no—
116C2×C4—3622no—
117C2×C4—1811no—
118C2×C4—1811no—
119C2×C4—1811no—
120C2×C4—1811no—
121C2×C4—7241no—
122C2×C4—7242no—
123C2×C4C22⋊#1062438211yescharacteristic
124C2×C4C22⋊#1062438211yescharacteristic
125C8—7242no—
126C8—7242no—
127C22—21no—
128C22—21no—
129C22C2×C22⋊#1062438211yescharacteristic
130C22#1915390312yes—
131C4—21no—
132C4—42no—
133C4—3621no—
134C4—3621no—
135C4—3621no—
136C4—3621no—
137C4—7242no—
138C4#1915387712yes—
139C2—22no—
140C2#2604225311yescharacteristic
141C2#2604226011yescharacteristic
142C2C2×#1915387711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutator, prime radicalC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
cosocleC22×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1470
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
71. C181#1470semidirect

Maximal subgroups

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

subgroupindex
#260423002
#260422962
#260421242
C2×#191538072
#1470181