Finite Group Databasebeta

← #37532048

Subgroups — #37532048

Order 23168.

440 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 93 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#26041243C212yesmaximal, complemented
2#26041003C214yesmaximal, complemented
3C22×C22⋊C4×C181C211yesmaximal, characteristic
4C2×#15668433—22no—
5C22⋊#13089678—22no—
6C22⋊#13089678C2214yescomplemented
7C25×C181C411yescharacteristic
8C23×C4×C181C411yescharacteristic
9C23×C4×C181C2211yescharacteristic
10C2×C22⋊C4×C181—22no—
11C2×C22⋊C4×C181—22no—
12C2×C22⋊C4×C181C412yes—
13C2×C22⋊C4×C181C2212yes—
14#15668433—44no—
15C2×#13089678—24no—
16C24×C181—21no—
17C24×C181—21no—
18C24×C181—24no—
19C24×C181—42no—
20C24×C181—42no—
21C24×C181C2×C411yescharacteristic
22C24×C181C2×C412yes—
23C22×C4×C181—21no—
24C22×C4×C181—21no—
25C22×C4×C181—42no—
26C22×C4×C181—42no—
27C22×C4×C181C2×C412yes—
28C22×C4×C181C2×C411yescharacteristic
29C22×C4×C181D412yes—
30C22×C4×C181D412yes—
31C22×C4×C181C2311yescharacteristic
32C22⋊C4×C181—24no—
33C22⋊C4×C181—24no—
34#13089678—44no—
35C23×C181—22no—
36C23×C181—22no—
37C23×C181—22no—
38C23×C181—24no—
39C23×C181—24no—
40C23×C181—22no—
41C23×C181—22no—
42C23×C181—42no—
43C23×C181—42no—
44C23×C181—416no—
45C23×C181—42no—
46C23×C181—42no—
47C23×C181—42no—
48C23×C181—42no—
49C23×C181C22⋊C411yescharacteristic
50C23×C181C22⋊C411yescharacteristic
51C23×C181M1614yescomplemented
52C23×C181C22×C411yescharacteristic
53C2×C4×C181—24no—
54C2×C4×C181—22no—
55C2×C4×C181—41no—
56C2×C4×C181—42no—
57C2×C4×C181—41no—
58C2×C4×C181—42no—
59C2×C4×C181—42no—
60C2×C4×C181—42no—
61C2×C4×C181C22⋊C412yes—
62C2×C4×C181C2×D412yes—
63C22×C181—28no—
64C22×C181—21no—
65C22×C181—21no—
66C22×C181—21no—
67C22×C181—21no—
68C22×C181—21no—
69C22×C181—21no—
70C22×C181—24no—
71C22×C181—44no—
72C22×C181—48no—
73C22×C181—48no—
74C22×C181—44no—
75C22×C181—42no—
76C22×C181—42no—
77C22×C181#9912yes—
78C22×C181#10012yes—
79C22×C181C2×C22⋊C411yescharacteristic
80C22×C181C2×M1612yes—
81C4×C181—22no—
82C4×C181—22no—
83C4×C181—42no—
84C2×C181—22no—
85C2×C181—22no—
86C2×C181—22no—
87C2×C181—44no—
88C2×C181#40711yescharacteristic
89C2×C181C2×#9911yescharacteristic
90C2×C181C2×#10011yescharacteristic
91C181#146211yescharacteristic, complemented, Sylow
92#1462—1811nomaximal, Sylow
93C22×C22⋊C4D18111yescharacteristic
94#407—1812no—
95#323—1814no—
96C25Dic18111yescharacteristic
97C23×C4Dic18111yescharacteristic
98C23×C4C2×D18111yescharacteristic
99C2×M16—3622no—
100C2×C22⋊C4—22no—
101C2×C22⋊C4—22no—
102C2×C22⋊C4Dic18112yes—
103C2×C22⋊C4C2×D18112yes—
104C22⋊C8—3622no—
105C22⋊C8—1814no—
106C24—21no—
107C24—21no—
108C24—24no—
109C24—42no—
110C24—42no—
111C24C2×Dic18111yescharacteristic
112C24C2×Dic18112yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4C2×Dic18112yes—
118C22×C4C2×Dic18111yescharacteristic
119C22×C4C22⋊D18112yes—
120C22×C4C22⋊D18112yes—
121C22×C4C22×D18111yescharacteristic
122M16—7244no—
123C2×C8—3624no—
124C22⋊C4—24no—
125C22⋊C4—24no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—24no—
130C23—24no—
131C23—22no—
132C23—22no—
133C23—42no—
134C23—42no—
135C23—416no—
136C23—42no—
137C23—42no—
138C23—42no—
139C23—42no—
140C23C22⋊Dic18111yescharacteristic
141C23C22⋊Dic18111yescharacteristic
142C23#1566843314yescomplemented
143C23C22×Dic18111yescharacteristic
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4C22⋊Dic18112yes—
153C2×C4C2×C22⋊D18112yes—
154C8—7244no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—24no—
163C22—44no—
164C22—48no—
165C22—48no—
166C22—44no—
167C22—42no—
168C22—42no—
169C22#1915373112yes—
170C22#1915373312yes—
171C22C2×C22⋊Dic18111yescharacteristic
172C22C2×#1566843312yes—
173C4—22no—
174C4—22no—
175C4—42no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—44no—
180C2#2604124311yescharacteristic
181C2C2×#1915373111yescharacteristic
182C2C2×#1915373311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic181
commutatorC23×C181C22×C4
FrattiniC22×C4C22×D181
FittingC22×C22⋊C4×C181C2
socleC22×C181C2×C22⋊C4
prime radicalC25×C181C4
cosocleC22×C4×C181C23
hypercenterC22×C22⋊C4D181
hypocenterC181#1462
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #26041243C2semidirect
2. #26041003C2semidirect
6. C22⋊#13089678C22semidirect
51. C23×C181M16semidirect
91. C181#1462semidirect
142. C23#15668433semidirect

Maximal subgroups

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

subgroupindex
#260412432
#260410032
C22×C22⋊C4×C1812
#1462181