Finite Group Databasebeta

← #37549160

Subgroups — #37549160

Order 23168.

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

normal subgroups only

This group has 288 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
1D181⋊(C22⋊C8)C211yesmaximal, characteristic
2#26042221C211yesmaximal, characteristic
3#26042132C214yesmaximal, complemented
4C2×#19153796C211yesmaximal, characteristic
5C2×D181⋊C8—21no—
6C2×C4⋊#10624382—21no—
7C2×C22⋊#10624382—21no—
8#19153873C2212yes—
9C22⋊#13089685—21no—
10(C2×#10624382)⋊C4C2212yes—
11C22×Dic362C411yescharacteristic, complemented
12C22×C4×D181C2211yescharacteristic
13#19153796—21no—
14#19153796—21no—
15#19153796C412yescomplemented
16#19153796C2212yes—
17C2×C4⋊Dic181—21no—
18C2×#15668426—21no—
19C2×C4⋊C4×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21D181⋊C8—42no—
22C2×#13089685—22no—
23C4⋊#10624382—42no—
24C22⋊#10624382—42no—
25C23×D181D411yescharacteristic
26C2×Dic362—21no—
27C2×Dic362—42no—
28C2×Dic362C2×C412yes—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C2×C4×D181—42no—
32C2×C4×D181C2×C411yescharacteristic
33C2×C4×D181D411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181C2311yescharacteristic
36C4⋊Dic181—22no—
37C4⋊Dic181—22no—
38#15668426—22no—
39#15668426—22no—
40C22×C4×C181—21no—
41C22×C4×C181C2×C411yescharacteristic
42C4⋊C4×C181—21no—
43C4⋊C4×C181C2×C412yes—
44C2×#10624382—42no—
45C2×#10624382—42no—
46C2×#10624382—42no—
47#13089685—42no—
48C22×D181—41no—
49C22×D181—41no—
50C22×D181C22⋊C411yescharacteristic
51C22×D181SD1612yes—
52C22×D181Q1612yes—
53C22×D181C2×D411yescharacteristic
54Dic362—42no—
55Dic362—42no—
56C2×Dic181—22no—
57C2×Dic181—41no—
58C2×Dic181—42no—
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C2×D411yescharacteristic
61C4×D181—22no—
62C4×D181—22no—
63C4×D181—41no—
64C4×D181—41no—
65C23×C181C22⋊C411yescharacteristic
66C2×C4×C181—22no—
67C2×C4×C181—22no—
68C2×C4×C181—42no—
69C2×C4×C181C22⋊C411yescharacteristic
70C2×C4×C181C22×C411yescharacteristic
71C22×C181—21no—
72C22×C181—21no—
73C22×C181#10312yes—
74C22×C181C2×C22⋊C411yescharacteristic
75C2×D181—21no—
76C2×D181—21no—
77C2×D181—21no—
78C2×D181—21no—
79C2×D181—42no—
80C2×D181—42no—
81C2×D181#10312yes—
82C2×D181C2×SD1611yescharacteristic
83C2×D181C2×Q1611yescharacteristic
84#10624382—82no—
85C4×C181—21no—
86C4×C181—42no—
87C4×C181#9912yes—
88Dic181—21no—
89Dic181—21no—
90Dic181—42no—
91C2×C181—22no—
92C2×C181C2×#9911yescharacteristic
93C2×C181C2×#10311yescharacteristic
94C2×C181#42111yescharacteristic
95D181—21no—
96D181—22no—
97D181—21no—
98C181#152011yescharacteristic, complemented, Sylow
99#1520—1811nomaximal, Sylow
100C2×C22⋊Q8—1811no—
101C2×C22⋊C8—1811no—
102#380—1811no—
103#328—1814no—
104C22×Q8—1811no—
105C23×C4—1811no—
106C22×C8—3621no—
107C22⋊Q8—3621no—
108C22⋊Q8—3621no—
109C22⋊Q8—1812no—
110C22⋊Q8—1812no—
111C2×C4⋊C4—3621no—
112C2×C4⋊C4—3621no—
113C2×C4⋊C4#1062438211yescharacteristic, complemented
114C2×C22⋊C4—3621no—
115C2×C22⋊C4—3621no—
116C22⋊C8—3621no—
117C22⋊C8—1812no—
118#95—1812no—
119C24—1811no—
120C2×Q8—3621no—
121C2×Q8—1812no—
122C2×Q8—7242no—
123C22×C4—21no—
124C22×C4—3621no—
125C22×C4—3622no—
126C22×C4—1811no—
127C22×C4—1811no—
128C22×C4—1811no—
129C22×C4—1811no—
130C22×C4—1811no—
131C22×C4—7242no—
132C22×C4C2×#1062438211yescharacteristic
133C2×C8—3622no—
134C2×C8—7242no—
135C4⋊C4—21no—
136C4⋊C4—3622no—
137C4⋊C4—3622no—
138C4⋊C4—7242no—
139C4⋊C4C2×#1062438212yes—
140C22⋊C4—3622no—
141C22⋊C4—3622no—
142C22⋊C4—7242no—
143C23—1811no—
144C23—1811no—
145C23—1812no—
146C23—1812no—
147C23—7241no—
148C23—7241no—
149C23C22⋊#1062438211yescharacteristic
150Q8—7242no—
151Q8—7242no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—3622no—
156C2×C4—3622no—
157C2×C4—3622no—
158C2×C4—1811no—
159C2×C4—1811no—
160C2×C4—7241no—
161C2×C4—7241no—
162C2×C4—7241no—
163C2×C4—7242no—
164C2×C4—7242no—
165C2×C4—7242no—
166C2×C4—7242no—
167C2×C4C22⋊#1062438211yescharacteristic
168C2×C4C22×#1062438211yescharacteristic
169C8—7242no—
170C22—21no—
171C22—21no—
172C22—3621no—
173C22—3621no—
174C22—3621no—
175C22—3621no—
176C22—1811no—
177C22—1812no—
178C22—1811no—
179C22—7242no—
180C22—7242no—
181C22#1915387912yes—
182C22C2×C22⋊#1062438211yescharacteristic
183C4—21no—
184C4—42no—
185C4—3621no—
186C4—3621no—
187C4—14482no—
188C4—7242no—
189C4#1915387512yes—
190C2—22no—
191C2—3621no—
192C2—3621no—
193C2—3622no—
194C2C2×#1915387511yescharacteristic
195C2C2×#1915387911yescharacteristic
196C2#2604227711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181D4
cosocleC2×C4×D181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1520
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #26042132C2semidirect
11. C22×Dic362C4semidirect
15. #19153796C4semidirect
19. C2×C4⋊C4×C181C4semidirect
98. C181#1520semidirect
113. C2×C4⋊C4#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C22⋊C8)2
#260422212
#260421322
C2×#191537962
#1520181