Finite Group Databasebeta

← #37549457

Subgroups — #37549457

Order 23168.

360 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 110 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
2C2×#19153870C212yesmaximal, complemented
3C4×C22⋊#10624382C211yesmaximal, characteristic
4(C2×#10624382)⋊C8C212yesmaximal, complemented
5C22×C8×D181C211yesmaximal, characteristic
6C2×D181⋊C8C2212yes—
7C2×C22⋊#10624382C412yes—
8C2×C4×#10624382C2212yes—
9#19153873C412yescomplemented
10C22⋊#13089685C412yescomplemented
11#19153870—24no—
12(C2×#10624382)⋊C4C412yes—
13C22×C4×D181C2211yescharacteristic
14C22×#13089678C411yescharacteristic, complemented
15C2×C8×D181—24no—
16C2×C8×D181C411yescharacteristic, complemented
17C2×C8×D181C411yescharacteristic, complemented
18C2×C8×D181C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20C22×C8×C181C411yescharacteristic, complemented
21C22×#10624382C2×C414yes—
22D181⋊C8—22no—
23D181⋊C8—22no—
24C2×#13089685C2×C414yes—
25C22⋊#10624382—24no—
26C4×#10624382—22no—
27C4×#10624382—22no—
28C23×D181C2×C411yescharacteristic
29C22×Dic181C2×C411yescharacteristic
30C2×C4×D181—22no—
31C2×C4×D181—22no—
32C2×C4×D181C2×C411yescharacteristic
33C2×C4×D181C2×C411yescharacteristic
34C2×C4×D181C2×C411yescharacteristic
35C2×C4×D181C2311yescharacteristic
36C2×#13089678—22no—
37C2×#13089678C2×C411yescharacteristic
38C2×#13089678C2×C411yescharacteristic
39C8×D181—22no—
40C8×D181—22no—
41C8×D181—22no—
42C8×D181D414yes—
43C22×C4×C181C2×C411yescharacteristic
44C2×C8×C181—22no—
45C2×C8×C181C2×C411yescharacteristic
46C2×C8×C181C2×C411yescharacteristic
47C2×#10624382—24no—
48C2×#10624382—24no—
49C2×#10624382—24no—
50#13089685—24no—
51C22×D181—22no—
52C22×D181—22no—
53C22×D181C4211yescharacteristic
54C22×D181M1614yes—
55C22×D181C22×C411yescharacteristic
56C2×Dic181—22no—
57C2×Dic181C4211yescharacteristic
58C2×Dic181C22×C411yescharacteristic
59C4×D181—22no—
60C4×D181—21no—
61C4×D181—21no—
62C4×D181—22no—
63C4×D181C2×D412yes—
64C4×D181#4112yes—
65#13089678—21no—
66#13089678C22⋊C412yescomplemented
67C23×C181C4211yescharacteristic
68C2×C4×C181—21no—
69C2×C4×C181—21no—
70C2×C4×C181C4211yescharacteristic
71C2×C4×C181C22×C411yescharacteristic
72C8×C181—21no—
73C8×C181C22⋊C412yescomplemented
74C22×C181—21no—
75C22×C181—21no—
76C22×C181#9712yescomplemented
77C22×C181C2×C4211yescharacteristic
78C2×D181—21no—
79C2×D181—21no—
80C2×D181—28no—
81C2×D181#9712yescomplemented
82C2×D181C4×D412yes—
83C2×D181C2×M1612yes—
84C2×D181#13112yes—
85#10624382—44no—
86C4×C181—21no—
87C4×C181C2×C22⋊C411yescharacteristic
88C4×C181#11711yescharacteristic
89Dic181—21no—
90Dic181C4×D412yes—
91C2×C181—22no—
92C2×C181C4×C22⋊C411yescharacteristic
93C2×C181C2×#9711yescharacteristic
94C2×C181#40511yescharacteristic
95D181—22no—
96D181#43514yes—
97C181#175211yescharacteristic, complemented, Sylow
98#1752—1811nomaximal, Sylow
99C23×C8—1811no—
100C2×C22⋊C8—1811no—
101C2×#97—1812no—
102C4×C22⋊C4—1811no—
103#336—1812no—
104C23×C4—1811no—
105C22×C8—3624no—
106C22×C8—1812no—
107C22×C8—1811no—
108C22×C8—1811no—
109C22×C8—1811no—
110C22×C8—1811no—
111C22×C8—1811no—
112C22×C8#1062438211yescharacteristic, complemented
113C2×C22⋊C4—1812no—
114C2×C42—1812no—
115C22⋊C8—1812no—
116C22⋊C8—1812no—
117#97—3624no—
118#95—1812no—
119C24—1811no—
120C22×C4—3622no—
121C22×C4—3622no—
122C22×C4—1814no—
123C22×C4—1811no—
124C22×C4—1811no—
125C22×C4—1811no—
126C22×C4—1811no—
127C22×C4—1811no—
128C22×C4C2×#1062438211yescharacteristic
129C2×C8—22no—
130C2×C8—3622no—
131C2×C8—3622no—
132C2×C8—3622no—
133C2×C8—3622no—
134C2×C8—3622no—
135C2×C8—3622no—
136C2×C8—1814no—
137C2×C8—1811no—
138C2×C8—1811no—
139C2×C8—1814no—
140C2×C8C2×#1062438211yescharacteristic
141C2×C8C2×#1062438211yescharacteristic
142C22⋊C4—3624no—
143C42—3622no—
144C42—3622no—
145C23—3622no—
146C23—3622no—
147C23—1814no—
148C23—1811no—
149C23—1811no—
150C23C4×#1062438211yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3622no—
154C2×C4—3622no—
155C2×C4—3622no—
156C2×C4—3621no—
157C2×C4—3621no—
158C2×C4—3624no—
159C2×C4—3624no—
160C2×C4—3624no—
161C2×C4—1811no—
162C2×C4—1811no—
163C2×C4—1812no—
164C2×C4—1812no—
165C2×C4C4×#1062438211yescharacteristic
166C2×C4C22×#1062438211yescharacteristic
167C8—21no—
168C8—3624no—
169C8—3621no—
170C8—1812no—
171C8C22⋊#1062438212yescomplemented
172C22—21no—
173C22—21no—
174C22—3628no—
175C22—3621no—
176C22—3621no—
177C22—1812no—
178C22—1812no—
179C22—1812no—
180C22—1812no—
181C22#1915387012yescomplemented
182C22C2×C4×#1062438211yescharacteristic
183C4—21no—
184C4—3621no—
185C4—1812no—
186C4—7244no—
187C4C2×C22⋊#1062438211yescharacteristic
188C4#1915389511yescharacteristic
189C2—22no—
190C2—3622no—
191C2—1814no—
192C2C4×C22⋊#1062438211yescharacteristic
193C2C2×#1915387011yescharacteristic
194C2#2604224211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#10624382
commutator, socleC22×C181C2×C42
FittingC22×C8×C181C4
prime radicalC23×D181C2×C4
cosocleC2×C4×D181C23
hypercenterC22×C8#10624382
hypocenterC181#1752
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#19153870C2semidirect
4. (C2×#10624382)⋊C8C2semidirect
9. #19153873C4semidirect
10. C22⋊#13089685C4semidirect
14. C22×#13089678C4semidirect
16. C2×C8×D181C4semidirect
17. C2×C8×D181C4semidirect
20. C22×C8×C181C4semidirect
66. #13089678C22⋊C4semidirect
73. C8×C181C22⋊C4semidirect
76. C22×C181#97semidirect
81. C2×D181#97semidirect
97. C181#1752semidirect
112. C22×C8#10624382semidirect
171. C8C22⋊#10624382semidirect
181. C22#19153870semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C22⋊C8)2
C2×#191538702
C4×C22⋊#106243822
(C2×#10624382)⋊C82
C22×C8×D1812
#1752181