Finite Group Databasebeta

← #26041913

Subgroups — #26041913

Order 11584.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22×D724C211yesmaximal, characteristic, complemented
2C2×D4×D181C212yesmaximal, complemented
3C2×D4×D181C211yesmaximal, characteristic, complemented
4#19153812C211yesmaximal, characteristic, complemented
5#19153791C211yesmaximal, characteristic, complemented
6#19153789C212yesmaximal, complemented
7#19153786C212yesmaximal, complemented
8#19153784C212yesmaximal, complemented
9#19153778C211yesmaximal, characteristic, complemented
10C4×C22⋊D181C211yesmaximal, characteristic, complemented
11#121×C181C211yesmaximal, characteristic, complemented
12C23×D181C2212yescomplemented
13C23×D181C2212yescomplemented
14C2×D724—24no—
15C2×D724C2211yescharacteristic
16C2×D724C2212yescomplemented
17C2×D724C2212yescomplemented
18C2×D724C2211yescharacteristic, complemented
19C2×C22⋊D181C2211yescharacteristic
20C2×C22⋊D181C2212yescomplemented
21C2×C22⋊D181C2212yescomplemented
22C2×C22⋊D181C2212yescomplemented
23D4×D181—24no—
24D4×D181—28no—
25C2×C4×D181C2211yescharacteristic, complemented
26C2×C4×D181C2212yescomplemented
27#15668428C2211yescharacteristic, complemented
28C22⋊Dic181C2211yescharacteristic, complemented
29#15668426C2211yescharacteristic, complemented
30#15668426C2212yescomplemented
31#15668426C2212yescomplemented
32C4×Dic181C2211yescharacteristic, complemented
33C2×D4×C181C2212yescomplemented
34C2×D4×C181C2211yescharacteristic, complemented
35C22×C4×C181C2211yescharacteristic, complemented
36C4⋊C4×C181C2211yescharacteristic, complemented
37C22⋊C4×C181C2212yescomplemented
38C22×D181—24no—
39C22×D181—24no—
40C22×D181—24no—
41C22×D181—24no—
42C22×D181—42no—
43C22×D181—42no—
44C22×D181C2312yes—
45C22×D181C2311yescharacteristic
46C22×D181C2312yes—
47D724—24no—
48D724—24no—
49D724—22no—
50D724D414yescomplemented
51C22⋊D181—24no—
52C22⋊D181—24no—
53C22⋊D181—42no—
54C22⋊D181D414yescomplemented
55C2×Dic181C2311yescharacteristic
56C2×Dic181C2311yescharacteristic
57C2×Dic181C2311yescharacteristic
58C4×D181—22no—
59C4×D181—24no—
60C23×C181C2312yes—
61C23×C181C2311yescharacteristic
62D4×C181—24no—
63D4×C181—22no—
64C2×C4×C181—22no—
65C2×C4×C181C2311yescharacteristic
66C2×C4×C181C2312yes—
67C2×C4×C181C2311yescharacteristic
68C22×C181—21no—
69C22×C181—21no—
70C22×C181—22no—
71C22×C181—22no—
72C22×C181—22no—
73C22×C181C2×D412yescomplemented
74C22×C181C2411yescharacteristic
75C2×D181—21no—
76C2×D181—22no—
77C2×D181—21no—
78C2×D181—22no—
79C2×D181—22no—
80C2×D181—22no—
81C2×D181—22no—
82C2×D181—48no—
83C2×D181—48no—
84C2×D181C2×D414yescomplemented
85C2×D181C2×D412yescomplemented
86C4×C181—21no—
87C4×C181—22no—
88C4×C181C2×D412yescomplemented
89Dic181—21no—
90Dic181—21no—
91Dic181C2×D412yescomplemented
92C2×C181—22no—
93C2×C181—42no—
94C2×C181C22×D411yescharacteristic
95C2×C181C22×D411yescharacteristic
96C2×C181H(5,𝔽2)11yescharacteristic
97D181—22no—
98D181—24no—
99D181—42no—
100C181D4211yescharacteristic, complemented, Sylow
101D42—1811nomaximal, Sylow
102C22×D4—1811no—
103C22×D4—1812no—
104C22×D4—1811no—
105#127—1811no—
106#121—1811no—
107#121—1812no—
108#121D18111yescharacteristic, complemented
109#120—1812no—
110#120—1812no—
111C4×D4—1811no—
112C4×D4—1811no—
113C24—1812no—
114C24—1812no—
115C2×D4—3624no—
116C2×D4—3628no—
117C2×D4—3624no—
118C2×D4—1812no—
119C2×D4—1812no—
120C2×D4—1811no—
121C2×D4—1812no—
122C2×D4—1812no—
123C2×D4—1812no—
124C2×D4—1811no—
125C2×D4—1811no—
126C2×D4C2×D18112yescomplemented
127C2×D4C2×D18111yescharacteristic, complemented
128C22×C4—1812no—
129C22×C4—1811no—
130C22×C4C2×D18111yescharacteristic, complemented
131C4⋊C4—1811no—
132C4⋊C4C2×D18111yescharacteristic, complemented
133C22⋊C4—1811no—
134C22⋊C4—1812no—
135C22⋊C4—1811no—
136C22⋊C4—1812no—
137C22⋊C4C2×D18112yescomplemented
138C42—1811no—
139C23—3624no—
140C23—3624no—
141C23—3624no—
142C23—3624no—
143C23—1812no—
144C23—1812no—
145C23—1811no—
146C23—7242no—
147C23—7242no—
148C23C22×D18112yes—
149C23C22×D18111yescharacteristic
150D4—24no—
151D4—22no—
152D4—3624no—
153D4—3624no—
154D4—3624no—
155D4—3624no—
156D4—3622no—
157D4—1814no—
158D4—1814no—
159D4—7242no—
160C2×C4—22no—
161C2×C4—3624no—
162C2×C4—3622no—
163C2×C4—1811no—
164C2×C4—1811no—
165C2×C4—1811no—
166C2×C4C22×D18112yes—
167C2×C4C22×D18111yescharacteristic
168C2×C4C22×D18111yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—3622no—
175C22—3621no—
176C22—3622no—
177C22—3621no—
178C22—3622no—
179C22—3622no—
180C22—3622no—
181C22—1812no—
182C22—1814no—
183C22—7248no—
184C22—7248no—
185C22D4×D18112yescomplemented
186C22C23×D18111yescharacteristic
187C4—21no—
188C4—22no—
189C4—3621no—
190C4—3621no—
191C4—1812no—
192C4D4×D18112yescomplemented
193C2—22no—
194C2—42no—
195C2—3624no—
196C2—3622no—
197C2—7242no—
198C2C2×D4×D18111yescharacteristic
199C2C2×D4×D18111yescharacteristic
200C2#1915386211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D181
commutator, socle, cosocleC22×C181C24
Fitting#121×C181C2
hypercenter#121D181
hypocenterC181D42
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D724C2semidirect
2. C2×D4×D181C2semidirect
3. C2×D4×D181C2semidirect
4. #19153812C2semidirect
5. #19153791C2semidirect
6. #19153789C2semidirect
7. #19153786C2semidirect
8. #19153784C2semidirect
9. #19153778C2semidirect
10. C4×C22⋊D181C2semidirect
11. #121×C181C2semidirect
12. C23×D181C22semidirect
13. C23×D181C22semidirect
16. C2×D724C22semidirect
17. C2×D724C22semidirect
18. C2×D724C22semidirect
20. C2×C22⋊D181C22semidirect
21. C2×C22⋊D181C22semidirect
22. C2×C22⋊D181C22semidirect
25. C2×C4×D181C22semidirect
26. C2×C4×D181C22semidirect
27. #15668428C22semidirect
28. C22⋊Dic181C22semidirect
29. #15668426C22semidirect
30. #15668426C22semidirect
31. #15668426C22semidirect
32. C4×Dic181C22semidirect
33. C2×D4×C181C22semidirect
34. C2×D4×C181C22semidirect
35. C22×C4×C181C22semidirect
36. C4⋊C4×C181C22semidirect
37. C22⋊C4×C181C22semidirect
50. D724D4semidirect
54. C22⋊D181D4semidirect
73. C22×C181C2×D4semidirect
84. C2×D181C2×D4semidirect
85. C2×D181C2×D4semidirect
88. C4×C181C2×D4semidirect
91. Dic181C2×D4semidirect
100. C181D42semidirect
108. #121D181semidirect
126. C2×D4C2×D181semidirect
127. C2×D4C2×D181semidirect
130. C22×C4C2×D181semidirect
132. C4⋊C4C2×D181semidirect
137. C22⋊C4C2×D181semidirect
185. C22D4×D181semidirect
192. C4D4×D181semidirect

Maximal subgroups

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

subgroupindex
C22×D7242
C2×D4×D1812
#191538122
#191537912
#191537892
#191537862
#191537842
#191537782
C4×C22⋊D1812
#121×C1812
D42181