Finite Group Databasebeta

← C2×#26041914 #37547160

Subgroups — C2×#26041914 #37547160

Order 23168.

2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 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×D4×D181C214yesmaximal, complemented
2#26041914C2116yesmaximal, direct product factor
3C2×#19153787C214yesmaximal, complemented
4C2×#19153784C214yesmaximal, complemented
5C2×C4×D724C212yesmaximal, complemented
6C2×#127×C181C211yesmaximal, characteristic, complemented
7C24×D181C2214yescomplemented
8C22×D724C2212yes—
9C22×C22⋊D181C2218yescomplemented
10C2×D4×D181—232no—
11C2×D4×D181C22132yescomplemented
12C22×C4×D181C2214yescomplemented
13#19153787C22132yescomplemented
14#19153784C22132yescomplemented
15C4×D724C22116yescomplemented
16C2×C4⋊Dic181C2212yescomplemented
17C2×C22⋊Dic181C2214yescomplemented
18C2×#15668426C2214yescomplemented
19C22×D4×C181C2214yescomplemented
20C22×D4×C181C2212yescomplemented
21#127×C181C2218yescomplemented
22C2×C42×C181C2211yescharacteristic, complemented
23C23×D181—232no—
24C23×D181—48no—
25C23×D181C2314yes—
26C23×D181C23116yescomplemented
27C2×D724D4116yescomplemented
28C2×D724C2318yes—
29C2×C22⋊D181—232no—
30C2×C22⋊D181C23132yescomplemented
31D4×D181—2128no—
32C22×Dic181C2314yes—
33C2×C4×D181—216no—
34C2×C4×D181C23116yescomplemented
35C4⋊Dic181C2318yescomplemented
36C22⋊Dic181C23116yescomplemented
37#15668426C23116yescomplemented
38C24×C181C2314yes—
39C2×D4×C181—216no—
40C2×D4×C181—44no—
41C2×D4×C181C23116yescomplemented
42C2×D4×C181C2318yescomplemented
43C22×C4×C181C2311yescharacteristic
44C22×C4×C181C2312yes—
45C42×C181C2314yescomplemented
46C22×D181—28no—
47C22×D181—28no—
48C22×D181—264no—
49C22×D181—416no—
50C22×D181—464no—
51C22×D181C2×D4116yescomplemented
52C22×D181C2418yes—
53D724C2×D4132yescomplemented
54C22⋊D181—264no—
55C2×Dic181—28no—
56C2×Dic181C2418yes—
57C4×D181—232no—
58C23×C181—216no—
59C23×C181—28no—
60C23×C181C2418yes—
61C23×C181C2411yescharacteristic
62D4×C181—232no—
63D4×C181—48no—
64C2×C4×C181—22no—
65C2×C4×C181C2×D418yescomplemented
66C2×C4×C181C2412yes—
67C2×C4×C181C2414yes—
68C22×C181—216no—
69C22×C181—28no—
70C22×C181—416no—
71C22×C181C22×D414yes—
72C22×C181H(5,𝔽2)12yes—
73C22×C181C2511yescharacteristic
74C2×D181—232no—
75C2×D181—28no—
76C2×D181—28no—
77C2×D181—464no—
78C2×D181C22×D4116yescomplemented
79C4×C181—22no—
80C4×C181C22×D418yescomplemented
81Dic181—28no—
82C2×C181—48no—
83C2×C181D4214yescomplemented
84C2×C181C23×D412yes—
85C2×C181C2×H(5,𝔽2)11yescharacteristic
86D181—216no—
87C181C2×D4211yescharacteristic, complemented, Sylow
88C2×D42—1811nomaximal, Sylow
89C23×D4—1814no—
90D42—18116no—
91C2×#127D18111yescharacteristic, complemented
92C2×#121—1814no—
93C2×#120—1814no—
94C2×C4×D4—1812no—
95C25—1814no—
96C22×D4—36232no—
97C22×D4—1818no—
98C22×D4—18132no—
99C22×D4—1812no—
100C22×D4C2×D18114yescomplemented
101C22×D4C2×D18112yescomplemented
102C23×C4—1814no—
103#127C2×D18118yescomplemented
104#121—18132no—
105#120—18132no—
106C4×D4—18116no—
107C2×C4⋊C4—1812no—
108C2×C22⋊C4—1814no—
109C2×C22⋊C4—1814no—
110C2×C42C2×D18111yescharacteristic, complemented
111C24—36232no—
112C24—1814no—
113C24—18116no—
114C24—7248no—
115C24C22×D18114yes—
116C2×D4—216no—
117C2×D4—44no—
118C2×D4—362128no—
119C2×D4—36232no—
120C2×D4—18132no—
121C2×D4—18116no—
122C2×D4—1818no—
123C2×D4C22×D181116yescomplemented
124C2×D4C22×D18118yescomplemented
125C22×C4—36216no—
126C22×C4—1814no—
127C22×C4—18116no—
128C22×C4C22×D18111yescharacteristic
129C22×C4C22×D18112yes—
130C4⋊C4—1818no—
131C22⋊C4—18116no—
132C22⋊C4—18116no—
133C42C22×D18114yescomplemented
134C23—216no—
135C23—28no—
136C23—36264no—
137C23—3628no—
138C23—3628no—
139C23—18116no—
140C23—1818no—
141C23—72416no—
142C23—72464no—
143C23C23×D18118yes—
144C23C23×D18111yescharacteristic
145D4—232no—
146D4—48no—
147D4—36264no—
148D4—18132no—
149C2×C4—22no—
150C2×C4—3628no—
151C2×C4—36232no—
152C2×C4—1818no—
153C2×C4D4×D18118yescomplemented
154C2×C4C23×D18112yes—
155C2×C4C23×D18114yes—
156C22—216no—
157C22—28no—
158C22—416no—
159C22—36232no—
160C22—3628no—
161C22—3628no—
162C22—18116no—
163C22—72464no—
164C22C2×D4×D18114yes—
165C22#1915386112yes—
166C22C24×D18111yescharacteristic
167C4—22no—
168C4—3628no—
169C4C2×D4×D18118yescomplemented
170C2—48no—
171C2—36216no—
172C2#2604191414yesdirect product factor
173C2C22×D4×D18112yes—
174C2C2×#1915386111yescharacteristic
subgroupG/H
centerC23C23×D181
commutator, cosocleC22×C181C25
FrattiniC22C24×D181
FittingC2×#127×C181C2
socleC23×C181C24
hypercenterC2×#127D181
hypocenterC181C2×D42
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D181C2semidirect
2. #26041914C2direct (N × H)
3. C2×#19153787C2semidirect
4. C2×#19153784C2semidirect
5. C2×C4×D724C2semidirect
6. C2×#127×C181C2semidirect
7. C24×D181C22semidirect
9. C22×C22⋊D181C22semidirect
11. C2×D4×D181C22semidirect
12. C22×C4×D181C22semidirect
13. #19153787C22semidirect
14. #19153784C22semidirect
15. C4×D724C22semidirect
16. C2×C4⋊Dic181C22semidirect
17. C2×C22⋊Dic181C22semidirect
18. C2×#15668426C22semidirect
19. C22×D4×C181C22semidirect
20. C22×D4×C181C22semidirect
21. #127×C181C22semidirect
22. C2×C42×C181C22semidirect
26. C23×D181C23semidirect
27. C2×D724D4semidirect
30. C2×C22⋊D181C23semidirect
34. C2×C4×D181C23semidirect
35. C4⋊Dic181C23semidirect
36. C22⋊Dic181C23semidirect
37. #15668426C23semidirect
41. C2×D4×C181C23semidirect
42. C2×D4×C181C23semidirect
45. C42×C181C23semidirect
51. C22×D181C2×D4semidirect
53. D724C2×D4semidirect
65. C2×C4×C181C2×D4semidirect
78. C2×D181C22×D4semidirect
80. C4×C181C22×D4semidirect
83. C2×C181D42semidirect
87. C181C2×D42semidirect
91. C2×#127D181semidirect
100. C22×D4C2×D181semidirect
101. C22×D4C2×D181semidirect
103. #127C2×D181semidirect
110. C2×C42C2×D181semidirect
123. C2×D4C22×D181semidirect
124. C2×D4C22×D181semidirect
133. C42C22×D181semidirect
153. C2×C4D4×D181semidirect
169. C4C2×D4×D181semidirect
172. C2#26041914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1812
#260419142
C2×#191537872
C2×#191537842
C2×C4×D7242
C2×#127×C1812
C2×D42181