Finite Group Databasebeta

← D4×C22⋊D37 #14558166

Subgroups — D4×C22⋊D37 #14558166

Order 2368.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×C22⋊D37C212yesmaximal, complemented
2C2×D4×D37C211yesmaximal, characteristic, complemented
3#11924532C211yesmaximal, characteristic, complemented
4#11924510C211yesmaximal, characteristic, complemented
5#11924508C212yesmaximal, complemented
6#11924507C211yesmaximal, characteristic, complemented
7#11924505C212yesmaximal, complemented
8#11924504C212yesmaximal, complemented
9D4×Dic37C211yesmaximal, characteristic, complemented
10C4×C22⋊D37C211yesmaximal, characteristic, complemented
11C22×D4×C37C211yesmaximal, characteristic, complemented
12C24×C37C2212yescomplemented
13C23×D37C2212yescomplemented
14C2×D4×C37—24no—
15C2×D4×C37C2211yescharacteristic
16C2×D4×C37C2212yescomplemented
17C2×D4×C37C2211yescharacteristic, complemented
18C22×C4×C37C2211yescharacteristic, complemented
19C2×C22⋊D37—28no—
20C2×C22⋊D37C2211yescharacteristic
21C2×C22⋊D37C2212yescomplemented
22C2×C22⋊D37C2212yescomplemented
23C2×C22⋊D37C2212yescomplemented
24C2×C22⋊D37C2212yescomplemented
25C2×C22⋊D37C2212yescomplemented
26C22×Dic37C2212yescomplemented
27D4×D37—24no—
28C2×D148C2211yescharacteristic, complemented
29C2×C4×D37C2211yescharacteristic, complemented
30C22⋊Dic37C2211yescharacteristic, complemented
31C22⋊Dic37C2212yescomplemented
32C22⋊Dic37C2212yescomplemented
33#10596938C2211yescharacteristic, complemented
34#10596938C2212yescomplemented
35C4⋊Dic37C2211yescharacteristic, complemented
36#10596936C2211yescharacteristic, complemented
37C4×Dic37C2211yescharacteristic, complemented
38C23×C37—24no—
39C23×C37—24no—
40C23×C37—42no—
41C23×C37C2312yes—
42C23×C37C2312yes—
43C23×C37C2311yescharacteristic
44C22×D37—24no—
45C22×D37—24no—
46C22×D37—42no—
47C22×D37C2312yes—
48C22×D37C2311yescharacteristic
49D4×C37—24no—
50D4×C37—22no—
51D4×C37D414yescomplemented
52C2×C4×C37—22no—
53C2×C4×C37C2311yescharacteristic
54C2×C4×C37C2311yescharacteristic
55C22⋊D37—24no—
56C22⋊D37—24no—
57C22⋊D37—24no—
58C22⋊D37—24no—
59C22⋊D37—42no—
60C22⋊D37D414yesdirect product factor
61C2×Dic37—24no—
62C2×Dic37C2311yescharacteristic
63C2×Dic37C2311yescharacteristic
64C2×Dic37C2312yes—
65C2×Dic37C2311yescharacteristic
66D148—22no—
67C4×D37—22no—
68C22×C37—22no—
69C22×C37—21no—
70C22×C37—22no—
71C22×C37—21no—
72C22×C37—22no—
73C22×C37—22no—
74C22×C37—22no—
75C22×C37—48no—
76C22×C37C2×D412yescomplemented
77C22×C37C2×D414yescomplemented
78C22×C37C2411yescharacteristic
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—22no—
82C2×D37—22no—
83C2×D37—22no—
84C2×D37—48no—
85C2×D37C2×D412yescomplemented
86C4×C37—21no—
87C4×C37C2×D412yescomplemented
88Dic37—21no—
89Dic37—22no—
90Dic37—21no—
91Dic37C2×D412yescomplemented
92C2×C37—24no—
93C2×C37—22no—
94C2×C37—42no—
95C2×C37C22×D411yescharacteristic
96C2×C37C22×D411yescharacteristic
97C2×C37H(5,𝔽2)11yescharacteristic
98D37—22no—
99D37—42no—
100D42—371nomaximal, Sylow
101C37D4211yescharacteristic, complemented, Sylow
102C22×D4—372no—
103C22×D4—371no—
104C22×D4D3711yescharacteristic, complemented
105#127—371no—
106#121—371no—
107#121—372no—
108#121—371no—
109#120—372no—
110#120—372no—
111C4×D4—371no—
112C4×D4—371no—
113C24—372no—
114C24C2×D3712yescomplemented
115C2×D4—24no—
116C2×D4—371no—
117C2×D4—372no—
118C2×D4—372no—
119C2×D4—372no—
120C2×D4—372no—
121C2×D4—372no—
122C2×D4—371no—
123C2×D4—748no—
124C2×D4—744no—
125C2×D4C2×D3711yescharacteristic
126C2×D4C2×D3712yescomplemented
127C2×D4C2×D3711yescharacteristic, complemented
128C22×C4—372no—
129C22×C4—371no—
130C22×C4C2×D3711yescharacteristic, complemented
131C4⋊C4—371no—
132C4⋊C4—371no—
133C22⋊C4—371no—
134C22⋊C4—372no—
135C22⋊C4—372no—
136C22⋊C4—371no—
137C22⋊C4—372no—
138C42—371no—
139C23—24no—
140C23—24no—
141C23—42no—
142C23—371no—
143C23—372no—
144C23—744no—
145C23—744no—
146C23—1482no—
147C23C22×D3712yes—
148C23C22×D3711yescharacteristic
149C23C22×D3712yes—
150D4—24no—
151D4—22no—
152D4—374no—
153D4—744no—
154D4—744no—
155D4—744no—
156D4—744no—
157D4—742no—
158D4—1482no—
159D4C22⋊D3714yesdirect product factor
160C2×C4—22no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—372no—
164C2×C4—371no—
165C2×C4—744no—
166C2×C4—742no—
167C2×C4C22×D3711yescharacteristic
168C2×C4C22×D3711yescharacteristic
169C22—22no—
170C22—21no—
171C22—21no—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—22no—
176C22—48no—
177C22—372no—
178C22—741no—
179C22—741no—
180C22—742no—
181C22—742no—
182C22—742no—
183C22—1488no—
184C22D4×D3712yescomplemented
185C22C2×C22⋊D3714yescomplemented
186C22C23×D3711yescharacteristic
187C4—21no—
188C4—372no—
189C4—742no—
190C4—741no—
191C4—741no—
192C4C2×C22⋊D3712yescomplemented
193C2—22no—
194C2—24no—
195C2—42no—
196C2—742no—
197C2—1482no—
198C2C2×D4×D3711yescharacteristic
199C2C22×C22⋊D3711yescharacteristic
200C2#1192458111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
FittingC22×D4×C37C2
hypercenterC22×D4D37
hypocenterC37D42
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D37C2semidirect
2. C2×D4×D37C2semidirect
3. #11924532C2semidirect
4. #11924510C2semidirect
5. #11924508C2semidirect
6. #11924507C2semidirect
7. #11924505C2semidirect
8. #11924504C2semidirect
9. D4×Dic37C2semidirect
10. C4×C22⋊D37C2semidirect
11. C22×D4×C37C2semidirect
12. C24×C37C22semidirect
13. C23×D37C22semidirect
16. C2×D4×C37C22semidirect
17. C2×D4×C37C22semidirect
18. C22×C4×C37C22semidirect
21. C2×C22⋊D37C22semidirect
22. C2×C22⋊D37C22semidirect
23. C2×C22⋊D37C22semidirect
24. C2×C22⋊D37C22semidirect
25. C2×C22⋊D37C22semidirect
26. C22×Dic37C22semidirect
28. C2×D148C22semidirect
29. C2×C4×D37C22semidirect
30. C22⋊Dic37C22semidirect
31. C22⋊Dic37C22semidirect
32. C22⋊Dic37C22semidirect
33. #10596938C22semidirect
34. #10596938C22semidirect
35. C4⋊Dic37C22semidirect
36. #10596936C22semidirect
37. C4×Dic37C22semidirect
51. D4×C37D4semidirect
60. C22⋊D37D4direct (N × H)
76. C22×C37C2×D4semidirect
77. C22×C37C2×D4semidirect
85. C2×D37C2×D4semidirect
87. C4×C37C2×D4semidirect
91. Dic37C2×D4semidirect
101. C37D42semidirect
104. C22×D4D37semidirect
114. C24C2×D37semidirect
126. C2×D4C2×D37semidirect
127. C2×D4C2×D37semidirect
130. C22×C4C2×D37semidirect
159. D4C22⋊D37direct (N × H)
184. C22D4×D37semidirect
185. C22C2×C22⋊D37semidirect
192. C4C2×C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D372
C2×D4×D372
#119245322
#119245102
#119245082
#119245072
#119245052
#119245042
D4×Dic372
C4×C22⋊D372
C22×D4×C372
D4237