Finite Group Databasebeta

← #14558167

Subgroups — #14558167

Order 2368.

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×D148C211yesmaximal, characteristic, complemented
2C2×D4×D37C211yesmaximal, characteristic, complemented
3C2×D4×D37C212yesmaximal, complemented
4#11924532C211yesmaximal, characteristic, complemented
5#11924511C211yesmaximal, characteristic, complemented
6#11924509C212yesmaximal, complemented
7#11924506C212yesmaximal, complemented
8#11924504C212yesmaximal, complemented
9#11924498C211yesmaximal, characteristic, complemented
10C4×C22⋊D37C211yesmaximal, characteristic, complemented
11#121×C37C211yesmaximal, characteristic, complemented
12C23×D37C2212yescomplemented
13C23×D37C2212yescomplemented
14C2×D4×C37C2212yescomplemented
15C2×D4×C37C2211yescharacteristic, complemented
16C22×C4×C37C2211yescharacteristic, complemented
17C2×C22⋊D37C2211yescharacteristic
18C2×C22⋊D37C2212yescomplemented
19C2×C22⋊D37C2212yescomplemented
20C2×C22⋊D37C2212yescomplemented
21D4×D37—28no—
22D4×D37—24no—
23C2×D148—24no—
24C2×D148C2211yescharacteristic
25C2×D148C2212yescomplemented
26C2×D148C2212yescomplemented
27C2×D148C2211yescharacteristic, complemented
28C2×C4×D37C2211yescharacteristic, complemented
29C2×C4×D37C2212yescomplemented
30C4⋊C4×C37C2211yescharacteristic, complemented
31C22⋊C4×C37C2212yescomplemented
32C22⋊Dic37C2211yescharacteristic, complemented
33#10596938C2211yescharacteristic, complemented
34#10596938C2212yescomplemented
35#10596938C2212yescomplemented
36#10596936C2211yescharacteristic, complemented
37C4×Dic37C2211yescharacteristic, complemented
38C23×C37C2312yes—
39C23×C37C2311yescharacteristic
40C22×D37—24no—
41C22×D37—24no—
42C22×D37—24no—
43C22×D37—24no—
44C22×D37—42no—
45C22×D37—42no—
46C22×D37C2312yes—
47C22×D37C2312yes—
48C22×D37C2311yescharacteristic
49D4×C37—24no—
50D4×C37—22no—
51C2×C4×C37—22no—
52C2×C4×C37C2311yescharacteristic
53C2×C4×C37C2312yes—
54C2×C4×C37C2311yescharacteristic
55C22⋊D37—24no—
56C22⋊D37—24no—
57C22⋊D37—42no—
58C22⋊D37D414yescomplemented
59C2×Dic37C2311yescharacteristic
60C2×Dic37C2311yescharacteristic
61C2×Dic37C2311yescharacteristic
62D148—24no—
63D148—24no—
64D148—22no—
65D148D414yescomplemented
66C4×D37—22no—
67C4×D37—24no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—22no—
71C22×C37—22no—
72C22×C37—22no—
73C22×C37C2×D412yescomplemented
74C22×C37C2411yescharacteristic
75C2×D37—21no—
76C2×D37—22no—
77C2×D37—22no—
78C2×D37—21no—
79C2×D37—22no—
80C2×D37—22no—
81C2×D37—22no—
82C2×D37—48no—
83C2×D37—48no—
84C2×D37C2×D412yescomplemented
85C2×D37C2×D414yescomplemented
86C4×C37—22no—
87C4×C37—21no—
88C4×C37C2×D412yescomplemented
89Dic37—21no—
90Dic37—21no—
91Dic37C2×D412yescomplemented
92C2×C37—22no—
93C2×C37—42no—
94C2×C37C22×D411yescharacteristic
95C2×C37C22×D411yescharacteristic
96C2×C37H(5,𝔽2)11yescharacteristic
97D37—22no—
98D37—24no—
99D37—42no—
100D42—371nomaximal, Sylow
101C37D4211yescharacteristic, complemented, Sylow
102C22×D4—372no—
103C22×D4—371no—
104C22×D4—371no—
105#127—371no—
106#121—371no—
107#121—372no—
108#121D3711yescharacteristic, complemented
109#120—372no—
110#120—372no—
111C4×D4—371no—
112C4×D4—371no—
113C24—372no—
114C24—372no—
115C2×D4—371no—
116C2×D4—372no—
117C2×D4—372no—
118C2×D4—372no—
119C2×D4—371no—
120C2×D4—372no—
121C2×D4—372no—
122C2×D4—371no—
123C2×D4—744no—
124C2×D4—748no—
125C2×D4—744no—
126C2×D4C2×D3712yescomplemented
127C2×D4C2×D3711yescharacteristic, complemented
128C22×C4—372no—
129C22×C4—371no—
130C22×C4C2×D3711yescharacteristic, complemented
131C4⋊C4—371no—
132C4⋊C4C2×D3711yescharacteristic, complemented
133C22⋊C4—371no—
134C22⋊C4—372no—
135C22⋊C4—371no—
136C22⋊C4—372no—
137C22⋊C4C2×D3712yescomplemented
138C42—371no—
139C23—371no—
140C23—372no—
141C23—372no—
142C23—744no—
143C23—744no—
144C23—744no—
145C23—744no—
146C23—1482no—
147C23—1482no—
148C23C22×D3712yes—
149C23C22×D3711yescharacteristic
150D4—24no—
151D4—22no—
152D4—374no—
153D4—374no—
154D4—744no—
155D4—744no—
156D4—744no—
157D4—744no—
158D4—742no—
159D4—1482no—
160C2×C4—22no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—744no—
165C2×C4—742no—
166C2×C4C22×D3712yes—
167C2×C4C22×D3711yescharacteristic
168C2×C4C22×D3711yescharacteristic
169C22—21no—
170C22—21no—
171C22—22no—
172C22—22no—
173C22—22no—
174C22—372no—
175C22—374no—
176C22—742no—
177C22—741no—
178C22—742no—
179C22—741no—
180C22—742no—
181C22—742no—
182C22—742no—
183C22—1488no—
184C22—1488no—
185C22D4×D3712yescomplemented
186C22C23×D3711yescharacteristic
187C4—21no—
188C4—22no—
189C4—372no—
190C4—741no—
191C4—741no—
192C4D4×D3712yescomplemented
193C2—22no—
194C2—42no—
195C2—744no—
196C2—742no—
197C2—1482no—
198C2C2×D4×D3711yescharacteristic
199C2C2×D4×D3711yescharacteristic
200C2#1192458211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
Fitting#121×C37C2
hypercenter#121D37
hypocenterC37D42
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×D148C2semidirect
2. C2×D4×D37C2semidirect
3. C2×D4×D37C2semidirect
4. #11924532C2semidirect
5. #11924511C2semidirect
6. #11924509C2semidirect
7. #11924506C2semidirect
8. #11924504C2semidirect
9. #11924498C2semidirect
10. C4×C22⋊D37C2semidirect
11. #121×C37C2semidirect
12. C23×D37C22semidirect
13. C23×D37C22semidirect
14. C2×D4×C37C22semidirect
15. C2×D4×C37C22semidirect
16. C22×C4×C37C22semidirect
18. C2×C22⋊D37C22semidirect
19. C2×C22⋊D37C22semidirect
20. C2×C22⋊D37C22semidirect
25. C2×D148C22semidirect
26. C2×D148C22semidirect
27. C2×D148C22semidirect
28. C2×C4×D37C22semidirect
29. C2×C4×D37C22semidirect
30. C4⋊C4×C37C22semidirect
31. C22⋊C4×C37C22semidirect
32. C22⋊Dic37C22semidirect
33. #10596938C22semidirect
34. #10596938C22semidirect
35. #10596938C22semidirect
36. #10596936C22semidirect
37. C4×Dic37C22semidirect
58. C22⋊D37D4semidirect
65. D148D4semidirect
73. C22×C37C2×D4semidirect
84. C2×D37C2×D4semidirect
85. C2×D37C2×D4semidirect
88. C4×C37C2×D4semidirect
91. Dic37C2×D4semidirect
101. C37D42semidirect
108. #121D37semidirect
126. C2×D4C2×D37semidirect
127. C2×D4C2×D37semidirect
130. C22×C4C2×D37semidirect
132. C4⋊C4C2×D37semidirect
137. C22⋊C4C2×D37semidirect
185. C22D4×D37semidirect
192. C4D4×D37semidirect

Maximal subgroups

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

subgroupindex
C22×D1482
C2×D4×D372
#119245322
#119245112
#119245092
#119245062
#119245042
#119244982
C4×C22⋊D372
#121×C372
D4237