Finite Group Databasebeta

← #30682504

Subgroups — #30682504

Order 16832.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#16862376C211yesmaximal, characteristic, complemented
2C2×D4×D263C211yesmaximal, characteristic, complemented
3#22554466C212yesmaximal, complemented
4#22554456C212yesmaximal, complemented
5#22554445C211yesmaximal, characteristic, complemented
6#22554444C211yesmaximal, characteristic, complemented
7#22554441C211yesmaximal, characteristic, complemented
8#22554440C212yesmaximal, complemented
9#22554438C212yesmaximal, complemented
10#22554428C211yesmaximal, characteristic, complemented
11#121×C263C211yesmaximal, characteristic, complemented
12C23×D263C2212yes—
13#16862376—24no—
14C2×Dic526C2211yescharacteristic, complemented
15C2×D1052C2211yescharacteristic
16C2×D1052C2211yescharacteristic
17C2×D1052C2212yescomplemented
18C2×C22⋊D263C2211yescharacteristic
19C2×C22⋊D263C2212yes—
20C2×C22⋊D263C2211yescharacteristic, complemented
21C2×C22⋊D263C2212yescomplemented
22C2×C22⋊D263C2212yescomplemented
23D4×D263—24no—
24C2×C4×D263C2211yescharacteristic
25C2×C4×D263C2211yescharacteristic, complemented
26C4⋊Dic263C2211yescharacteristic, complemented
27C22⋊Dic263C2212yescomplemented
28(C2×D263)⋊C4C2212yes—
29(C2×D263)⋊C4C2212yescomplemented
30(C2×D263)⋊C4C2212yescomplemented
31C4×Dic263C2212yescomplemented
32C2×D4×C263C2211yescharacteristic
33C2×D4×C263C2212yescomplemented
34C22×C4×C263C2211yescharacteristic, complemented
35C4⋊C4×C263C2211yescharacteristic, complemented
36C22⋊C4×C263C2212yescomplemented
37C22×D263—24no—
38C22×D263—42no—
39C22×D263—42no—
40C22×D263C2312yes—
41C22×D263C2311yescharacteristic
42C22×D263C2311yescharacteristic
43Dic526—22no—
44D1052—22no—
45D1052—22no—
46D1052—42no—
47C22⋊D263—22no—
48C22⋊D263—24no—
49C22⋊D263—22no—
50C22⋊D263—42no—
51C22⋊D263—42no—
52C2×Dic263C2312yes—
53C2×Dic263C2311yescharacteristic
54C2×Dic263C2311yescharacteristic
55C4×D263—22no—
56C4×D263D414yescomplemented
57C23×C263C2312yes—
58C23×C263C2311yescharacteristic
59D4×C263—22no—
60D4×C263—42no—
61C2×C4×C263—22no—
62C2×C4×C263C2311yescharacteristic
63C2×C4×C263C2312yes—
64C2×C4×C263C2311yescharacteristic
65C22×C263—21no—
66C22×C263—22no—
67C22×C263—21no—
68C22×C263—22no—
69C22×C263—21no—
70C22×C263—22no—
71C22×C263C2411yescharacteristic
72C2×D263—21no—
73C2×D263—21no—
74C2×D263—21no—
75C2×D263—22no—
76C2×D263—21no—
77C2×D263—22no—
78C2×D263—21no—
79C2×D263—22no—
80C2×D263—48no—
81C2×D263C2×D412yes—
82C4×C263—21no—
83C4×C263—22no—
84C4×C263C2×D412yes—
85Dic263—21no—
86Dic263—22no—
87Dic263C2×D412yes—
88C2×C263—42no—
89C2×C263—41no—
90C2×C263C22×D411yescharacteristic
91C2×C263H(5,𝔽2)11yescharacteristic
92C2×C263H(5,𝔽2)11yescharacteristic
93D263—22no—
94D263—41no—
95D263—42no—
96C263#53511yescharacteristic, complemented, Sylow
97#535—2631nomaximal, Sylow
98C2×#41—2631no—
99C22×D4—2631no—
100#127—2632no—
101#124—2632no—
102#121—2631no—
103#121—2631no—
104#121—2631no—
105#121D26311yescharacteristic, complemented
106#120—2632no—
107#120—2632no—
108#117—2631no—
109C24—2632no—
110#41—5264no—
111C2×Q8—2631no—
112C2×D4—2631no—
113C2×D4—2632no—
114C2×D4—2631no—
115C2×D4—2632no—
116C2×D4—2632no—
117C2×D4—2631no—
118C2×D4—2631no—
119C2×D4—2632no—
120C2×D4—5264no—
121C2×D4C2×D26311yescharacteristic
122C2×D4C2×D26312yescomplemented
123C22×C4—2631no—
124C22×C4—2631no—
125C22×C4C2×D26311yescharacteristic, complemented
126C4⋊C4—2631no—
127C4⋊C4C2×D26311yescharacteristic, complemented
128C22⋊C4—2632no—
129C22⋊C4—2632no—
130C22⋊C4—2632no—
131C22⋊C4—2632no—
132C22⋊C4C2×D26312yescomplemented
133C42—2632no—
134C23—2631no—
135C23—2632no—
136C23—2631no—
137C23—5264no—
138C23—10522no—
139C23—10522no—
140C23C22×D26312yes—
141C23C22×D26311yescharacteristic
142Q8—5262no—
143D4—22no—
144D4—42no—
145D4—5262no—
146D4—5264no—
147D4—5262no—
148D4—5262no—
149D4—5262no—
150D4—10522no—
151D4—10522no—
152D4—10522no—
153C2×C4—22no—
154C2×C4—2631no—
155C2×C4—2634no—
156C2×C4—2632no—
157C2×C4—2631no—
158C2×C4—5262no—
159C2×C4C22×D26312yes—
160C2×C4C22×D26311yescharacteristic
161C2×C4C22×D26311yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—2632no—
169C22—5261no—
170C22—5261no—
171C22—5261no—
172C22—5262no—
173C22—5261no—
174C22—5262no—
175C22—5261no—
176C22—5262no—
177C22—10528no—
178C22C23×D26311yescharacteristic
179C4—21no—
180C4—22no—
181C4—2632no—
182C4—5261no—
183C4—5262no—
184C4D4×D26312yes—
185C2—42no—
186C2—41no—
187C2—5262no—
188C2—10522no—
189C2—10521no—
190C2C2×D4×D26311yescharacteristic
191C2#2255451511yescharacteristic
192C2#2255451611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D263
commutator, socle, cosocleC22×C263C24
Fitting#121×C263C2
hypercenter#121D263
hypocenterC263#535
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#16862376C2semidirect
2. C2×D4×D263C2semidirect
3. #22554466C2semidirect
4. #22554456C2semidirect
5. #22554445C2semidirect
6. #22554444C2semidirect
7. #22554441C2semidirect
8. #22554440C2semidirect
9. #22554438C2semidirect
10. #22554428C2semidirect
11. #121×C263C2semidirect
14. C2×Dic526C22semidirect
17. C2×D1052C22semidirect
20. C2×C22⋊D263C22semidirect
21. C2×C22⋊D263C22semidirect
22. C2×C22⋊D263C22semidirect
25. C2×C4×D263C22semidirect
26. C4⋊Dic263C22semidirect
27. C22⋊Dic263C22semidirect
29. (C2×D263)⋊C4C22semidirect
30. (C2×D263)⋊C4C22semidirect
31. C4×Dic263C22semidirect
33. C2×D4×C263C22semidirect
34. C22×C4×C263C22semidirect
35. C4⋊C4×C263C22semidirect
36. C22⋊C4×C263C22semidirect
56. C4×D263D4semidirect
96. C263#535semidirect
105. #121D263semidirect
122. C2×D4C2×D263semidirect
125. C22×C4C2×D263semidirect
127. C4⋊C4C2×D263semidirect
132. C22⋊C4C2×D263semidirect

Maximal subgroups

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

subgroupindex
C2×#168623762
C2×D4×D2632
#225544662
#225544562
#225544452
#225544442
#225544412
#225544402
#225544382
#225544282
#121×C2632
#535263