Finite Group Databasebeta

← #30682584

Subgroups — #30682584

Order 16832.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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
2C22×D1052C211yesmaximal, characteristic, complemented
3#22554458C211yesmaximal, characteristic, complemented
4#22554455C212yesmaximal, complemented
5#22554449C211yesmaximal, characteristic, complemented
6#22554444C211yesmaximal, characteristic, complemented
7#22554443C212yesmaximal, complemented
8#22554438C212yesmaximal, complemented
9C4×D1052C211yesmaximal, characteristic, complemented
10C22⋊C4×D263C212yesmaximal, complemented
11C4×D4×C263C211yesmaximal, characteristic, complemented
12C23×D263C2212yes—
13#16862376—24no—
14C2×Dic526C2211yescharacteristic, complemented
15C2×D1052—24no—
16C2×D1052C2212yes—
17C2×D1052C2211yescharacteristic
18C2×D1052C2211yescharacteristic
19C2×C22⋊D263C2212yescomplemented
20C2×C22⋊D263C2212yescomplemented
21C2×C4×D263C2212yescomplemented
22C2×C4×D263C2212yescomplemented
23C4⋊Dic263C2211yescharacteristic, complemented
24Dic263⋊C4C2212yescomplemented
25C22⋊Dic263C2212yes—
26(C2×D263)⋊C4C2212yescomplemented
27(C2×D263)⋊C4C2212yescomplemented
28(C2×D263)⋊C4C2212yescomplemented
29(C2×D263)⋊C4C2212yescomplemented
30C2×D4×C263C2211yescharacteristic
31C22×C4×C263C2211yescharacteristic
32C22×C4×C263C2211yescharacteristic, complemented
33C4⋊C4×C263C2211yescharacteristic, complemented
34C22⋊C4×C263C2211yescharacteristic
35C22⋊C4×C263C2211yescharacteristic, complemented
36C42×C263C2211yescharacteristic, complemented
37C22×D263—24no—
38C22×D263—24no—
39C22×D263—42no—
40C22×D263C2312yes—
41C22×D263C2312yes—
42Dic526—22no—
43D1052—24no—
44D1052—22no—
45D1052D414yescomplemented
46C22⋊D263—24no—
47C22⋊D263—42no—
48C2×Dic263C2312yes—
49C2×Dic263C2312yes—
50C4×D263—24no—
51C4×D263—42no—
52C23×C263C2311yescharacteristic
53C23×C263C2311yescharacteristic
54D4×C263—22no—
55C2×C4×C263—22no—
56C2×C4×C263—22no—
57C2×C4×C263C2311yescharacteristic
58C2×C4×C263C2311yescharacteristic
59C2×C4×C263C2311yescharacteristic
60C2×C4×C263C2311yescharacteristic
61C2×C4×C263C2311yescharacteristic
62C22×C263—21no—
63C22×C263—21no—
64C22×C263—21no—
65C22×C263—21no—
66C22×C263—21no—
67C22×C263#4112yescomplemented
68C22×C263C2411yescharacteristic
69C2×D263—22no—
70C2×D263—22no—
71C2×D263—22no—
72C2×D263—22no—
73C2×D263—22no—
74C2×D263—48no—
75C2×D263C2×D414yes—
76C4×C263—21no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263—21no—
80C4×C263C2×D412yes—
81Dic263—22no—
82Dic263—22no—
83C2×C263—22no—
84C2×C263—41no—
85C2×C263C22×D411yescharacteristic
86C2×C263C2×#4111yescharacteristic
87C2×C263H(5,𝔽2)11yescharacteristic
88D263—24no—
89D263—42no—
90C263#54611yescharacteristic, complemented, Sylow
91#546—2631nomaximal, Sylow
92C2×#41—2631no—
93C22×D4—2631no—
94#124—2631no—
95#123—2632no—
96C22⋊Q8—2631no—
97#121—2631no—
98#121—2632no—
99#120—2632no—
100C4×D4—2631no—
101C4×D4D26311yescharacteristic, complemented
102C2×C22⋊C4—2632no—
103C24—2632no—
104#41—5264no—
105C2×Q8—2631no—
106C2×D4—2632no—
107C2×D4—2632no—
108C2×D4—2631no—
109C2×D4—2632no—
110C2×D4—2631no—
111C2×D4—5264no—
112C2×D4C2×D26311yescharacteristic
113C22×C4—2632no—
114C22×C4—2632no—
115C22×C4C2×D26311yescharacteristic
116C22×C4C2×D26311yescharacteristic, complemented
117C4⋊C4—2631no—
118C4⋊C4—2632no—
119C4⋊C4C2×D26311yescharacteristic, complemented
120C22⋊C4—2632no—
121C22⋊C4—2632no—
122C22⋊C4—2632no—
123C22⋊C4—2632no—
124C22⋊C4—2632no—
125C22⋊C4C2×D26311yescharacteristic
126C22⋊C4C2×D26311yescharacteristic, complemented
127C42C2×D26311yescharacteristic, complemented
128C23—2632no—
129C23—2632no—
130C23—5264no—
131C23—5264no—
132C23—10522no—
133C23C22×D26311yescharacteristic
134C23C22×D26311yescharacteristic
135Q8—5262no—
136D4—22no—
137D4—2634no—
138D4—5264no—
139D4—5264no—
140D4—5262no—
141D4—10522no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—2632no—
145C2×C4—2632no—
146C2×C4—5264no—
147C2×C4—10522no—
148C2×C4C22×D26311yescharacteristic
149C2×C4C22×D26311yescharacteristic
150C2×C4C22×D26311yescharacteristic
151C2×C4C22×D26311yescharacteristic
152C2×C4C22×D26311yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—2634no—
159C22—5262no—
160C22—5262no—
161C22—5262no—
162C22—5262no—
163C22—5262no—
164C22—10528no—
165C22#1686237612yescomplemented
166C22C23×D26311yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—5262no—
172C4—5262no—
173C4D4×D26312yes—
174C2—22no—
175C2—41no—
176C2—5264no—
177C2—10522no—
178C2C2×D4×D26311yescharacteristic
179C2C2×#1686237611yescharacteristic
180C2#2255451611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D263
commutator, socle, cosocleC22×C263C24
FittingC4×D4×C263C2
hypercenterC4×D4D263
hypocenterC263#546
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16862376C2semidirect
2. C22×D1052C2semidirect
3. #22554458C2semidirect
4. #22554455C2semidirect
5. #22554449C2semidirect
6. #22554444C2semidirect
7. #22554443C2semidirect
8. #22554438C2semidirect
9. C4×D1052C2semidirect
10. C22⋊C4×D263C2semidirect
11. C4×D4×C263C2semidirect
14. C2×Dic526C22semidirect
19. C2×C22⋊D263C22semidirect
20. C2×C22⋊D263C22semidirect
21. C2×C4×D263C22semidirect
22. C2×C4×D263C22semidirect
23. C4⋊Dic263C22semidirect
24. Dic263⋊C4C22semidirect
26. (C2×D263)⋊C4C22semidirect
27. (C2×D263)⋊C4C22semidirect
28. (C2×D263)⋊C4C22semidirect
29. (C2×D263)⋊C4C22semidirect
32. C22×C4×C263C22semidirect
33. C4⋊C4×C263C22semidirect
35. C22⋊C4×C263C22semidirect
36. C42×C263C22semidirect
45. D1052D4semidirect
67. C22×C263#41semidirect
90. C263#546semidirect
101. C4×D4D263semidirect
116. C22×C4C2×D263semidirect
119. C4⋊C4C2×D263semidirect
126. C22⋊C4C2×D263semidirect
127. C42C2×D263semidirect
165. C22#16862376semidirect

Maximal subgroups

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

subgroupindex
C2×#168623762
C22×D10522
#225544582
#225544552
#225544492
#225544442
#225544432
#225544382
C4×D10522
C22⋊C4×D2632
C4×D4×C2632
#546263