Finite Group Databasebeta

← #30682581

Subgroups — #30682581

Order 16832.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16862377C211yesmaximal, characteristic, complemented
2C2×D4×D263C211yesmaximal, characteristic, complemented
3#22554452C212yesmaximal, complemented
4#22554446C211yesmaximal, characteristic, complemented
5#22554443C212yesmaximal, complemented
6#22554441C211yesmaximal, characteristic, complemented
7#22554440C212yesmaximal, complemented
8C4×D1052C211yesmaximal, characteristic, complemented
9C4×D1052C211yesmaximal, characteristic, complemented
10C22⋊C4×D263C212yesmaximal, complemented
11#124×C263C211yesmaximal, characteristic, complemented
12C23×D263C2212yes—
13#16862377—24no—
14C2×D1052C2211yescharacteristic
15C2×D1052C2211yescharacteristic
16C2×D1052C2212yescomplemented
17C2×C22⋊D263C2212yes—
18C2×C22⋊D263C2212yescomplemented
19D4×D263—24no—
20C2×C4×D263C2211yescharacteristic
21C2×C4×D263C2212yescomplemented
22C2×C4×D263C2211yescharacteristic, complemented
23C2×C4×D263C2212yescomplemented
24C4⋊Dic263C2211yescharacteristic, complemented
25C4⋊Dic263C2211yescharacteristic, complemented
26Dic263⋊C4C2212yescomplemented
27C22⋊Dic263C2212yescomplemented
28(C2×D263)⋊C4C2211yescharacteristic
29(C2×D263)⋊C4C2212yes—
30(C2×D263)⋊C4C2212yescomplemented
31(C2×D263)⋊C4C2211yescharacteristic, complemented
32C2×Q8×C263C2211yescharacteristic, complemented
33C2×D4×C263C2211yescharacteristic
34C22⋊C4×C263C2212yescomplemented
35C22⋊C4×C263C2212yescomplemented
36C42×C263C2211yescharacteristic, complemented
37C22×D263—24no—
38C22×D263—24no—
39C22×D263—42no—
40C22×D263C2311yescharacteristic
41C22×D263C2312yes—
42C22×D263C2311yescharacteristic
43D1052—24no—
44D1052—22no—
45D1052D414yescomplemented
46C22⋊D263—24no—
47C22⋊D263—42no—
48C2×Dic263C2312yes—
49C2×Dic263C2311yescharacteristic
50C2×Dic263C2311yescharacteristic
51C4×D263—24no—
52C4×D263—22no—
53C4×D263—22no—
54C4×D263—42no—
55C23×C263C2312yes—
56Q8×C263—22no—
57D4×C263—22no—
58C2×C4×C263C2311yescharacteristic
59C2×C4×C263C2311yescharacteristic
60C2×C4×C263C2312yes—
61C2×C4×C263C2311yescharacteristic
62C22×C263—22no—
63C22×C263—22no—
64C22×C263—22no—
65C22×C263C2411yescharacteristic
66C2×D263—21no—
67C2×D263—22no—
68C2×D263—22no—
69C2×D263—21no—
70C2×D263—21no—
71C2×D263—21no—
72C2×D263—21no—
73C2×D263—48no—
74C2×D263C2×D414yes—
75C2×D263#4112yescomplemented
76C4×C263—22no—
77C4×C263—21no—
78C4×C263—21no—
79C4×C263C2×D412yes—
80Dic263—21no—
81Dic263—21no—
82Dic263—22no—
83C2×C263—42no—
84C2×C263C22×D411yescharacteristic
85C2×C263C2×#4111yescharacteristic
86C2×C263H(5,𝔽2)11yescharacteristic
87D263—22no—
88D263—24no—
89D263—41no—
90C263#54611yescharacteristic, complemented, Sylow
91#546—2631nomaximal, Sylow
92C2×#41—2631no—
93C22×D4—2631no—
94#124D26311yescharacteristic, complemented
95#123—2632no—
96C22⋊Q8—2631no—
97#121—2631no—
98#121—2632no—
99#120—2632no—
100C4×D4—2631no—
101C4×D4—2631no—
102C2×C22⋊C4—2632no—
103C24—2632no—
104#41—5264no—
105C2×Q8C2×D26311yescharacteristic, complemented
106C2×D4—2632no—
107C2×D4—2632no—
108C2×D4—2631no—
109C2×D4—2631no—
110C2×D4—2632no—
111C2×D4—5264no—
112C2×D4C2×D26311yescharacteristic
113C22×C4—2632no—
114C22×C4—2631no—
115C22×C4—2631no—
116C22×C4—2632no—
117C4⋊C4—2631no—
118C4⋊C4—2631no—
119C4⋊C4—2632no—
120C22⋊C4—2632no—
121C22⋊C4—2631no—
122C22⋊C4—2632no—
123C22⋊C4—2632no—
124C22⋊C4—2631no—
125C22⋊C4C2×D26312yescomplemented
126C22⋊C4C2×D26312yescomplemented
127C42C2×D26311yescharacteristic, complemented
128C23—2631no—
129C23—2632no—
130C23—2631no—
131C23—5264no—
132C23—5264no—
133C23—10522no—
134C23C22×D26312yes—
135Q8—22no—
136D4—22no—
137D4—2634no—
138D4—5264no—
139D4—5262no—
140D4—5264no—
141D4—10522no—
142C2×C4—2632no—
143C2×C4—2631no—
144C2×C4—2631no—
145C2×C4—5264no—
146C2×C4—5262no—
147C2×C4—5262no—
148C2×C4—10522no—
149C2×C4C22×D26311yescharacteristic
150C2×C4C22×D26311yescharacteristic
151C2×C4C22×D26312yes—
152C2×C4C22×D26311yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—2634no—
157C22—2632no—
158C22—5261no—
159C22—5262no—
160C22—5262no—
161C22—5261no—
162C22—5261no—
163C22—5261no—
164C22—5261no—
165C22—10528no—
166C22C23×D26311yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—5261no—
171C4—5261no—
172C4—5262no—
173C4D4×D26312yes—
174C2—42no—
175C2—5262no—
176C2—5264no—
177C2—10521no—
178C2C2×D4×D26311yescharacteristic
179C2#41×D26311yescharacteristic
180C2#2255451611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D263
commutator, socle, cosocleC22×C263C24
Fitting#124×C263C2
hypercenter#124D263
hypocenterC263#546
LCSG ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#16862377C2semidirect
2. C2×D4×D263C2semidirect
3. #22554452C2semidirect
4. #22554446C2semidirect
5. #22554443C2semidirect
6. #22554441C2semidirect
7. #22554440C2semidirect
8. C4×D1052C2semidirect
9. C4×D1052C2semidirect
10. C22⋊C4×D263C2semidirect
11. #124×C263C2semidirect
16. C2×D1052C22semidirect
18. C2×C22⋊D263C22semidirect
21. C2×C4×D263C22semidirect
22. C2×C4×D263C22semidirect
23. C2×C4×D263C22semidirect
24. C4⋊Dic263C22semidirect
25. C4⋊Dic263C22semidirect
26. Dic263⋊C4C22semidirect
27. C22⋊Dic263C22semidirect
30. (C2×D263)⋊C4C22semidirect
31. (C2×D263)⋊C4C22semidirect
32. C2×Q8×C263C22semidirect
34. C22⋊C4×C263C22semidirect
35. C22⋊C4×C263C22semidirect
36. C42×C263C22semidirect
45. D1052D4semidirect
75. C2×D263#41semidirect
90. C263#546semidirect
94. #124D263semidirect
105. C2×Q8C2×D263semidirect
125. C22⋊C4C2×D263semidirect
126. C22⋊C4C2×D263semidirect
127. C42C2×D263semidirect

Maximal subgroups

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

subgroupindex
C2×#168623772
C2×D4×D2632
#225544522
#225544462
#225544432
#225544412
#225544402
C4×D10522
C22⋊C4×D2632
#124×C2632
#546263