Finite Group Databasebeta

← #30682117

Subgroups — #30682117

Order 16832.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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
1#22554516C211yesmaximal, characteristic
2#22554503C211yesmaximal, characteristic, complemented
3#22554500C211yesmaximal, characteristic, complemented
4#22554458C211yesmaximal, characteristic, complemented
5#22554398C211yesmaximal, characteristic, complemented
6#22554386C211yesmaximal, characteristic, complemented
7#104×C263C211yesmaximal, characteristic, complemented
8#16862377—21no—
9#16862376—21no—
10#16862376C2211yescharacteristic
11C2×Dic526C2211yescharacteristic, complemented
12C2×D1052—21no—
13C2×D1052C2211yescharacteristic
14D4×D263—22no—
15D4×D263—21no—
16Dic1052—21no—
17#16862366—21no—
18#16862365—21no—
19#16862364—21no—
20#16862360C2211yescharacteristic, complemented
21(C2×D263)⋊C4—22no—
22#41×C263C2211yescharacteristic
23M16×C263C2211yescharacteristic, complemented
24C42×C263C2211yescharacteristic, complemented
25C22×D263—22no—
26C22×D263D412yes—
27Dic526—21no—
28Dic526—21no—
29Dic526D411yescharacteristic
30D1052—22no—
31D1052—21no—
32D1052—21no—
33D1052D411yescharacteristic
34C22⋊D263—22no—
35C22⋊D263—21no—
36C2×Dic263—21no—
37C4×D263—22no—
38C4×D263—21no—
39C263⋊C8—21no—
40Q8×C263D411yescharacteristic
41D4×C263—21no—
42D4×C263D411yescharacteristic
43C2×C4×C263—21no—
44C2×C4×C263—21no—
45C2×C4×C263C2311yescharacteristic
46C8×C263—21no—
47C22×C263—21no—
48C22×C263C2×D411yescharacteristic
49C2×D263—22no—
50C2×D263—21no—
51C2×D263—42no—
52C2×D263—82no—
53C4×C263—21no—
54C4×C263—41no—
55C4×C263C2×D411yescharacteristic
56C4×C263C2×D411yescharacteristic
57Dic263—21no—
58Dic263—41no—
59C2×C263—21no—
60C2×C263—41no—
61C2×C263#12011yescharacteristic
62D263—42no—
63D263—41no—
64C263#45511yescharacteristic, complemented, Sylow
65#455—2631nomaximal, Sylow
66H(5,𝔽2)—2631no—
67#137—2631no—
68#137—2631no—
69#124—2631no—
70#104—2631no—
71#104D26311yescharacteristic, complemented
72#100—2631no—
73#41—2631no—
74#41—5261no—
75#41—5261no—
76#41C2×D26311yescharacteristic
77C2×Q8—2631no—
78C2×D4—2631no—
79C2×D4—5261no—
80C2×D4—5262no—
81C2×D4—5261no—
82Q16—5261no—
83Q16—5261no—
84SD16—5261no—
85SD16—5261no—
86M16—2631no—
87M16C2×D26311yescharacteristic, complemented
88C22⋊C4—5262no—
89C42C2×D26311yescharacteristic, complemented
90C23—2632no—
91C23—5262no—
92Q8—2631no—
93Q8—5261no—
94Q8—5261no—
95Q8D105211yescharacteristic
96D4—21no—
97D4—2631no—
98D4—5262no—
99D4—5262no—
100D4—5261no—
101D4—5261no—
102D4—5261no—
103D4D105211yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—5262no—
107C2×C4—5261no—
108C2×C4—5261no—
109C2×C4C22×D26311yescharacteristic
110C8—21no—
111C8—5261no—
112C22—21no—
113C22—5261no—
114C22—5262no—
115C22—10522no—
116C22—21042no—
117C22D4×D26311yescharacteristic
118C4—21no—
119C4—41no—
120C4—5261no—
121C4—10521no—
122C4D4×D26311yescharacteristic
123C4C2×D105211yescharacteristic
124C2—21no—
125C2—41no—
126C2—10522no—
127C2—10521no—
128C2#2255444011yescharacteristic
subgroupG/H
centerC2#22554440
commutator, cosocleC2×C4×C263C23
FrattiniC2×C4C22×D263
Fitting#104×C263C2
socleC2×C263#120
prime radical#22554516C2
hypercenter#104D263
hypocenterC263#455
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #22554503C2semidirect
3. #22554500C2semidirect
4. #22554458C2semidirect
5. #22554398C2semidirect
6. #22554386C2semidirect
7. #104×C263C2semidirect
11. C2×Dic526C22semidirect
20. #16862360C22semidirect
23. M16×C263C22semidirect
24. C42×C263C22semidirect
64. C263#455semidirect
71. #104D263semidirect
87. M16C2×D263semidirect
89. C42C2×D263semidirect

Maximal subgroups

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

subgroupindex
#225545162
#225545032
#225545002
#225544582
#225543982
#225543862
#104×C2632
#455263