Finite Group Databasebeta

← #23782480

Subgroups — #23782480

Order 10432.

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

normal subgroups only

This group has 248 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
1#19104782C211yesmaximal, characteristic, complemented
2#19104766C213yesmaximal, complemented
3#19104765C213yesmaximal, complemented
4#19104755C213yesmaximal, complemented
5C2×#14579689C213yesmaximal, complemented
6#19104742C211yesmaximal, characteristic, complemented
72−1+4×C163C211yesmaximal, characteristic, complemented
8#14579699C2213yes—
9#14579698—23no—
10C2×Dic326C2213yes—
11Q8×D163—21no—
12#14579689C2213yes—
13#14579689C2216yes—
14#14579687C2213yes—
15#14579686C2213yes—
16#14579684C2211yescharacteristic
17#14579683C2213yes—
18C2×C163⋊C8C2213yes—
19#41×C163—23no—
20#41×C163C2213yes—
21#41×C163C2211yescharacteristic
22C2×Q8×C163—21no—
23C2×Q8×C163C2213yes—
24Dic326—23no—
25Dic326C2313yes—
26D652C2311yescharacteristic
27C22⋊D163—23no—
28C2×Dic163—23no—
29C4×D163—23no—
30C163⋊C8C2311yescharacteristic
31C163⋊C8C2313yes—
32Q8×C163—23no—
33Q8×C163D411yescharacteristic
34Q8×C163C2313yes—
35D4×C163—23no—
36D4×C163D413yes—
37D4×C163C2311yescharacteristic
38C2×C4×C163—23no—
39C2×C4×C163—23no—
40C2×C4×C163C2313yes—
41C22×C163—21no—
42C22×C163C2×D413yes—
43C2×D163—21no—
44C4×C163—23no—
45C4×C163C2×D413yes—
46C4×C163C2411yescharacteristic
47Dic163—23no—
48C2×C163—23no—
49C2×C163—41no—
50C2×C163C22×D411yescharacteristic
51D163—41no—
52C163#57811yescharacteristic, complemented, Sylow
53#578—1631nomaximal, Sylow
542−1+4—1631no—
552−1+4D16311yescharacteristic, complemented
56#137—1633no—
57#137—1633no—
58#135—1633no—
59C2×Q16—1633no—
60#131—1631no—
61#41—23no—
62#41—3263no—
63#41—1633no—
64#41C2×D16313yes—
65#41C2×D16311yescharacteristic
66C2×Q8—21no—
67C2×Q8—3261no—
68C2×Q8—1633no—
69C2×Q8C2×D16313yes—
70Q16—1633no—
71Q16—1636no—
72SD16—1633no—
73SD16—1633no—
74D8—1631no—
75M16—1633no—
76C2×C8—1633no—
77Q8—23no—
78Q8—3263no—
79Q8—1633no—
80Q8C22⋊D16311yescharacteristic
81Q8C22×D16313yes—
82D4—23no—
83D4—3263no—
84D4—1631no—
85D4C22⋊D16313yes—
86D4C22×D16311yescharacteristic
87C2×C4—23no—
88C2×C4—23no—
89C2×C4—3263no—
90C2×C4—3263no—
91C2×C4C22×D16313yes—
92C8—1631no—
93C8—1633no—
94C22—21no—
95C22—3261no—
96C22C2×C22⋊D16313yes—
97C4—23no—
98C4—3263no—
99C4C2×C22⋊D16313yes—
100C4C23×D16311yescharacteristic
101C2—23no—
102C2—41no—
103C2—6521no—
104C2C22×C22⋊D16311yescharacteristic
subgroupG/H
centerC2C22×C22⋊D163
commutator, cosocleC4×C163C24
FrattiniC4C23×D163
Fitting2−1+4×C163C2
socleC2×C163C22×D4
hypercenter2−1+4D163
hypocenterC163#578
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ #41 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #19104782C2semidirect
2. #19104766C2semidirect
3. #19104765C2semidirect
4. #19104755C2semidirect
5. C2×#14579689C2semidirect
6. #19104742C2semidirect
7. 2−1+4×C163C2semidirect
52. C163#578semidirect
55. 2−1+4D163semidirect