Finite Group Databasebeta

← #23781841

Subgroups — #23781841

Order 10432.

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#19104781C211yesmaximal, characteristic
2#19104766C211yesmaximal, characteristic, complemented
3#19104724C211yesmaximal, characteristic, complemented
4#19104662C211yesmaximal, characteristic, complemented
5#19104661C211yesmaximal, characteristic, complemented
6#19104651C211yesmaximal, characteristic, complemented
7#137×C163C211yesmaximal, characteristic, complemented
8#14579700—21no—
9#14579699—21no—
10#14579699C2211yescharacteristic
11C2×D652—21no—
12C2×D652C2211yescharacteristic
13D4×D163—22no—
14D4×D163—21no—
15#14579689—21no—
16#14579686—21no—
17#14579683C2211yescharacteristic, complemented
18(C2×D163)⋊C4—22no—
19C4×Dic163C2211yescharacteristic, complemented
20#41×C163C2211yescharacteristic
21C2×Q8×C163C2211yescharacteristic, complemented
22Q16×C163—21no—
23SD16×C163—21no—
24M16×C163C2211yescharacteristic, complemented
25C22×D163—22no—
26C22×D163D412yes—
27Dic326D411yescharacteristic
28D652—22no—
29D652—21no—
30D652—21no—
31D652D411yescharacteristic
32C22⋊D163—22no—
33C22⋊D163—21no—
34C2×Dic163—21no—
35C4×D163—22no—
36C4×D163—21no—
37C163⋊C8—21no—
38Q8×C163—21no—
39Q8×C163—21no—
40Q8×C163D411yescharacteristic
41D4×C163—21no—
42D4×C163D411yescharacteristic
43C2×C4×C163—21no—
44C2×C4×C163—21no—
45C2×C4×C163C2311yescharacteristic
46C8×C163—21no—
47C22×C163—21no—
48C22×C163C2×D411yescharacteristic
49C2×D163—22no—
50C2×D163—21no—
51C2×D163—42no—
52C2×D163—82no—
53C4×C163—21no—
54C4×C163—41no—
55C4×C163C2×D411yescharacteristic
56C4×C163C2×D411yescharacteristic
57Dic163—21no—
58Dic163—41no—
59C2×C163—21no—
60C2×C163—41no—
61C2×C163#12011yescharacteristic
62D163—42no—
63D163—41no—
64C163#45511yescharacteristic, complemented, Sylow
65#455—1631nomaximal, Sylow
66H(5,𝔽2)—1631no—
67#137—1631no—
68#137D16311yescharacteristic, complemented
69#124—1631no—
70#104—1631no—
71#104—1631no—
72#100—1631no—
73#41—3261no—
74#41—3261no—
75#41—1631no—
76#41C2×D16311yescharacteristic
77C2×Q8C2×D16311yescharacteristic, complemented
78C2×D4—3261no—
79C2×D4—3262no—
80C2×D4—3261no—
81C2×D4—1631no—
82Q16—21no—
83Q16—3261no—
84SD16—21no—
85SD16—3261no—
86M16—1631no—
87M16C2×D16311yescharacteristic, complemented
88C22⋊C4—3262no—
89C42—1631no—
90C23—3262no—
91C23—1632no—
92Q8—21no—
93Q8—21no—
94Q8—1631no—
95Q8C22⋊D16311yescharacteristic
96D4—21no—
97D4—3262no—
98D4—3262no—
99D4—3261no—
100D4—3261no—
101D4—3261no—
102D4—1631no—
103D4C22⋊D16311yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—3262no—
107C2×C4—3261no—
108C2×C4—3261no—
109C2×C4C22×D16311yescharacteristic
110C8—21no—
111C8—3261no—
112C22—21no—
113C22—13042no—
114C22—3262no—
115C22—3261no—
116C22—6522no—
117C22D4×D16311yescharacteristic
118C4—21no—
119C4—41no—
120C4—3261no—
121C4—6521no—
122C4D4×D16311yescharacteristic
123C4C2×C22⋊D16311yescharacteristic
124C2—21no—
125C2—41no—
126C2—6521no—
127C2—6522no—
128C2#1910470311yescharacteristic
subgroupG/H
centerC2#19104703
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#137×C163C2
socleC2×C163#120
prime radical#19104781C2
hypercenter#137D163
hypocenterC163#455
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #19104766C2semidirect
3. #19104724C2semidirect
4. #19104662C2semidirect
5. #19104661C2semidirect
6. #19104651C2semidirect
7. #137×C163C2semidirect
17. #14579683C22semidirect
19. C4×Dic163C22semidirect
21. C2×Q8×C163C22semidirect
24. M16×C163C22semidirect
64. C163#455semidirect
68. #137D163semidirect
77. C2×Q8C2×D163semidirect
87. M16C2×D163semidirect